@article{15013, abstract = {We consider random n×n matrices X with independent and centered entries and a general variance profile. We show that the spectral radius of X converges with very high probability to the square root of the spectral radius of the variance matrix of X when n tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge.}, author = {Alt, Johannes and Erdös, László and Krüger, Torben H}, issn = {2690-1005}, journal = {Probability and Mathematical Physics}, number = {2}, pages = {221--280}, publisher = {Mathematical Sciences Publishers}, title = {{Spectral radius of random matrices with independent entries}}, doi = {10.2140/pmp.2021.2.221}, volume = {2}, year = {2021}, } @article{6965, abstract = {The central object of investigation of this paper is the Hirzebruch class, a deformation of the Todd class, given by Hirzebruch (for smooth varieties). The generalization for singular varieties is due to Brasselet–Schürmann–Yokura. Following the work of Weber, we investigate its equivariant version for (possibly singular) toric varieties. The local decomposition of the Hirzebruch class to the fixed points of the torus action and a formula for the local class in terms of the defining fan are recalled. After this review part, we prove the positivity of local Hirzebruch classes for all toric varieties, thus proving false the alleged counterexample given by Weber.}, author = {Rychlewicz, Kamil P}, issn = {1469-2120}, journal = {Bulletin of the London Mathematical Society}, number = {2}, pages = {560--574}, publisher = {Wiley}, title = {{The positivity of local equivariant Hirzebruch class for toric varieties}}, doi = {10.1112/blms.12442}, volume = {53}, year = {2021}, } @misc{6995, abstract = {Human brain organoids represent a powerful tool for the study of human neurological diseases particularly those that impact brain growth and structure. However, many neurological diseases lack obvious anatomical abnormalities, yet significantly impact neural network functions, raising the question of whether organoids possess sufficient neural network architecture and complexity to model these conditions. Here, we explore the network level functions of brain organoids using calcium sensor imaging and extracellular recording approaches that together reveal the existence of complex oscillatory network behaviors reminiscent of intact brain preparations. We further demonstrate strikingly abnormal epileptiform network activity in organoids derived from a Rett Syndrome patient despite only modest anatomical differences from isogenically matched controls, and rescue with an unconventional neuromodulatory drug Pifithrin-α. Together, these findings provide an essential foundation for the utilization of human brain organoids to study intact and disordered human brain network formation and illustrate their utility in therapeutic discovery.}, author = {Samarasinghe, Ranmal A. and Miranda, Osvaldo and Buth, Jessie E. and Mitchell, Simon and Ferando, Isabella and Watanabe, Momoko and Kurdian, Arinnae and Golshani, Peyman and Plath, Kathrin and Lowry, William E. and Parent, Jack M. and Mody, Istvan and Novitch, Bennett G.}, issn = {1546-1726}, pages = {32}, publisher = {Springer Nature}, title = {{Identification of neural oscillations and epileptiform changes in human brain organoids}}, doi = {10.1038/s41593-021-00906-5}, volume = {24}, year = {2021}, } @article{7463, abstract = {Resting-state brain activity is characterized by the presence of neuronal avalanches showing absence of characteristic size. Such evidence has been interpreted in the context of criticality and associated with the normal functioning of the brain. A distinctive attribute of systems at criticality is the presence of long-range correlations. Thus, to verify the hypothesis that the brain operates close to a critical point and consequently assess deviations from criticality for diagnostic purposes, it is of primary importance to robustly and reliably characterize correlations in resting-state brain activity. Recent works focused on the analysis of narrow-band electroencephalography (EEG) and magnetoencephalography (MEG) signal amplitude envelope, showing evidence of long-range temporal correlations (LRTC) in neural oscillations. However, brain activity is a broadband phenomenon, and a significant piece of information useful to precisely discriminate between normal (critical) and pathological behavior (non-critical), may be encoded in the broadband spatio-temporal cortical dynamics. Here we propose to characterize the temporal correlations in the broadband brain activity through the lens of neuronal avalanches. To this end, we consider resting-state EEG and long-term MEG recordings, extract the corresponding neuronal avalanche sequences, and study their temporal correlations. We demonstrate that the broadband resting-state brain activity consistently exhibits long-range power-law correlations in both EEG and MEG recordings, with similar values of the scaling exponents. Importantly, although we observe that the avalanche size distribution depends on scale parameters, scaling exponents characterizing long-range correlations are quite robust. In particular, they are independent of the temporal binning (scale of analysis), indicating that our analysis captures intrinsic characteristics of the underlying dynamics. Because neuronal avalanches constitute a fundamental feature of neural systems with universal characteristics, the proposed approach may serve as a general, systems- and experiment-independent procedure to infer the existence of underlying long-range correlations in extended neural systems, and identify pathological behaviors in the complex spatio-temporal interplay of cortical rhythms.}, author = {Lombardi, Fabrizio and Shriki, Oren and Herrmann, Hans J and de Arcangelis, Lucilla}, issn = {1872-8286}, journal = {Neurocomputing}, pages = {657--666}, publisher = {Elsevier}, title = {{Long-range temporal correlations in the broadband resting state activity of the human brain revealed by neuronal avalanches}}, doi = {10.1016/j.neucom.2020.05.126}, volume = {461}, year = {2021}, } @article{7551, abstract = {Novelty facilitates formation of memories. The detection of novelty and storage of contextual memories are both mediated by the hippocampus, yet the mechanisms that link these two functions remain to be defined. Dentate granule cells (GCs) of the dorsal hippocampus fire upon novelty exposure forming engrams of contextual memory. However, their key excitatory inputs from the entorhinal cortex are not responsive to novelty and are insufficient to make dorsal GCs fire reliably. Here we uncover a powerful glutamatergic pathway to dorsal GCs from ventral hippocampal mossy cells (MCs) that relays novelty, and is necessary and sufficient for driving dorsal GCs activation. Furthermore, manipulation of ventral MCs activity bidirectionally regulates novelty-induced contextual memory acquisition. Our results show that ventral MCs activity controls memory formation through an intra-hippocampal interaction mechanism gated by novelty.}, author = {Fredes Tolorza, Felipe A and Silva Sifuentes, Maria A and Koppensteiner, Peter and Kobayashi, Kenta and Jösch, Maximilian A and Shigemoto, Ryuichi}, journal = {Current Biology}, number = {1}, pages = {P25--38.E5}, publisher = {Elsevier}, title = {{Ventro-dorsal hippocampal pathway gates novelty-induced contextual memory formation}}, doi = {10.1016/j.cub.2020.09.074}, volume = {31}, year = {2021}, } @article{7553, abstract = {Normative theories and statistical inference provide complementary approaches for the study of biological systems. A normative theory postulates that organisms have adapted to efficiently solve essential tasks, and proceeds to mathematically work out testable consequences of such optimality; parameters that maximize the hypothesized organismal function can be derived ab initio, without reference to experimental data. In contrast, statistical inference focuses on efficient utilization of data to learn model parameters, without reference to any a priori notion of biological function, utility, or fitness. Traditionally, these two approaches were developed independently and applied separately. Here we unify them in a coherent Bayesian framework that embeds a normative theory into a family of maximum-entropy “optimization priors.” This family defines a smooth interpolation between a data-rich inference regime (characteristic of “bottom-up” statistical models), and a data-limited ab inito prediction regime (characteristic of “top-down” normative theory). We demonstrate the applicability of our framework using data from the visual cortex, and argue that the flexibility it affords is essential to address a number of fundamental challenges relating to inference and prediction in complex, high-dimensional biological problems.}, author = {Mlynarski, Wiktor F and Hledik, Michal and Sokolowski, Thomas R and Tkačik, Gašper}, journal = {Neuron}, number = {7}, pages = {1227--1241.e5}, publisher = {Cell Press}, title = {{Statistical analysis and optimality of neural systems}}, doi = {10.1016/j.neuron.2021.01.020}, volume = {109}, year = {2021}, } @article{7685, abstract = {We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.}, author = {Boccato, Chiara}, issn = {0129-055X}, journal = {Reviews in Mathematical Physics}, number = {1}, publisher = {World Scientific}, title = {{The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime}}, doi = {10.1142/S0129055X20600065}, volume = {33}, year = {2021}, } @article{7883, abstract = {All vertebrates have a spinal cord with dimensions and shape specific to their species. Yet how species‐specific organ size and shape are achieved is a fundamental unresolved question in biology. The formation and sculpting of organs begins during embryonic development. As it develops, the spinal cord extends in anterior–posterior direction in synchrony with the overall growth of the body. The dorsoventral (DV) and apicobasal lengths of the spinal cord neuroepithelium also change, while at the same time a characteristic pattern of neural progenitor subtypes along the DV axis is established and elaborated. At the basis of these changes in tissue size and shape are biophysical determinants, such as the change in cell number, cell size and shape, and anisotropic tissue growth. These processes are controlled by global tissue‐scale regulators, such as morphogen signaling gradients as well as mechanical forces. Current challenges in the field are to uncover how these tissue‐scale regulatory mechanisms are translated to the cellular and molecular level, and how regulation of distinct cellular processes gives rise to an overall defined size. Addressing these questions will help not only to achieve a better understanding of how size is controlled, but also of how tissue size is coordinated with the specification of pattern.}, author = {Kuzmicz-Kowalska, Katarzyna and Kicheva, Anna}, issn = {17597692}, journal = {Wiley Interdisciplinary Reviews: Developmental Biology}, publisher = {Wiley}, title = {{Regulation of size and scale in vertebrate spinal cord development}}, doi = {10.1002/wdev.383}, year = {2021}, } @article{7900, abstract = {Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation.}, author = {Benedikter, Niels P}, issn = {1793-6659}, journal = {Reviews in Mathematical Physics}, number = {1}, publisher = {World Scientific}, title = {{Bosonic collective excitations in Fermi gases}}, doi = {10.1142/s0129055x20600090}, volume = {33}, year = {2021}, } @article{7901, abstract = {We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.}, author = {Benedikter, Niels P and Nam, Phan Thành and Porta, Marcello and Schlein, Benjamin and Seiringer, Robert}, issn = {1432-1297}, journal = {Inventiones Mathematicae}, pages = {885--979}, publisher = {Springer}, title = {{Correlation energy of a weakly interacting Fermi gas}}, doi = {10.1007/s00222-021-01041-5}, volume = {225}, year = {2021}, } @article{7905, abstract = {We investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a partially ordered set with the Alexandroff topology. We prove that the resulting decomposition is the unique minimal stratification for which the strata are homogeneous and the given sheaf is constructible. In particular, when we choose to work with the local homology sheaf, our algorithm gives an alternative to the local homology transfer algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the cohomology stratification algorithm given in Nanda (Found. Comput. Math. 20(2), 195–222, 2020). Additionally, we give examples of stratifications based on the geometric techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018), illustrating how the sheaf-theoretic approach can be used to study stratifications from both topological and geometric perspectives. This approach also points toward future applications of sheaf theory in the study of topological data analysis by illustrating the utility of the language of sheaf theory in generalizing existing algorithms.}, author = {Brown, Adam and Wang, Bei}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {1166--1198}, publisher = {Springer Nature}, title = {{Sheaf-theoretic stratification learning from geometric and topological perspectives}}, doi = {10.1007/s00454-020-00206-y}, volume = {65}, year = {2021}, } @article{7925, abstract = {In this paper, we introduce a relaxed CQ method with alternated inertial step for solving split feasibility problems. We give convergence of the sequence generated by our method under some suitable assumptions. Some numerical implementations from sparse signal and image deblurring are reported to show the efficiency of our method.}, author = {Shehu, Yekini and Gibali, Aviv}, issn = {1862-4480}, journal = {Optimization Letters}, pages = {2109--2126}, publisher = {Springer Nature}, title = {{New inertial relaxed method for solving split feasibilities}}, doi = {10.1007/s11590-020-01603-1}, volume = {15}, year = {2021}, } @article{7939, abstract = {We design fast deterministic algorithms for distance computation in the Congested Clique model. Our key contributions include: A (2+ϵ)-approximation for all-pairs shortest paths in O(log2n/ϵ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. A (1+ϵ)-approximation for multi-source shortest paths from O(n−−√) sources in O(log2n/ϵ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in O~(n1/6) rounds. }, author = {Censor-Hillel, Keren and Dory, Michal and Korhonen, Janne and Leitersdorf, Dean}, issn = {1432-0452}, journal = {Distributed Computing}, pages = {463--487}, publisher = {Springer Nature}, title = {{Fast approximate shortest paths in the congested clique}}, doi = {10.1007/s00446-020-00380-5}, volume = {34}, year = {2021}, } @inbook{7941, abstract = {Expansion microscopy is a recently developed super-resolution imaging technique, which provides an alternative to optics-based methods such as deterministic approaches (e.g. STED) or stochastic approaches (e.g. PALM/STORM). The idea behind expansion microscopy is to embed the biological sample in a swellable gel, and then to expand it isotropically, thereby increasing the distance between the fluorophores. This approach breaks the diffraction barrier by simply separating the emission point-spread-functions of the fluorophores. The resolution attainable in expansion microscopy is thus directly dependent on the separation that can be achieved, i.e. on the expansion factor. The original implementation of the technique achieved an expansion factor of fourfold, for a resolution of 70–80 nm. The subsequently developed X10 method achieves an expansion factor of 10-fold, for a resolution of 25–30 nm. This technique can be implemented with minimal technical requirements on any standard fluorescence microscope, and is more easily applied for multi-color imaging than either deterministic or stochastic super-resolution approaches. This renders X10 expansion microscopy a highly promising tool for new biological discoveries, as discussed here, and as demonstrated by several recent applications.}, author = {Truckenbrodt, Sven M and Rizzoli, Silvio O.}, booktitle = {Methods in Cell Biology}, isbn = {978012820807-6}, issn = {0091-679X}, pages = {33--56}, publisher = {Elsevier}, title = {{Simple multi-color super-resolution by X10 microscopy}}, doi = {10.1016/bs.mcb.2020.04.016}, volume = {161}, year = {2021}, } @article{8196, abstract = {This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of two set-valued maximal monotone operators without any further assumption of uniform monotonicity on any of the involved maximal monotone operators. Furthermore, our proposed method is easy to implement and the inertial factor in our proposed method is a natural choice. Our method of proof is of independent interest. Finally, some numerical implementations are given to confirm the theoretical analysis.}, author = {Shehu, Yekini and Dong, Qiao-Li and Liu, Lu-Lu and Yao, Jen-Chih}, issn = {1573-2924}, journal = {Optimization and Engineering}, pages = {2627--2653}, publisher = {Springer Nature}, title = {{New strong convergence method for the sum of two maximal monotone operators}}, doi = {10.1007/s11081-020-09544-5}, volume = {22}, year = {2021}, } @article{8198, abstract = {We investigate how the critical driving amplitude at the Floquet many-body localized (MBL) to ergodic phase transition differs between smooth and nonsmooth drives. To this end, we numerically study a disordered spin-1/2 chain which is periodically driven by a sine or square-wave drive over a wide range of driving frequencies. In both cases the critical driving amplitude increases monotonically with the frequency, and at large frequencies it is identical for the two drives. However, at low and intermediate frequencies the critical amplitude of the square-wave drive depends strongly on the frequency, while that of the sinusoidal drive is almost constant over a wide frequency range. By analyzing the density of drive-induced resonances we conclude that this difference is due to resonances induced by the higher harmonics which are present (absent) in the Fourier spectrum of the square-wave (sine) drive. Furthermore, we suggest a numerically efficient method for estimating the frequency dependence of the critical driving amplitudes for different drives which is based on calculating the density of drive-induced resonances. We conclude that delocalization occurs once the density of drive-induced resonances reaches a critical value determined only by the static system.}, author = {Diringer, Asaf A. and Gulden, Tobias}, issn = {24699969}, journal = {Physical Review B}, number = {21}, publisher = {American Physical Society}, title = {{Impact of drive harmonics on the stability of Floquet many-body localization}}, doi = {10.1103/PhysRevB.103.214204}, volume = {103}, year = {2021}, } @article{8248, abstract = {We consider the following setting: suppose that we are given a manifold M in Rd with positive reach. Moreover assume that we have an embedded simplical complex A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then A is a triangulation of the manifold, that is, they are homeomorphic.}, author = {Boissonnat, Jean-Daniel and Dyer, Ramsay and Ghosh, Arijit and Lieutier, Andre and Wintraecken, Mathijs}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {666--686}, publisher = {Springer Nature}, title = {{Local conditions for triangulating submanifolds of Euclidean space}}, doi = {10.1007/s00454-020-00233-9}, volume = {66}, year = {2021}, } @article{8253, abstract = {Brains process information in spiking neural networks. Their intricate connections shape the diverse functions these networks perform. In comparison, the functional capabilities of models of spiking networks are still rudimentary. This shortcoming is mainly due to the lack of insight and practical algorithms to construct the necessary connectivity. Any such algorithm typically attempts to build networks by iteratively reducing the error compared to a desired output. But assigning credit to hidden units in multi-layered spiking networks has remained challenging due to the non-differentiable nonlinearity of spikes. To avoid this issue, one can employ surrogate gradients to discover the required connectivity in spiking network models. However, the choice of a surrogate is not unique, raising the question of how its implementation influences the effectiveness of the method. Here, we use numerical simulations to systematically study how essential design parameters of surrogate gradients impact learning performance on a range of classification problems. We show that surrogate gradient learning is robust to different shapes of underlying surrogate derivatives, but the choice of the derivative’s scale can substantially affect learning performance. When we combine surrogate gradients with a suitable activity regularization technique, robust information processing can be achieved in spiking networks even at the sparse activity limit. Our study provides a systematic account of the remarkable robustness of surrogate gradient learning and serves as a practical guide to model functional spiking neural networks.}, author = {Zenke, Friedemann and Vogels, Tim P}, issn = {1530-888X}, journal = {Neural Computation}, number = {4}, pages = {899--925}, publisher = {MIT Press}, title = {{The remarkable robustness of surrogate gradient learning for instilling complex function in spiking neural networks}}, doi = {10.1162/neco_a_01367}, volume = {33}, year = {2021}, } @article{8286, abstract = {We consider the following dynamic load-balancing process: given an underlying graph G with n nodes, in each step t≥ 0, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks a random neighbor, and the two nodes balance their loads by averaging them. We are interested in the expected gap between the minimum and maximum loads at nodes as the process progresses, and its dependence on n and on the graph structure. Variants of the above graphical balanced allocation process have been studied previously by Peres, Talwar, and Wieder [Peres et al., 2015], and by Sauerwald and Sun [Sauerwald and Sun, 2015]. These authors left as open the question of characterizing the gap in the case of cycle graphs in the dynamic case, where weights are created during the algorithm’s execution. For this case, the only known upper bound is of 𝒪(n log n), following from a majorization argument due to [Peres et al., 2015], which analyzes a related graphical allocation process. In this paper, we provide an upper bound of 𝒪 (√n log n) on the expected gap of the above process for cycles of length n. We introduce a new potential analysis technique, which enables us to bound the difference in load between k-hop neighbors on the cycle, for any k ≤ n/2. We complement this with a "gap covering" argument, which bounds the maximum value of the gap by bounding its value across all possible subsets of a certain structure, and recursively bounding the gaps within each subset. We provide analytical and experimental evidence that our upper bound on the gap is tight up to a logarithmic factor. }, author = {Alistarh, Dan-Adrian and Nadiradze, Giorgi and Sabour, Amirmojtaba}, issn = {1432-0541}, journal = {Algorithmica}, location = {Virtual, Online; Germany}, publisher = {Springer Nature}, title = {{Dynamic averaging load balancing on cycles}}, doi = {10.1007/s00453-021-00905-9}, year = {2021}, } @article{8317, abstract = {When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.}, author = {Aichholzer, Oswin and Akitaya, Hugo A. and Cheung, Kenneth C. and Demaine, Erik D. and Demaine, Martin L. and Fekete, Sándor P. and Kleist, Linda and Kostitsyna, Irina and Löffler, Maarten and Masárová, Zuzana and Mundilova, Klara and Schmidt, Christiane}, issn = {09257721}, journal = {Computational Geometry: Theory and Applications}, publisher = {Elsevier}, title = {{Folding polyominoes with holes into a cube}}, doi = {10.1016/j.comgeo.2020.101700}, volume = {93}, year = {2021}, }