Synchronization in collectively moving active matter - Riedl, Michael
Most motions of many-body systems at any scale in nature with sufficient degrees of freedom tend to be chaotic; reaching from the orbital motion of planets, the air currents in our atmosphere, down to the water flowing through our pipelines or the movement of a population of bacteria. To the observer it is therefore intriguing when a moving collective exhibits order. Collective motion of flocks of birds, schools of fish or swarms of self-propelled particles or robots have been studied extensively over the past decades but the mechanisms involved in the transition from chaos to order remain unclear. Here, the interactions, that in most systems give rise to chaos, sustain order. In this thesis we investigate mechanisms that preserve, destabilize or lead to the ordered state. We show that endothelial cells migrating in circular confinements transition to a collective rotating state and concomitantly synchronize the frequencies of nucleating actin waves within individual cells. Consequently, the frequency dependent cell migration speed uniformizes across the population. Complementary to the WAVE dependent nucleation of traveling actin waves, we show that in leukocytes the actin polymerization depending on WASp generates pushing forces locally at stationary patches. Next, in pipe flows, we study methods to disrupt the self–sustaining cycle of turbulence and therefore relaminarize the flow. While we find in pulsating flow conditions that turbulence emerges through a helical instability during the decelerating phase. Finally, we show quantitatively in brain slices of mice that wild-type control neurons can compensate the migratory deficits of a genetically modified neuronal sub–population in the developing cortex.

Synchronization in collectively moving active matter - Riedl, Michael
Most motions of many-body systems at any scale in nature with sufficient degrees of freedom tend to be chaotic; reaching from the orbital motion of planets, the air currents in our atmosphere, down to the water flowing through our pipelines or the movement of a population of bacteria. To the observer it is therefore intriguing when a moving collective exhibits order. Collective motion of flocks of birds, schools of fish or swarms of self-propelled particles or robots have been studied extensively over the past decades but the mechanisms involved in the transition from chaos to order remain unclear. Here, the interactions, that in most systems give rise to chaos, sustain order. In this thesis we investigate mechanisms that preserve, destabilize or lead to the ordered state. We show that endothelial cells migrating in circular confinements transition to a collective rotating state and concomitantly synchronize the frequencies of nucleating actin waves within individual cells. Consequently, the frequency dependent cell migration speed uniformizes across the population. Complementary to the WAVE dependent nucleation of traveling actin waves, we show that in leukocytes the actin polymerization depending on WASp generates pushing forces locally at stationary patches. Next, in pipe flows, we study methods to disrupt the self--sustaining cycle of turbulence and therefore relaminarize the flow. While we find in pulsating flow conditions that turbulence emerges through a helical instability during the decelerating phase. Finally, we show quantitatively in brain slices of mice that wild-type control neurons can compensate the migratory deficits of a genetically modified neuronal sub--population in the developing cortex.
Keywords: Synchronization; Collective Movement; Active Matter; Cell Migration; Active Colloids

Resonant microwave spectroscopy of Al-InAs - Phan, Duc T
Superconductor-semiconductor heterostructures currently capture a significant amount of research interest and they serve as the physical platform in many proposals towards topological quantum computation. Despite being under extensive investigations, historically using transport techniques, the basic properties of the interface between the superconductor and the semiconductor remain to be understood. In this thesis, two separate studies on the Al-InAs heterostructures are reported with the first focusing on the physics of the material motivated by the emergence of a new phase, the Bogoliubov-Fermi surface. The second focuses on a technological application, a gate-tunable Josephson parametric amplifier. In the first study, we investigate the hypothesized unconventional nature of the induced superconductivity at the interface between the Al thin film and the InAs quantum well. We embed a two-dimensional Al-InAs hybrid system in a resonant microwave circuit allowing measurements of change in inductance. The behaviour of the resonance in a range of temperature and in-plane magnetic field has been studied and compared with the theory of conventional s-wave superconductor and a two-component theory that includes both contribution of the $s$-wave pairing in Al and the intraband $p ± ip$ pairing in InAs. Measuring the temperature dependence of resonant frequency, no discrepancy is found between data and the conventional theory. We observe the breakdown of superconductivity due to an applied magnetic field which contradicts the conventional theory. In contrast, the data can be captured quantitatively by fitting to a two-component model. We find the evidence of the intraband $p ± ip$ pairing in the InAs and the emergence of the Bogoliubov-Fermi surfaces due to magnetic field with the characteristic value $B^* = 0.33~T$. From the fits, the sheet resistance of Al, the carrier density and mobility in InAs are determined. By systematically studying the anisotropy of the circuit response, we find weak anisotropy for $B < B^*$ and increasingly strong anisotropy for $B > B^*$ resulting in a pronounced two-lobe structure in polar plot of frequency versus field angle. Strong resemblance between the field dependence of dissipation and superfluid density hints at a hidden signature of the Bogoliubov-Fermi surface that is burried in the dissipation data. In the second study, we realize a parametric amplifier with a Josephson field effect transistor as the active element. The device's modest construction consists of a gated SNS weak link embedded at the center of a coplanar waveguide resonator. By applying a gate voltage, the resonant frequency is field-effect tunable over a range of 2 GHz. Modelling the JoFET minimally as a parallel RL circuit, the dissipation introduced by the JoFET can be quantitatively related to the gate voltage. We observed gate-tunable Kerr nonlinearity qualitatively in line with expectation. The JoFET amplifier has 20 dB of gain, 4 MHz of instantaneous bandwidth, and a 1dB compression point of -125.5 dBm when operated at a fixed resonant frequency. In general, the signal-to-noise ratio is improved by 5-7 dB when the JoFET amplifier is activated compared. The noise of the measurement chain and insertion loss of relevant circuit elements are calibrated to determine the expected and the real noise performance of the JoFET amplifier. As a quantification of the noise performance, the measured total input-referred noise of the JoFET amplifier is in good agreement with the estimated expectation which takes device loss into account. We found that the noise performance of the device reported in this document approaches one photon of total input-referred added noise which is the quantum limit imposed in nondegenerate parametric amplifier.
Keywords: superconductor-semiconductor; superconductivity; Al; InAs; p-wave; superconductivity; JPA; microwave

Procedural metamaterials: A unified procedural graph for metamaterial design - Makatura, Liane; Wang, Bohan; Chen, Yi-Lu; Deng, Bolei; Wojtan, Christopher J; Bickel, Bernd; Matusik, Wojciech (ACM Transactions on Graphics)
We introduce a compact, intuitive procedural graph representation for cellular metamaterials, which are small-scale, tileable structures that can be architected to exhibit many useful material properties. Because the structures’ “architectures” vary widely—with elements such as beams, thin shells, and solid bulks—it is difficult to explore them using existing representations. Generic approaches like voxel grids are versatile, but it is cumbersome to represent and edit individual structures; architecture-specific approaches address these issues, but are incompatible with one another. By contrast, our procedural graph succinctly represents the construction process for any structure using a simple skeleton annotated with spatially varying thickness. To express the highly constrained triply periodic minimal surfaces (TPMS) in this manner, we present the first fully automated version of the conjugate surface construction method, which allows novices to create complex TPMS from intuitive input. We demonstrate our representation’s expressiveness, accuracy, and compactness by constructing a wide range of established structures and hundreds of novel structures with diverse architectures and material properties. We also conduct a user study to verify our representation’s ease-of-use and ability to expand engineers’ capacity for exploration.
Keywords: Computer Graphics and Computer-Aided Design

Advanced motion tracking for interactive mass spectrometry imaging (IMSI) - Kluibenschedl, Florian; Ploner, Anna; Meisenbichler, Christina; Konrat, Robert; Müller, Thomas (International Journal of Mass Spectrometry)
Mass spectrometry imaging (MSI) is a powerful analytical technique for the two-dimensional (2D) localization of chemicals on surfaces. Conventional MSI experiments require to predefine the surface of interest based on photographic or microscopic images. Typically, these boundaries can no longer be changed or adjusted once the experiment has been started. In terms of a more interactive approach we recently developed a pen-like ionization interface which is directly connected to the mass spectrometer. The device allows the user to ionize chemicals by desorption electrospray ionization (DESI) and to freely move the interface over a surface of interest. A mini camera, which is mounted on the tip of the pen, magnifies the desorption area and enables a simple positioning of the pen. The combination of optical data from the camera module and chemical data obtained by mass analysis facilitates a novel type of imaging experiment: interactive mass spectrometry imaging (IMSI). For this application, we present a novel approach for a robust, optical flow-based motion detection. While the live video stream from the camera is used to track the pen's motion across the surface a post-acquisition algorithm correlates the coordinates of the pen trajectory with respective mass spectra obtained from a simultaneous mass spectrometric data acquisition. This algorithm is no longer dependent on a single, manually applied optical marker on the sample surface, which has to be visible on all video frames throughout the analysis. The advanced DESI-IMSI method was successfully tested on inkjet-printed letters as well as mouse brain tissue samples. Validation of the results was done by comparing DESI-IMSI with standard DESI-MSI data.

Direct path from turbulence to time-periodic solutions - Paranjape, Chaitanya S; Yalniz, Gökhan; Duguet, Yohann; Budanur, Nazmi B; Hof, Björn (Physical Review Letters)
Viscous flows through pipes and channels are steady and ordered until, with increasing velocity, the laminar motion catastrophically breaks down and gives way to turbulence. How this apparently discontinuous change from low- to high-dimensional motion can be rationalized within the framework of the Navier-Stokes equations is not well understood. Exploiting geometrical properties of transitional channel flow we trace turbulence to far lower Reynolds numbers (Re) than previously possible and identify the complete path that reversibly links fully turbulent motion to an invariant solution. This precursor of turbulence destabilizes rapidly with Re, and the accompanying explosive increase in attractor dimension effectively marks the transition between deterministic and de facto stochastic dynamics.
Keywords: General Physics and Astronomy

The molecular basis of sexual dimorphism: Experimental and theoretical characterization of phenotypic, transcriptomic and genetic patterns of sex-specific adaptation - Puixeu Sala, Gemma
Females and males across species are subject to divergent selective pressures arising from di↵erent reproductive interests and ecological niches. This often translates into a intricate array of sex-specific natural and sexual selection on traits that have a shared genetic basis between both sexes, causing a genetic sexual conflict. The resolution of this conflict mostly relies on the evolution of sex-specific expression of the shared genes, leading to phenotypic sexual dimorphism. Such sex-specific gene expression is thought to evolve via modifications of the genetic networks ultimately linked to sex-determining transcription factors. Although much empirical and theoretical evidence supports this standard picture of the molecular basis of sexual conflict resolution, there still are a few open questions regarding the complex array of selective forces driving phenotypic di↵erentiation between the sexes, as well as the molecular mechanisms underlying sexspecific adaptation. I address some of these open questions in my PhD thesis. First, how do patterns of phenotypic sexual dimorphism vary within populations, as a response to the temporal and spatial changes in sex-specific selective forces? To tackle this question, I analyze the patterns of sex-specific phenotypic variation along three life stages and across populations spanning the whole geographical range of Rumex hastatulus, a wind-pollinated angiosperm, in the first Chapter of the thesis. Second, how do gene expression patterns lead to phenotypic dimorphism, and what are the molecular mechanisms underlying the observed transcriptomic variation? I address this question by examining the sex- and tissue-specific expression variation in newly-generated datasets of sex-specific expression in heads and gonads of Drosophila melanogaster. I additionally used two complementary approaches for the study of the genetic basis of sex di↵erences in gene expression in the second and third Chapters of the thesis. Third, how does intersex correlation, thought to be one of the main aspects constraining the ability for the two sexes to decouple, interact with the evolution of sexual dimorphism? I develop models of sex-specific stabilizing selection, mutation and drift to formalize common intuition regarding the patterns of covariation between intersex correlation and sexual dimorphism in the fourth Chapter of the thesis. Alltogether, the work described in this PhD thesis provides useful insights into the links between genetic, transcriptomic and phenotypic layers of sex-specific variation, and contributes to our general understanding of the dynamics of sexual dimorphism evolution.

Sex-specific estimation of cis and trans regulation of gene expression in heads and gonads of Drosophila melanogaster - Puixeu Sala, Gemma; Macon, Ariana; Vicoso, Beatriz (G3: Genes, Genomes, Genetics)
The regulatory architecture of gene expression is known to differ substantially between sexes in Drosophila, but most studies performed so far used whole-body data and only single crosses, which may have limited their scope to detect patterns that are robust across tissues and biological replicates. Here, we use allele-specific gene expression of parental and reciprocal hybrid crosses between 6 Drosophila melanogaster inbred lines to quantify cis- and trans-regulatory variation in heads and gonads of both sexes separately across 3 replicate crosses. Our results suggest that female and male heads, as well as ovaries, have a similar regulatory architecture. On the other hand, testes display more and substantially different cis-regulatory effects, suggesting that sex differences in the regulatory architecture that have been previously observed may largely derive from testis-specific effects. We also examine the difference in cis-regulatory variation of genes across different levels of sex bias in gonads and heads. Consistent with the idea that intersex correlations constrain expression and can lead to sexual antagonism, we find more cis variation in unbiased and moderately biased genes in heads. In ovaries, reduced cis variation is observed for male-biased genes, suggesting that cis variants acting on these genes in males do not lead to changes in ovary expression. Finally, we examine the dominance patterns of gene expression and find that sex- and tissue-specific patterns of inheritance as well as trans-regulatory variation are highly variable across biological crosses, although these were performed in highly controlled experimental conditions. This highlights the importance of using various genetic backgrounds to infer generalizable patterns.
Keywords: Genetics (clinical); Genetics; Molecular Biology

Data from: Sex-specific estimation of cis and trans regulation of gene expression in heads and gonads of Drosophila melanogaster - Puixeu Sala, Gemma
Datasets of the publication "Sex-specific estimation of cis and trans regulation of gene expression in heads and gonads of Drosophila melanogaster".

Gaussian fluctuations in the equipartition principle for Wigner matrices - Cipolloni, Giorgio; Erdös, László; Henheik, Sven Joscha; Kolupaiev, Oleksii (Forum of Mathematics, Sigma)
The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.

Creation rate of Dirac particles at a point source - Henheik, Sven Joscha; Tumulka, Roderich (Journal of Physics A: Mathematical and Theoretical)
Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process $(Q_t)_{t\in\mathbb{R}}$ in the configuration space of a variable number of particles that is $|ψ_t|^2$-distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell's jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission).

Mechanistic insight on water dissociation on pristine low-index TiO2 surfaces from machine learning molecular dynamics simulations - Zeng, Zezhu; Wodaczek, Felix; Liu, Keyang; Stein, Frederick; Hutter, Jürg; Chen, Ji; Cheng, Bingqing (Nature Communications)
Water adsorption and dissociation processes on pristine low-index TiO2 interfaces are important but poorly understood outside the well-studied anatase (101) and rutile (110). To understand these, we construct three sets of machine learning potentials that are simultaneously applicable to various TiO2 surfaces, based on three density-functional-theory approximations. Here we show the water dissociation free energies on seven pristine TiO2 surfaces, and predict that anatase (100), anatase (110), rutile (001), and rutile (011) favor water dissociation, anatase (101) and rutile (100) have mostly molecular adsorption, while the simulations of rutile (110) sensitively depend on the slab thickness and molecular adsorption is preferred with thick slabs. Moreover, using an automated algorithm, we reveal that these surfaces follow different types of atomistic mechanisms for proton transfer and water dissociation: one-step, two-step, or both. These mechanisms can be rationalized based on the arrangements of water molecules on the different surfaces. Our finding thus demonstrates that the different pristine TiO2 surfaces react with water in distinct ways, and cannot be represented using just the low-energy anatase (101) and rutile (110) surfaces.

Improving variational quantum algorithms: Innovative initialization techniques and extensions to qudit systems - Sack, Stefan

Neutrophils on the hunt: Migratory strategies employed by neutrophils to fulfill their effector function - Stopp, Julian A

Investigating inbreeding depression and the self-incompatibility locus of Antirrhinum majus - Arathoon, Louise S
For self-incompatibility (SI) to be stable in a population, theory predicts that sufficient inbreeding depression (ID) is required: the fitness of offspring from self-mated individuals must be low enough to prevent the spread of self-compatibility (SC). Reviews of natural plant populations have supported this theory, with SI species generally showing high levels of ID. However, there is thought to be an under-sampling of self-incompatible taxa in the current literature. In this thesis, I study inbreeding depression in the SI plant species Antirrhinum majus using both greenhouse crosses and a large collected field dataset. Additionally, the gametophytic S-locus of A. majus is highly heterozygous and polymorphic, thus making assembly and discovery of S-alleles very difficult. Here, 206 new alleles of the male component SLFs are presented, along with a phylogeny showing the high conservation with alleles from another Antirrhinum species. Lastly, selected sites within the protein structure of SLFs are investigated, with one site in particular highlighted as potentially being involved in the SI recognition mechanism.

Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation - Ishida, Sadashige; Lavenant, Hugo (arXiv)
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also obtain the convergence rates for the gradient of the optimal potentials and the velocity field under mild regularity assumptions. To obtain such rates we discretize the dual formulation of the dynamic optimal transport problem and use the mature literature related to the error due to discretizing the Hamilton-Jacobi equation.
Keywords: Optimal transport; Hamilton-Jacobi equation; convex optimization

Executing and proving over dirty ledgers - Stefo, Christos; Xiang, Zhuolun; Kokoris Kogias, Eleftherios (27th International Conference on Financial Cryptography and Data Security)
Scaling blockchain protocols to perform on par with the expected needs of Web3.0 has been proven to be a challenging task with almost a decade of research. In the forefront of the current solution is the idea of separating the execution of the updates encoded in a block from the ordering of blocks. In order to achieve this, a new class of protocols called rollups has emerged. Rollups have as input a total ordering of valid and invalid transactions and as output a new valid state-transition. If we study rollups from a distributed computing perspective, we uncover that rollups take as input the output of a Byzantine Atomic Broadcast (BAB) protocol and convert it to a State Machine Replication (SMR) protocol. BAB and SMR, however, are considered equivalent as far as distributed computing is concerned and a solution to one can easily be retrofitted to solve the other simply by adding/removing an execution step before the validation of the input. This “easy” step of retrofitting an atomic broadcast solution to implement an SMR has, however, been overlooked in practice. In this paper, we formalize the problem and show that after BAB is solved, traditional impossibility results for consensus no longer apply towards an SMR. Leveraging this we propose a distributed execution protocol that allows reduced execution and storage cost per executor (O(log2n/n)) without relaxing the network assumptions of the underlying BAB protocol and providing censorship-resistance. Finally, we propose efficient non-interactive light client constructions that leverage our efficient execution protocols and do not require any synchrony assumptions or expensive ZK-proofs.

Automated verification and control of infinite state stochastic systems - Zikelic, Dorde
Stochastic systems provide a formal framework for modelling and quantifying uncertainty in systems and have been widely adopted in many application domains. Formal verification and control of finite state stochastic systems, a subfield of formal methods also known as probabilistic model checking, is well studied. In contrast, formal verification and control of infinite state stochastic systems have received comparatively less attention. However, infinite state stochastic systems commonly arise in practice. For instance, probabilistic models that contain continuous probability distributions such as normal or uniform, or stochastic dynamical systems which are a classical model for control under uncertainty, both give rise to infinite state systems. The goal of this thesis is to contribute to laying theoretical and algorithmic foundations of fully automated formal verification and control of infinite state stochastic systems, with a particular focus on systems that may be executed over a long or infinite time. We consider formal verification of infinite state stochastic systems in the setting of static analysis of probabilistic programs and formal control in the setting of controller synthesis in stochastic dynamical systems. For both problems, we present some of the first fully automated methods for probabilistic (a.k.a. quantitative) reachability and safety analysis applicable to infinite time horizon systems. We also advance the state of the art of probability 1 (a.k.a. qualitative) reachability analysis for both problems. Finally, for formal controller synthesis in stochastic dynamical systems, we present a novel framework for learning neural network control policies in stochastic dynamical systems with formal guarantees on correctness with respect to quantitative reachability, safety or reach-avoid specifications.

Intensification mechanisms of tropical cyclones - Polesello, Andrea; Muller, Caroline J; Pasquero, Claudia; Meroni, Agostino N. (EGU General Assembly 2023)

PCBend: Light up your 3D shapes with foldable circuit boards - Freire, Marco; Bhargava, Manas; Schreck, Camille; Hugron, Pierre-Alexandre; Bickel, Bernd; Lefebvre, Sylvain (Transactions on Graphics)
We propose a computational design approach for covering a surface with individually addressable RGB LEDs, effectively forming a low-resolution surface screen. To achieve a low-cost and scalable approach, we propose creating designs from flat PCB panels bent in-place along the surface of a 3D printed core. Working with standard rigid PCBs enables the use of established PCB manufacturing services, allowing the fabrication of designs with several hundred LEDs. Our approach optimizes the PCB geometry for folding, and then jointly optimizes the LED packing, circuit and routing, solving a challenging layout problem under strict manufacturing requirements. Unlike paper, PCBs cannot bend beyond a certain point without breaking. Therefore, we introduce parametric cut patterns acting as hinges, designed to allow bending while remaining compact. To tackle the joint optimization of placement, circuit and routing, we propose a specialized algorithm that splits the global problem into one sub-problem per triangle, which is then individually solved. Our technique generates PCB blueprints in a completely automated way. After being fabricated by a PCB manufacturing service, the boards are bent and glued by the user onto the 3D printed support. We demonstrate our technique on a range of physical models and virtual examples, creating intricate surface light patterns from hundreds of LEDs.
Keywords: PCB design and layout; Mesh geometry models

Superconductivity from a melted insulator in Josephson junction arrays - Mukhopadhyay, Soham; Senior, Jorden L; Saez Mollejo, Jaime; Puglia, Denise; Zemlicka, Martin; Fink, Johannes M; Higginbotham, Andrew P (Nature Physics)
Arrays of Josephson junctions are governed by a competition between superconductivity and repulsive Coulomb interactions, and are expected to exhibit diverging low-temperature resistance when interactions exceed a critical level. Here we report a study of the transport and microwave response of Josephson arrays with interactions exceeding this level. Contrary to expectations, we observe that the array resistance drops dramatically as the temperature is decreased—reminiscent of superconducting behaviour—and then saturates at low temperature. Applying a magnetic field, we eventually observe a transition to a highly resistive regime. These observations can be understood within a theoretical picture that accounts for the effect of thermal fluctuations on the insulating phase. On the basis of the agreement between experiment and theory, we suggest that apparent superconductivity in our Josephson arrays arises from melting the zero-temperature insulator.
Keywords: General Physics and Astronomy

An energy decomposition theorem for matrices and related questions - Mohammadi, Ali; Pham, Thang; Wang, Yiting (Canadian Mathematical Bulletin)
Given A⊆GL2(Fq), we prove that there exist disjoint subsets B,C⊆A such that A=B⊔C and their additive and multiplicative energies satisfying max{E+(B),E×(C)}≪|A|3/M(|A|), where M(|A|)=min{q4/3/|A|1/3(log|A|)2/3,|A|4/5/q13/5(log|A|)27/10}. We also study some related questions on moderate expanders over matrix rings, namely, for A,B,C⊆GL2(Fq), we have |AB+C|, |(A+B)C|≫q4, whenever |A||B||C|≫q10+1/2. These improve earlier results due to Karabulut, Koh, Pham, Shen, and Vinh ([2019], Expanding phenomena over matrix rings, ForumMath., 31, 951–970).

Spontaneous flows and dynamics of full-integer topological defects in polar active matter - Rønning, Jonas; Renaud, Julian B; Doostmohammadi, Amin; Angheluta, Luiza (Soft Matter)
Polar active matter of self-propelled particles sustain spontaneous flows through the full-integer topological defects. We study theoretically the incompressible flow profiles around ±1 defects induced by polar and dipolar active forces. We show that dipolar forces induce vortical flows around the +1 defect, while the flow around the −1 defect has an 8-fold rotational symmetry. The vortical flow changes its chirality near the +1 defect core in the absence of the friction with a substrate. We show analytically that the flow induced by polar active forces is vortical near the +1 defect and is 4-fold symmetric near the −1 defect, while it becomes uniform in the far-field. For a pair of oppositely charged defects, this polar flow contributes to a mutual interaction force that depends only on the orientation of the defect pair relative to the background polarization, and that enhances defect pair annihilation. This is in contradiction with the effect of dipolar active forces which decay inversely proportional with the defect separation distance. As such, our analyses reveals a long-ranged mechanism for the pairwise interaction between topological defects in polar active matter.

Beyond the universal law of robustness: Sharper laws for random features and neural tangent kernels - Bombari, Simone; Kiyani, Shayan; Mondelli, Marco (Proceedings of the 40th International Conference on Machine Learning)
Machine learning models are vulnerable to adversarial perturbations, and a thought-provoking paper by Bubeck and Sellke has analyzed this phenomenon through the lens of over-parameterization: interpolating smoothly the data requires significantly more parameters than simply memorizing it. However, this "universal" law provides only a necessary condition for robustness, and it is unable to discriminate between models. In this paper, we address these gaps by focusing on empirical risk minimization in two prototypical settings, namely, random features and the neural tangent kernel (NTK). We prove that, for random features, the model is not robust for any degree of over-parameterization, even when the necessary condition coming from the universal law of robustness is satisfied. In contrast, for even activations, the NTK model meets the universal lower bound, and it is robust as soon as the necessary condition on over-parameterization is fulfilled. This also addresses a conjecture in prior work by Bubeck, Li and Nagaraj. Our analysis decouples the effect of the kernel of the model from an "interaction matrix", which describes the interaction with the test data and captures the effect of the activation. Our theoretical results are corroborated by numerical evidence on both synthetic and standard datasets (MNIST, CIFAR-10).

The metabolism of the developing brain : How large neutral amino acids modulate perinatal neuronal excitability and survival - Knaus, Lisa
Within the human body, the brain exhibits the highest rate of energy consumption amongst all organs, with the majority of generated ATP being utilized to sustain neuronal activity. Therefore, the metabolism of the mature cerebral cortex is geared towards preserving metabolic homeostasis whilst generating significant amounts of energy. This requires a precise interplay between diverse metabolic pathways, spanning from a tissue-wide scale to the level of individual neurons. Disturbances to this delicate metabolic equilibrium, such as those resulting from maternal malnutrition or mutations affecting metabolic enzymes, often result in neuropathological variants of neurodevelopment. For instance, mutations in SLC7A5, a transporter of metabolically essential large neutral amino acids (LNAAs), have been associated with autism and microcephaly. However, despite recent progress in the field, the extent of metabolic restructuring that occurs within the developing brain and the corresponding alterations in nutrient demands during various critical periods remain largely unknown. To investigate this, we performed metabolomic profiling of the murine cerebral cortex to characterize the metabolic state of the forebrain at different developmental stages. We found that the developing cortex undergoes substantial metabolic reprogramming, with specific sets of metabolites displaying stage-specific changes. According to our observations, we determined a distinct temporal period in postnatal development during which the cortex displays heightened reliance on LNAAs. Hence, using a conditional knock-out mouse model, we deleted Slc7a5 in neural cells, allowing us to monitor the impact of a perturbed neuronal metabolic state across multiple developmental stages of corticogenesis. We found that manipulating the levels of essential LNAAs in cortical neurons in vivo affects one particular perinatal developmental period critical for cortical network refinement. Abnormally low intracellular LNAA levels result in cell-autonomous alterations in neuronal lipid metabolism, excitability, and survival during this particular time window. Although most of the effects of Slc7a5 deletion on neuronal physiology are transient, derailment of these processes during this brief but crucial window leads to long-term circuit dysfunction in mice. In conclusion, out data indicate that the cerebral cortex undergoes significant metabolic reorganization during development. This process involves the intricate integration of multiple metabolic pathways to ensure optimal neuronal function throughout different developmental stages. Our findings offer a paradigm for understanding how neurons synchronize the expression of nutrient-related genes with their activity to allow proper brain maturation. Further, our results demonstrate that disruptions in these precisely calibrated metabolic processes during critical periods of brain development may result in neuropathological outcomes in mice and in humans.

Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows - Marensi, Elena; Yalniz, Gökhan; Hof, Björn (Journal of Fluid Mechanics)
The first long-lived turbulent structures observable in planar shear flows take the form of localized stripes, inclined with respect to the mean flow direction. The dynamics of these stripes is central to transition, and recent studies proposed an analogy to directed percolation where the stripes’ proliferation is ultimately responsible for the turbulence becoming sustained. In the present study we focus on the internal stripe dynamics as well as on the eventual stripe expansion, and we compare the underlying mechanisms in pressure- and shear-driven planar flows, respectively, plane-Poiseuille and plane-Couette flow. Despite the similarities of the overall laminar–turbulence patterns, the stripe proliferation processes in the two cases are fundamentally different. Starting from the growth and sustenance of individual stripes, we find that in plane-Couette flow new streaks are created stochastically throughout the stripe whereas in plane-Poiseuille flow streak creation is deterministic and occurs locally at the downstream tip. Because of the up/downstream symmetry, Couette stripes, in contrast to Poiseuille stripes, have two weak and two strong laminar turbulent interfaces. These differences in symmetry as well as in internal growth give rise to two fundamentally different stripe splitting mechanisms. In plane-Poiseuille flow splitting is connected to the elongational growth of the original stripe, and it results from a break-off/shedding of the stripe's tail. In plane-Couette flow splitting follows from a broadening of the original stripe and a division along the stripe into two slimmer stripes.
Keywords: turbulence; transition to turbulence; patterns

To DISP or not? The far‐reaching reaction mechanisms underpinning Lithium‐air batteries - Jethwa, Rajesh B; Mondal, Soumyadip; Pant, Bhargavi; Freunberger, Stefan Alexander (Angewandte Chemie International Edition)
The short history of research on Li-O2 batteries has seen a remarkable number of mechanistic U-turns over the years. From the initial use of carbonate electrolytes, that were then found to be entirely unsuitable, to the belief that (su)peroxide was solely responsible for degradation, before the more reactive singlet oxygen was found to form, to the hypothesis that capacity depends on a competing surface/solution mechanism before a practically exclusive solution mechanism was identified. Herein, we argue for an ever-fresh look at the reported data without bias towards supposedly established explanations. We explain how the latest findings on rate and capacity limits, as well as the origin of side reactions, are connected via the disproportionation (DISP) step in the (dis)charge mechanism. Therefrom, directions emerge for the design of electrolytes and mediators on how to suppress side reactions and to enable high rate and high reversible capacity.
Keywords: General Chemistry; Catalysis

The rigid core and flexible surface of amyloid fibrils probed by Magic‐Angle Spinning NMR of aromatic residues - Becker, Lea Marie; Berbon, Mélanie; Vallet, Alicia; Grelard, Axelle; Morvan, Estelle; Bardiaux, Benjamin; Lichtenecker, Roman; Ernst, Matthias; Loquet, Antoine; Schanda, Paul (Angewandte Chemie International Edition)
Aromatic side chains are important reporters of the plasticity of proteins, and often form important contacts in protein--protein interactions. By studying a pair of structurally homologous cross-β amyloid fibrils, HET-s and HELLF, with a specific isotope-labeling approach and magic-angle-spinning (MAS) NMR, we have characterized the dynamic behavior of Phe and Tyr aromatic rings to show that the hydrophobic amyloid core is rigid, without any sign of "breathing motions" over hundreds of milliseconds at least. Aromatic residues exposed at the fibril surface have a rigid ring axis but undergo ring flips, on a variety of time scales from ns to µs. Our approach provides direct insight into hydrophobic-core motions, enabling a better evaluation of the conformational heterogeneity generated from a NMR structural ensemble of such amyloid cross-β architecture.
Keywords: General Chemistry; Catalysis

Research data to: The rigid core and flexible surface of amyloid fibrils probed by magic-angle-spinning NMR spectroscopy of aromatic residues - Becker, Lea Marie; Schanda, Paul
Aromatic side chains are important reporters of the plasticity of proteins, and often form important contacts in protein–protein interactions. We studied aromatic residues in the two structurally homologous cross-β amyloid fibrils HET-s, and HELLF by employing a specific isotope-labeling approach and magic-angle-spinning NMR. The dynamic behavior of the aromatic residues Phe and Tyr indicates that the hydrophobic amyloid core is rigid, without any sign of "breathing motions" over hundreds of milliseconds at least. Aromatic residues exposed at the fibril surface have a rigid ring axis but undergo ring flips on a variety of time scales from nanoseconds to microseconds. Our approach provides direct insight into hydrophobic-core motions, enabling a better evaluation of the conformational heterogeneity generated from an NMR structural ensemble of such amyloid cross-β architecture.
Keywords: aromatic side chains; isotopic labeling; protein dynamics; ring flips; spin relaxation

Chiral and nematic phases of flexible active filaments - Dunajova, Zuzana; Prats Mateu, Batirtze; Radler, Philipp; Lim, Keesiang; Brandis, Dörte; Velicky, Philipp; Danzl, Johann G; Wong, Richard W.; Elgeti, Jens; Hannezo, Edouard B; Loose, Martin (Nature Physics)
The emergence of large-scale order in self-organized systems relies on local interactions between individual components. During bacterial cell division, FtsZ—a prokaryotic homologue of the eukaryotic protein tubulin—polymerizes into treadmilling filaments that further organize into a cytoskeletal ring. In vitro, FtsZ filaments can form dynamic chiral assemblies. However, how the active and passive properties of individual filaments relate to these large-scale self-organized structures remains poorly understood. Here we connect single-filament properties with the mesoscopic scale by combining minimal active matter simulations and biochemical reconstitution experiments. We show that the density and flexibility of active chiral filaments define their global order. At intermediate densities, curved, flexible filaments organize into chiral rings and polar bands. An effectively nematic organization dominates for high densities and for straight, mutant filaments with increased rigidity. Our predicted phase diagram quantitatively captures these features, demonstrating how the flexibility, density and chirality of the active filaments affect their collective behaviour. Our findings shed light on the fundamental properties of active chiral matter and explain how treadmilling FtsZ filaments organize during bacterial cell division.

Spatiotemporal signaling during assembly of the bacterial divisome - Radler, Philipp
Cell division in Escherichia coli is performed by the divisome, a multi-protein complex composed of more than 30 proteins. The divisome spans from the cytoplasm through the inner membrane to the cell wall and the outer membrane. Divisome assembly is initiated by a cytoskeletal structure, the so-called Z-ring, which localizes at the center of the E. coli cell and determines the position of the future cell septum. The Z-ring is composed of the highly conserved bacterial tubulin homologue FtsZ, which forms treadmilling filaments. These filaments are recruited to the inner membrane by FtsA, a highly conserved bacterial actin homologue. FtsA interacts with other proteins in the periplasm and thus connects the cytoplasmic and periplasmic components of the divisome. A previous model postulated that FtsA regulates maturation of the divisome by switching from an oligomeric, inactive state to a monomeric and active state. This model was based mostly on in vivo studies, as a biochemical characterization of FtsA has been hampered by difficulties in purifying the protein. Here, we studied FtsA using an in vitro reconstitution approach and aimed to answer two questions: (i) How are dynamics from cytoplasmic, treadmilling FtsZ filaments coupled to proteins acting in the periplasmic space and (ii) How does FtsA regulate the maturation of the divisome? We found that the cytoplasmic peptides of the transmembrane proteins FtsN and FtsQ interact directly with FtsA and can follow the spatiotemporal signal of FtsA/Z filaments. When we investigated the underlying mechanism by imaging single molecules of FtsNcyto, we found the peptide to interact transiently with FtsA. An in depth analysis of the single molecule trajectories helped to postulate a model where PG synthases follow the dynamics of FtsZ by a diffusion and capture mechanism. Following up on these findings we were interested in how the self-interaction of FtsA changes when it encounters FtsNcyto and if we can confirm the proposed oligomer-monomer switch. For this, we compared the behavior of the previously identified, hyperactive mutant FtsA R286W with wildtype FtsA. The mutant outperforms WT in mirroring and transmitting the spatiotemporal signal of treadmilling FtsZ filaments. Surprisingly however, we found that this was not due to a difference in the self-interaction strength of the two variants, but a difference in their membrane residence time. Furthermore, in contrast to our expectations, upon binding of FtsNcyto the measured self-interaction of FtsA actually increased. We propose that FtsNcyto induces a rearrangement of the oligomeric architecture of FtsA. In further consequence this change leads to more persistent FtsZ filaments which results in a defined signalling zone, allowing formation of the mature divisome. The observed difference between FtsA WT and R286W is due to the vastly different membrane turnover of the proteins. R286W cycles 5-10x faster compared to WT which allows to sample FtsZ filaments at faster frequencies. These findings can explain the observed differences in toxicity for overexpression of FtsA WT and R286W and help to understand how FtsA regulates divisome maturation.
Keywords: Cell Division; Reconstitution; FtsZ; FtsA; Divisome; E.coli

Mesoscopic phenomena in hybrid semiconductor-superconductor nanodevices : From full-shell nanowires to two-dimensional hole gas in germanium - Valentini, Marco
Semiconductor-superconductor hybrid systems are the harbour of many intriguing mesoscopic phenomena. This material combination leads to spatial variations of the superconducting properties, which gives rise to Andreev bound states (ABSs). Some of these states might exhibit remarkable properties that render them highly desirable for topological quantum computing. The most prominent and hunted of such states are Majorana zero modes (MZMs), quasiparticles equals to their own quasiparticles that they follow non-abelian statistics. In this thesis, we first introduce the general framework of such hybrid systems and, then, we unveil a series of mesoscopic phenomena that we discovered. Firstly, we show tunneling spectroscopy experiments on full-shell nanowires (NWs) showing that unwanted quantum-dot states coupled to superconductors (Yu-Shiba-Rusinov states) can mimic MZMs signatures. Then, we introduce a novel protocol which allowed the integration of tunneling spectroscopy with Coulomb spectroscopy within the same device. Employing this approach on both full-shell NWs and partial-shell NWs, we demonstrated that longitudinally confined states reveal charge transport phenomenology similar to the one expected for MZMs. These findings shed light on the intricate interplay between superconductivity and quantum confinement, which brought us to explore another material platform, i.e. a two-dimensional Germanium hole gas. After developing a robust way to induce superconductivity in such system, we showed how to engineer the proximity effect and we revealed a superconducting hard gap. Finally, we created a superconducting radio frequency driven ideal diode and a generator of non-sinusoidal current-phase relations. Our results open the path for the exploration of protected superconducting qubits and more complex hybrid devices in planar Germanium, like Kitaev chains and hybrid qubit devices.

Lincheck: A practical framework for testing concurrent data structures on JVM - Koval, Nikita; Fedorov, Alexander; Sokolova, Maria; Tsitelov, Dmitry; Alistarh, Dan-Adrian (35th International Conference on Computer Aided Verification)
This paper presents Lincheck, a new practical and user-friendly framework for testing concurrent algorithms on the Java Virtual Machine (JVM). Lincheck provides a simple and declarative way to write concurrent tests: instead of describing how to perform the test, users specify what to test by declaring all the operations to examine; the framework automatically handles the rest. As a result, tests written with Lincheck are concise and easy to understand. The framework automatically generates a set of concurrent scenarios, examines them using stress-testing or bounded model checking, and verifies that the results of each invocation are correct. Notably, if an error is detected via model checking, Lincheck provides an easy-to-follow trace to reproduce it, significantly simplifying the bug investigation. To the best of our knowledge, Lincheck is the first production-ready tool on the JVM that offers such a simple way of writing concurrent tests, without requiring special skills or expertise. We successfully integrated Lincheck in the development process of several large projects, such as Kotlin Coroutines, and identified new bugs in popular concurrency libraries, such as a race in Java’s standard ConcurrentLinkedDeque and a liveliness bug in Java’s AbstractQueuedSynchronizer framework, which is used in most of the synchronization primitives. We believe that Lincheck can significantly improve the quality and productivity of concurrent algorithms research and development and become the state-of-the-art tool for checking their correctness.

Individual and social immunity against viral infections in ants - Franschitz, Anna
Social insects fight disease using their individual immune systems and the cooperative sanitary behaviors of colony members. These social defenses are well explored against externally-infecting pathogens, but little is known about defense strategies against internally-infecting pathogens, such as viruses. Viruses are ubiquitous and in the last decades it has become evident that also many ant species harbor viruses. We present one of the first studies addressing transmission dynamics and collective disease defenses against viruses in ants on a mechanistic level. I successfully established an experimental ant host – viral pathogen system as a model for the defense strategies used by social insects against internal pathogen infections, as outlined in the third chapter. In particular, we studied how garden ants (Lasius neglectus) defend themselves and their colonies against the generalist insect virus CrPV (cricket paralysis virus). We chose microinjections of virus directly into the ants’ hemolymph because it allowed us to use a defined exposure dose. Here we show that this is a good model system, as the virus is replicating and thus infecting the host. The ants mount a clear individual immune response against the viral infection, which is characterized by a specific siRNA pattern, namely siRNAs mapping against the viral genome with a peak of 21 and 22 bp long fragments. The onset of this immune response is consistent with the timeline of viral replication that starts already within two days post injection. The disease manifests in decreased survival over a course of two to three weeks. Regarding group living, we find that infected ants show a strong individual immune response, but that their course of disease is little affected by nestmate presence, as described in chapter four. Hence, we do not find social immunity in the context of viral infections in ants. Nestmates, however, can contract the virus. Using Drosophila S2R+ cells in culture, we showed that 94 % of the nestmates contract active virus within four days of social contact to an infected individual. Virus is transmitted in low doses, thus not causing disease transmission within the colony. While virus can be transmitted during short direct contacts, we also assume transmission from deceased ants and show that the nestmates’ immune system gets activated after contracting a low viral dose. We find considerable potential for indirect transmission via the nest space. Virus is shed to the nest, where it stays viable for one week and is also picked up by other ants. Apart from that, we want to underline the potential of ant poison as antiviral agent. We determined that ant poison successfully inactivates CrPV in vitro. However, we found no evidence for effective poison use to sanitize the nest space. On the other hand, local application of ant poison by oral poison uptake, which is part of the ants prophylactic behavioral repertoire, probably contributes to keeping the gut of each individual sanitized. We hypothesize that oral poison uptake might be the reason why we did not find viable virus in the trophallactic fluid. The fifth chapter encompasses preliminary data on potential social immunization. However, our experiments do not confirm an actual survival benefit for the nestmates upon pathogen challenge under the given experimental settings. Nevertheless, we do not want to rule out the possibility for nestmate immunization, but rather emphasize that considering different experimental timelines and viral doses would provide a multitude of options for follow-up experiments. In conclusion, we find that prophylactic individual behaviors, such as oral poison uptake, might play a role in preventing viral disease transmission. Compared to colony defense against external pathogens, internal pathogen infections require a stronger component of individual physiological immunity than behavioral social immunity, yet could still lead to collective protection.

1-Lipschitz neural networks are more expressive with N-activations - Prach, Bernd; Lampert, Christoph (arXiv)
A crucial property for achieving secure, trustworthy and interpretable deep learning systems is their robustness: small changes to a system's inputs should not result in large changes to its outputs. Mathematically, this means one strives for networks with a small Lipschitz constant. Several recent works have focused on how to construct such Lipschitz networks, typically by imposing constraints on the weight matrices. In this work, we study an orthogonal aspect, namely the role of the activation function. We show that commonly used activation functions, such as MaxMin, as well as all piece-wise linear ones with two segments unnecessarily restrict the class of representable functions, even in the simplest one-dimensional setting. We furthermore introduce the new N-activation function that is provably more expressive than currently popular activation functions. We provide code at this https URL.

Regulation of neural progenitor survival by Shh and BMP in the developing spinal cord - Kuzmicz-Kowalska, Katarzyna
Morphogens are signaling molecules that are known for their prominent role in pattern formation within developing tissues. In addition to patterning, morphogens also control tissue growth. However, the underlying mechanisms are poorly understood. We studied the role of morphogens in regulating tissue growth in the developing vertebrate neural tube. In this system, opposing morphogen gradients of Shh and BMP establish the dorsoventral pattern of neural progenitor domains. Perturbations in these morphogen pathways result in alterations in tissue growth and cell cycle progression, however, it has been unclear what cellular process is affected. To address this, we analysed the rates of cell proliferation and cell death in mouse mutants in which signaling is perturbed, as well as in chick neural plate explants exposed to defined concentrations of signaling activators or inhibitors. Our results indicated that the rate of cell proliferation was not altered in these assays. By contrast, both the Shh and BMP signaling pathways had profound effects on neural progenitor survival. Our results indicate that these pathways synergise to promote cell survival within neural progenitors. Consistent with this, we found that progenitors within the intermediate region of the neural tube, where the combined levels of Shh and BMP are the lowest, are most prone to cell death when signaling activity is inhibited. In addition, we found that downregulation of Shh results in increased apoptosis within the roof plate, which is the dorsal source of BMP ligand production. This revealed a cross-interaction between the Shh and BMP morphogen signaling pathways that may be relevant for understanding how gradients scale in neural tubes with different overall sizes. We further studied the mechanism acting downstream of Shh in cell survival regulation using genetic and genomic approaches. We propose that Shh transcriptionally regulates a non-canonical apoptotic pathway. Altogether, our study points to a novel role of opposing morphogen gradients in tissue size regulation and provides new insights into complex interactions between Shh and BMP signaling gradients in the neural tube.

Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences - Marveggio, Alice
This thesis concerns the application of variational methods to the study of evolution problems arising in fluid mechanics and in material sciences. The main focus is on weak-strong stability properties of some curvature driven interface evolution problems, such as the two-phase Navier–Stokes flow with surface tension and multiphase mean curvature flow, and on the phase-field approximation of the latter. Furthermore, we discuss a variational approach to the study of a class of doubly nonlinear wave equations. First, we consider the two-phase Navier–Stokes flow with surface tension within a bounded domain. The two fluids are immiscible and separated by a sharp interface, which intersects the boundary of the domain at a constant contact angle of ninety degree. We devise a suitable concept of varifolds solutions for the associated interface evolution problem and we establish a weak-strong uniqueness principle in case of a two dimensional ambient space. In order to focus on the boundary effects and on the singular geometry of the evolving domains, we work for simplicity in the regime of same viscosities for the two fluids. The core of the thesis consists in the rigorous proof of the convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow for a suitable class of multi- well potentials and for well-prepared initial data. We even establish a rate of convergence. Our relative energy approach relies on the concept of gradient-flow calibration for branching singularities in multiphase mean curvature flow and thus enables us to overcome the limitations of other approaches. To the best of the author’s knowledge, our result is the first quantitative and unconditional one available in the literature for the vectorial/multiphase setting. This thesis also contains a first study of weak-strong stability for planar multiphase mean curvature flow beyond the singularity resulting from a topology change. Previous weak-strong results are indeed limited to time horizons before the first topology change of the strong solution. We consider circular topology changes and we prove weak-strong stability for BV solutions to planar multiphase mean curvature flow beyond the associated singular times by dynamically adapting the strong solutions to the weak one by means of a space-time shift. In the context of interface evolution problems, our proofs for the main results of this thesis are based on the relative energy technique, relying on novel suitable notions of relative energy functionals, which in particular measure the interface error. Our statements follow from the resulting stability estimates for the relative energy associated to the problem. At last, we introduce a variational approach to the study of nonlinear evolution problems. This approach hinges on the minimization of a parameter dependent family of convex functionals over entire trajectories, known as Weighted Inertia-Dissipation-Energy (WIDE) functionals. We consider a class of doubly nonlinear wave equations and establish the convergence, up to subsequences, of the associated WIDE minimizers to a solution of the target problem as the parameter goes to zero.

Mesoscopic eigenvalue statistics for Wigner-type matrices - Riabov, Volodymyr (arXiv)
We prove a universal mesoscopic central limit theorem for linear eigenvalue statistics of a Wigner-type matrix inside the bulk of the spectrum with compactly supported twice continuously differentiable test functions. The main novel ingredient is an optimal local law for the two-point function $T(z,ζ)$ and a general class of related quantities involving two resolvents at nearby spectral parameters.

Provably-efficient and internally-deterministic parallel Union-Find - Fedorov, Alexander; Hashemi, Diba; Nadiradze, Giorgi; Alistarh, Dan-Adrian (Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures)
Determining the degree of inherent parallelism in classical sequential algorithms and leveraging it for fast parallel execution is a key topic in parallel computing, and detailed analyses are known for a wide range of classical algorithms. In this paper, we perform the first such analysis for the fundamental Union-Find problem, in which we are given a graph as a sequence of edges, and must maintain its connectivity structure under edge additions. We prove that classic sequential algorithms for this problem are well-parallelizable under reasonable assumptions, addressing a conjecture by [Blelloch, 2017]. More precisely, we show via a new potential argument that, under uniform random edge ordering, parallel union-find operations are unlikely to interfere: T concurrent threads processing the graph in parallel will encounter memory contention O(T2 · log |V| · log |E|) times in expectation, where |E| and |V| are the number of edges and nodes in the graph, respectively. We leverage this result to design a new parallel Union-Find algorithm that is both internally deterministic, i.e., its results are guaranteed to match those of a sequential execution, but also work-efficient and scalable, as long as the number of threads T is O(|E|1 over 3 - ε), for an arbitrarily small constant ε > 0, which holds for most large real-world graphs. We present lower bounds which show that our analysis is close to optimal, and experimental results suggesting that the performance cost of internal determinism is limited.

Adaptive mutation in E. coli modulated by luxS - Hennessey-Wesen, Mike
Keywords: microfluidics; miceobiology; mutations; quorum sensing

Nanoparticle-based semiconductor solids: From synthesis to consolidation - Calcabrini, Mariano
High-performance semiconductors rely upon precise control of heat and charge transport. This can be achieved by precisely engineering defects in polycrystalline solids. There are multiple approaches to preparing such polycrystalline semiconductors, and the transformation of solution-processed colloidal nanoparticles is appealing because colloidal nanoparticles combine low cost with structural and compositional tunability along with rich surface chemistry. However, the multiple processes from nanoparticle synthesis to the final bulk nanocomposites are very complex. They involve nanoparticle purification, post-synthetic modifications, and finally consolidation (thermal treatments and densification). All these properties dictate the final material’s composition and microstructure, ultimately affecting its functional properties. This thesis explores the synthesis, surface chemistry and consolidation of colloidal semiconductor nanoparticles into dense solids. In particular, the transformations that take place during these processes, and their effect on the material’s transport properties are evaluated.

Ultrastructural characterization of natively preserved extracellular matrix by cryo-electron tomography - Zens, Bettina
The extracellular matrix (ECM) is a hydrated and complex three-dimensional network consisting of proteins, polysaccharides, and water. It provides structural scaffolding for the cells embedded within it and is essential in regulating numerous physiological processes, including cell migration and proliferation, wound healing, and stem cell fate. Despite extensive study, detailed structural knowledge of ECM components in physiologically relevant conditions is still rudimentary. This is due to methodological limitations in specimen preparation protocols which are incompatible with keeping large samples, such as the ECM, in their native state for subsequent imaging. Conventional electron microscopy (EM) techniques rely on fixation, dehydration, contrasting, and sectioning. This results in the alteration of a highly hydrated environment and the potential introduction of artifacts. Other structural biology techniques, such as nuclear magnetic resonance (NMR) spectroscopy and X-ray crystallography, allow high-resolution analysis of protein structures but only work on homogenous and purified samples, hence lacking contextual information. Currently, no approach exists for the ultrastructural and structural study of extracellular components under native conditions in a physiological, 3D environment. In this thesis, I have developed a workflow that allows for the ultrastructural analysis of the ECM in near-native conditions at molecular resolution. The developments I introduced include implementing a novel specimen preparation workflow for cell-derived matrices (CDMs) to render them compatible with ion-beam milling and subsequent high-resolution cryo-electron tomography (ET). To this end, I have established protocols to generate CDMs grown over several weeks on EM grids that are compatible with downstream cryo-EM sample preparation and imaging techniques. Characterization of these ECMs confirmed that they contain essential ECM components such as collagen I, collagen VI, and fibronectin I in high abundance and hence represent a bona fide biologically-relevant sample. I successfully optimized vitrification of these specimens by testing various vitrification techniques and cryoprotectants. In order to obtain high-resolution molecular insights into the ultrastructure and organization of CDMs, I established cryo-focused ion beam scanning electron microscopy (FIBSEM) on these challenging and complex specimens. I explored different approaches for the creation of thin cryo-lamellae by FIB milling and succeeded in optimizing the cryo-lift-out technique, resulting in high-quality lamellae of approximately 200 nm thickness. High-resolution Cryo-ET of these lamellae revealed for the first time the architecture of native CDM in the context of matrix-secreting cells. This allowed for the in situ visualization of fibrillar matrix proteins such as collagen, laying the foundation for future structural and ultrastructural characterization of these proteins in their near-native environment. In summary, in this thesis, I present a novel workflow that combines state-of-the-art cryo-EM specimen preparation and imaging technologies to permit characterization of the ECM, an important tissue component in higher organisms. This innovative and highly versatile workflow will enable addressing far-reaching questions on ECM architecture, composition, and reciprocal ECM-cell interactions.
Keywords: cryo-EM; cryo-ET; FIB milling; method development; FIBSEM; extracellular matrix; ECM; cell-derived matrices; CDMs; cell culture; high pressure freezing; HPF; structural biology; tomography; collagen

Mechanochemical pattern formation across biological scales - Boocock, Daniel R
Pattern formation is of great importance for its contribution across different biological behaviours. During developmental processes for example, patterns of chemical gradients are established to determine cell fate and complex tissue patterns emerge to define structures such as limbs and vascular networks. Patterns are also seen in collectively migrating groups, for instance traveling waves of density emerging in moving animal flocks as well as collectively migrating cells and tissues. To what extent these biological patterns arise spontaneously through the local interaction of individual constituents or are dictated by higher level instructions is still an open question however there is evidence for the involvement of both types of process. Where patterns arise spontaneously there is a long standing interest in how far the interplay of mechanics, e.g. force generation and deformation, and chemistry, e.g. gene regulation and signaling, contributes to the behaviour. This is because many systems are able to both chemically regulate mechanical force production and chemically sense mechanical deformation, forming mechano-chemical feedback loops which can potentially become unstable towards spatio and/or temporal patterning. We work with experimental collaborators to investigate the possibility that this type of interaction drives pattern formation in biological systems at different scales. We focus first on tissue-level ERK-density waves observed during the wound healing response across different systems where many previous studies have proposed that patterns depend on polarized cell migration and arise from a mechanical flocking-like mechanism. By combining theory with mechanical and optogenetic perturbation experiments on in vitro monolayers we instead find evidence for mechanochemical pattern formation involving only scalar bilateral feedbacks between ERK signaling and cell contraction. We perform further modeling and experiment to study how this instability couples with polar cell migration in order to produce a robust and efficient wound healing response. In a following chapter we implement ERK-density coupling and cell migration in a 2D active vertex model to investigate the interaction of ERK-density patterning with different tissue rheologies and find that the spatio-temporal dynamics are able to both locally and globally fluidize a tissue across the solid-fluid glass transition. In a last chapter we move towards lower spatial scales in the context of subcellular patterning of the cell cytoskeleton where we investigate the transition between phases of spatially homogeneous temporal oscillations and chaotic spatio-temporal patterning in the dynamics of myosin and ROCK activities (a motor component of the actomyosin cytoskeleton and its activator). Experimental evidence supports an intrinsic chemical oscillator which we encode in a reaction model and couple to a contractile active gel description of the cell cortex. The model exhibits phases of chemical oscillations and contractile spatial patterning which reproduce many features of the dynamics seen in Drosophila oocyte epithelia in vivo. However, additional pharmacological perturbations to inhibit myosin contractility leaves the role of contractile instability unclear. We discuss alternative hypotheses and investigate the possibility of reaction-diffusion instability.

Mesendoderm formation in zebrafish gastrulation: The role of extraembryonic tissues - Schauer, Alexandra
The tight spatiotemporal coordination of signaling activity determining embryo patterning and the physical processes driving embryo morphogenesis renders embryonic development robust, such that key developmental processes can unfold relatively normally even outside of the full embryonic context. For instance, embryonic stem cell cultures can recapitulate the hallmarks of gastrulation, i.e. break symmetry leading to germ layer formation and morphogenesis, in a very reduced environment. This leads to questions on specific contributions of embryo-specific features, such as the presence of extraembryonic tissues, which are inherently involved in gastrulation in the full embryonic context. To address this, we established zebrafish embryonic explants without the extraembryonic yolk cell, an important player as a signaling source and for morphogenesis during gastrulation, as a model of ex vivo development. We found that dorsal-marginal determinants are required and sufficient in these explants to form and pattern all three germ layers. However, formation of tissues, which require the highest Nodal-signaling levels, is variable, demonstrating a contribution of extraembryonic tissues for reaching peak Nodal signaling levels. Blastoderm explants also undergo gastrulation-like axis elongation. We found that this elongation movement shows hallmarks of oriented mesendoderm cell intercalations typically associated with dorsal tissues in the intact embryo. These are disrupted by uniform upregulation of BMP signaling activity and concomitant explant ventralization, suggesting that tight spatial control of BMP signaling is a prerequisite for explant morphogenesis. This control is achieved by Nodal signaling, which is critical for effectively downregulating BMP signaling in the mesendoderm, highlighting that Nodal signaling is not only directly required for mesendoderm cell fate specification and morphogenesis, but also by maintaining low levels of BMP signaling at the dorsal side. Collectively, we provide insights into the capacity and organization of signaling and morphogenetic domains to recapitulate features of zebrafish gastrulation outside of the full embryonic context.

Plasticity in the cerebellum: What molecular mechanisms are behind physiological learning - Alcarva, Catarina
Understanding the mechanisms of learning and memory formation has always been one of the main goals in neuroscience. Already Pavlov (1927) in his early days has used his classic conditioning experiments to study the neural mechanisms governing behavioral adaptation. What was not known back then was that the part of the brain that is largely responsible for this type of associative learning is the cerebellum. Since then, plenty of theories on cerebellar learning have emerged. Despite their differences, one thing they all have in common is that learning relies on synaptic and intrinsic plasticity. The goal of my PhD project was to unravel the molecular mechanisms underlying synaptic plasticity in two synapses that have been shown to be implicated in motor learning, in an effort to understand how learning and memory formation are processed in the cerebellum. One of the earliest and most well-known cerebellar theories postulates that motor learning largely depends on long-term depression at the parallel fiber-Purkinje cell (PC-PC) synapse. However, the discovery of other types of plasticity in the cerebellar circuitry, like long-term potentiation (LTP) at the PC-PC synapse, potentiation of molecular layer interneurons (MLIs), and plasticity transfer from the cortex to the cerebellar/ vestibular nuclei has increased the popularity of the idea that multiple sites of plasticity might be involved in learning. Still a lot remains unknown about the molecular mechanisms responsible for these types of plasticity and whether they occur during physiological learning. In the first part of this thesis we have analyzed the variation and nanodistribution of voltagegated calcium channels (VGCCs) and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid type glutamate receptors (AMPARs) on the parallel fiber-Purkinje cell synapse after vestibuloocular reflex phase reversal adaptation, a behavior that has been suggested to rely on PF-PC LTP. We have found that on the last day of adaptation there is no learning trace in form of VGCCs nor AMPARs variation at the PF-PC synapse, but instead a decrease in the number of PF-PC synapses. These data seem to support the view that learning is only stored in the cerebellar cortex in an initial learning phase, being transferred later to the vestibular nuclei. Next, we have studied the role of MLIs in motor learning using a relatively simple and well characterized behavioral paradigm – horizontal optokinetic reflex (HOKR) adaptation. We have found behavior-induced MLI potentiation in form of release probability increase that could be explained by the increase of VGCCs at the presynaptic side. Our results strengthen the idea of distributed cerebellar plasticity contributing to learning and provide a novel mechanism for release probability increase.

Structural and mechanistic study of bacterial complex I and its cyanobacterial ortholog - Kravchuk, Vladyslav
Most energy in humans is produced in form of ATP by the mitochondrial respiratory chain consisting of several protein assemblies embedded into lipid membrane (complexes I-V). Complex I is the first and the largest enzyme of the respiratory chain which is essential for energy production. It couples the transfer of two electrons from NADH to ubiquinone with proton translocation across bacterial or inner mitochondrial membrane. The coupling mechanism between electron transfer and proton translocation is one of the biggest enigma in bioenergetics and structural biology. Even though the enzyme has been studied for decades, only recent technological advances in cryo-EM allowed its extensive structural investigation. Complex I from E.coli appears to be of special importance because it is a perfect model system with a rich mutant library, however the structure of the entire complex was unknown. In this thesis I have resolved structures of the minimal complex I version from E. coli in different states including reduced, inhibited, under reaction turnover and several others. Extensive structural analyses of these structures and comparison to structures from other species allowed to derive general features of conformational dynamics and propose a universal coupling mechanism. The mechanism is straightforward, robust and consistent with decades of experimental data available for complex I from different species. Cyanobacterial NDH (cyanobacterial complex I) is a part of broad complex I superfamily and was studied as well in this thesis. It plays an important role in cyclic electron transfer (CET), during which electrons are cycled within PSI through ferredoxin and plastoquinone to generate proton gradient without NADPH production. Here, I solved structure of NDH and revealed additional state, which was not observed before. The novel “resting” state allowed to propose the mechanism of CET regulation. Moreover, conformational dynamics of NDH resembles one in complex I which suggest more broad universality of the proposed coupling mechanism. In summary, results presented here helped to interpret decades of experimental data for complex I and contributed to fundamental mechanistic understanding of protein function.

Generalizing medial axes with homology switches - Stephenson, Elizabeth R
We introduce the notion of a Faustian interchange in a 1-parameter family of smooth functions to generalize the medial axis to critical points of index larger than 0. We construct and implement a general purpose algorithm for approximating such generalized medial axes.

Panoramic functional gradients across the mouse retina - Kirillova, Kseniia
All visual experiences of the vertebrates begin with light being converted into electrical signals by the eye retina. Retinal ganglion cells (RGCs) are the neurons of the innermost layer of the mammal retina, and they transmit visual information to the rest of the brain. It has been shown that RGCs vary in their morphology and genetic profiles, moreover they can be unambiguously grouped into subtypes that share the same morphological and/or molecular properties. However, in terms of RGCs function, it remains unclear how many distinct types there are and what response properties their typology relies on. Even given the recent studies that successfully classified RGCs in a patch of the retina [1] and in scotopic conditions [2], the question remains whether the found subtypes persist across the entire retina. In this work, using a novel imaging method, we show that, when sampled from a large portion of the retina, RGCs can not be clearly divided into functional subtypes. We found that in photopic conditions, which implies more prominent natural scene statistic differences across the visual field, response properties can be exhibited by cells differently depending on their location in the retina, which leads to formation of a gradient of features rather than distinct classes. This finding suggests that RGCs follow a global organization across the visual field of the animal, adapting each RGC subtype to the requirements imposed by the natural scene statistics.

The effect of local population structure on genetic variation at selected loci in the A. majus hybrid zone - Julseth, Mara
The evolutionary processes that brought about today’s plethora of living species and the many billions more ancient ones all underlie biology. Evolutionary pathways are neither directed nor deterministic, but rather an interplay between selection, migration, mutation, genetic drift and other environmental factors. Hybrid zones, as natural crossing experiments, offer a great opportunity to use cline analysis to deduce different evolutionary processes - for example, selection strength. Theoretical cline models, largely assuming uniform distribution of individuals, often lack the capability of incorporating population structure. Since in reality organisms mostly live in patchy distributions and their dispersal is hardly ever Gaussian, it is necessary to unravel the effect of these different elements of population structure on cline parameters and shape. In this thesis, I develop a simulation inspired by the A. majus hybrid zone of a single selected locus under frequency dependent selection. This simulation enables us to untangle the effects of different elements of population structure as for example a low-density center and long-range dispersal. This thesis is therefore a first step towards theoretically untangling the effects of different elements of population structure on cline parameters and shape.

Mechanism of clathrin-coated vesicle formation during endocytosis in plants - Gnyliukh, Nataliia
Keywords: Clathrin-Mediated Endocytosis; vesicle scission; Dynamin-Related Protein 2; SH3P2; TPLATE complex; Total internal reflection fluorescence microscopy; Arabidopsis thaliana

Inverse shape design with parametric representations: Kirchhoff Rods and parametric surface models - Hafner, Christian
Inverse design problems in fabrication-aware shape optimization are typically solved on discrete representations such as polygonal meshes. This thesis argues that there are benefits to treating these problems in the same domain as human designers, namely, the parametric one. One reason is that discretizing a parametric model usually removes the capability of making further manual changes to the design, because the human intent is captured by the shape parameters. Beyond this, knowledge about a design problem can sometimes reveal a structure that is present in a smooth representation, but is fundamentally altered by discretizing. In this case, working in the parametric domain may even simplify the optimization task. We present two lines of research that explore both of these aspects of fabrication-aware shape optimization on parametric representations. The first project studies the design of plane elastic curves and Kirchhoff rods, which are common mathematical models for describing the deformation of thin elastic rods such as beams, ribbons, cables, and hair. Our main contribution is a characterization of all curved shapes that can be attained by bending and twisting elastic rods having a stiffness that is allowed to vary across the length. Elements like these can be manufactured using digital fabrication devices such as 3d printers and digital cutters, and have applications in free-form architecture and soft robotics. We show that the family of curved shapes that can be produced this way admits geometric description that is concise and computationally convenient. In the case of plane curves, the geometric description is intuitive enough to allow a designer to determine whether a curved shape is physically achievable by visual inspection alone. We also present shape optimization algorithms that convert a user-defined curve in the plane or in three dimensions into the geometry of an elastic rod that will naturally deform to follow this curve when its endpoints are attached to a support structure. Implemented in an interactive software design tool, the rod geometry is generated in real time as the user edits a curve and enables fast prototyping. The second project tackles the problem of general-purpose shape optimization on CAD models using a novel variant of the extended finite element method (XFEM). Our goal is the decoupling between the simulation mesh and the CAD model, so no geometry-dependent meshing or remeshing needs to be performed when the CAD parameters change during optimization. This is achieved by discretizing the embedding space of the CAD model, and using a new high-accuracy numerical integration method to enable XFEM on free-form elements bounded by the parametric surface patches of the model. Our simulation is differentiable from the CAD parameters to the simulation output, which enables us to use off-the-shelf gradient-based optimization procedures. The result is a method that fits seamlessly into the CAD workflow because it works on the same representation as the designer, enabling the alternation of manual editing and fabrication-aware optimization at will.

A versatile toolbox for the comprehensive analysis of nervous tissue organization with light microscopy - Michalska, Julia M
The brain is an exceptionally sophisticated organ consisting of billions of cells and trillions of connections that orchestrate our cognition and behavior. To decode its complex connectivity, it is pivotal to disentangle its intricate architecture spanning from cm-sized circuits down to tens of nm-small synapses. To achieve this goal, I developed CATS – Comprehensive Analysis of nervous Tissue across Scales, a versatile toolbox for obtaining a holistic view of nervous tissue context with (superresolution) fluorescence microscopy. CATS combines comprehensive labeling of the extracellular space, that is compatible with chemical fixation, with information on molecular markers, superresolved data acquisition and machine-learning based data analysis for segmentation and synapse identification. I used CATS to analyze key features of nervous tissue connectivity, ranging from whole tissue architecture, neuronal in- and output-fields, down to synapse morphology. Focusing on the hippocampal circuitry, I quantified synaptic transmission properties of mossy fiber boutons and analyzed the connectivity pattern of dentate gyrus granule cells with CA3 pyramidal neurons. This shows that CATS is a viable tool to study hallmarks of neuronal connectivity with light microscopy.

Existence and density problems in Diophantine geometry: From norm forms to Campana points - Shute, Alec L
In this thesis, we study two of the most important questions in Arithmetic geometry: that of the existence and density of solutions to Diophantine equations. In order for a Diophantine equation to have any solutions over the rational numbers, it must have solutions everywhere locally, i.e., over R and over Qp for every prime p. The converse, called the Hasse principle, is known to fail in general. However, it is still a central question in Arithmetic geometry to determine for which varieties the Hasse principle does hold. In this work, we establish the Hasse principle for a wide new family of varieties of the form f(t) = NK/Q(x) ̸= 0, where f is a polynomial with integer coefficients and NK/Q denotes the norm form associated to a number field K. Our results cover products of arbitrarily many linear, quadratic or cubic factors, and generalise an argument of Irving [69], which makes use of the beta sieve of Rosser and Iwaniec. We also demonstrate how our main sieve results can be applied to treat new cases of a conjecture of Harpaz and Wittenberg on locally split values of polynomials over number fields, and discuss consequences for rational points in fibrations. In the second question, about the density of solutions, one defines a height function and seeks to estimate asymptotically the number of points of height bounded by B as B → ∞. Traditionally, one either counts rational points, or integral points with respect to a suitable model. However, in this thesis, we study an emerging area of interest in Arithmetic geometry known as Campana points, which in some sense interpolate between rational and integral points. More precisely, we count the number of nonzero integers z1, z2, z3 such that gcd(z1, z2, z3) = 1, and z1, z2, z3, z1 + z2 + z3 are all squareful and bounded by B. Using the circle method, we obtain an asymptotic formula which agrees in the power of B and log B with a bold new generalisation of Manin’s conjecture to the setting of Campana points, recently formulated by Pieropan, Smeets, Tanimoto and Várilly-Alvarado [96]. However, in this thesis we also provide the first known counterexamples to leading constant predicted by their conjecture.

Algorithms and hardness results for computing cores of Markov chains - Ahmadi, Ali; Chatterjee, Krishnendu; Goharshady, Amir Kafshdar; Meggendorfer, Tobias; Safavi Hemami, Roodabeh; Zikelic, Dorde (42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science)
Given a Markov chain M = (V, v_0, δ), with state space V and a starting state v_0, and a probability threshold ε, an ε-core is a subset C of states that is left with probability at most ε. More formally, C ⊆ V is an ε-core, iff ℙ[reach (V\C)] ≤ ε. Cores have been applied in a wide variety of verification problems over Markov chains, Markov decision processes, and probabilistic programs, as a means of discarding uninteresting and low-probability parts of a probabilistic system and instead being able to focus on the states that are likely to be encountered in a real-world run. In this work, we focus on the problem of computing a minimal ε-core in a Markov chain. Our contributions include both negative and positive results: (i) We show that the decision problem on the existence of an ε-core of a given size is NP-complete. This solves an open problem posed in [Jan Kretínský and Tobias Meggendorfer, 2020]. We additionally show that the problem remains NP-complete even when limited to acyclic Markov chains with bounded maximal vertex degree; (ii) We provide a polynomial time algorithm for computing a minimal ε-core on Markov chains over control-flow graphs of structured programs. A straightforward combination of our algorithm with standard branch prediction techniques allows one to apply the idea of cores to find a subset of program lines that are left with low probability and then focus any desired static analysis on this core subset.

Tangible topology through the lens of limits - Shipman, Barbara A.; Stephenson, Elizabeth R (PRIMUS)
Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences.
Keywords: Education; General Mathematics

Repeated prophet inequality with near-optimal bounds - Chatterjee, Krishnendu; Mohammadi, Mona; Saona Urmeneta, Raimundo J (arXiv)
In modern sample-driven Prophet Inequality, an adversary chooses a sequence of n items with values v1,v2,…,vn to be presented to a decision maker (DM). The process follows in two phases. In the first phase (sampling phase), some items, possibly selected at random, are revealed to the DM, but she can never accept them. In the second phase, the DM is presented with the other items in a random order and online fashion. For each item, she must make an irrevocable decision to either accept the item and stop the process or reject the item forever and proceed to the next item. The goal of the DM is to maximize the expected value as compared to a Prophet (or offline algorithm) that has access to all information. In this setting, the sampling phase has no cost and is not part of the optimization process. However, in many scenarios, the samples are obtained as part of the decision-making process. We model this aspect as a two-phase Prophet Inequality where an adversary chooses a sequence of 2n items with values v1,v2,…,v2n and the items are randomly ordered. Finally, there are two phases of the Prophet Inequality problem with the first n-items and the rest of the items, respectively. We show that some basic algorithms achieve a ratio of at most 0.450. We present an algorithm that achieves a ratio of at least 0.495. Finally, we show that for every algorithm the ratio it can achieve is at most 0.502. Hence our algorithm is near-optimal.

Towards differential relational privacy and its use in question answering - Bombari, Simone; Achille, Alessandro; Wang, Zijian; Wang, Yu-Xiang; Xie, Yusheng; Singh, Kunwar Yashraj; Appalaraju, Srikar; Mahadevan, Vijay; Soatto, Stefano (arXiv)
Memorization of the relation between entities in a dataset can lead to privacy issues when using a trained model for question answering. We introduce Relational Memorization (RM) to understand, quantify and control this phenomenon. While bounding general memorization can have detrimental effects on the performance of a trained model, bounding RM does not prevent effective learning. The difference is most pronounced when the data distribution is long-tailed, with many queries having only few training examples: Impeding general memorization prevents effective learning, while impeding only relational memorization still allows learning general properties of the underlying concepts. We formalize the notion of Relational Privacy (RP) and, inspired by Differential Privacy (DP), we provide a possible definition of Differential Relational Privacy (DrP). These notions can be used to describe and compute bounds on the amount of RM in a trained model. We illustrate Relational Privacy concepts in experiments with large-scale models for Question Answering.

Almost-orthogonal layers for efficient general-purpose Lipschitz networks - Prach, Bernd; Lampert, Christoph (Computer Vision – ECCV 2022)
It is a highly desirable property for deep networks to be robust against small input changes. One popular way to achieve this property is by designing networks with a small Lipschitz constant. In this work, we propose a new technique for constructing such Lipschitz networks that has a number of desirable properties: it can be applied to any linear network layer (fully-connected or convolutional), it provides formal guarantees on the Lipschitz constant, it is easy to implement and efficient to run, and it can be combined with any training objective and optimization method. In fact, our technique is the first one in the literature that achieves all of these properties simultaneously. Our main contribution is a rescaling-based weight matrix parametrization that guarantees each network layer to have a Lipschitz constant of at most 1 and results in the learned weight matrices to be close to orthogonal. Hence we call such layers almost-orthogonal Lipschitz (AOL). Experiments and ablation studies in the context of image classification with certified robust accuracy confirm that AOL layers achieve results that are on par with most existing methods. Yet, they are simpler to implement and more broadly applicable, because they do not require computationally expensive matrix orthogonalization or inversion steps as part of the network architecture. We provide code at https://github.com/berndprach/AOL.

High-dimensional expansion and crossing numbers of simplicial complexes - Wild, Pascal
In this dissertation we study coboundary expansion of simplicial complex with a view of giving geometric applications. Our main novel tool is an equivariant version of Gromov's celebrated Topological Overlap Theorem. The equivariant topological overlap theorem leads to various geometric applications including a quantitative non-embeddability result for sufficiently thick buildings (which partially resolves a conjecture of Tancer and Vorwerk) and an improved lower bound on the pair-crossing number of (bounded degree) expander graphs. Additionally, we will give new proofs for several known lower bounds for geometric problems such as the number of Tverberg partitions or the crossing number of complete bipartite graphs. For the aforementioned applications one is naturally lead to study expansion properties of joins of simplicial complexes. In the presence of a special certificate for expansion (as it is the case, e.g., for spherical buildings), the join of two expanders is an expander. On the flip-side, we report quite some evidence that coboundary expansion exhibits very non-product-like behaviour under taking joins. For instance, we exhibit infinite families of graphs $(G_n)_{n\in \mathbb{N}}$ and $(H_n)_{n\in\mathbb{N}}$ whose join $G_n*H_n$ has expansion of lower order than the product of the expansion constant of the graphs. Moreover, we show an upper bound of $(d+1)/2^d$ on the normalized coboundary expansion constants for the complete multipartite complex $[n]^{*(d+1)}$ (under a mild divisibility condition on $n$). Via the probabilistic method the latter result extends to an upper bound of $(d+1)/2^d+ε$ on the coboundary expansion constant of the spherical building associated with $PGL_{d+2}(\mathbb{F}_q)$ for any $ε>0$ and sufficiently large $q=q(ε)$. This disproves a conjecture of Lubotzky, Meshulam and Mozes -- in a rather strong sense. By improving on existing lower bounds we make further progress towards closing the gap between the known lower and upper bounds on the coboundary expansion constants of $[n]^{*(d+1)}$. The best improvements we achieve using computer-aided proofs and flag algebras. The exact value even for the complete $3$-partite $2$-dimensional complex $[n]^{*3}$ remains unknown but we are happy to conjecture a precise value for every $n$. %Moreover, we show that a previously shown lower bound on the expansion constant of the spherical building associated with $PGL_{2}(\mathbb{F}_q)$ is not tight. In a loosely structured, last chapter of this thesis we collect further smaller observations related to expansion. We point out a link between discrete Morse theory and a technique for showing coboundary expansion, elaborate a bit on the hardness of computing coboundary expansion constants, propose a new criterion for coboundary expansion (in a very dense setting) and give one way of making the folklore result that expansion of links is a necessary condition for a simplicial complex to be an expander precise.

Genetic basis of flower colour as a model for adaptive evolution - Matejovicova, Lenka
Although we often see studies focusing on simple or even discrete traits in studies of colouration, the variation of “appearance” phenotypes found in nature is often more complex, continuous and high-dimensional. Therefore, we developed automated methods suitable for large datasets of genomes and images, striving to account for their complex nature, while minimising human bias. We used these methods on a dataset of more than 20, 000 plant SNP genomes and corresponding fower images from a hybrid zone of two subspecies of Antirrhinum majus with distinctly coloured fowers to improve our understanding of the genetic nature of the fower colour in our study system. Firstly, we use the advantage of large numbers of genotyped plants to estimate the haplotypes in the main fower colour regulating region. We study colour- and geography-related characteristics of the estimated haplotypes and how they connect to their relatedness. We show discrepancies from the expected fower colour distributions given the genotype and identify particular haplotypes leading to unexpected phenotypes. We also confrm a signifcant defcit of the double recessive recombinant and quite surprisingly, we show that haplotypes of the most frequent parental type are much less variable than others. Secondly, we introduce our pipeline capable of processing tens of thousands of full fower images without human interaction and summarising each image into a set of informative scores. We show the compatibility of these machine-measured fower colour scores with the previously used manual scores and study impact of external efect on the resulting scores. Finally, we use the machine-measured fower colour scores to ft and examine a phenotype cline across the hybrid zone in Planoles using full fower images as opposed to discrete, manual scores and compare it with the genotypic cline.

Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap - Henheik, Sven Joscha; Teufel, Stefan (Journal of Mathematical Physics)
We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.
Keywords: mathematical physics; statistical and nonlinear physics

Local stability of ground states in locally gapped and weakly interacting quantum spin systems - Henheik, Sven Joscha; Teufel, Stefan; Wessel, Tom (Letters in Mathematical Physics)
Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences.
Keywords: mathematical physics; statistical and nonlinear physics

Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk - Henheik, Sven Joscha; Teufel, Stefan (Forum of Mathematics, Sigma)
We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.
Keywords: computational mathematics; discrete mathematics and combinatorics; geometry and topology; mathematical physics; statistics and probability; algebra and number theory; theoretical computer science; analysis

The BCS critical temperature at high density - Henheik, Sven Joscha (Mathematical Physics, Analysis and Geometry)
We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.
Keywords: geometry and topology; mathematical physics

Dynamics of hole singlet-triplet qubits with large g-factor differences - Jirovec, Daniel; Mutter, Philipp M.; Hofmann, Andrea C; Crippa, Alessandro; Rychetsky, Marek; Craig, David L.; Kukucka, Josip; Martins, Frederico; Ballabio, Andrea; Ares, Natalia; Chrastina, Daniel; Isella, Giovanni; et al. (Physical Review Letters)
The spin-orbit interaction permits to control the state of a spin qubit via electric fields. For holes it is particularly strong, allowing for fast all electrical qubit manipulation, and yet an in-depth understanding of this interaction in hole systems is missing. Here we investigate, experimentally and theoretically, the effect of the cubic Rashba spin-orbit interaction on the mixing of the spin states by studying singlet-triplet oscillations in a planar Ge hole double quantum dot. Landau-Zener sweeps at different magnetic field directions allow us to disentangle the effects of the spin-orbit induced spin-flip term from those caused by strongly site-dependent and anisotropic quantum dot g tensors. Our work, therefore, provides new insights into the hole spin-orbit interaction, necessary for optimizing future qubit experiments.

On the wavenumber-frequency spectrum of the wall pressure fluctuations in turbulent channel flow - Yang, Bowen; Yang, Zixuan (Journal of Fluid Mechanics)
Direct numerical simulations (DNS) of turbulent channel flows up to Reτ≈1000 are conducted to investigate the three-dimensional (consisting of streamwise wavenumber, spanwise wavenumber and frequency) spectrum of wall pressure fluctuations. To develop a predictive model of the wavenumber–frequency spectrum from the wavenumber spectrum, the time decorrelation mechanisms of wall pressure fluctuations are investigated. It is discovered that the energy-containing part of the wavenumber–frequency spectrum of wall pressure fluctuations can be well predicted using a similar random sweeping model for streamwise velocity fluctuations. To refine the investigation, we further decompose the spectrum of the total wall pressure fluctuations into the autospectra of rapid and slow pressure fluctuations, and the cross-spectrum between them. We focus on evaluating the assumption applied in many predictive models, that is, the magnitude of the cross-spectrum is negligibly small. The present DNS shows that neglecting the cross-spectrum causes a maximum error up to 4.7 dB in the subconvective region for all Reynolds numbers under test. Our analyses indicate that the approximation of neglecting the cross-spectrum needs to be applied carefully in the investigations of acoustics at low Mach numbers, in which the subconvective components of wall pressure fluctuations make important contributions to the radiated acoustic power.

On the operator norm of a Hermitian random matrix with correlated entries - Reker, Jana (Random Matrices: Theory and Applications)
We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.
Keywords: Discrete Mathematics and Combinatorics; Statistics; Probability and Uncertainty; Statistics and Probability; Algebra and Number Theory

Differential cost analysis with simultaneous potentials and anti-potentials - Zikelic, Dorde; Chang, Bor-Yuh Evan; Bolignano, Pauline; Raimondi, Franco (Proceedings of the 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation)
We present a novel approach to differential cost analysis that, given a program revision, attempts to statically bound the difference in resource usage, or cost, between the two program versions. Differential cost analysis is particularly interesting because of the many compelling applications for it, such as detecting resource-use regressions at code-review time or proving the absence of certain side-channel vulnerabilities. One prior approach to differential cost analysis is to apply relational reasoning that conceptually constructs a product program on which one can over-approximate the difference in costs between the two program versions. However, a significant challenge in any relational approach is effectively aligning the program versions to get precise results. In this paper, our key insight is that we can avoid the need for and the limitations of program alignment if, instead, we bound the difference of two cost-bound summaries rather than directly bounding the concrete cost difference. In particular, our method computes a threshold value for the maximal difference in cost between two program versions simultaneously using two kinds of cost-bound summaries---a potential function that evaluates to an upper bound for the cost incurred in the first program and an anti-potential function that evaluates to a lower bound for the cost incurred in the second. Our method has a number of desirable properties: it can be fully automated, it allows optimizing the threshold value on relative cost, it is suitable for programs that are not syntactically similar, and it supports non-determinism. We have evaluated an implementation of our approach on a number of program pairs collected from the literature, and we find that our method computes tight threshold values on relative cost in most examples.

Heterogeneity of the GFP fitness landscape and data-driven protein design - Gonzalez Somermeyer, Louisa; Fleiss, Aubin; Mishin, Alexander S; Bozhanova, Nina G; Igolkina, Anna A; Meiler, Jens; Alaball Pujol, Maria-Elisenda; Putintseva, Ekaterina V; Sarkisyan, Karen S; Kondrashov, Fyodor (eLife)
Studies of protein fitness landscapes reveal biophysical constraints guiding protein evolution and empower prediction of functional proteins. However, generalisation of these findings is limited due to scarceness of systematic data on fitness landscapes of proteins with a defined evolutionary relationship. We characterized the fitness peaks of four orthologous fluorescent proteins with a broad range of sequence divergence. While two of the four studied fitness peaks were sharp, the other two were considerably flatter, being almost entirely free of epistatic interactions. Mutationally robust proteins, characterized by a flat fitness peak, were not optimal templates for machine-learning-driven protein design – instead, predictions were more accurate for fragile proteins with epistatic landscapes. Our work paves insights for practical application of fitness landscape heterogeneity in protein engineering.
Keywords: General Immunology and Microbiology; General Biochemistry; Genetics and Molecular Biology; General Medicine; General Neuroscience

Relation between the number of peaks and the number of reciprocal sign epistatic interactions - Saona Urmeneta, Raimundo J; Kondrashov, Fyodor; Khudiakova, Kseniia (Bulletin of Mathematical Biology)
Empirical essays of fitness landscapes suggest that they may be rugged, that is having multiple fitness peaks. Such fitness landscapes, those that have multiple peaks, necessarily have special local structures, called reciprocal sign epistasis (Poelwijk et al. in J Theor Biol 272:141–144, 2011). Here, we investigate the quantitative relationship between the number of fitness peaks and the number of reciprocal sign epistatic interactions. Previously, it has been shown (Poelwijk et al. in J Theor Biol 272:141–144, 2011) that pairwise reciprocal sign epistasis is a necessary but not sufficient condition for the existence of multiple peaks. Applying discrete Morse theory, which to our knowledge has never been used in this context, we extend this result by giving the minimal number of reciprocal sign epistatic interactions required to create a given number of peaks.
Keywords: Computational Theory and Mathematics; General Agricultural and Biological Sciences; Pharmacology; General Environmental Science; General Biochemistry; Genetics and Molecular Biology; General Mathematics; Immunology; General Neuroscience

Laser frequency-offset locking at 10-Hz-level instability using hybrid electronic filters - Li, Vyacheslav; Diorico, Fritz R; Hosten, Onur (Physical Review Applied)
Lasers with well-controlled relative frequencies are indispensable for many applications in science and technology. We present a frequency-offset locking method for lasers based on beat-frequency discrimination utilizing hybrid electronic LC filters. The method is specifically designed for decoupling the tightness of the lock from the broadness of its capture range. The presented demonstration locks two free-running diode lasers at 780 nm with a 5.5-GHz offset. It displays an offset frequency instability below 55 Hz for time scales in excess of 1000 s and a minimum of 12 Hz at 10-s averaging. The performance is complemented with a 190-MHz lock-capture range, a tuning range of up to 1 GHz, and a frequency ramp agility of 200kHz/μs.
Keywords: General Physics and Astronomy

CoCoA: Concurrent continuous group key agreement - Alwen, Joël; Auerbach, Benedikt; Cueto Noval, Miguel; Klein, Karen; Pascual Perez, Guillermo; Pietrzak, Krzysztof Z; Walter, Michael (Advances in Cryptology – EUROCRYPT 2022)
Messaging platforms like Signal are widely deployed and provide strong security in an asynchronous setting. It is a challenging problem to construct a protocol with similar security guarantees that can efficiently scale to large groups. A major bottleneck are the frequent key rotations users need to perform to achieve post compromise forward security. In current proposals – most notably in TreeKEM (which is part of the IETF’s Messaging Layer Security (MLS) protocol draft) – for users in a group of size n to rotate their keys, they must each craft a message of size log(n) to be broadcast to the group using an (untrusted) delivery server. In larger groups, having users sequentially rotate their keys requires too much bandwidth (or takes too long), so variants allowing any T≤n users to simultaneously rotate their keys in just 2 communication rounds have been suggested (e.g. “Propose and Commit” by MLS). Unfortunately, 2-round concurrent updates are either damaging or expensive (or both); i.e. they either result in future operations being more costly (e.g. via “blanking” or “tainting”) or are costly themselves requiring Ω(T) communication for each user [Bienstock et al., TCC’20]. In this paper we propose CoCoA; a new scheme that allows for T concurrent updates that are neither damaging nor costly. That is, they add no cost to future operations yet they only require Ω(log2(n)) communication per user. To circumvent the [Bienstock et al.] lower bound, CoCoA increases the number of rounds needed to complete all updates from 2 up to (at most) log(n); though typically fewer rounds are needed. The key insight of our protocol is the following: in the (non-concurrent version of) TreeKEM, a delivery server which gets T concurrent update requests will approve one and reject the remaining T−1. In contrast, our server attempts to apply all of them. If more than one user requests to rotate the same key during a round, the server arbitrarily picks a winner. Surprisingly, we prove that regardless of how the server chooses the winners, all previously compromised users will recover after at most log(n) such update rounds. To keep the communication complexity low, CoCoA is a server-aided CGKA. That is, the delivery server no longer blindly forwards packets, but instead actively computes individualized packets tailored to each user. As the server is untrusted, this change requires us to develop new mechanisms ensuring robustness of the protocol.

Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics - Kalinov, Aleksei; Osinskiy, A.I.; Matveev, S.A.; Otieno, W.; Brilliantov, N.V. (Journal of Computational Physics)
We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and compare their performance with efficient deterministic finite-difference method applied to the same model. We validate the stochastic methods on the test problems and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation kinetics recently detected in deterministic simulations. We confirm the emergence of steady oscillations of densities in such systems and prove the stability of the oscillations with respect to fluctuations and noise.
Keywords: Computer Science Applications; Physics and Astronomy (miscellaneous); Applied Mathematics; Computational Mathematics; Modeling and Simulation; Numerical Analysis

RALF1 peptide triggers biphasic root growth inhibition upstream of auxin biosynthesis - Li, Lanxin; Chen, Huihuang; Alotaibi, Saqer S.; Pěnčík, Aleš; Adamowski, Maciek; Novák, Ondřej; Friml, Jiří (Proceedings of the National Academy of Sciences)
Plant cell growth responds rapidly to various stimuli, adapting architecture to environmental changes. Two major endogenous signals regulating growth are the phytohormone auxin and the secreted peptides rapid alkalinization factors (RALFs). Both trigger very rapid cellular responses and also exert long-term effects [Du et al., Annu. Rev. Plant Biol. 71, 379–402 (2020); Blackburn et al., Plant Physiol. 182, 1657–1666 (2020)]. However, the way, in which these distinct signaling pathways converge to regulate growth, remains unknown. Here, using vertical confocal microscopy combined with a microfluidic chip, we addressed the mechanism of RALF action on growth. We observed correlation between RALF1-induced rapid Arabidopsis thaliana root growth inhibition and apoplast alkalinization during the initial phase of the response, and revealed that RALF1 reversibly inhibits primary root growth through apoplast alkalinization faster than within 1 min. This rapid apoplast alkalinization was the result of RALF1-induced net H+ influx and was mediated by the receptor FERONIA (FER). Furthermore, we investigated the cross-talk between RALF1 and the auxin signaling pathways during root growth regulation. The results showed that RALF-FER signaling triggered auxin signaling with a delay of approximately 1 h by up-regulating auxin biosynthesis, thus contributing to sustained RALF1-induced growth inhibition. This biphasic RALF1 action on growth allows plants to respond rapidly to environmental stimuli and also reprogram growth and development in the long term.
Keywords: Multidisciplinary

Chimeric G protein-coupled receptors mimic distinct signaling pathways and modulate microglia function - Schulz, Rouven
G protein-coupled receptors (GPCRs) respond to specific ligands and regulate multiple processes ranging from cell growth and immune responses to neuronal signal transmission. However, ligands for many GPCRs remain unknown, suffer from off-target effects or have poor bioavailability. Additional challenges exist to dissect cell-type specific responses when the same GPCR is expressed on several cell types within the body. Here, we overcome these limitations by engineering DREADD-based GPCR chimeras that selectively bind their agonist clozapine-N-oxide (CNO) and mimic a GPCR-of-interest in a desired cell type. We validated our approach with β2-adrenergic receptor (β2AR/ADRB2) and show that our chimeric DREADD-β2AR triggers comparable responses on second messenger and kinase activity, post-translational modifications, and protein-protein interactions. Since β2AR is also enriched in microglia, which can drive inflammation in the central nervous system, we expressed chimeric DREADD-β2AR in primary microglia and successfully recapitulate β2AR-mediated filopodia formation through CNO stimulation. To dissect the role of selected GPCRs during microglial inflammation, we additionally generated DREADD-based chimeras for microglia-enriched GPR65 and GPR109A/HCAR2. In a microglia cell line, DREADD-β2AR and DREADD-GPR65 both modulated the inflammatory response with a similar profile as endogenously expressed β2AR, while DREADD-GPR109A showed no impact. Our DREADD-based approach provides the means to obtain mechanistic and functional insights into GPCR signaling on a cell-type specific level.

Abstract monitors for quantitative specifications - Henzinger, Thomas A; Mazzocchi, Nicolas Adrien; Sarac, Naci E (22nd International Conference on Runtime Verification)
Quantitative monitoring can be universal and approximate: For every finite sequence of observations, the specification provides a value and the monitor outputs a best-effort approximation of it. The quality of the approximation may depend on the resources that are available to the monitor. By taking to the limit the sequences of specification values and monitor outputs, we obtain precision-resource trade-offs also for limit monitoring. This paper provides a formal framework for studying such trade-offs using an abstract interpretation for monitors: For each natural number n, the aggregate semantics of a monitor at time n is an equivalence relation over all sequences of at most n observations so that two equivalent sequences are indistinguishable to the monitor and thus mapped to the same output. This abstract interpretation of quantitative monitors allows us to measure the number of equivalence classes (or “resource use”) that is necessary for a certain precision up to a certain time, or at any time. Our framework offers several insights. For example, we identify a family of specifications for which any resource-optimal exact limit monitor is independent of any error permitted over finite traces. Moreover, we present a specification for which any resource-optimal approximate limit monitor does not minimize its resource use at any time.

Translation-invariant quantum systems with effectively broken symmetry - Brooks, Morris
The scope of this thesis is to study quantum systems exhibiting a continuous symmetry that is broken on the level of the corresponding effective theory. In particular we are going to investigate translation-invariant Bose gases in the mean field limit, effectively described by the Hartree functional, and the Fröhlich Polaron in the regime of strong coupling, effectively described by the Pekar functional. The latter is a model describing the interaction between a charged particle and the optical modes of a polar crystal. Regarding the former, we assume in addition that the particles in the gas are unconfined, and typically we will consider particles that are subject to an attractive interaction. In both cases the ground state energy of the Hamiltonian is not a proper eigenvalue due to the underlying translation-invariance, while on the contrary there exists a whole invariant orbit of minimizers for the corresponding effective functionals. Both, the absence of proper eigenstates and the broken symmetry of the effective theory, make the study significantly more involved and it is the content of this thesis to develop a frameworks which allows for a systematic way to circumvent these issues. It is a well-established result that the ground state energy of Bose gases in the mean field limit, as well as the ground state energy of the Fröhlich Polaron in the regime of strong coupling, is to leading order given by the minimal energy of the corresponding effective theory. As part of this thesis we identify the sub-leading term in the expansion of the ground state energy, which can be interpreted as the quantum correction to the classical energy, since the effective theories under consideration can be seen as classical counterparts. We are further going to establish an asymptotic expression for the energy-momentum relation of the Fröhlich Polaron in the strong coupling limit. In the regime of suitably small momenta, this asymptotic expression agrees with the energy-momentum relation of a free particle having an effectively increased mass, and we find that this effectively increased mass agrees with the conjectured value in the physics literature. In addition we will discuss two unrelated papers written by the author during his stay at ISTA in the appendix. The first one concerns the realization of anyons, which are quasi-particles acquiring a non-trivial phase under the exchange of two particles, as molecular impurities. The second one provides a classification of those vector fields defined on a given manifold that can be written as the gradient of a given functional with respect to a suitable metric, provided that some mild smoothness assumptions hold. This classification is subsequently used to identify those quantum Markov semigroups that can be written as a gradient flow of the relative entropy.

Learning verifiable representations - Lechner, Mathias
Deep learning has enabled breakthroughs in challenging computing problems and has emerged as the standard problem-solving tool for computer vision and natural language processing tasks. One exception to this trend is safety-critical tasks where robustness and resilience requirements contradict the black-box nature of neural networks. To deploy deep learning methods for these tasks, it is vital to provide guarantees on neural network agents' safety and robustness criteria. This can be achieved by developing formal verification methods to verify the safety and robustness properties of neural networks. Our goal is to design, develop and assess safety verification methods for neural networks to improve their reliability and trustworthiness in real-world applications. This thesis establishes techniques for the verification of compressed and adversarially trained models as well as the design of novel neural networks for verifiably safe decision-making. First, we establish the problem of verifying quantized neural networks. Quantization is a technique that trades numerical precision for the computational efficiency of running a neural network and is widely adopted in industry. We show that neglecting the reduced precision when verifying a neural network can lead to wrong conclusions about the robustness and safety of the network, highlighting that novel techniques for quantized network verification are necessary. We introduce several bit-exact verification methods explicitly designed for quantized neural networks and experimentally confirm on realistic networks that the network's robustness and other formal properties are affected by the quantization. Furthermore, we perform a case study providing evidence that adversarial training, a standard technique for making neural networks more robust, has detrimental effects on the network's performance. This robustness-accuracy tradeoff has been studied before regarding the accuracy obtained on classification datasets where each data point is independent of all other data points. On the other hand, we investigate the tradeoff empirically in robot learning settings where a both, a high accuracy and a high robustness, are desirable. Our results suggest that the negative side-effects of adversarial training outweigh its robustness benefits in practice. Finally, we consider the problem of verifying safety when running a Bayesian neural network policy in a feedback loop with systems over the infinite time horizon. Bayesian neural networks are probabilistic models for learning uncertainties in the data and are therefore often used on robotic and healthcare applications where data is inherently stochastic. We introduce a method for recalibrating Bayesian neural networks so that they yield probability distributions over safe decisions only. Our method learns a safety certificate that guarantees safety over the infinite time horizon to determine which decisions are safe in every possible state of the system. We demonstrate the effectiveness of our approach on a series of reinforcement learning benchmarks.
Keywords: neural networks; verification; machine learning

Finite-memory strategies in POMDPs with long-run average objectives - Chatterjee, Krishnendu; Saona Urmeneta, Raimundo J; Ziliotto, Bruno (Mathematics of Operations Research)
Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the decision maker has approximately optimal strategies with finite memory. This implies notably that approximating the long-run value is recursively enumerable, as well as a weak continuity property of the value with respect to the transition function.
Keywords: Management Science and Operations Research; General Mathematics; Computer Science Applications

The BCS energy gap at high density - Henheik, Sven Joscha; Lauritsen, Asbjørn Bækgaard (Journal of Statistical Physics)
We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature.
Keywords: Mathematical Physics; Statistical and Nonlinear Physics

Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes - Köse, Seyda; Özbudak, Ferruh (Cryptography and Communications)
We determine the unique factorization of some polynomials over a finite local commutative ring with identity explicitly. This solves and generalizes the main conjecture of Qian, Shi and Solé in [13]. We also give some applications to enumeration of certain generalized double circulant self-dual and linear complementary dual (LCD) codes over some finite rings together with an application in asymptotic coding theory.
Keywords: Applied Mathematics; Computational Theory and Mathematics; Computer Networks and Communications

Polarons in Bose gases and polar crystals: Some rigorous energy estimates - Mysliwy, Krzysztof
The polaron model is a basic model of quantum field theory describing a single particle interacting with a bosonic field. It arises in many physical contexts. We are mostly concerned with models applicable in the context of an impurity atom in a Bose-Einstein condensate as well as the problem of electrons moving in polar crystals. The model has a simple structure in which the interaction of the particle with the field is given by a term linear in the field’s creation and annihilation operators. In this work, we investigate the properties of this model by providing rigorous estimates on various energies relevant to the problem. The estimates are obtained, for the most part, by suitable operator techniques which constitute the principal mathematical substance of the thesis. The first application of these techniques is to derive the polaron model rigorously from first principles, i.e., from a full microscopic quantum-mechanical many-body problem involving an impurity in an otherwise homogeneous system. We accomplish this for the N + 1 Bose gas in the mean-field regime by showing that a suitable polaron-type Hamiltonian arises at weak interactions as a low-energy effective theory for this problem. In the second part, we investigate rigorously the ground state of the model at fixed momentum and for large values of the coupling constant. Qualitatively, the system is expected to display a transition from the quasi-particle behavior at small momenta, where the dispersion relation is parabolic and the particle moves through the medium dragging along a cloud of phonons, to the radiative behavior at larger momenta where the polaron decelerates and emits free phonons. At the same time, in the strong coupling regime, the bosonic field is expected to behave purely classically. Accordingly, the effective mass of the polaron at strong coupling is conjectured to be asymptotically equal to the one obtained from the semiclassical counterpart of the problem, first studied by Landau and Pekar in the 1940s. For polaron models with regularized form factors and phonon dispersion relations of superfluid type, i.e., bounded below by a linear function of the wavenumbers for all phonon momenta as in the interacting Bose gas, we prove that for a large window of momenta below the radiation threshold, the energy-momentum relation at strong coupling is indeed essentially a parabola with semi-latus rectum equal to the Landau–Pekar effective mass, as expected. For the Fröhlich polaron describing electrons in polar crystals where the dispersion relation is of the optical type and the form factor is formally UV–singular due to the nature of the point charge-dipole interaction, we are able to give the corresponding upper bound. In contrast to the regular case, this requires the inclusion of the quantum fluctuations of the phonon field, which makes the problem considerably more difficult. The results are supplemented by studies on the absolute ground-state energy at strong coupling, a proof of the divergence of the effective mass with the coupling constant for a wide class of polaron models, as well as the discussion of the apparent UV singularity of the Fröhlich model and the application of the techniques used for its removal for the energy estimates.

Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models - Brighi, Pietro; Ljubotina, Marko; Serbyn, Maksym (arXiv)
Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring a conserved particle number and strong inversion-symmetry breaking due to facilitated hopping. We demonstrate that these models provide a generic example of so-called quantum Hilbert space fragmentation, that is manifested in disconnected sectors in the Hilbert space that are not apparent in the computational basis. Quantum Hilbert space fragmentation leads to an exponential in system size number of eigenstates with exactly zero entanglement entropy across several bipartite cuts. These eigenstates can be probed dynamically using quenches from simple initial product states. In addition, we study the particle spreading under unitary dynamics launched from the domain wall state, and find faster than diffusive dynamics at high particle densities, that crosses over into logarithmically slow relaxation at smaller densities. Using a classically simulable cellular automaton, we reproduce the logarithmic dynamics observed in the quantum case. Our work suggests that particle conserving constrained models with inversion symmetry breaking realize so far unexplored universality classes of dynamics and invite their further theoretical and experimental studies.

A homozygous MED11 C-terminal variant causes a lethal neurodegenerative disease - Cali, Elisa; Lin, Sheng-Jia; Rocca, Clarissa; Sahin, Yavuz; Al Shamsi, Aisha; El Chehadeh, Salima; Chaabouni, Myriam; Mankad, Kshitij; Galanaki, Evangelia; Efthymiou, Stephanie; Sudhakar, Sniya; Athanasiou-Fragkouli, Alkyoni; et al. (Genetics in Medicine)
Purpose: The mediator (MED) multisubunit-complex modulates the activity of the transcriptional machinery, and genetic defects in different MED subunits (17, 20, 27) have been implicated in neurologic diseases. In this study, we identified a recurrent homozygous variant in MED11 (c.325C>T; p.Arg109Ter) in 7 affected individuals from 5 unrelated families. Methods: To investigate the genetic cause of the disease, exome or genome sequencing were performed in 5 unrelated families identified via different research networks and Matchmaker Exchange. Deep clinical and brain imaging evaluations were performed by clinical pediatric neurologists and neuroradiologists. The functional effect of the candidate variant on both MED11 RNA and protein was assessed using reverse transcriptase polymerase chain reaction and western blotting using fibroblast cell lines derived from 1 affected individual and controls and through computational approaches. Knockouts in zebrafish were generated using clustered regularly interspaced short palindromic repeats/Cas9. Results: The disease was characterized by microcephaly, profound neurodevelopmental impairment, exaggerated startle response, myoclonic seizures, progressive widespread neurodegeneration, and premature death. Functional studies on patient-derived fibroblasts did not show a loss of protein function but rather disruption of the C-terminal of MED11, likely impairing binding to other MED subunits. A zebrafish knockout model recapitulates key clinical phenotypes. Conclusion: Loss of the C-terminal of MED subunit 11 may affect its binding efficiency to other MED subunits, thus implicating the MED-complex stability in brain development and neurodegeneration. (C) 2022 The Authors. Published by Elsevier Inc. on behalf of American College of Medical Genetics and Genomics.
Keywords: Human mediator complex; MED11; MEDopathies

Combining of synthetic VHH and immune scFv libraries for pregnancy-associated glycoproteins ELISA development - Dormeshkin, Dmitri; Shapira, Michail; Karputs, Alena; Kavaleuski, Anton; Kuzminski, Ivan; Stepanova, Elena; Gilep, Andrei (Applied Microbiology and Biotechnology)
Nanobodies (VHH) from camelid antibody libraries hold great promise as therapeutic agents and components of immunoassay systems. Synthetic antibody libraries that could be designed and generated once and for various applications could yield binders to virtually any targets, even for non-immunogenic or toxic ones, in a short term. One of the most difficult tasks is to obtain antibodies with a high affinity and specificity to polyglycosylated proteins. It requires antibody libraries with extremely high functional diversity and the use of sophisticated selection techniques. Here we report a development of a novel sandwich immunoassay involving a combination of the synthetic library-derived VHH-Fc fusion protein as a capture antibody and the immune single-chain fragment variable (scFv) as a tracer for the detection of pregnancy-associated glycoprotein (PAG) of cattle (Bos taurus). We succeeded in the generation of a number of specific scFv antibodies against PAG from the mouse immune library. Subsequent selection using the immobilized scFv-Fc capture antibody allowed to isolate 1.9 nM VHH binder from the diverse synthetic library without any overlapping with the capture antibody binding site. The prototype sandwich ELISA based on the synthetic VHH and the immune scFv was established. This is the first successful example of the combination of synthetic and immune antibody libraries in a single sandwich immunoassay. Thus, our approach could be used for the express isolation of antibody pairs and the development of sandwich immunoassays for challenging antigens.

Robustness and fairness in machine learning - Konstantinov, Nikola H
Because of the increasing popularity of machine learning methods, it is becoming important to understand the impact of learned components on automated decision-making systems and to guarantee that their consequences are beneficial to society. In other words, it is necessary to ensure that machine learning is sufficiently trustworthy to be used in real-world applications. This thesis studies two properties of machine learning models that are highly desirable for the sake of reliability: robustness and fairness. In the first part of the thesis we study the robustness of learning algorithms to training data corruption. Previous work has shown that machine learning models are vulnerable to a range of training set issues, varying from label noise through systematic biases to worst-case data manipulations. This is an especially relevant problem from a present perspective, since modern machine learning methods are particularly data hungry and therefore practitioners often have to rely on data collected from various external sources, e.g. from the Internet, from app users or via crowdsourcing. Naturally, such sources vary greatly in the quality and reliability of the data they provide. With these considerations in mind, we study the problem of designing machine learning algorithms that are robust to corruptions in data coming from multiple sources. We show that, in contrast to the case of a single dataset with outliers, successful learning within this model is possible both theoretically and practically, even under worst-case data corruptions. The second part of this thesis deals with fairness-aware machine learning. There are multiple areas where machine learning models have shown promising results, but where careful considerations are required, in order to avoid discrimanative decisions taken by such learned components. Ensuring fairness can be particularly challenging, because real-world training datasets are expected to contain various forms of historical bias that may affect the learning process. In this thesis we show that data corruption can indeed render the problem of achieving fairness impossible, by tightly characterizing the theoretical limits of fair learning under worst-case data manipulations. However, assuming access to clean data, we also show how fairness-aware learning can be made practical in contexts beyond binary classification, in particular in the challenging learning to rank setting.
Keywords: robustness; fairness; machine learning; PAC learning; adversarial learning

Two-particle bound states at interfaces and corners - Roos, Barbara; Seiringer, Robert (Journal of Functional Analysis)
We study two interacting quantum particles forming a bound state in d-dimensional free space, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with Neumann boundary conditions. First, we prove that the ground state energy strictly decreases upon going from k to k+1. This shows that the particles stick to the corner where all boundary planes intersect. Second, we show that for all k the resulting Hamiltonian, after removing the free part of the kinetic energy, has only finitely many eigenvalues below the essential spectrum. This paper generalizes the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444, 2020) to dimensions d > 1.
Keywords: Analysis

Assessing human iPSC-derived microglia identity and function by immunostaining, phagocytosis, calcium activity, and inflammation assay - Hübschmann, Verena; Korkut, Medina; Siegert, Sandra (STAR Protocols)
To understand how potential gene manipulations affect in vitro microglia, we provide a set of short protocols to evaluate microglia identity and function. We detail steps for immunostaining to determine microglia identity. We describe three functional assays for microglia: phagocytosis, calcium response following ATP stimulation, and cytokine expression upon inflammatory stimuli. We apply these protocols to human induced-pluripotent-stem-cell (hiPSC)-derived microglia, but they can be also applied to other in vitro microglial models including primary mouse microglia. For complete details on the use and execution of this protocol, please refer to Bartalska et al. (2022).1
Keywords: General Immunology and Microbiology; General Biochemistry; Genetics and Molecular Biology; General Neuroscience

ABP1–TMK auxin perception for global phosphorylation and auxin canalization - Friml, Jiří; Gallei, Michelle C; Gelová, Zuzana; Johnson, Alexander J; Mazur, Ewa; Monzer, Aline; Rodriguez Solovey, Lesia; Roosjen, Mark; Verstraeten, Inge; Živanović, Branka D.; Zou, Minxia; Fiedler, Lukas; et al. (Nature)
The phytohormone auxin triggers transcriptional reprogramming through a well-characterized perception machinery in the nucleus. By contrast, mechanisms that underlie fast effects of auxin, such as the regulation of ion fluxes, rapid phosphorylation of proteins or auxin feedback on its transport, remain unclear1,2,3. Whether auxin-binding protein 1 (ABP1) is an auxin receptor has been a source of debate for decades1,4. Here we show that a fraction of Arabidopsis thaliana ABP1 is secreted and binds auxin specifically at an acidic pH that is typical of the apoplast. ABP1 and its plasma-membrane-localized partner, transmembrane kinase 1 (TMK1), are required for the auxin-induced ultrafast global phospho-response and for downstream processes that include the activation of H+-ATPase and accelerated cytoplasmic streaming. abp1 and tmk mutants cannot establish auxin-transporting channels and show defective auxin-induced vasculature formation and regeneration. An ABP1(M2X) variant that lacks the capacity to bind auxin is unable to complement these defects in abp1 mutants. These data indicate that ABP1 is the auxin receptor for TMK1-based cell-surface signalling, which mediates the global phospho-response and auxin canalization.

Auxin and strigolactone non-canonical signaling regulating development in Arabidopsis thaliana - Gallei, Michelle C
Plant growth and development is well known to be both, flexible and dynamic. The high capacity for post-embryonic organ formation and tissue regeneration requires tightly regulated intercellular communication and coordinated tissue polarization. One of the most important drivers for patterning and polarity in plant development is the phytohormone auxin. Auxin has the unique characteristic to establish polarized channels for its own active directional cell to cell transport. This fascinating phenomenon is called auxin canalization. Those auxin transport channels are characterized by the expression and polar, subcellular localization of PIN auxin efflux carriers. PIN proteins have the ability to dynamically change their localization and auxin itself can affect this by interfering with trafficking. Most of the underlying molecular mechanisms of canalization still remain enigmatic. What is known so far is that canonical auxin signaling is indispensable but also other non-canonical signaling components are thought to play a role. In order to shed light into the mysteries auf auxin canalization this study revisits the branches of auxin signaling in detail. Further a new auxin analogue, PISA, is developed which triggers auxin-like responses but does not directly activate canonical transcriptional auxin signaling. We revisit the direct auxin effect on PIN trafficking where we found that, contradictory to previous observations, auxin is very specifically promoting endocytosis of PIN2 but has no overall effect on endocytosis. Further, we evaluate which cellular processes related to PIN subcellular dynamics are involved in the establishment of auxin conducting channels and the formation of vascular tissue. We are re-evaluating the function of AUXIN BINDING PROTEIN 1 (ABP1) and provide a comprehensive picture about its developmental phneotypes and involvement in auxin signaling and canalization. Lastly, we are focusing on the crosstalk between the hormone strigolactone (SL) and auxin and found that SL is interfering with essentially all processes involved in auxin canalization in a non-transcriptional manner. Lastly we identify a new way of SL perception and signaling which is emanating from mitochondria, is independent of canonical SL signaling and is modulating primary root growth.

Measuring airborne nanoplastics using aerosol physics - Stöllner, Andrea (Nature Reviews Earth and Environment)

In vitro reconstitution of Escherichia coli divisome activation - Radler, Philipp
FtsA is crucial for assembly of the E. coli divisome, as it dynamically links cytoplasmic FtsZ filaments with transmembrane cell division proteins. FtsA allegedly initiates cell division by switching from an inactive polymeric to an active monomeric confirmation, which recruits downstream proteins and stabilizes FtsZ filaments. Here, we use biochemical reconstitution experiments combined with quantitative fluorescence microscopy to study divisome activation in vitro. We compare wildtype-FtsA with FtsA-R286W, a constantly active gain-of-function mutant and find that R286W outperforms the wildtype protein in replicating FtsZ treadmilling dynamics, stabilizing FtsZ filaments and recruiting FtsN. We attribute these differences to a faster membrane exchange of FtsA-R286W and its higher packing density below FtsZ filaments. Using FRET microscopy, we find that FtsN binding does not compete with, but promotes FtsA self-interaction. Our findings suggest a model where FtsA always forms dynamic polymers on the membrane, which re-organize during assembly and activation of the divisome.
Keywords: Bacterial cell division; in vitro reconstitution; FtsZ; FtsN; FtsA

Source Data (Chimeric GPCRs mimic distinct signaling pathways and modulate microglia responses) - Schulz, Rouven

Effects of fine-scale population structure on the distribution of heterozygosity in a long-term study of Antirrhinum majus - Surendranadh, Parvathy; Arathoon, Louise S; Baskett, Carina; Field, David; Pickup, Melinda; Barton, Nicholas H (Genetics)
Many studies have quantified the distribution of heterozygosity and relatedness in natural populations, but few have examined the demographic processes driving these patterns. In this study, we take a novel approach by studying how population structure affects both pairwise identity and the distribution of heterozygosity in a natural population of the self-incompatible plant Antirrhinum majus. Excess variance in heterozygosity between individuals is due to identity disequilibrium, which reflects the variance in inbreeding between individuals; it is measured by the statistic g2. We calculated g2 together with FST and pairwise relatedness (Fij) using 91 SNPs in 22,353 individuals collected over 11 years. We find that pairwise Fij declines rapidly over short spatial scales, and the excess variance in heterozygosity between individuals reflects significant variation in inbreeding. Additionally, we detect an excess of individuals with around half the average heterozygosity, indicating either selfing or matings between close relatives. We use 2 types of simulation to ask whether variation in heterozygosity is consistent with fine-scale spatial population structure. First, by simulating offspring using parents drawn from a range of spatial scales, we show that the known pollen dispersal kernel explains g2. Second, we simulate a 1,000-generation pedigree using the known dispersal and spatial distribution and find that the resulting g2 is consistent with that observed from the field data. In contrast, a simulated population with uniform density underestimates g2, indicating that heterogeneous density promotes identity disequilibrium. Our study shows that heterogeneous density and leptokurtic dispersal can together explain the distribution of heterozygosity.

Effects of fine-scale population structure on the distribution of heterozygosity in a long-term study of Antirrhinum majus - Surendranadh, Parvathy; Arathoon, Louise S; Baskett, Carina; Field, David; Pickup, Melinda; Barton, Nicholas H
Here are the research data underlying the publication "Effects of fine-scale population structure on the distribution of heterozygosity in a long-term study of Antirrhinum majus" Further information are summed up in the README document.

Homogenizing yarn simulations: Large-scale mechanics, small-scale detail, and quantitative fitting - Sperl, Georg
The complex yarn structure of knitted and woven fabrics gives rise to both a mechanical and visual complexity. The small-scale interactions of yarns colliding with and pulling on each other result in drastically different large-scale stretching and bending behavior, introducing anisotropy, curling, and more. While simulating cloth as individual yarns can reproduce this complexity and match the quality of real fabric, it may be too computationally expensive for large fabrics. On the other hand, continuum-based approaches do not need to discretize the cloth at a stitch-level, but it is non-trivial to find a material model that would replicate the large-scale behavior of yarn fabrics, and they discard the intricate visual detail. In this thesis, we discuss three methods to try and bridge the gap between small-scale and large-scale yarn mechanics using numerical homogenization: fitting a continuum model to periodic yarn simulations, adding mechanics-aware yarn detail onto thin-shell simulations, and quantitatively fitting yarn parameters to physical measurements of real fabric. To start, we present a method for animating yarn-level cloth effects using a thin-shell solver. We first use a large number of periodic yarn-level simulations to build a model of the potential energy density of the cloth, and then use it to compute forces in a thin-shell simulator. The resulting simulations faithfully reproduce expected effects like the stiffening of woven fabrics and the highly deformable nature and anisotropy of knitted fabrics at a fraction of the cost of full yarn-level simulation. While our thin-shell simulations are able to capture large-scale yarn mechanics, they lack the rich visual detail of yarn-level simulations. Therefore, we propose a method to animate yarn-level cloth geometry on top of an underlying deforming mesh in a mechanics-aware fashion in real time. Using triangle strains to interpolate precomputed yarn geometry, we are able to reproduce effects such as knit loops tightening under stretching at negligible cost. Finally, we introduce a methodology for inverse-modeling of yarn-level mechanics of cloth, based on the mechanical response of fabrics in the real world. We compile a database from physical tests of several knitted fabrics used in the textile industry spanning diverse physical properties like stiffness, nonlinearity, and anisotropy. We then develop a system for approximating these mechanical responses with yarn-level cloth simulation, using homogenized shell models to speed up computation and adding some small-but-necessary extensions to yarn-level models used in computer graphics.

Analytic and machine learning approaches to composite quantum impurities - Rzadkowski, Wojciech
In this Thesis, I study composite quantum impurities with variational techniques, both inspired by machine learning as well as fully analytic. I supplement this with exploration of other applications of machine learning, in particular artificial neural networks, in many-body physics. In Chapters 3 and 4, I study quasiparticle systems with variational approach. I derive a Hamiltonian describing the angulon quasiparticle in the presence of a magnetic field. I apply analytic variational treatment to this Hamiltonian. Then, I introduce a variational approach for non-additive systems, based on artificial neural networks. I exemplify this approach on the example of the polaron quasiparticle (Fröhlich Hamiltonian). In Chapter 5, I continue using artificial neural networks, albeit in a different setting. I apply artificial neural networks to detect phases from snapshots of two types physical systems. Namely, I study Monte Carlo snapshots of multilayer classical spin models as well as molecular dynamics maps of colloidal systems. The main type of networks that I use here are convolutional neural networks, known for their applicability to image data.

A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs - Biswas, Ranita; Cultrera di Montesano, Sebastiano; Edelsbrunner, Herbert; Saghafian, Morteza (LIPIcs)
We characterize critical points of 1-dimensional maps paired in persistent homology geometrically and this way get elementary proofs of theorems about the symmetry of persistence diagrams and the variation of such maps. In particular, we identify branching points and endpoints of networks as the sole source of asymmetry and relate the cycle basis in persistent homology with a version of the stable marriage problem. Our analysis provides the foundations of fast algorithms for maintaining collections of interrelated sorted lists together with their persistence diagrams.

The response of a metapopulation to a changing environment - Barton, Nicholas H; Olusanya, Oluwafunmilola O (Philosophical Transactions of the Royal Society B: Biological Sciences)
A species distributed across diverse environments may adapt to local conditions. We ask how quickly such a species changes its range in response to changed conditions. Szép et al. (Szép E, Sachdeva H, Barton NH. 2021 Polygenic local adaptation in metapopulations: a stochastic eco-evolutionary model. Evolution75, 1030–1045 (doi:10.1111/evo.14210)) used the infinite island model to find the stationary distribution of allele frequencies and deme sizes. We extend this to find how a metapopulation responds to changes in carrying capacity, selection strength, or migration rate when deme sizes are fixed. We further develop a ‘fixed-state’ approximation. Under this approximation, polymorphism is only possible for a narrow range of habitat proportions when selection is weak compared to drift, but for a much wider range otherwise. When rates of selection or migration relative to drift change in a single deme of the metapopulation, the population takes a time of order m−1 to reach the new equilibrium. However, even with many loci, there can be substantial fluctuations in net adaptation, because at each locus, alleles randomly get lost or fixed. Thus, in a finite metapopulation, variation may gradually be lost by chance, even if it would persist in an infinite metapopulation. When conditions change across the whole metapopulation, there can be rapid change, which is predicted well by the fixed-state approximation. This work helps towards an understanding of how metapopulations extend their range across diverse environments. This article is part of the theme issue ‘Species’ ranges in the face of changing environments (Part II)’.
Keywords: General Agricultural and Biological Sciences; General Biochemistry; Genetics and Molecular Biology

Genetic load and extinction in peripheral populations: The roles of migration, drift and demographic stochasticity - Sachdeva, Himani; Olusanya, Oluwafunmilola O; Barton, Nicholas H (Philosophical Transactions of the Royal Society B)
We analyse how migration from a large mainland influences genetic load and population numbers on an island, in a scenario where fitness-affecting variants are unconditionally deleterious, and where numbers decline with increasing load. Our analysis shows that migration can have qualitatively different effects, depending on the total mutation target and fitness effects of deleterious variants. In particular, we find that populations exhibit a genetic Allee effect across a wide range of parameter combinations, when variants are partially recessive, cycling between low-load (large-population) and high-load (sink) states. Increased migration reduces load in the sink state (by increasing heterozygosity) but further inflates load in the large-population state (by hindering purging). We identify various critical parameter thresholds at which one or other stable state collapses, and discuss how these thresholds are influenced by the genetic versus demographic effects of migration. Our analysis is based on a ‘semi-deterministic’ analysis, which accounts for genetic drift but neglects demographic stochasticity. We also compare against simulations which account for both demographic stochasticity and drift. Our results clarify the importance of gene flow as a key determinant of extinction risk in peripheral populations, even in the absence of ecological gradients. This article is part of the theme issue ‘Species’ ranges in the face of changing environments (part I)’.