Concentration without independence via information measures - Esposito, Amedeo Roberto; Mondelli, Marco (Proceedings of 2023 IEEE International Symposium on Information Theory)
We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being independent. This price is encapsulated in the Hellinger integral between the joint and the product of the marginals, which is then upper bounded leveraging tensorisation properties. Our bounds represent a natural generalisation of concentration inequalities in the presence of dependence: we recover exactly the classical bounds (McDiarmid's inequality) when the random variables are independent. Furthermore, in a ``large deviations'' regime, we obtain the same decay in the probability as for the independent case, even when the random variables display non-trivial dependencies. To show this, we consider a number of applications of interest. First, we provide a bound for Markov chains with finite state space. Then, we consider the Simple Symmetric Random Walk, which is a non-contracting Markov chain, and a non-Markovian setting in which the stochastic process depends on its entire past. To conclude, we propose an application to Markov Chain Monte Carlo methods, where our approach leads to an improved lower bound on the minimum burn-in period required to reach a certain accuracy. In all of these settings, we provide a regime of parameters in which our bound fares better than what the state of the art can provide.

Enumerating matroids and linear spaces - Kwan, Matthew Alan; Sah, Ashwin; Sawhney, Mehtaab (Comptes Rendus Mathematique)
We show that the number of linear spaces on a set of n points and the number of rank-3 matroids on a ground set of size n are both of the form (cn+o(n))n2/6, where c=e3√/2−3(1+3–√)/2. This is the final piece of the puzzle for enumerating fixed-rank matroids at this level of accuracy: the numbers of rank-1 and rank-2 matroids on a ground set of size n have exact representations in terms of well-known combinatorial functions, and it was recently proved by van der Hofstad, Pendavingh, and van der Pol that for constant r≥4 there are (e1−rn+o(n))nr−1/r! rank-r matroids on a ground set of size n. In our proof, we introduce a new approach for bounding the number of clique decompositions of a complete graph, using quasirandomness instead of the so-called entropy method that is common in this area.

Maximal Lp-regularity and H∞-calculus for block operator matrices and applications - Agresti, Antonio; Hussein, Amru (Journal of Functional Analysis)
Many coupled evolution equations can be described via 2×2-block operator matrices of the form A=[ A B C D ] in a product space X=X1×X2 with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator A can be seen as a relatively bounded perturbation of its diagonal part with D(A)=D(A)×D(D) though with possibly large relative bound. For such operators the properties of sectoriality, R-sectoriality and the boundedness of the H∞-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time dependent parabolic problem associated with A can be analyzed in maximal Lpt -regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.
Keywords: Analysis

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.

Genetic load, eco-evolutionary feedback and extinction in a metapopulation - Olusanya, Oluwafunmilola O; Khudiakova, Kseniia; Sachdeva, Himani (bioRxiv)
Fragmented landscapes pose a significant threat to the persistence of species as they are highly susceptible to heightened risk of extinction due to the combined effects of genetic and demographic factors such as genetic drift and demographic stochasticity. This paper explores the intricate interplay between genetic load and extinction risk within metapopulations with a focus on understanding the impact of eco-evolutionary feedback mechanisms. We distinguish between two models of selection: soft selection, characterised by subpopulations maintaining carrying capacity despite load, and hard selection, where load can significantly affect population size. Within the soft selection framework, we investigate the impact of gene flow on genetic load at a single locus, while also considering the effect of selection strength and dominance coefficient. We subsequently build on this to examine how gene flow influences both population size and load under hard selection as well as identify critical thresholds for metapopulation persistence. Our analysis employs the diffusion, semi-deterministic and effective migration approximations. Our findings reveal that under soft selection, even modest levels of migration can significantly alleviate the burden of load. In sharp contrast, with hard selection, a much higher degree of gene flow is required to mitigate load and prevent the collapse of the metapopulation. Overall, this study sheds light into the crucial role migration plays in shaping the dynamics of genetic load and extinction risk in fragmented landscapes, offering valuable insights for conservation strategies and the preservation of diversity in a changing world.

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.

Gloss-aware color correction for 3D printing - Condor, Jorge; Piovarci, Michael; Bickel, Bernd; Didyk, Piotr (SIGGRAPH ’23 Conference Proceedings)
Color and gloss are fundamental aspects of surface appearance. State-of-the-art fabrication techniques can manipulate both properties of the printed 3D objects. However, in the context of appearance reproduction, perceptual aspects of color and gloss are usually handled separately, even though previous perceptual studies suggest their interaction. Our work is motivated by previous studies demonstrating a perceived color shift due to a change in the object's gloss, i.e., two samples with the same color but different surface gloss appear as they have different colors. In this paper, we conduct new experiments which support this observation and provide insights into the magnitude and direction of the perceived color change. We use the observations as guidance to design a new method that estimates and corrects the color shift enabling the fabrication of objects with the same perceived color but different surface gloss. We formulate the problem as an optimization procedure solved using differentiable rendering. We evaluate the effectiveness of our method in perceptual experiments with 3D objects fabricated using a multi-material 3D printer and demonstrate potential applications.
Keywords: color; gloss; perception; color compensation; color management

Runtime monitoring of dynamic fairness properties - Henzinger, Thomas A; Karimi, Mahyar; Kueffner, Konstantin; Mallik, Kaushik (FAccT '23: Proceedings of the 2023 ACM Conference on Fairness, Accountability, and Transparency)
A machine-learned system that is fair in static decision-making tasks may have biased societal impacts in the long-run. This may happen when the system interacts with humans and feedback patterns emerge, reinforcing old biases in the system and creating new biases. While existing works try to identify and mitigate long-run biases through smart system design, we introduce techniques for monitoring fairness in real time. Our goal is to build and deploy a monitor that will continuously observe a long sequence of events generated by the system in the wild, and will output, with each event, a verdict on how fair the system is at the current point in time. The advantages of monitoring are two-fold. Firstly, fairness is evaluated at run-time, which is important because unfair behaviors may not be eliminated a priori, at design-time, due to partial knowledge about the system and the environment, as well as uncertainties and dynamic changes in the system and the environment, such as the unpredictability of human behavior. Secondly, monitors are by design oblivious to how the monitored system is constructed, which makes them suitable to be used as trusted third-party fairness watchdogs. They function as computationally lightweight statistical estimators, and their correctness proofs rely on the rigorous analysis of the stochastic process that models the assumptions about the underlying dynamics of the system. We show, both in theory and experiments, how monitors can warn us (1) if a bank’s credit policy over time has created an unfair distribution of credit scores among the population, and (2) if a resource allocator’s allocation policy over time has made unfair allocations. Our experiments demonstrate that the monitors introduce very low overhead. We believe that runtime monitoring is an important and mathematically rigorous new addition to the fairness toolbox.

Whole-genome phylogeography of the intertidal snail Littorina saxatilis - Stankowski, Sean; Zagrodzka, Zuzanna B; Galindo, Juan; Montaño-Rendón, Mauricio; Faria, Rui; Mikhailova, Natalia; Blakeslee, April M H; Arnason, Einar; Broquet, Thomas; Morales, Hernán E; Grahame, John W; Westram, Anja M; et al. (Evolutionary Journal of the Linnean Society)
Understanding the factors that have shaped the current distributions and diversity of species is a central and longstanding aim of evolutionary biology. The recent inclusion of genomic data into phylogeographic studies has dramatically improved our understanding in organisms where evolutionary relationships have been challenging to infer. We used whole-genome sequences to study the phylogeography of the intertidal snail Littorina saxatilis, which has successfully colonized and diversified across a broad range of coastal environments in the Northern Hemisphere amid repeated cycles of glaciation. Building on past studies based on short DNA sequences, we used genome-wide data to provide a clearer picture of the relationships among samples spanning most of the species natural range. Our results confirm the trans-Atlantic colonization of North America from Europe, and have allowed us to identify rough locations of glacial refugia and to infer likely routes of colonization within Europe. We also investigated the signals in different datasets to account for the effects of genomic architecture and non-neutral evolution, which provides new insights about diversification of four ecotypes of L. saxatilis (the crab, wave, barnacle, and brackish ecotypes) at different spatial scales. Overall, we provide a much clearer picture of the biogeography of L. saxatilis, providing a foundation for more detailed phylogenomic and demographic studies.

The scorpionfly (Panorpa cognata) genome highlights conserved and derived features of the peculiar dipteran X chromosome - Lasne, Clementine; Elkrewi, Marwan N; Toups, Melissa A; Layana Franco, Lorena Alexandra; Macon, Ariana; Vicoso, Beatriz (Molecular Biology and Evolution)
Many insects carry an ancient X chromosome - the Drosophila Muller element F - that likely predates their origin. Interestingly, the X has undergone turnover in multiple fly species (Diptera) after being conserved for more than 450 MY. The long evolutionary distance between Diptera and other sequenced insect clades makes it difficult to infer what could have contributed to this sudden increase in rate of turnover. Here, we produce the first genome and transcriptome of a long overlooked sister-order to Diptera: Mecoptera. We compare the scorpionfly Panorpa cognata X-chromosome gene content, expression, and structure, to that of several dipteran species as well as more distantly-related insect orders (Orthoptera and Blattodea). We find high conservation of gene content between the mecopteran X and the dipteran Muller F element, as well as several shared biological features, such as the presence of dosage compensation and a low amount of genetic diversity, consistent with a low recombination rate. However, the two homologous X chromosomes differ strikingly in their size and number of genes they carry. Our results therefore support a common ancestry of the mecopteran and ancestral dipteran X chromosomes, and suggest that Muller element F shrank in size and gene content after the split of Diptera and Mecoptera, which may have contributed to its turnover in dipteran insects.
Keywords: Genetics; Molecular Biology; Ecology; Evolution; Behavior and Systematics

The scorpionfly (Panorpa cognata) genome highlights conserved and derived features of the peculiar dipteran X chromosome - Lasne, Clementine; Elkrewi, Marwan N
Many insects carry an ancient X chromosome—the Drosophila Muller element F—that likely predates their origin. Interestingly, the X has undergone turnover in multiple fly species (Diptera) after being conserved for more than 450 My. The long evolutionary distance between Diptera and other sequenced insect clades makes it difficult to infer what could have contributed to this sudden increase in rate of turnover. Here, we produce the first genome and transcriptome of scorpionflies (genus Panorpa), an insect belonging to a long overlooked sister-order to Diptera: Mecoptera. Combining our genome assembly with genomic short-read data, we obtain genome coverage and identify X-linked super-scaffolds. We further perform a gene homology analysis between the Panorpa X and a closely related Diptera species, and we assess the conservation of the Panorpa X-linked gene content with that of more distantly related insect species. We explored the structure of the Panorpa X by determining its repeat content, GC content, and nucleotide diversity. Finally, we used RNAseq data to detect the presence of dosage compensation in somatic tissues, as well as to explore gene expression tissue-specificity, and sex-bias in gene expression. We find high conservation of gene content between the mecopteran X and the dipteran Muller F element, as well as several shared biological features, such as the presence of dosage compensation and a low amount of genetic diversity, consistent with a low recombination rate. However, the 2 homologous X chromosomes differ strikingly in their size and number of genes they carry. Our results therefore support a common ancestry of the mecopteran and ancestral dipteran X chromosomes, and suggest that Muller element F shrank in size and gene content after the split of Diptera and Mecoptera, which may have contributed to its turnover in dipteran insects.
Keywords: Panorpa; scorpionfly; genome; transcriptome

Role of dynamin-related proteins 2 and SH3P2 in clathrin-mediated endocytosis in plants - Gnyliukh, Nataliia; Johnson, Alexander J; Nagel, Marie-Kristin; Monzer, Aline; Hlavata, Annamaria; Isono, Erika; Loose, Martin; Friml, Jiří (bioRxiv)
Clathrin-mediated endocytosis (CME) is vital for the regulation of plant growth and development by controlling plasma membrane protein composition and cargo uptake. CME relies on the precise recruitment of regulators for vesicle maturation and release. Homologues of components of mammalian vesicle scission are strong candidates to be part of the scissin machinery in plants, but the precise roles of these proteins in this process is not fully understood. Here, we characterised the roles of Plant Dynamin-Related Proteins 2 (DRP2s) and SH3-domain containing protein 2 (SH3P2), the plant homologue to Dynamins’ recruiters, like Endophilin and Amphiphysin, in the CME by combining high-resolution imaging of endocytic events in vivo and characterisation of the purified proteins in vitro. Although DRP2s and SH3P2 arrive similarly late during CME and physically interact, genetic analysis of the Dsh3p1,2,3 triple-mutant and complementation assays with non-SH3P2-interacting DRP2 variants suggests that SH3P2 does not directly recruit DRP2s to the site of endocytosis. These observations imply that despite the presence of many well-conserved endocytic components, plants have acquired a distinct mechanism for CME. One Sentence Summary In contrast to predictions based on mammalian systems, plant Dynamin-related proteins 2 are recruited to the site of Clathrin-mediated endocytosis independently of BAR-SH3 proteins.

Skin-Screen: A computational fabrication framework for color tattoos - Piovarci, Michael; Chapiro, Alexandre; Bickel, Bernd (ACM Transactions on Graphics)
Tattoos are a highly popular medium, with both artistic and medical applications. Although the mechanical process of tattoo application has evolved historically, the results are reliant on the artisanal skill of the artist. This can be especially challenging for some skin tones, or in cases where artists lack experience. We provide the first systematic overview of tattooing as a computational fabrication technique. We built an automated tattooing rig and a recipe for the creation of silicone sheets mimicking realistic skin tones, which allowed us to create an accurate model predicting tattoo appearance. This enables several exciting applications including tattoo previewing, color retargeting, novel ink spectra optimization, color-accurate prosthetics, and more.
Keywords: appearance; modeling; reproduction; tattoo; skin color; gamut mapping; ink-optimization; prosthetic

On lexicographic proof rules for probabilistic termination - Chatterjee, Krishnendu; Kafshdar Goharshady, Ehsan; Novotný, Petr; Zárevúcky, Jiří; Zikelic, Dorde (Formal Aspects of Computing)
We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs. Lexicographic ranking functions provide a sound and practical approach for termination of non-probabilistic programs, and their extension to probabilistic programs is achieved via lexicographic ranking supermartingales (LexRSMs). However, LexRSMs introduced in the previous work have a limitation that impedes their automation: all of their components have to be non-negative in all reachable states. This might result in a LexRSM not existing even for simple terminating programs. Our contributions are twofold. First, we introduce a generalization of LexRSMs that allows for some components to be negative. This standard feature of non-probabilistic termination proofs was hitherto not known to be sound in the probabilistic setting, as the soundness proof requires a careful analysis of the underlying stochastic process. Second, we present polynomial-time algorithms using our generalized LexRSMs for proving a.s. termination in broad classes of linear-arithmetic programs.
Keywords: Theoretical Computer Science; Software

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.

Professor Kerstin Johannesson–winner of the 2022 Molecular Ecology Prize - Westram, Anja M; Butlin, Roger (Molecular Ecology)
Kerstin Johannesson is a marine ecologist and evolutionary biologist based at the Tjärnö Marine Laboratory of the University of Gothenburg, which is situated in the beautiful Kosterhavet National Park on the Swedish west coast. Her work, using marine periwinkles (especially Littorina saxatilis and L. fabalis) as main model systems, has made a remarkable contribution to marine evolutionary biology and our understanding of local adaptation and its genetic underpinnings.
Keywords: Genetics; Ecology; Evolution; Behavior and Systematics

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.

The nitrate transporter NRT2.1 directly antagonizes PIN7-mediated auxin transport for root growth adaptation - Wang, Yalu; Yuan, Zhi; Wang, Jinyi; Xiao, Huixin; Wan, Lu; Li, Lanxin; Guo, Yan; Gong, Zhizhong; Friml, Jiří; Zhang, Jing (Proceedings of the National Academy of Sciences of the United States of America)
As a crucial nitrogen source, nitrate (NO3−) is a key nutrient for plants. Accordingly, root systems adapt to maximize NO3− availability, a developmental regulation also involving the phytohormone auxin. Nonetheless, the molecular mechanisms underlying this regulation remain poorly understood. Here, we identify low-nitrate-resistant mutant (lonr) in Arabidopsis (Arabidopsis thaliana), whose root growth fails to adapt to low-NO3− conditions. lonr2 is defective in the high-affinity NO3− transporter NRT2.1. lonr2 (nrt2.1) mutants exhibit defects in polar auxin transport, and their low-NO3−-induced root phenotype depends on the PIN7 auxin exporter activity. NRT2.1 directly associates with PIN7 and antagonizes PIN7-mediated auxin efflux depending on NO3− levels. These results reveal a mechanism by which NRT2.1 in response to NO3− limitation directly regulates auxin transport activity and, thus, root growth. This adaptive mechanism contributes to the root developmental plasticity to help plants cope with changes in NO3− availability.

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.

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.

The design space of Kirchhoff rods - Hafner, Christian; Bickel, Bernd (ACM Transactions on Graphics)
The Kirchhoff rod model describes the bending and twisting of slender elastic rods in three dimensions, and has been widely studied to enable the prediction of how a rod will deform, given its geometry and boundary conditions. In this work, we study a number of inverse problems with the goal of computing the geometry of a straight rod that will automatically deform to match a curved target shape after attaching its endpoints to a support structure. Our solution lets us finely control the static equilibrium state of a rod by varying the cross-sectional profiles along its length. We also show that the set of physically realizable equilibrium states admits a concise geometric description in terms of linear line complexes, which leads to very efficient computational design algorithms. Implemented in an interactive software tool, they allow us to convert three-dimensional hand-drawn spline curves to elastic rods, and give feedback about the feasibility and practicality of a design in real time. We demonstrate the efficacy of our method by designing and manufacturing several physical prototypes with applications to interior design and soft robotics.
Keywords: Computer Graphics; Computational Design; Computational Geometry; Shape Modeling

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.

Constraints on probing quantum coherence to infer gravitational entanglement - Hosten, Onur (Physical Review Research)
Finding a feasible scheme for testing the quantum mechanical nature of the gravitational interaction has been attracting an increasing level of attention. Gravity mediated entanglement generation so far appears to be the key ingredient for a potential experiment. In a recent proposal [D. Carney et al., PRX Quantum 2, 030330 (2021)] combining an atom interferometer with a low-frequency mechanical oscillator, a coherence revival test is proposed for verifying this entanglement generation. With measurements performed only on the atoms, this protocol bypasses the need for correlation measurements. Here, we explore formulations of such a protocol, and specifically find that in the envisioned regime of operation with high thermal excitation, semiclassical models, where there is no concept of entanglement, also give the same experimental signatures. We elucidate in a fully quantum mechanical calculation that entanglement is not the source of the revivals in the relevant parameter regime. We argue that, in its current form, the suggested test is only relevant if the oscillator is nearly in a pure quantum state, and in this regime the effects are too small to be measurable. We further discuss potential open ends. The results highlight the importance and subtleties of explicitly considering how the quantum case differs from the classical expectations when testing for the quantum mechanical nature of a physical system.

1H NMR chemical exchange techniques reveal local and global effects of oxidized cytosine derivatives - Dubini, Romeo C. A.; Korytiaková, Eva; Schinkel, Thea; Heinrichs, Pia; Carell, Thomas; Rovo, Petra (ACS Physical Chemistry Au)
5-Carboxycytosine (5caC) is a rare epigenetic modification found in nucleic acids of all domains of life. Despite its sparse genomic abundance, 5caC is presumed to play essential regulatory roles in transcription, maintenance and base-excision processes in DNA. In this work, we utilize nuclear magnetic resonance (NMR) spectroscopy to address the effects of 5caC incorporation into canonical DNA strands at multiple pH and temperature conditions. Our results demonstrate that 5caC has a pH-dependent global destabilizing and a base-pair mobility enhancing local impact on dsDNA, albeit without any detectable influence on the ground-state B-DNA structure. Measurement of hybridization thermodynamics and kinetics of 5caC-bearing DNA duplexes highlighted how acidic environment (pH 5.8 and 4.7) destabilizes the double-stranded structure by ∼10–20 kJ mol–1 at 37 °C when compared to the same sample at neutral pH. Protonation of 5caC results in a lower activation energy for the dissociation process and a higher barrier for annealing. Studies on conformational exchange on the microsecond time scale regime revealed a sharply localized base-pair motion involving exclusively the modified site and its immediate surroundings. By direct comparison with canonical and 5-formylcytosine (5fC)-edited strands, we were able to address the impact of the two most oxidized naturally occurring cytosine derivatives in the genome. These insights on 5caC’s subtle sensitivity to acidic pH contribute to the long-standing questions of its capacity as a substrate in base excision repair processes and its purpose as an independent, stable epigenetic mark.

Flavors of sequential information flow - Bartocci, Ezio; Ferrere, Thomas; Henzinger, Thomas A; Nickovic, Dejan; Da Costa, Ana Oliveira (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics))
We study the problem of specifying sequential information-flow properties of systems. Information-flow properties are hyperproperties, as they compare different traces of a system. Sequential information-flow properties can express changes, over time, in the information-flow constraints. For example, information-flow constraints during an initialization phase of a system may be different from information-flow constraints that are required during the operation phase. We formalize several variants of interpreting sequential information-flow constraints, which arise from different assumptions about what can be observed of the system. For this purpose, we introduce a first-order logic, called Hypertrace Logic, with both trace and time quantifiers for specifying linear-time hyperproperties. We prove that HyperLTL, which corresponds to a fragment of Hypertrace Logic with restricted quantifier prefixes, cannot specify the majority of the studied variants of sequential information flow, including all variants in which the transition between sequential phases (such as initialization and operation) happens asynchronously. Our results rely on new equivalences between sets of traces that cannot be distinguished by certain classes of formulas from Hypertrace Logic. This presents a new approach to proving inexpressiveness results for HyperLTL.

Non relativistic quantum field theory: Dynamics and irreversibility - Daguerre, L.; Torroba, G.; Medina Ramos, Raimel A; Solís, M. (Anales de la Asociacion Fisica Argentina)
studiamos aspectos de Teoría Cuántica de Campos a densidad finita usando técnicas y conceptos de información cuántica. Nos enfocamos en fermiones de Dirac masivos con potencial químico en 1+1 dimensiones espacio-temporales. Usando la entropía de entrelazamiento en un intervalo, construimos la función c entrópica que es finita. Esta función c no es monótona, e incorpora el entrelazamiento de largo alcance proveniente de la superficie de Fermi. Motivados por trabajos previos de modelos en la red, calculamos numéricamente las entropías de Renyi y encontramos oscilaciones de Friedel. Seguidamente, analizamos la información mutua como una medida de correlación entre diferentes regiones. Usando una expansión de distancia grande desarrollada por Cardy, argumentamos que la información mutua detecta las correlaciones inducidas por la superficie de Fermi todavía al orden dominante en la expansión. Finalmente, analizamos la entropía relativa y sus generalizaciones de Renyi para distinguir estados con diferente carga. Encontramos que estados en diferentes sectores de superselección dan origen a un comportamiento super-extensivo en la entropía relativa.

Alpha rhythm induces attenuation-amplification dynamics in neural activity cascades - Lombardi, Fabrizio; Herrmann, Hans J.; Parrino, Liborio; Plenz, Dietmar; Scarpetta, Silvia; Vaudano, Anna Elisabetta; de Arcangelis, Lucilla; Shriki, Oren (bioRxiv)
Rhythmical cortical activity has long been recognized as a pillar in the architecture of brain functions. Yet, the dynamic organization of its underlying neuronal population activity remains elusive. Here we uncover a unique organizational principle regulating collective neural dynamics associated with the alpha rhythm in the awake resting-state. We demonstrate that cascades of neural activity obey attenuation-amplification dynamics (AAD), with a transition from the attenuation regime—within alpha cycles—to the amplification regime—across a few alpha cycles—that correlates with the characteristic frequency of the alpha rhythm. We find that this short-term AAD is part of a large-scale, size-dependent temporal structure of neural cascades that obeys the Omori law: Following large cascades, smaller cascades occur at a rate that decays as a power-law of the time elapsed from such events—a long-term AAD regulating brain activity over the timescale of seconds. We show that such an organization corresponds to the "waxing and waning" of the alpha rhythm. Importantly, we observe that short- and long-term AAD are unique to the awake resting-state, being absent during NREM sleep. These results provide a quantitative, dynamical description of the so-far-qualitative notion of the "waxing and waning" phenomenon, and suggest the AAD as a key principle governing resting-state dynamics across timescales.

Impurity with a resonance in the vicinity of the Fermi energy - Maslov, Mikhail; Lemeshko, Mikhail; Volosniev, Artem (Physical Review Research)
We study an impurity with a resonance level whose position coincides with the Fermi energy of the surrounding Fermi gas. An impurity causes a rapid variation of the scattering phase shift for fermions at the Fermi surface, introducing a new characteristic length scale into the problem. We investigate manifestations of this length scale in the self-energy of the impurity and in the density of the bath. Our calculations reveal a model-independent deformation of the density of the Fermi gas, which is determined by the width of the resonance. To provide a broader picture, we investigate time evolution of the density in quench dynamics, and study the behavior of the system at finite temperatures. Finally, we briefly discuss implications of our findings for the Fermi-polaron problem.

Parameter inference for stochastic biochemical models from perturbation experiments parallelised at the single cell level - Davidović, Anđela; Chait, Remy P; Batt, Gregory; Ruess, Jakob (PLoS Computational Biology)
Understanding and characterising biochemical processes inside single cells requires experimental platforms that allow one to perturb and observe the dynamics of such processes as well as computational methods to build and parameterise models from the collected data. Recent progress with experimental platforms and optogenetics has made it possible to expose each cell in an experiment to an individualised input and automatically record cellular responses over days with fine time resolution. However, methods to infer parameters of stochastic kinetic models from single-cell longitudinal data have generally been developed under the assumption that experimental data is sparse and that responses of cells to at most a few different input perturbations can be observed. Here, we investigate and compare different approaches for calculating parameter likelihoods of single-cell longitudinal data based on approximations of the chemical master equation (CME) with a particular focus on coupling the linear noise approximation (LNA) or moment closure methods to a Kalman filter. We show that, as long as cells are measured sufficiently frequently, coupling the LNA to a Kalman filter allows one to accurately approximate likelihoods and to infer model parameters from data even in cases where the LNA provides poor approximations of the CME. Furthermore, the computational cost of filtering-based iterative likelihood evaluation scales advantageously in the number of measurement times and different input perturbations and is thus ideally suited for data obtained from modern experimental platforms. To demonstrate the practical usefulness of these results, we perform an experiment in which single cells, equipped with an optogenetic gene expression system, are exposed to various different light-input sequences and measured at several hundred time points and use parameter inference based on iterative likelihood evaluation to parameterise a stochastic model of the system.

Fast graphical population protocols - Alistarh, Dan-Adrian; Gelashvili, Rati; Rybicki, Joel (25th International Conference on Principles of Distributed Systems)
Let G be a graph on n nodes. In the stochastic population protocol model, a collection of n indistinguishable, resource-limited nodes collectively solve tasks via pairwise interactions. In each interaction, two randomly chosen neighbors first read each other’s states, and then update their local states. A rich line of research has established tight upper and lower bounds on the complexity of fundamental tasks, such as majority and leader election, in this model, when G is a clique. Specifically, in the clique, these tasks can be solved fast, i.e., in n polylog n pairwise interactions, with high probability, using at most polylog n states per node. In this work, we consider the more general setting where G is an arbitrary regular graph, and present a technique for simulating protocols designed for fully-connected networks in any connected regular graph. Our main result is a simulation that is efficient on many interesting graph families: roughly, the simulation overhead is polylogarithmic in the number of nodes, and quadratic in the conductance of the graph. As a sample application, we show that, in any regular graph with conductance φ, both leader election and exact majority can be solved in φ^{-2} ⋅ n polylog n pairwise interactions, with high probability, using at most φ^{-2} ⋅ polylog n states per node. This shows that there are fast and space-efficient population protocols for leader election and exact majority on graphs with good expansion properties. We believe our results will prove generally useful, as they allow efficient technology transfer between the well-mixed (clique) case, and the under-explored spatial setting.

Beyond distributed subgraph detection: Induced subgraphs, multicolored problems and graph parameters - Nikabadi, Amir; Korhonen, Janne (25th International Conference on Principles of Distributed Systems)
Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on induced subgraph detection. The main line of this work presents lower bounds and parameterized algorithms w.r.t structural parameters of the input graph: - On general graphs, we give unconditional lower bounds for induced detection of cycles and patterns of treewidth 2 in CONGEST. Moreover, by adapting reductions from centralized parameterized complexity, we prove lower bounds in CONGEST for detecting patterns with a 4-clique, and for induced path detection conditional on the hardness of triangle detection in the congested clique. - On graphs of bounded degeneracy, we show that induced paths can be detected fast in CONGEST using techniques from parameterized algorithms, while detecting cycles and patterns of treewidth 2 is hard. - On graphs of bounded vertex cover number, we show that induced subgraph detection is easy in CONGEST for any pattern graph. More specifically, we adapt a centralized parameterized algorithm for a more general maximum common induced subgraph detection problem to the distributed setting. In addition to these induced subgraph detection results, we study various related problems in the CONGEST and congested clique models, including for multicolored versions of subgraph-detection-like problems.

Quantifying the probing and selection of microenvironmental pores by motile immune cells - Kroll, Janina; Ruiz-Fernandez, Mauricio J.A.; Braun, Malte B.; Merrin, Jack; Renkawitz, Jörg (Current Protocols)
Immune cells are constantly on the move through multicellular organisms to explore and respond to pathogens and other harmful insults. While moving, immune cells efficiently traverse microenvironments composed of tissue cells and extracellular fibers, which together form complex environments of various porosity, stiffness, topography, and chemical composition. In this protocol we describe experimental procedures to investigate immune cell migration through microenvironments of heterogeneous porosity. In particular, we describe micro-channels, micro-pillars, and collagen networks as cell migration paths with alternative pore size choices. Employing micro-channels or micro-pillars that divide at junctions into alternative paths with initially differentially sized pores allows us to precisely (1) measure the cellular translocation time through these porous path junctions, (2) quantify the cellular preference for individual pore sizes, and (3) image cellular components like the nucleus and the cytoskeleton. This reductionistic experimental setup thus can elucidate how immune cells perform decisions in complex microenvironments of various porosity like the interstitium. The setup further allows investigation of the underlying forces of cellular squeezing and the consequences of cellular deformation on the integrity of the cell and its organelles. As a complementary approach that does not require any micro-engineering expertise, we describe the usage of three-dimensional collagen networks with different pore sizes. Whereas we here focus on dendritic cells as a model for motile immune cells, the described protocols are versatile as they are also applicable for other immune cell types like neutrophils and non-immune cell types such as mesenchymal and cancer cells. In summary, we here describe protocols to identify the mechanisms and principles of cellular probing, decision making, and squeezing during cellular movement through microenvironments of heterogeneous porosity.

A cautionary tale: Burning the medial axis is unstable - Chambers, Erin; Fillmore, Christopher D; Stephenson, Elizabeth R; Wintraecken, Mathijs (38th International Symposium on Computational Geometry)
The medial axis of a set consists of the points in the ambient space without a unique closest point on the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a topologically equivalent skeleton. Unfortunately, one limiting factor in the use of the medial axis of a smooth manifold is that it is not necessarily topologically stable under small perturbations of the manifold. To counter these instabilities various prunings of the medial axis have been proposed. Here, we examine one type of pruning, called burning. Because of the good experimental results, it was hoped that the burning method of simplifying the medial axis would be stable. In this work we show a simple example that dashes such hopes based on Bing’s house with two rooms, demonstrating an isotopy of a shape where the medial axis goes from collapsible to non-collapsible.

Mean-field analysis of piecewise linear solutions for wide ReLU networks - Shevchenko, Aleksandr; Kungurtsev, Vyacheslav; Mondelli, Marco (Journal of Machine Learning Research)
Understanding the properties of neural networks trained via stochastic gradient descent (SGD) is at the heart of the theory of deep learning. In this work, we take a mean-field view, and consider a two-layer ReLU network trained via noisy-SGD for a univariate regularized regression problem. Our main result is that SGD with vanishingly small noise injected in the gradients is biased towards a simple solution: at convergence, the ReLU network implements a piecewise linear map of the inputs, and the number of “knot” points -- i.e., points where the tangent of the ReLU network estimator changes -- between two consecutive training inputs is at most three. In particular, as the number of neurons of the network grows, the SGD dynamics is captured by the solution of a gradient flow and, at convergence, the distribution of the weights approaches the unique minimizer of a related free energy, which has a Gibbs form. Our key technical contribution consists in the analysis of the estimator resulting from this minimizer: we show that its second derivative vanishes everywhere, except at some specific locations which represent the “knot” points. We also provide empirical evidence that knots at locations distinct from the data points might occur, as predicted by our theory.

The persistent homology of dual digital image constructions - Bleile, Bea; Garin, Adélie; Heiss, Teresa; Maggs, Kelly; Robins, Vanessa (Research in Computational Topology 2)
To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital adjacencies) can give different results for the same image. The two constructions are almost dual to each other, and we use this relationship to extend and modify the cubical complexes to become dual filtered cell complexes. We derive a general relationship between the persistent homology of two dual filtered cell complexes, and also establish how various modifications to a filtered complex change the persistence diagram. Applying these results to images, we derive a method to transform the persistence diagram computed using one type of cubical complex into a persistence diagram for the other construction. This means software for computing persistent homology from images can now be easily adapted to produce results for either of the two cubical complex constructions without additional low-level code implementation.

From the prefect’s desk: Gerard van Swieten’s library correspondence - Chlebak, Clara A; Reid, Peter H. (Library and Information History)
This article investigates library-related documents written by Gerard van Swieten (1700–72) during his tenure as Library Prefect in the Imperial Library of Vienna (1745–72). Van Swieten’s time as Library Prefect is considered through a textual analysis. Handwritten letters were deconstructed in terms of their appearance, layout, and tone in order to mine them for meaning. Furthermore, the contents were examined for library matters such as censorship, catalogues, and collection development. The Imperial Court Library held a prominent role as a repository for rare and valuable works, later becoming the National Library of Austria. Gerard van Swieten’s work as a librarian tends to be overlooked, perhaps because he is better known as the private physician of Maria Theresia, as well as a medical reformer. Nevertheless, he was a hard-working chief librarian deeply involved in all aspects of librarianship. Van Swieten endorsed modern scientific works, which were otherwise banned officially by the censorship commission, for the use of scholars in the library, expanded the collection by acquiring books through his network of scholars and publishers, and reissued library catalogues. He also provided for the comfort of users in the library reading room, at a time when such considerations were unusual. In conclusion, a proposal is made that van Swieten viewed his role as librarian with some importance and pride.

The dynamics of complex box mappings - Clark, Trevor; Drach, Kostiantyn; Kozlovski, Oleg; Strien, Sebastian Van (Arnold Mathematical Journal)
In holomorphic dynamics, complex box mappings arise as first return maps to wellchosen domains. They are a generalization of polynomial-like mapping, where the domain of the return map can have infinitely many components. They turned out to be extremely useful in tackling diverse problems. The purpose of this paper is: • To illustrate some pathologies that can occur when a complex box mapping is not induced by a globally defined map and when its domain has infinitely many components, and to give conditions to avoid these issues. • To show that once one has a box mapping for a rational map, these conditions can be assumed to hold in a very natural setting. Thus, we call such complex box mappings dynamically natural. Having such box mappings is the first step in tackling many problems in one-dimensional dynamics. • Many results in holomorphic dynamics rely on an interplay between combinatorial and analytic techniques. In this setting, some of these tools are: • the Enhanced Nest (a nest of puzzle pieces around critical points) from Kozlovski, Shen, van Strien (AnnMath 165:749–841, 2007), referred to below as KSS; • the Covering Lemma (which controls the moduli of pullbacks of annuli) from Kahn and Lyubich (Ann Math 169(2):561–593, 2009); • the QC-Criterion and the Spreading Principle from KSS. The purpose of this paper is to make these tools more accessible so that they can be used as a ‘black box’, so one does not have to redo the proofs in new settings. • To give an intuitive, but also rather detailed, outline of the proof from KSS and Kozlovski and van Strien (Proc Lond Math Soc (3) 99:275–296, 2009) of the following results for non-renormalizable dynamically natural complex box mappings: • puzzle pieces shrink to points, • (under some assumptions) topologically conjugate non-renormalizable polynomials and box mappings are quasiconformally conjugate. • We prove the fundamental ergodic properties for dynamically natural box mappings. This leads to some necessary conditions for when such a box mapping supports a measurable invariant line field on its filled Julia set. These mappings are the analogues of Lattès maps in this setting. • We prove a version of Mañé’s Theorem for complex box mappings concerning expansion along orbits of points that avoid a neighborhood of the set of critical points.

Inferring couplings in networks across order-disorder phase transitions - Ngampruetikorn, Vudtiwat; Sachdeva, Vedant; Torrence, Johanna; Humplik, Jan; Schwab, David J.; Palmer, Stephanie E. (Physical Review Research)
Statistical inference is central to many scientific endeavors, yet how it works remains unresolved. Answering this requires a quantitative understanding of the intrinsic interplay between statistical models, inference methods, and the structure in the data. To this end, we characterize the efficacy of direct coupling analysis (DCA)—a highly successful method for analyzing amino acid sequence data—in inferring pairwise interactions from samples of ferromagnetic Ising models on random graphs. Our approach allows for physically motivated exploration of qualitatively distinct data regimes separated by phase transitions. We show that inference quality depends strongly on the nature of data-generating distributions: optimal accuracy occurs at an intermediate temperature where the detrimental effects from macroscopic order and thermal noise are minimal. Importantly our results indicate that DCA does not always outperform its local-statistics-based predecessors; while DCA excels at low temperatures, it becomes inferior to simple correlation thresholding at virtually all temperatures when data are limited. Our findings offer insights into the regime in which DCA operates so successfully, and more broadly, how inference interacts with the structure in the data.

The "New Synthesis" - Barton, Nicholas H (Proceedings of the National Academy of Sciences of the United States of America)
When Mendel’s work was rediscovered in 1900, and extended to establish classical genetics, it was initially seen in opposition to Darwin’s theory of evolution by natural selection on continuous variation, as represented by the biometric research program that was the foundation of quantitative genetics. As Fisher, Haldane, and Wright established a century ago, Mendelian inheritance is exactly what is needed for natural selection to work efficiently. Yet, the synthesis remains unfinished. We do not understand why sexual reproduction and a fair meiosis predominate in eukaryotes, or how far these are responsible for their diversity and complexity. Moreover, although quantitative geneticists have long known that adaptive variation is highly polygenic, and that this is essential for efficient selection, this is only now becoming appreciated by molecular biologists—and we still do not have a good framework for understanding polygenic variation or diffuse function.

Quantifying heterologous gene expression during ectopic MazF production in Escherichia coli - Nikolic, Nela; Sauert, Martina; Albanese, Tanino G.; Moll, Isabella (BMC Research Notes)
Objective: MazF is a sequence-specific endoribonuclease-toxin of the MazEF toxin–antitoxin system. MazF cleaves single-stranded ribonucleic acid (RNA) regions at adenine–cytosine–adenine (ACA) sequences in the bacterium Escherichia coli. The MazEF system has been used in various biotechnology and synthetic biology applications. In this study, we infer how ectopic mazF overexpression affects production of heterologous proteins. To this end, we quantified the levels of fluorescent proteins expressed in E. coli from reporters translated from the ACA-containing or ACA-less messenger RNAs (mRNAs). Additionally, we addressed the impact of the 5′-untranslated region of these reporter mRNAs under the same conditions by comparing expression from mRNAs that comprise (canonical mRNA) or lack this region (leaderless mRNA). Results: Flow cytometry analysis indicates that during mazF overexpression, fluorescent proteins are translated from the canonical as well as leaderless mRNAs. Our analysis further indicates that longer mazF overexpression generally increases the concentration of fluorescent proteins translated from ACA-less mRNAs, however it also substantially increases bacterial population heterogeneity. Finally, our results suggest that the strength and duration of mazF overexpression should be optimized for each experimental setup, to maximize the heterologous protein production and minimize the amount of phenotypic heterogeneity in bacterial populations, which is unfavorable in biotechnological processes.
Keywords: General Biochemistry; Genetics and Molecular Biology; General Medicine

Kac regularity and domination of quadratic forms - Wirth, Melchior (Advances in Operator Theory)
A domain is called Kac regular for a quadratic form on L2 if every functions vanishing almost everywhere outside the domain can be approximated in form norm by functions with compact support in the domain. It is shown that this notion is stable under domination of quadratic forms. As applications measure perturbations of quasi-regular Dirichlet forms, Cheeger energies on metric measure spaces and Schrödinger operators on manifolds are studied. Along the way a characterization of the Sobolev space with Dirichlet boundary conditions on domains in infinitesimally Riemannian metric measure spaces is obtained.
Keywords: Algebra and Number Theory; Analysis

An invitation to the promise constraint satisfaction problem - Krokhin, Andrei; Opršal, Jakub (ACM SIGLOG News)
The study of the complexity of the constraint satisfaction problem (CSP), centred around the Feder-Vardi Dichotomy Conjecture, has been very prominent in the last two decades. After a long concerted effort and many partial results, the Dichotomy Conjecture has been proved in 2017 independently by Bulatov and Zhuk. At about the same time, a vast generalisation of CSP, called promise CSP, has started to gain prominence. In this survey, we explain the importance of promise CSP and highlight many new very interesting features that the study of promise CSP has brought to light. The complexity classification quest for the promise CSP is wide open, and we argue that, despite the promise CSP being more general, this quest is rather more accessible to a wide range of researchers than the dichotomy-led study of the CSP has been.

Latent imagination facilitates zero-shot transfer in autonomous racing - Brunnbauer, Axel; Berducci, Luigi; Brandstatter, Andreas; Lechner, Mathias; Hasani, Ramin; Rus, Daniela; Grosu, Radu (2022 International Conference on Robotics and Automation)
World models learn behaviors in a latent imagination space to enhance the sample-efficiency of deep reinforcement learning (RL) algorithms. While learning world models for high-dimensional observations (e.g., pixel inputs) has become practicable on standard RL benchmarks and some games, their effectiveness in real-world robotics applications has not been explored. In this paper, we investigate how such agents generalize to real-world autonomous vehicle control tasks, where advanced model-free deep RL algorithms fail. In particular, we set up a series of time-lap tasks for an F1TENTH racing robot, equipped with a high-dimensional LiDAR sensor, on a set of test tracks with a gradual increase in their complexity. In this continuous-control setting, we show that model-based agents capable of learning in imagination substantially outperform model-free agents with respect to performance, sample efficiency, successful task completion, and generalization. Moreover, we show that the generalization ability of model-based agents strongly depends on the choice of their observation model. We provide extensive empirical evidence for the effectiveness of world models provided with long enough memory horizons in sim2real tasks.

The capacity of causal adversarial channels - Zhang, Yihan; Jaggi, Sidharth; Langberg, Michael; Sarwate, Anand D. (2022 IEEE International Symposium on Information Theory)
We characterize the capacity for the discrete-time arbitrarily varying channel with discrete inputs, outputs, and states when (a) the encoder and decoder do not share common randomness, (b) the input and state are subject to cost constraints, (c) the transition matrix of the channel is deterministic given the state, and (d) at each time step the adversary can only observe the current and past channel inputs when choosing the state at that time. The achievable strategy involves stochastic encoding together with list decoding and a disambiguation step. The converse uses a two-phase "babble-and-push" strategy where the adversary chooses the state randomly in the first phase, list decodes the output, and then chooses state inputs to symmetrize the channel in the second phase. These results generalize prior work on specific channels models (additive, erasure) to general discrete alphabets and models.

Polar coded computing: The role of the scaling exponent - Fathollahi, Dorsa; Mondelli, Marco (2022 IEEE International Symposium on Information Theory)
We consider the problem of coded distributed computing using polar codes. The average execution time of a coded computing system is related to the error probability for transmission over the binary erasure channel in recent work by Soleymani, Jamali and Mahdavifar, where the performance of binary linear codes is investigated. In this paper, we focus on polar codes and unveil a connection between the average execution time and the scaling exponent μ of the family of codes. In the finite-length characterization of polar codes, the scaling exponent is a key object capturing the speed of convergence to capacity. In particular, we show that (i) the gap between the normalized average execution time of polar codes and that of optimal MDS codes is O(n –1/μ ), and (ii) this upper bound can be improved to roughly O(n –1/2 ) by considering polar codes with large kernels. We conjecture that these bounds could be improved to O(n –2/μ ) and O(n –1 ), respectively, and provide a heuristic argument as well as numerical evidence supporting this view.

Heterogeneous differential privacy via graphs - Torkamani, Sahel; Ebrahimi, Javad B.; Sadeghi, Parastoo; D'Oliveira, Rafael G.L.; Médard, Muriel (2022 IEEE International Symposium on Information Theory)
This paper is eligible for the Jack Keil Wolf ISIT Student Paper Award. We generalize a previous framework for designing utility-optimal differentially private (DP) mechanisms via graphs, where datasets are vertices in the graph and edges represent dataset neighborhood. The boundary set contains datasets where an individual’s response changes the binary-valued query compared to its neighbors. Previous work was limited to the homogeneous case where the privacy parameter ε across all datasets was the same and the mechanism at boundary datasets was identical. In our work, the mechanism can take different distributions at the boundary and the privacy parameter ε is a function of neighboring datasets, which recovers an earlier definition of personalized DP as special case. The problem is how to extend the mechanism, which is only defined at the boundary set, to other datasets in the graph in a computationally efficient and utility optimal manner. Using the concept of strongest induced DP condition we solve this problem efficiently in polynomial time (in the size of the graph).

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.

Complexity of spatial games - Chatterjee, Krishnendu; Ibsen-Jensen, Rasmus; Jecker, Ismael R; Svoboda, Jakub (42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science)
Spatial games form a widely-studied class of games from biology and physics modeling the evolution of social behavior. Formally, such a game is defined by a square (d by d) payoff matrix M and an undirected graph G. Each vertex of G represents an individual, that initially follows some strategy i ∈ {1,2,…,d}. In each round of the game, every individual plays the matrix game with each of its neighbors: An individual following strategy i meeting a neighbor following strategy j receives a payoff equal to the entry (i,j) of M. Then, each individual updates its strategy to its neighbors' strategy with the highest sum of payoffs, and the next round starts. The basic computational problems consist of reachability between configurations and the average frequency of a strategy. For general spatial games and graphs, these problems are in PSPACE. In this paper, we examine restricted setting: the game is a prisoner’s dilemma; and G is a subgraph of grid. We prove that basic computational problems for spatial games with prisoner’s dilemma on a subgraph of a grid are PSPACE-hard.

Entanglement-based observables for quantum impurities - Stocker, Lidia; Sack, Stefan; Ferguson, Michael S.; Zilberberg, Oded (Physical Review Research)
Quantum impurities exhibit fascinating many-body phenomena when the small interacting impurity changes the physics of a large noninteracting environment. The characterisation of such strongly correlated nonperturbative effects is particularly challenging due to the infinite size of the environment, and the inability of local correlators to capture the buildup of long-ranged entanglement in the system. Here, we harness an entanglement-based observable—the purity of the impurity—as a witness for the formation of strong correlations. We showcase the utility of our scheme by exactly solving the open Kondo box model in the small box limit, and thus describe all-electronic dot-cavity devices. Specifically, we conclusively characterize the metal-to-insulator phase transition in the system and identify how the (conducting) dot-lead Kondo singlet is quenched by an (insulating) intraimpurity singlet formation. Furthermore, we propose an experimentally feasible tomography protocol for the measurement of the purity, which motivates the observation of impurity physics through their entanglement build up.

Gloss management for consistent reproduction of real and virtual objects - Chen, Bin; Piovarci, Michael; Wang, Chao; Seidel, Hans-Peter; Didyk, Piotr; Myszkowski, Karol; Serrano, Ana (SIGGRAPH Asia 2022 Conference Papers)
A good match of material appearance between real-world objects and their digital on-screen representations is critical for many applications such as fabrication, design, and e-commerce. However, faithful appearance reproduction is challenging, especially for complex phenomena, such as gloss. In most cases, the view-dependent nature of gloss and the range of luminance values required for reproducing glossy materials exceeds the current capabilities of display devices. As a result, appearance reproduction poses significant problems even with accurately rendered images. This paper studies the gap between the gloss perceived from real-world objects and their digital counterparts. Based on our psychophysical experiments on a wide range of 3D printed samples and their corresponding photographs, we derive insights on the influence of geometry, illumination, and the display’s brightness and measure the change in gloss appearance due to the display limitations. Our evaluation experiments demonstrate that using the prediction to correct material parameters in a rendering system improves the match of gloss appearance between real objects and their visualization on a display device.

Explosive transitions in epidemic dynamics - Börner, Georg; Schröder, Malte; Scarselli, Davide; Budanur, Nazmi B; Hof, Björn; Timme, Marc (Journal of Physics: Complexity)
Standard epidemic models exhibit one continuous, second order phase transition to macroscopic outbreaks. However, interventions to control outbreaks may fundamentally alter epidemic dynamics. Here we reveal how such interventions modify the type of phase transition. In particular, we uncover three distinct types of explosive phase transitions for epidemic dynamics with capacity-limited interventions. Depending on the capacity limit, interventions may (i) leave the standard second order phase transition unchanged but exponentially suppress the probability of large outbreaks, (ii) induce a first-order discontinuous transition to macroscopic outbreaks, or (iii) cause a secondary explosive yet continuous third-order transition. These insights highlight inherent limitations in predicting and containing epidemic outbreaks. More generally our study offers a cornerstone example of a third-order explosive phase transition in complex systems.
Keywords: Artificial Intelligence; Computer Networks and Communications; Computer Science Applications; Information Systems

Eukaryotic gene regulation at equilibrium, or non? - Zoller, Benjamin; Gregor, Thomas; Tkačik, Gašper (Current Opinion in Systems Biology)
Models of transcriptional regulation that assume equilibrium binding of transcription factors have been less successful at predicting gene expression from sequence in eukaryotes than in bacteria. This could be due to the non-equilibrium nature of eukaryotic regulation. Unfortunately, the space of possible non-equilibrium mechanisms is vast and predominantly uninteresting. The key question is therefore how this space can be navigated efficiently, to focus on mechanisms and models that are biologically relevant. In this review, we advocate for the normative role of theory—theory that prescribes rather than just describes—in providing such a focus. Theory should expand its remit beyond inferring mechanistic models from data, towards identifying non-equilibrium gene regulatory schemes that may have been evolutionarily selected, despite their energy consumption, because they are precise, reliable, fast, or otherwise outperform regulation at equilibrium. We illustrate our reasoning by toy examples for which we provide simulation code.
Keywords: Applied Mathematics; Computer Science Applications; Drug Discovery; General Biochemistry; Genetics and Molecular Biology; Modeling and Simulation

Synthesis of parametric hybrid automata from time series - Garcia Soto, Miriam; Henzinger, Thomas A; Schilling, Christian (20th International Symposium on Automated Technology for Verification and Analysis)
We propose an algorithmic approach for synthesizing linear hybrid automata from time-series data. Unlike existing approaches, our approach provides a whole family of models with the same discrete structure but different dynamics. Each model in the family is guaranteed to capture the input data up to a precision error ε, in the following sense: For each time series, the model contains an execution that is ε-close to the data points. Our construction allows to effectively choose a model from this family with minimal precision error ε. We demonstrate the algorithm’s efficiency and its ability to find precise models in two case studies.

Brief announcement: Temporal locality in online algorithms - Pacut, Maciej; Parham, Mahmoud; Rybicki, Joel; Schmid, Stefan; Suomela, Jukka; Tereshchenko, Aleksandr (36th International Symposium on Distributed Computing)
Online algorithms make decisions based on past inputs, with the goal of being competitive against an algorithm that sees also future inputs. In this work, we introduce time-local online algorithms; these are online algorithms in which the output at any given time is a function of only T latest inputs. Our main observation is that time-local online algorithms are closely connected to local distributed graph algorithms: distributed algorithms make decisions based on the local information in the spatial dimension, while time-local online algorithms make decisions based on the local information in the temporal dimension. We formalize this connection, and show how we can directly use the tools developed to study distributed approximability of graph optimization problems to prove upper and lower bounds on the competitive ratio achieved with time-local online algorithms. Moreover, we show how to use computational techniques to synthesize optimal time-local algorithms.

Effective contraction of Skinning maps - Cremaschi, Tommaso; Dello Schiavo, Lorenzo (Proceedings of the American Mathematical Society, Series B)
Using elementary hyperbolic geometry, we give an explicit formula for the contraction constant of the skinning map over moduli spaces of relatively acylindrical hyperbolic manifolds.

On the condition number of the shifted real Ginibre ensemble - Cipolloni, Giorgio; Erdös, László; Schröder, Dominik J (SIAM Journal on Matrix Analysis and Applications)
We derive an accurate lower tail estimate on the lowest singular value σ1(X−z) of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z. Such shift effectively changes the upper tail behavior of the condition number κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away from the real axis. This sharpens and resolves a recent conjecture in [J. Banks et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of the real Ginibre ensemble with a genuinely complex shift. As a consequence we obtain an improved upper bound on the eigenvalue condition numbers (known also as the eigenvector overlaps) for real Ginibre matrices. The main technical tool is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys., 1 (2020), pp. 101--146].
Keywords: Analysis

Bullshark: DAG BFT protocols made practical - Spiegelman, Alexander; Giridharan, Neil; Sonnino, Alberto; Kokoris Kogias, Eleftherios (Proceedings of the 2022 ACM SIGSAC Conference on Computer and Communications Security)
We present Bullshark, the first directed acyclic graph (DAG) based asynchronous Byzantine Atomic Broadcast protocol that is optimized for the common synchronous case. Like previous DAG-based BFT protocols [19, 25], Bullshark requires no extra communication to achieve consensus on top of building the DAG. That is, parties can totally order the vertices of the DAG by interpreting their local view of the DAG edges. Unlike other asynchronous DAG-based protocols, Bullshark provides a practical low latency fast-path that exploits synchronous periods and deprecates the need for notoriously complex view-change and view-synchronization mechanisms. Bullshark achieves this while maintaining all the desired properties of its predecessor DAG-Rider [25]. Namely, it has optimal amortized communication complexity, it provides fairness and asynchronous liveness, and safety is guaranteed even under a quantum adversary. In order to show the practicality and simplicity of our approach, we also introduce a standalone partially synchronous version of Bullshark, which we evaluate against the state of the art. The implemented protocol is embarrassingly simple (200 LOC on top of an existing DAG-based mempool implementation). It is highly efficient, achieving for example, 125,000 transactions per second with a 2 seconds latency for a deployment of 50 parties. In the same setting, the state of the art pays a steep 50% latency increase as it optimizes for asynchrony.

Optimal steering of matrix product states and quantum many-body scars - Ljubotina, Marko; Roos, Barbara; Abanin, Dmitry A.; Serbyn, Maksym (PRX Quantum)
Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of nontrivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states (MPSs). We compare counterdiabatic and leakage minimization approaches to the so-called local steering problem that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counterdiabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally, we apply our leakage minimization approach to construct quantum scars in the periodically driven nonintegrable Ising model.
Keywords: General Medicine

Practical asynchronous distributed key generation - Das, Sourav; Yurek, Thomas; Xiang, Zhuolun; Miller, Andrew; Kokoris Kogias, Eleftherios; Ren, Ling (2022 IEEE Symposium on Security and Privacy)
Distributed Key Generation (DKG) is a technique to bootstrap threshold cryptosystems without a trusted third party and is a building block to decentralized protocols such as randomness beacons, threshold signatures, and general multiparty computation. Until recently, DKG protocols have assumed the synchronous model and thus are vulnerable when their underlying network assumptions do not hold. The recent advancements in asynchronous DKG protocols are insufficient as they either have poor efficiency or limited functionality, resulting in a lack of concrete implementations. In this paper, we present a simple and concretely efficient asynchronous DKG (ADKG) protocol. In a network of n nodes, our ADKG protocol can tolerate up to t<n/3 malicious nodes and have an expected O(κn3) communication cost, where κ is the security parameter. Our ADKG protocol produces a field element as the secret and is thus compatible with off-the-shelf threshold cryptosystems. We implement our ADKG protocol and evaluate it using a network of up to 128 nodes in geographically distributed AWS instances. Our evaluation shows that our protocol takes as low as 3 and 9.5 seconds to terminate for 32 and 64 nodes, respectively. Also, each node sends only 0.7 Megabytes and 2.9 Megabytes of data during the two experiments, respectively.

Loop Grassmannians of Quivers and Affine Quantum Groups - Mirković, Ivan; Yang, Yaping; Zhao, Gufang (Representation Theory and Algebraic Geometry)
We construct for each choice of a quiver Q, a cohomology theory A, and a poset P a “loop Grassmannian” GP(Q,A). This generalizes loop Grassmannians of semisimple groups and the loop Grassmannians of based quadratic forms. The addition of a “dilation” torus D⊆G2m gives a quantization GPD(Q,A). This construction is motivated by the program of introducing an inner cohomology theory in algebraic geometry adequate for the Geometric Langlands program (Mirković, Some extensions of the notion of loop Grassmannians. Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., the Mardešić issue. No. 532, 53–74, 2017) and on the construction of affine quantum groups from generalized cohomology theories (Yang and Zhao, Quiver varieties and elliptic quantum groups, preprint. arxiv1708.01418).

History-deterministic timed automata - Henzinger, Thomas A; Lehtinen, Karoliina; Totzke, Patrick (33rd International Conference on Concurrency Theory)
We explore the notion of history-determinism in the context of timed automata (TA). History-deterministic automata are those in which nondeterminism can be resolved on the fly, based on the run constructed thus far. History-determinism is a robust property that admits different game-based characterisations, and history-deterministic specifications allow for game-based verification without an expensive determinization step. We show yet another characterisation of history-determinism in terms of fair simulation, at the general level of labelled transition systems: a system is history-deterministic precisely if and only if it fairly simulates all language smaller systems. For timed automata over infinite timed words it is known that universality is undecidable for Büchi TA. We show that for history-deterministic TA with arbitrary parity acceptance, timed universality, inclusion, and synthesis all remain decidable and are ExpTime-complete. For the subclass of TA with safety or reachability acceptance, we show that checking whether such an automaton is history-deterministic is decidable (in ExpTime), and history-deterministic TA with safety acceptance are effectively determinizable without introducing new automata states.

An updated survey of bidding games on graphs - Avni, Guy; Henzinger, Thomas A (47th International Symposium on Mathematical Foundations of Computer Science)
A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. In bidding games, both players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token. In this survey, we consider several bidding mechanisms and their effect on the properties of the game. Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly. We summarize how minor changes in the bidding mechanism lead to unexpected differences in the equivalence with random-turn games.

Estimation in rotationally invariant generalized linear models via approximate message passing - Venkataramanan, Ramji; Kögler, Kevin; Mondelli, Marco (Proceedings of the 39th International Conference on Machine Learning)
We consider the problem of signal estimation in generalized linear models defined via rotationally invariant design matrices. Since these matrices can have an arbitrary spectral distribution, this model is well suited for capturing complex correlation structures which often arise in applications. We propose a novel family of approximate message passing (AMP) algorithms for signal estimation, and rigorously characterize their performance in the high-dimensional limit via a state evolution recursion. Our rotationally invariant AMP has complexity of the same order as the existing AMP derived under the restrictive assumption of a Gaussian design; our algorithm also recovers this existing AMP as a special case. Numerical results showcase a performance close to Vector AMP (which is conjectured to be Bayes-optimal in some settings), but obtained with a much lower complexity, as the proposed algorithm does not require a computationally expensive singular value decomposition.

The price of ignorance: How much does it cost to forget noise structure in low-rank matrix estimation? - Barbier, Jean; Hou, TianQi; Mondelli, Marco; Saenz, Manuel (arXiv)
We consider the problem of estimating a rank-1 signal corrupted by structured rotationally invariant noise, and address the following question: how well do inference algorithms perform when the noise statistics is unknown and hence Gaussian noise is assumed? While the matched Bayes-optimal setting with unstructured noise is well understood, the analysis of this mismatched problem is only at its premises. In this paper, we make a step towards understanding the effect of the strong source of mismatch which is the noise statistics. Our main technical contribution is the rigorous analysis of a Bayes estimator and of an approximate message passing (AMP) algorithm, both of which incorrectly assume a Gaussian setup. The first result exploits the theory of spherical integrals and of low-rank matrix perturbations; the idea behind the second one is to design and analyze an artificial AMP which, by taking advantage of the flexibility in the denoisers, is able to "correct" the mismatch. Armed with these sharp asymptotic characterizations, we unveil a rich and often unexpected phenomenology. For example, despite AMP is in principle designed to efficiently compute the Bayes estimator, the former is outperformed by the latter in terms of mean-square error. We show that this performance gap is due to an incorrect estimation of the signal norm. In fact, when the SNR is large enough, the overlaps of the AMP and the Bayes estimator coincide, and they even match those of optimal estimators taking into account the structure of the noise.

Risk-aware stochastic shortest path - Meggendorfer, Tobias (Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022)
We treat the problem of risk-aware control for stochastic shortest path (SSP) on Markov decision processes (MDP). Typically, expectation is considered for SSP, which however is oblivious to the incurred risk. We present an alternative view, instead optimizing conditional value-at-risk (CVaR), an established risk measure. We treat both Markov chains as well as MDP and introduce, through novel insights, two algorithms, based on linear programming and value iteration, respectively. Both algorithms offer precise and provably correct solutions. Evaluation of our prototype implementation shows that risk-aware control is feasible on several moderately sized models.

Cross-client Label Propagation for transductive federated learning - Scott, Jonathan A; Yeo, Michelle X; Lampert, Christoph (arXiv)
We present Cross-Client Label Propagation(XCLP), a new method for transductive federated learning. XCLP estimates a data graph jointly from the data of multiple clients and computes labels for the unlabeled data by propagating label information across the graph. To avoid clients having to share their data with anyone, XCLP employs two cryptographically secure protocols: secure Hamming distance computation and secure summation. We demonstrate two distinct applications of XCLP within federated learning. In the first, we use it in a one-shot way to predict labels for unseen test points. In the second, we use it to repeatedly pseudo-label unlabeled training data in a federated semi-supervised setting. Experiments on both real federated and standard benchmark datasets show that in both applications XCLP achieves higher classification accuracy than alternative approaches.

Generalization in Multi-objective machine learning - Súkeník, Peter; Lampert, Christoph (arXiv)
Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their combinations. Multi-objective learning offers a natural framework for handling such problems without having to commit to early trade-offs. Surprisingly, statistical learning theory so far offers almost no insight into the generalization properties of multi-objective learning. In this work, we make first steps to fill this gap: we establish foundational generalization bounds for the multi-objective setting as well as generalization and excess bounds for learning with scalarizations. We also provide the first theoretical analysis of the relation between the Pareto-optimal sets of the true objectives and the Pareto-optimal sets of their empirical approximations from training data. In particular, we show a surprising asymmetry: all Pareto-optimal solutions can be approximated by empirically Pareto-optimal ones, but not vice versa.

Intriguing properties of input-dependent randomized smoothing - Súkeník, Peter; Kuvshinov, Aleksei; Günnemann, Stephan (Proceedings of the 39th International Conference on Machine Learning)
Randomized smoothing is currently considered the state-of-the-art method to obtain certifiably robust classifiers. Despite its remarkable performance, the method is associated with various serious problems such as “certified accuracy waterfalls”, certification vs. accuracy trade-off, or even fairness issues. Input-dependent smoothing approaches have been proposed with intention of overcoming these flaws. However, we demonstrate that these methods lack formal guarantees and so the resulting certificates are not justified. We show that in general, the input-dependent smoothing suffers from the curse of dimensionality, forcing the variance function to have low semi-elasticity. On the other hand, we provide a theoretical and practical framework that enables the usage of input-dependent smoothing even in the presence of the curse of dimensionality, under strict restrictions. We present one concrete design of the smoothing variance function and test it on CIFAR10 and MNIST. Our design mitigates some of the problems of classical smoothing and is formally underlined, yet further improvement of the design is still necessary.

FLEA: Provably robust fair multisource learning from unreliable training data - Iofinova, Eugenia B; Konstantinov, Nikola H; Lampert, Christoph (Transactions on Machine Learning Research)
Fairness-aware learning aims at constructing classifiers that not only make accurate predictions, but also do not discriminate against specific groups. It is a fast-growing area of machine learning with far-reaching societal impact. However, existing fair learning methods are vulnerable to accidental or malicious artifacts in the training data, which can cause them to unknowingly produce unfair classifiers. In this work we address the problem of fair learning from unreliable training data in the robust multisource setting, where the available training data comes from multiple sources, a fraction of which might not be representative of the true data distribution. We introduce FLEA, a filtering-based algorithm that identifies and suppresses those data sources that would have a negative impact on fairness or accuracy if they were used for training. As such, FLEA is not a replacement of prior fairness-aware learning methods but rather an augmentation that makes any of them robust against unreliable training data. We show the effectiveness of our approach by a diverse range of experiments on multiple datasets. Additionally, we prove formally that –given enough data– FLEA protects the learner against corruptions as long as the fraction of affected data sources is less than half. Our source code and documentation are available at https://github.com/ISTAustria-CVML/FLEA.

On compatible matchings - Aichholzer, Oswin; Arroyo Guevara, Alan M; Masárová, Zuzana; Parada, Irene; Perz, Daniel; Pilz, Alexander; Tkadlec, Josef; Vogtenhuber, Birgit (Journal of Graph Algorithms and Applications)
A matching is compatible to two or more labeled point sets of size n with labels {1, . . . , n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled sets of n points in convex position there exists a compatible matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(log n) copies of any set of n points are necessary and sufficient for the existence of labelings of these point sets such that any compatible matching consists only of a single edge.

Open problems on billiards and geometric optics - Bialy, Misha; Fiorebe, Corentin; Glutsyuk, Alexey; Levi, Mark; Plakhov, Alexander; Tabachnikov, Serge (Arnold Mathematical Journal)
This is a collection of problems composed by some participants of the workshop “Differential Geometry, Billiards, and Geometric Optics” that took place at CIRM on October 4–8, 2021.

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.

CGX: Adaptive system support for communication-efficient deep learning - Markov, Ilia; Ramezanikebrya, Hamidreza; Alistarh, Dan-Adrian (Proceedings of the 23rd ACM/IFIP International Middleware Conference)
The ability to scale out training workloads has been one of the key performance enablers of deep learning. The main scaling approach is data-parallel GPU-based training, which has been boosted by hardware and software support for highly efficient point-to-point communication, and in particular via hardware bandwidth over-provisioning. Overprovisioning comes at a cost: there is an order of magnitude price difference between "cloud-grade" servers with such support, relative to their popular "consumer-grade" counterparts, although single server-grade and consumer-grade GPUs can have similar computational envelopes. In this paper, we show that the costly hardware overprovisioning approach can be supplanted via algorithmic and system design, and propose a framework called CGX, which provides efficient software support for compressed communication in ML applications, for both multi-GPU single-node training, as well as larger-scale multi-node training. CGX is based on two technical advances: At the system level, it relies on a re-developed communication stack for ML frameworks, which provides flexible, highly-efficient support for compressed communication. At the application level, it provides seamless, parameter-free integration with popular frameworks, so that end-users do not have to modify training recipes, nor significant training code. This is complemented by a layer-wise adaptive compression technique which dynamically balances compression gains with accuracy preservation. CGX integrates with popular ML frameworks, providing up to 3X speedups for multi-GPU nodes based on commodity hardware, and order-of-magnitude improvements in the multi-node setting, with negligible impact on accuracy.

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.

Integral points of bounded height on a certain toric variety - Wilsch, Florian Alexander (arXiv)
We determine an asymptotic formula for the number of integral points of bounded height on a certain toric variety, which is incompatible with part of a preprint by Chambert-Loir and Tschinkel. We provide an alternative interpretation of the asymptotic formula we get. To do so, we construct an analogue of Peyre's constant $α$ and describe its relation to a new obstruction to the Zariski density of integral points in certain regions of varieties.
Keywords: Integral point; toric variety; Manin's conjecture

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.

Where is the sweet spot? A procurement story of general purpose compute nodes - Schlögl, Alois; Hornoiu, Andrei; Elefante, Stefano; Stadlbauer, Stephan (ASHPC22 - Austrian-Slovenian HPC Meeting 2022)

Tissue-wide genetic and cellular landscape shapes the execution of sequential PRC2 functions in neural stem cell lineage progression - Amberg, Nicole; Pauler, Florian; Streicher, Carmen; Hippenmeyer, Simon (Science Advances)
The generation of a correctly-sized cerebral cortex with all-embracing neuronal and glial cell-type diversity critically depends on faithful radial glial progenitor (RGP) cell proliferation/differentiation programs. Temporal RGP lineage progression is regulated by Polycomb Repressive Complex 2 (PRC2) and loss of PRC2 activity results in severe neurogenesis defects and microcephaly. How PRC2-dependent gene expression instructs RGP lineage progression is unknown. Here we utilize Mosaic Analysis with Double Markers (MADM)-based single cell technology and demonstrate that PRC2 is not cell-autonomously required in neurogenic RGPs but rather acts at the global tissue-wide level. Conversely, cortical astrocyte production and maturation is cell-autonomously controlled by PRC2-dependent transcriptional regulation. We thus reveal highly distinct and sequential PRC2 functions in RGP lineage progression that are dependent on complex interplays between intrinsic and tissue-wide properties. In a broader context our results imply a critical role for the genetic and cellular niche environment in neural stem cell behavior.

Closed-loop control of direct ink writing via reinforcement learning - Piovarci, Michael; Foshey, Michael; Xu, Jie; Erps, Timothy; Babaei, Vahid; Didyk, Piotr; Rusinkiewicz, Szymon; Matusik, Wojciech; Bickel, Bernd (ACM Transactions on Graphics)
Enabling additive manufacturing to employ a wide range of novel, functional materials can be a major boost to this technology. However, making such materials printable requires painstaking trial-and-error by an expert operator, as they typically tend to exhibit peculiar rheological or hysteresis properties. Even in the case of successfully finding the process parameters, there is no guarantee of print-to-print consistency due to material differences between batches. These challenges make closed-loop feedback an attractive option where the process parameters are adjusted on-the-fly. There are several challenges for designing an efficient controller: the deposition parameters are complex and highly coupled, artifacts occur after long time horizons, simulating the deposition is computationally costly, and learning on hardware is intractable. In this work, we demonstrate the feasibility of learning a closed-loop control policy for additive manufacturing using reinforcement learning. We show that approximate, but efficient, numerical simulation is sufficient as long as it allows learning the behavioral patterns of deposition that translate to real-world experiences. In combination with reinforcement learning, our model can be used to discover control policies that outperform baseline controllers. Furthermore, the recovered policies have a minimal sim-to-real gap. We showcase this by applying our control policy in-vivo on a single-layer, direct ink writing printer.

Near-optimal leader election in population protocols on graphs - Alistarh, Dan-Adrian; Rybicki, Joel; Voitovych, Sasha (Proceedings of the Annual ACM Symposium on Principles of Distributed Computing)
In the stochastic population protocol model, we are given a connected graph with n nodes, and in every time step, a scheduler samples an edge of the graph uniformly at random and the nodes connected by this edge interact. A fundamental task in this model is stable leader election, in which all nodes start in an identical state and the aim is to reach a configuration in which (1) exactly one node is elected as leader and (2) this node remains as the unique leader no matter what sequence of interactions follows. On cliques, the complexity of this problem has recently been settled: time-optimal protocols stabilize in Θ(n log n) expected steps using Θ(log log n) states, whereas protocols that use O(1) states require Θ(n2) expected steps. In this work, we investigate the complexity of stable leader election on general graphs. We provide the first non-trivial time lower bounds for leader election on general graphs, showing that, when moving beyond cliques, the complexity landscape of leader election becomes very diverse: the time required to elect a leader can range from O(1) to Θ(n3) expected steps. On the upper bound side, we first observe that there exists a protocol that is time-optimal on many graph families, but uses polynomially-many states. In contrast, we give a near-time-optimal protocol that uses only O(log2n) states that is at most a factor log n slower. Finally, we show that the constant-state protocol of Beauquier et al. [OPODIS 2013] is at most a factor n log n slower than the fast polynomial-state protocol. Moreover, among constant-state protocols, this protocol has near-optimal average case complexity on dense random graphs.

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.

Predictive learning enables neural networks to learn complex working memory tasks - Van Der Plas, Thijs L.; Vogels, Tim P; Manohar, Sanjay G. (Proceedings of Machine Learning Research)
Brains are thought to engage in predictive learning - learning to predict upcoming stimuli - to construct an internal model of their environment. This is especially notable for spatial navigation, as first described by Tolman’s latent learning tasks. However, predictive learning has also been observed in sensory cortex, in settings unrelated to spatial navigation. Apart from normative frameworks such as active inference or efficient coding, what could be the utility of learning to predict the patterns of occurrence of correlated stimuli? Here we show that prediction, and thereby the construction of an internal model of sequential stimuli, can bootstrap the learning process of a working memory task in a recurrent neural network. We implemented predictive learning alongside working memory match-tasks, and networks emerged to solve the prediction task first by encoding information across time to predict upcoming stimuli, and then eavesdropped on this solution to solve the matching task. Eavesdropping was most beneficial when neural resources were limited. Hence, predictive learning acts as a general neural mechanism to learn to store sensory information that can later be essential for working memory tasks.

Revisiting the adversarial robustness-accuracy tradeoff in robot learning - Lechner, Mathias; Amini, Alexander; Rus, Daniela; Henzinger, Thomas A (arXiv)
Adversarial training (i.e., training on adversarially perturbed input data) is a well-studied method for making neural networks robust to potential adversarial attacks during inference. However, the improved robustness does not come for free but rather is accompanied by a decrease in overall model accuracy and performance. Recent work has shown that, in practical robot learning applications, the effects of adversarial training do not pose a fair trade-off but inflict a net loss when measured in holistic robot performance. This work revisits the robustness-accuracy trade-off in robot learning by systematically analyzing if recent advances in robust training methods and theory in conjunction with adversarial robot learning can make adversarial training suitable for real-world robot applications. We evaluate a wide variety of robot learning tasks ranging from autonomous driving in a high-fidelity environment amenable to sim-to-real deployment, to mobile robot gesture recognition. Our results demonstrate that, while these techniques make incremental improvements on the trade-off on a relative scale, the negative side-effects caused by adversarial training still outweigh the improvements by an order of magnitude. We conclude that more substantial advances in robust learning methods are necessary before they can benefit robot learning tasks in practice.

Coupling 3D liquid simulation with 2D wave propagation for large scale water surface animation using the equivalent sources method - Schreck, Camille; Wojtan, Christopher J (Computer Graphics Forum)
This paper proposes a method for simulating liquids in large bodies of water by coupling together a water surface wave simulator with a 3D Navier-Stokes simulator. The surface wave simulation uses the equivalent sources method (ESM) to efficiently animate large bodies of water with precisely controllable wave propagation behavior. The 3D liquid simulator animates complex non-linear fluid behaviors like splashes and breaking waves using off-the-shelf simulators using FLIP or the level set method with semi-Lagrangian advection. We combine the two approaches by using the 3D solver to animate localized non-linear behaviors, and the 2D wave solver to animate larger regions with linear surface physics. We use the surface motion from the 3D solver as boundary conditions for 2D surface wave simulator, and we use the velocity and surface heights from the 2D surface wave simulator as boundary conditions for the 3D fluid simulation. We also introduce a novel technique for removing visual artifacts caused by numerical errors in 3D fluid solvers: we use experimental data to estimate the artificial dispersion caused by the 3D solver and we then carefully tune the wave speeds of the 2D solver to match it, effectively eliminating any differences in wave behavior across the boundary. To the best of our knowledge, this is the first time such a empirically driven error compensation approach has been used to remove coupling errors from a physics simulator. Our coupled simulation approach leverages the strengths of each simulation technique, animating large environments with seamless transitions between 2D and 3D physics.

Even maps, the Colin de Verdière number and representations of graphs - Kaluza, Vojtech; Tancer, Martin (Combinatorica)
Van der Holst and Pendavingh introduced a graph parameter σ, which coincides with the more famous Colin de Verdière graph parameter μ for small values. However, the definition of a is much more geometric/topological directly reflecting embeddability properties of the graph. They proved μ(G) ≤ σ(G) + 2 and conjectured σ(G) ≤ σ(G) for any graph G. We confirm this conjecture. As far as we know, this is the first topological upper bound on σ(G) which is, in general, tight. Equality between μ and σ does not hold in general as van der Holst and Pendavingh showed that there is a graph G with μ(G) ≤ 18 and σ(G) ≥ 20. We show that the gap appears at much smaller values, namely, we exhibit a graph H for which μ(H) ≥ 7 and σ(H) ≥ 8. We also prove that, in general, the gap can be large: The incidence graphs Hq of finite projective planes of order q satisfy μ(Hq) ∈ O(q3/2) and σ(Hq) ≥ q2.

Equidistribution and freeness on Grassmannians - Browning, Timothy D; Horesh, Tal; Wilsch, Florian Alexander (Algebra & Number Theory)
We associate a certain tensor product lattice to any primitive integer lattice and ask about its typical shape. These lattices are related to the tangent bundle of Grassmannians and their study is motivated by Peyre's programme on "freeness" for rational points of bounded height on Fano varieties.

Multitier mechanics control stromal adaptations in swelling lymph nodes - Assen, Frank P; Abe, Jun; Hons, Miroslav; Hauschild, Robert; Shamipour, Shayan; Kaufmann, Walter; Costanzo, Tommaso; Krens, Gabriel; Brown, Markus; Ludewig, Burkhard; Hippenmeyer, Simon; Heisenberg, Carl-Philipp J; et al. (Nature Immunology)
Lymph nodes (LNs) comprise two main structural elements: fibroblastic reticular cells that form dedicated niches for immune cell interaction and capsular fibroblasts that build a shell around the organ. Immunological challenge causes LNs to increase more than tenfold in size within a few days. Here, we characterized the biomechanics of LN swelling on the cellular and organ scale. We identified lymphocyte trapping by influx and proliferation as drivers of an outward pressure force, causing fibroblastic reticular cells of the T-zone (TRCs) and their associated conduits to stretch. After an initial phase of relaxation, TRCs sensed the resulting strain through cell matrix adhesions, which coordinated local growth and remodeling of the stromal network. While the expanded TRC network readopted its typical configuration, a massive fibrotic reaction of the organ capsule set in and countered further organ expansion. Thus, different fibroblast populations mechanically control LN swelling in a multitier fashion.

The topological correctness of PL approximations of isomanifolds - Boissonnat, Jean-Daniel; Wintraecken, Mathijs (Foundations of Computational Mathematics)
Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f : Rd → Rd−n. A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation T of the ambient space Rd. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine triangulation T . This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary.

On the size of the maximum of incomplete Kloosterman sums - Bonolis, Dante (Mathematical Proceedings of the Cambridge Philosophical Society)
Let t : Fp → C be a complex valued function on Fp. A classical problem in analytic number theory is bounding the maximum M(t) := max 0≤H<p ∣ 1/√p ∑ 0≤n<H t (n) ∣ of the absolute value of the incomplete sums(1/√p)∑0≤n<H t (n). In this very general context one of the most important results is the Pólya–Vinogradov bound M(t)≤IIˆtII∞ log 3p, where ˆt : Fp → C is the normalized Fourier transform of t. In this paper we provide a lower bound for certain incomplete Kloosterman sums, namely we prove that for any ε > 0 there exists a large subset of a ∈ F×p such that for kl a,1,p : x → e((ax+x) / p) we have M(kla,1,p) ≥ (1−ε/√2π + o(1)) log log p, as p→∞. Finally, we prove a result on the growth of the moments of {M (kla,1,p)}a∈F×p. 2020 Mathematics Subject Classification: 11L03, 11T23 (Primary); 14F20, 60F10 (Secondary).

Resurgence analysis of quantum invariants of Seifert fibered homology spheres - Mistegaard, William; Andersen, Jørgen Ellegaard (Journal of the London Mathematical Society)
For a Seifert fibered homology sphere X we show that the q-series invariant Zˆ0(X; q) introduced by Gukov-Pei-Putrov-Vafa, is a resummation of the Ohtsuki series Z0(X). We show that for every even k ∈ N there exists a full asymptotic expansion of Zˆ0(X; q) for q tending to e 2πi/k, and in particular that the limit Zˆ0(X; e 2πi/k) exists and is equal to the WRT quantum invariant τk(X). We show that the poles of the Borel transform of Z0(X) coincide with the classical complex Chern-Simons values, which we further show classifies the corresponding components of the moduli space of flat SL(2, C)-connections.

Fourteen stations of auxin - Friml, Jiří (Cold Spring Harbor Perspectives in Biology)
Auxin has always been at the forefront of research in plant physiology and development. Since the earliest contemplations by Julius von Sachs and Charles Darwin, more than a century-long struggle has been waged to understand its function. This largely reflects the failures, successes, and inevitable progress in the entire field of plant signaling and development. Here I present 14 stations on our long and sometimes mystical journey to understand auxin. These highlights were selected to give a flavor of the field and to show the scope and limits of our current knowledge. A special focus is put on features that make auxin unique among phytohormones, such as its dynamic, directional transport network, which integrates external and internal signals, including self-organizing feedback. Accented are persistent mysteries and controversies. The unexpected discoveries related to rapid auxin responses and growth regulation recently disturbed our contentment regarding understanding of the auxin signaling mechanism. These new revelations, along with advances in technology, usher us into a new, exciting era in auxin research.

Integral points on singular del Pezzo surfaces - Derenthal, Ulrich; Wilsch, Florian Alexander (Journal of the Institute of Mathematics of Jussieu)
In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type A1 + A3 and prove an analogue of Manin's conjecture for integral points with respect to its singularities and its lines.
Keywords: Integral points; del Pezzo surface; universal torsor; Manin’s conjecture