Separation of variables for scalar-valued polynomials in the non-stable range - Beďatš, Daniel (Journal of Algebra)
Any complex-valued polynomial on (Rn)k decomposes into an algebraic combination of O(n)-invariant polynomials and harmonic polynomials. This decomposition, separation of variables, is granted to be unique if n≥2k−1. We prove that the condition n≥2k−1 is not only sufficient, but also necessary for uniqueness of the separation. Moreover, we describe the structure of non-uniqueness of the separation in the boundary cases when n=2k−2 and n=2k−3. Formally, we study the kernel of a multiplication map ϕ carrying out separation of variables. We devise a general algorithmic procedure for describing Ker ϕ in the restricted non-stable range k≤n<2k−1. In the full non-stable range n<2k−1, we give formulas for highest weights of generators of the kernel as well as formulas for its Hilbert series. Using the developed methods, we obtain a list of highest weight vectors generating Ker ϕ.

Enhanced many-body quantum scars from the non-hermitian fock skin effect - Shen, Ruizhe; Qin, Fang; Desaules, Jean-Yves Marc; Papić, Zlatko; Lee, Ching Hua (Physical Review Letters)
In contrast with extended Bloch waves, a single particle can become spatially localized due to the so-called skin effect originating from non-Hermitian pumping. Here we show that in kinetically constrained many-body systems, the skin effect can instead manifest as dynamical amplification within the Fock space, beyond the intuitively expected and previously studied particle localization and clustering. We exemplify this non-Hermitian Fock skin effect in an asymmetric version of the PXP model and show that it gives rise to ergodicity-breaking eigenstates—the non-Hermitian analogs of quantum many-body scars. A distinguishing feature of these non-Hermitian scars is their enhanced robustness against external disorders. We propose an experimental realization of the non-Hermitian scar enhancement in a tilted Bose-Hubbard optical lattice with laser-induced loss. Additionally, we implement digital simulations of such scar enhancement on the IBM quantum processor. Our results show that the Fock skin effect provides a powerful tool for creating robust nonergodic states in generic open quantum systems.

The importance of solving Subglaciar hydrology in modeling glacier retreat: A case study of Hansbreen, Svalbard - De Andrés, Eva; Muñoz Hermosilla, José M; Shahateet, Kaian; Otero, Jaime (Hydrology)
Arctic tidewater glaciers are retreating, serving as key indicators of global warming. This study aims to assess how subglacial hydrology affects glacier front retreat by comparing two glacier–fjord models of the Hansbreen glacier: one incorporating a detailed subglacial hydrology model and another simplifying the subglacial discharge to a single channel centered in the flow line. We first validate the subglacial hydrology model by comparing its discharge channels with observations of plume activity. Simulations conducted from April to December 2010 revealed that the glacier front position aligns more closely with the observations in the coupled model than in the simplified version. Furthermore, the mass loss due to calving and submarine melting is greater in the coupled model, with the calving mass loss reaching 6 Mt by the end of the simulation compared to 4 Mt in the simplified model. These findings highlight the critical role of subglacial hydrology in predicting glacier dynamics and emphasize the importance of detailed modeling in understanding the responses of Arctic tidewater glaciers to climate change.

Anisotropic potential immersed in a dipolar Bose-Einstein condensate - Shukla, Neelam; Volosniev, Artem; Armstrong, Jeremy R. (Physical Review A)
We study a three-dimensional Gross-Pitaevskii equation that describes a static impurity in a dipolar Bose-Einstein condensate. Our focus is on the interplay between the shape of the impurity and the anisotropy of the medium manifested in the energy and the density of the system. Without external confinement, properties of the system are derived with basic analytical approaches. For a system in a harmonic trap, the model is investigated numerically, using the split-step Crank-Nicolson method. Our results demonstrate that the impurity self-energy is minimized when its shape more closely aligns with the anisotropic character of the bath; in particular a prolate deformed impurity aligned with the direction of the dipoles has the smallest self-energy for a repulsive impurity. Our work complements studies of impurities in Bose gases with zero-range interactions and paves the way for studies of dipolar polarons with a Gross-Pitaevskii equation.

Stochastic processes with expected stopping time - Chatterjee, Krishnendu; Doyen, Laurent (Logical Methods in Computer Science)
Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.

Nucleosome-bound NR5A2 structure reveals pioneer factor mechanism by DNA minor groove anchor competition - Kobayashi, Wataru; Sappler, Anna H.; Bollschweiler, Daniel; Kümmecke, Maximilian; Basquin, Jérôme; Arslantas, Eda Nur; Ruangroengkulrith, Siwat; Hornberger, Renate; Duderstadt, Karl; Tachibana, Kikuë (Nature Structural & Molecular Biology)
Gene expression during natural and induced reprogramming is controlled by pioneer transcription factors that initiate transcription from closed chromatin. Nr5a2 is a key pioneer factor that regulates zygotic genome activation in totipotent embryos, pluripotency in embryonic stem cells and metabolism in adult tissues, but the mechanism of its pioneer activity remains poorly understood. Here, we present a cryo-electron microscopy structure of human NR5A2 bound to a nucleosome. The structure shows that the conserved carboxy-terminal extension (CTE) loop of the NR5A2 DNA-binding domain competes with a DNA minor groove anchor of the nucleosome and releases entry-exit site DNA. Mutational analysis showed that NR5A2 D159 of the CTE is dispensable for DNA binding but required for stable nucleosome association and persistent DNA ‘unwrapping’. These findings suggest that NR5A2 belongs to an emerging class of pioneer factors that can use DNA minor groove anchor competition to destabilize nucleosomes and facilitate gene expression during reprogramming.

Development: Turing mechanics - Hino, Naoya; Santos Fernandes Lasbarrères Camelo, Carolina; Heisenberg, Carl-Philipp J (Current Biology)
Embryo axis formation begins with the localized expression of biochemical signals, which organize cell movements and determine cell fate. A quail study finds that tissue contraction and resulting long-range changes in tissue tension restrict the area where these biochemical signals are expressed.

Codes for adversaries: Between worst-case and average-case jamming - Dey, Bikash Kumar; Jaggi, Sidharth; Langberg, Michael; Sarwate, Anand D.; Zhang, Yihan (Foundations and Trends in Communications and Information Theory)
Over the last 70 years, information theory and coding has enabled communication technologies that have had an astounding impact on our lives. This is possible due to the match between encoding/decoding strategies and corresponding channel models. Traditional studies of channels have taken one of two extremes: Shannon-theoretic models are inherently average-case in which channel noise is governed by a memoryless stochastic process, whereas coding-theoretic (referred to as “Hamming”) models take a worst-case, adversarial, view of the noise. However, for several existing and emerging communication systems the Shannon/average-case view may be too optimistic, whereas the Hamming/worstcase view may be too pessimistic. This monograph takes up the challenge of studying adversarial channel models that lie between the Shannon and Hamming extremes.

Automated long-range compensation of an rf quantum dot sensor - Hickie, Joseph; Van Straaten, Barnaby; Fedele, Federico; Jirovec, Daniel; Ballabio, Andrea; Chrastina, Daniel; Isella, Giovanni; Katsaros, Georgios; Ares, Natalia (Physical Review Applied)
Charge sensing is a sensitive technique for probing quantum devices, of particular importance for spin-qubit readout. To achieve good readout sensitivities, the proximity of the charge sensor to the device to be measured is a necessity. However, this proximity also means that the operation of the device affects, in turn, the sensor tuning and ultimately the readout sensitivity. We present an approach for compensating for this crosstalk effect allowing for the gate voltages of the measured device to be swept in a 1-V × 1-V window while maintaining a sensor configuration chosen by a Bayesian optimizer. Our algorithm will hopefully be a major contribution to the suite of fully automated solutions required for the operation of large quantum device architectures.

Scale-invariant magnetic anisotropy in α-RuCl3: A quantum Monte Carlo study - Sato, Toshihiro; Ramshaw, B. J.; Modic, Kimberly A; Assaad, Fakher F. (Physical Review B)
We compute the rotational anisotropy of the free energy of 𝛼−RuCl3 in an external magnetic field. This quantity, known as the magnetotropic susceptibility, 𝑘, relates to the second derivative of the free energy with respect to the angle of rotation. We have used approximation-free, auxiliary-field quantum Monte Carlo simulations for a realistic model of 𝛼−RuCl3 and optimized the path integral to alleviate the negative sign problem. This allows us to reach temperatures down to 30K—an energy scale below the dominant Kitaev coupling. We demonstrate that the magnetotropic spin susceptibility in this model of 𝛼−RuCl3 displays scaling behavior 𝑘=𝑇⁢𝑓⁡(𝐵/𝑇) at high temperatures. Once the uniform susceptibility departs from the Curie law (i.e., at the energy scale of the exchange interactions), it appears to transition to an emergent scalinglike behavior, characterized by a different function 𝑓 at lower temperatures, stemming from the locality of torque fluctuations. We observe a remarkable numerical match between experiment and simulations and we also find qualitative agreement with the pure Kitaev model. In comparison, for the XXZ Heisenberg Hamiltonian, the scaling 𝑘=𝑇⁢𝑓⁡(𝐵/𝑇) breaks down at a temperature scale where the uniform spin susceptibility deviates from the Curie law and never reemerges at low temperatures.

Climbing up a random subgraph of the hypercube - Anastos, Michael; Diskin, Sahar; Elboim, Dor; Krivelevich, Michael (Electronic Communications in Probability)
Let Qd be the d-dimensional binary hypercube. We say that P={v1,…,vk} is an increasing path of length k−1 in Qd, if for every i∈[k−1] the edge vivi+1 is obtained by switching some zero coordinate in vi to a one coordinate in vi+1. Form a random subgraph Qdp by retaining each edge in E(Qd) independently with probability p. We show that there is a phase transition with respect to the length of a longest increasing path around p=ed. Let α be a constant and let p=αd. When α<e, then there exists a δ∈[0,1) such that whp a longest increasing path in Qdp is of length at most δd. On the other hand, when α>e, whp there is a path of length d−2 in Qdp, and in fact, whether it is of length d−2,d−1, or d depends on whether the all-zero and all-one vertices percolate or not.

Out-of-time-ordered correlators for Wigner matrices - Cipolloni, Giorgio; Erdös, László; Henheik, Sven Joscha (Advances in Theoretical and Mathematical Physics)
We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables and in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three time regimes separated by the physically relevant scrambling and relaxation times. The main feature of our analysis is that we express the error terms in the optimal Schatten (tracial) norms of the observables, allowing us to track the exact dependence of the errors on their rank. In particular, for significantly overlapping observables with low rank the OTOC is shown to exhibit a significant local maximum at the scrambling time, a feature that may not have been noticed in the physics literature before. Our main tool is a novel multi-resolvent local law with Schatten norms that unifies and improves previous local laws involving either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf. [11]).

New methods for applying topological data analysis to materials science - Heiss, Teresa
Many chemical and physical properties of materials are determined by the material’s shape, for example the size of its pores and the width of its tunnels. This makes materials science a prime application area for geometrical and topological methods. Nevertheless many methods in topological data analysis have not been satisfyingly extended to the needs of materials science. This thesis provides new methods and new mathematical theorems targeted at those specific needs by answering four different research questions. While the motivation for each of the research questions arises from materials science, the methods are versatile and can be applied in different areas as well. The first research question is concerned with image data, for example a three-dimensional computed tomography (CT) scan of a material, like sand or stone. There are two commonly used topologies for digital images and depending on the application either of them might be required. However, software for computing the topological data analysis method persistence homology, usually supports only one of the two topologies. We answer the question how to compute persistent homology of an image with respect to one of the two topologies using software that is intended for the other topology. The second research question is concerned with image data as well, and asks how much of the topological information of an image is lost when the resolution is coarsened. As computer tomography scanners are more expensive the higher the resolution, it is an important question in materials science to know which resolution is enough to get satisfying persistent homology. We give theoretical bounds on the information loss based on different geometrical properties of the object to be scanned. In addition, we conduct experiments on sand and stone CT image data. The third research question is motivated by comparing crystalline materials efficiently. As the atoms within a crystal repeat periodically, crystalline materials are either modeled by unmanageable infinite periodic point sets, or by one of their fundamental domains, which is unstable under perturbation. Therefore a fingerprint of crystalline materials is needed, with appropriate properties such that comparing the crystals can be eased by comparing the fingerprints instead. We define the density fingerprint and prove the necessary properties. The fourth research question is motivated by studying the hole-structure or connectedness, i.e. persistent homology or merge trees, of crystalline materials. A common way to deal with periodicity is to take a fundamental domain and identify opposite boundaries to form a torus. However, computing persistent homology or merge trees on that torus loses some of the information materials scientists are interested in and is additionally not stable under certain noise. We therefore decorate the merge tree stemming from the torus with additional information describing the density and growth rate of the periodic copies of a component within a growing spherical window. We prove all desired properties, like stability and efficient computability.
Keywords: persistent homology; topological data analysis; periodic; crystalline materials; images; fingerprint

Merge trees of periodic filtrations - Edelsbrunner, Herbert; Heiss, Teresa (arXiv)
Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are invariant under isometries, changing bases, and indeed changing lattices. In addition, we prove stability under perturbations and provide an algorithm that under mild geometric conditions typically satisfied by crystalline materials takes O((n+m)logn) time, in which n and m are the numbers of vertices and edges in the quotient complex, respectively.

Image analysis for brain tissue reconstruction with super-resolution light microscopy - Lyudchik, Julia
Mapping the complex and dense arrangement of cells and their connectivity in brain tissue requires volumetric imaging at nanoscale spatial resolution. While light microscopy excels at visualizing specific molecules and individual cells, achieving dense, synapse-level circuit reconstruction has not been possible with any light microscopy technique. Thus, the goal of my work was to develop image and data analysis pipelines for brain tissue visualization and reconstruction with light microscopy. To achieve dense circuit reconstruction with single-synapse resolution, I developed both conventional and deep-learning-based synapse detection algorithms, as well as connectivity analysis pipelines that integrate synapse detection with volumetric segmentation of brain tissue.

Light-microscopy based dense connectomic reconstruction of mammalian brain tissue - Tavakoli, Mojtaba; Lyudchik, Julia; Januszewski, Michał; Vistunou, Vitali; Agudelo Duenas, Nathalie; Vorlaufer, Jakob; Sommer, Christoph M; Kreuzinger, Caroline; Oliveira, Bárbara; Cenameri, Alban; Novarino, Gaia; Jain, Viren; et al. (bioRxiv)
The information-processing capability of the brain’s cellular network depends on the physical wiring pattern between neurons and their molecular and functional characteristics. Mapping neurons and resolving their individual synaptic connections can be achieved by volumetric imaging at nanoscale resolution with dense cellular labeling. Light microscopy is uniquely positioned to visualize specific molecules but dense, synapse-level circuit reconstruction by light microscopy has been out of reach due to limitations in resolution, contrast, and volumetric imaging capability. Here we developed light-microscopy based connectomics (LICONN). We integrated specifically engineered hydrogel embedding and expansion with comprehensive deep-learning based segmentation and analysis of connectivity, thus directly incorporating molecular information in synapse-level brain tissue reconstructions. LICONN will allow synapse-level brain tissue phenotyping in biological experiments in a readily adoptable manner.

Developing molecular and structural tools for studying brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics reconstruction with light microscopy - Tavakoli, Mojtaba

Human hippocampal CA3 uses specific functional connectivity rules for efficient associative memory - Watson, Jake F.; Vargas-Barroso, Victor; Morse-Mora, Rebecca J.; Navas-Olive, Andrea; Tavakoli, Mojtaba; Danzl, Johann G; Tomschik, Matthias; Rössler, Karl; Jonas, Peter M (bioRxiv)
The human brain has remarkable computational power. It generates sophisticated behavioral sequences, stores engrams over an individual’s lifetime, and produces higher cognitive functions up to the level of consciousness. However, so little of our neuroscience knowledge covers the human brain, and it remains unknown whether this organ is truly unique, or is a scaled version of the extensively studied rodent brain. To address this fundamental question, we determined the cellular, synaptic, and connectivity rules of the hippocampal CA3 recurrent circuit using multicellular patch clamp-recording. This circuit is the largest autoassociative network in the brain, and plays a key role in memory and higher-order computations such as pattern separation and pattern completion. We demonstrate that human hippocampal CA3 employs sparse connectivity, in stark contrast to neocortical recurrent networks. Connectivity sparsifies from rodents to humans, providing a circuit architecture that maximizes associational power. Unitary synaptic events at human CA3–CA3 synapses showed both distinct species-specific and circuit-dependent properties, with high reliability, unique amplitude precision, and long integration times. We also identify differential scaling rules between hippocampal pathways from rodents to humans, with a moderate increase in the convergence of CA3 inputs per cell, but a marked increase in human mossy fiber innervation. Anatomically guided full-scale modeling suggests that the human brain’s sparse connectivity, expanded neuronal number, and reliable synaptic signaling combine to enhance the associative memory storage capacity of CA3. Together, our results reveal unique rules of connectivity and synaptic signaling in the human hippocampus, demonstrating the absolute necessity of human brain research and beginning to unravel the remarkable performance of our autoassociative memory circuits.

Super-resolution expansion microscopy in plant roots - Gallei, Michelle C; Truckenbrodt, Sven M; Kreuzinger, Caroline; Inumella, Syamala; Vistunou, Vitali; Sommer, Christoph M; Tavakoli, Mojtaba; Agudelo Duenas, Nathalie; Vorlaufer, Jakob; Jahr, Wiebke; Randuch, Marek; Johnson, Alexander J; et al. (bioRxiv)
Multiplexed fluorescence microscopy imaging is widely used in biomedical applications. However, simultaneous imaging of multiple fluorophores can result in spectral leaks and overlapping, which greatly degrades image quality and subsequent analysis. Existing popular spectral unmixing methods are mainly based on computational intensive linear models and the performance is heavily dependent on the reference spectra, which may greatly preclude its further applications. In this paper, we propose a deep learning-based blindly spectral unmixing method, termed AutoUnmix, to imitate the physical spectral mixing process. A tranfer learning framework is further devised to allow our AutoUnmix adapting to a variety of imaging systems without retraining the network. Our proposed method has demonstrated real-time unmixing capabilities, surpassing existing methods by up to 100-fold in terms of unmixing speed. We further validate the reconstruction performance on both synthetic datasets and biological samples. The unmixing results of AutoUnmix achieve a highest SSIM of 0.99 in both three- and four-color imaging, with nearly up to 20% higher than other popular unmixing methods. Due to the desirable property of data independency and superior blind unmixing performance, we believe AutoUnmix is a powerful tool to study the interaction process of different organelles labeled by multiple fluorophores.

The cost of maintaining keys in dynamic groups with applications to multicast encryption and group messaging - Anastos, Michael; Auerbach, Benedikt; Baig, Mirza Ahad; Cueto Noval, Miguel; Kwan, Matthew Alan; Pascual Perez, Guillermo; Pietrzak, Krzysztof Z (22nd International Conference on Theory of Cryptography)
In this work we prove lower bounds on the (communication) cost of maintaining a shared key among a dynamic group of users. Being “dynamic” means one can add and remove users from the group. This captures important protocols like multicast encryption (ME) and continuous group-key agreement (CGKA), which is the primitive underlying many group messaging applications. We prove our bounds in a combinatorial setting where the state of the protocol progresses in rounds. The state of the protocol in each round is captured by a set system, with each of its elements specifying a set of users who share a secret key. We show this combinatorial model implies bounds in symbolic models for ME and CGKA that capture, as building blocks, PRGs, PRFs, dual PRFs, secret sharing, and symmetric encryption in the setting of ME, and PRGs, PRFs, dual PRFs, secret sharing, public-key encryption, and key-updatable public-key encryption in the setting of CGKA. The models are related to the ones used by Micciancio and Panjwani (Eurocrypt’04) and Bienstock et al. (TCC’20) to analyze ME and CGKA, respectively. We prove – using the Bollobás’ Set Pairs Inequality – that the cost (number of uploaded ciphertexts) for replacing a set of d users in a group of size n is Ω(dln(n/d)). Our lower bound is asymptotically tight and both improves on a bound of Ω(d) by Bienstock et al. (TCC’20), and generalizes a result by Micciancio and Panjwani (Eurocrypt’04), who proved a lower bound of Ω(log(n)) for d=1.