@article{12705, abstract = {The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly cross-linked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the cross-links and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density and connect the cross-link localization length to the shear modulus of the system.}, author = {Sorichetti, Valerio and Ninarello, Andrea and Ruiz-Franco, José and Hugouvieux, Virginie and Zaccarelli, Emanuela and Micheletti, Cristian and Kob, Walter and Rovigatti, Lorenzo}, issn = {1089-7690}, journal = {Journal of Chemical Physics}, number = {7}, publisher = {American Institute of Physics}, title = {{Structure and elasticity of model disordered, polydisperse, and defect-free polymer networks}}, doi = {10.1063/5.0134271}, volume = {158}, year = {2023}, } @article{12738, abstract = {We study turn-based stochastic zero-sum games with lexicographic preferences over objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit both randomness as well as controllable and adversarial non-determinism. Lexicographic order allows one to consider multiple objectives with a strict preference order. To the best of our knowledge, stochastic games with lexicographic objectives have not been studied before. For a mixture of reachability and safety objectives, we show that deterministic lexicographically optimal strategies exist and memory is only required to remember the already satisfied and violated objectives. For a constant number of objectives, we show that the relevant decision problem is in NP∩coNP, matching the current known bound for single objectives; and in general the decision problem is PSPACE-hard and can be solved in NEXPTIME∩coNEXPTIME. We present an algorithm that computes the lexicographically optimal strategies via a reduction to the computation of optimal strategies in a sequence of single-objectives games. For omega-regular objectives, we restrict our analysis to one-player games, also known as Markov decision processes. We show that lexicographically optimal strategies exist and need either randomization or finite memory. We present an algorithm that solves the relevant decision problem in polynomial time. We have implemented our algorithms and report experimental results on various case studies.}, author = {Chatterjee, Krishnendu and Katoen, Joost P and Mohr, Stefanie and Weininger, Maximilian and Winkler, Tobias}, issn = {1572-8102}, journal = {Formal Methods in System Design}, publisher = {Springer Nature}, title = {{Stochastic games with lexicographic objectives}}, doi = {10.1007/s10703-023-00411-4}, year = {2023}, } @misc{14279, abstract = {The zip file includes source data used in the manuscript "CCR7 acts as both a sensor and a sink for CCL19 to coordinate collective leukocyte migration", as well as a representative Jupyter notebook to reproduce the main figures. Please see the preprint on bioRxiv and the DOI link there to access the final published version. Note the title change between the preprint and the published manuscript. A sample script for particle-based simulations of collective chemotaxis by self-generated gradients is also included (see Self-generated_chemotaxis_sample_script.ipynb) to generate exemplary cell trajectories. A detailed description of the simulation setup is provided in the supplementary information of the manuscipt.}, author = {Ucar, Mehmet C}, publisher = {Zenodo}, title = {{Source data for the manuscript "CCR7 acts as both a sensor and a sink for CCL19 to coordinate collective leukocyte migration"}}, doi = {10.5281/ZENODO.8133960}, year = {2023}, } @article{10405, abstract = {We consider large non-Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives. Previously this result was known only for a few special cases; either the test functions were required to be analytic [72], or the distribution of the matrix elements needed to be Gaussian [73], or at least match the Gaussian up to the first four moments [82, 56]. We find the exact dependence of the limiting variance on the fourth cumulant that was not known before. The proof relies on two novel ingredients: (i) a local law for a product of two resolvents of the Hermitisation of X with different spectral parameters and (ii) a coupling of several weakly dependent Dyson Brownian motions. These methods are also the key inputs for our analogous results on the linear eigenvalue statistics of real matrices X that are presented in the companion paper [32]. }, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {1097-0312}, journal = {Communications on Pure and Applied Mathematics}, number = {5}, pages = {946--1034}, publisher = {Wiley}, title = {{Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices}}, doi = {10.1002/cpa.22028}, volume = {76}, year = {2023}, } @article{10770, abstract = {Mathematical models often aim to describe a complicated mechanism in a cohesive and simple manner. However, reaching perfect balance between being simple enough or overly simplistic is a challenging task. Frequently, game-theoretic models have an underlying assumption that players, whenever they choose to execute a specific action, do so perfectly. In fact, it is rare that action execution perfectly coincides with intentions of individuals, giving rise to behavioural mistakes. The concept of incompetence of players was suggested to address this issue in game-theoretic settings. Under the assumption of incompetence, players have non-zero probabilities of executing a different strategy from the one they chose, leading to stochastic outcomes of the interactions. In this article, we survey results related to the concept of incompetence in classic as well as evolutionary game theory and provide several new results. We also suggest future extensions of the model and argue why it is important to take into account behavioural mistakes when analysing interactions among players in both economic and biological settings.}, author = {Graham, Thomas and Kleshnina, Maria and Filar, Jerzy A.}, issn = {2153-0793}, journal = {Dynamic Games and Applications}, pages = {231--264}, publisher = {Springer Nature}, title = {{Where do mistakes lead? A survey of games with incompetent players}}, doi = {10.1007/s13235-022-00425-3}, volume = {13}, year = {2023}, } @article{10145, abstract = {We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique.}, author = {Dello Schiavo, Lorenzo}, issn = {1572-929X}, journal = {Potential Analysis}, pages = {573--615}, publisher = {Springer Nature}, title = {{Ergodic decomposition of Dirichlet forms via direct integrals and applications}}, doi = {10.1007/s11118-021-09951-y}, volume = {58}, year = {2023}, } @article{11706, abstract = {We say that (Formula presented.) if, in every edge coloring (Formula presented.), we can find either a 1-colored copy of (Formula presented.) or a 2-colored copy of (Formula presented.). The well-known states that the threshold for the property (Formula presented.) is equal to (Formula presented.), where (Formula presented.) is given by (Formula presented.) for any pair of graphs (Formula presented.) and (Formula presented.) with (Formula presented.). In this article, we show the 0-statement of the Kohayakawa–Kreuter conjecture for every pair of cycles and cliques. }, author = {Liebenau, Anita and Mattos, Letícia and Mendonca Dos Santos, Walner and Skokan, Jozef}, issn = {1098-2418}, journal = {Random Structures and Algorithms}, number = {4}, pages = {1035--1055}, publisher = {Wiley}, title = {{Asymmetric Ramsey properties of random graphs involving cliques and cycles}}, doi = {10.1002/rsa.21106}, volume = {62}, year = {2023}, } @article{12707, abstract = {We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail.}, author = {Erdös, László and Xu, Yuanyuan}, issn = {1350-7265}, journal = {Bernoulli}, number = {2}, pages = {1063--1079}, publisher = {Bernoulli Society for Mathematical Statistics and Probability}, title = {{Small deviation estimates for the largest eigenvalue of Wigner matrices}}, doi = {10.3150/22-BEJ1490}, volume = {29}, year = {2023}, } @article{12837, abstract = {As developing tissues grow in size and undergo morphogenetic changes, their material properties may be altered. Such changes result from tension dynamics at cell contacts or cellular jamming. Yet, in many cases, the cellular mechanisms controlling the physical state of growing tissues are unclear. We found that at early developmental stages, the epithelium in the developing mouse spinal cord maintains both high junctional tension and high fluidity. This is achieved via a mechanism in which interkinetic nuclear movements generate cell area dynamics that drive extensive cell rearrangements. Over time, the cell proliferation rate declines, effectively solidifying the tissue. Thus, unlike well-studied jamming transitions, the solidification uncovered here resembles a glass transition that depends on the dynamical stresses generated by proliferation and differentiation. Our finding that the fluidity of developing epithelia is linked to interkinetic nuclear movements and the dynamics of growth is likely to be relevant to multiple developing tissues.}, author = {Bocanegra, Laura and Singh, Amrita and Hannezo, Edouard B and Zagórski, Marcin P and Kicheva, Anna}, issn = {1745-2481}, journal = {Nature Physics}, pages = {1050--1058}, publisher = {Springer Nature}, title = {{Cell cycle dynamics control fluidity of the developing mouse neuroepithelium}}, doi = {10.1038/s41567-023-01977-w}, volume = {19}, year = {2023}, } @article{12836, abstract = {Coherent control and manipulation of quantum degrees of freedom such as spins forms the basis of emerging quantum technologies. In this context, the robust valley degree of freedom and the associated valley pseudospin found in two-dimensional transition metal dichalcogenides is a highly attractive platform. Valley polarization and coherent superposition of valley states have been observed in these systems even up to room temperature. Control of valley coherence is an important building block for the implementation of valley qubit. Large magnetic fields or high-power lasers have been used in the past to demonstrate the control (initialization and rotation) of the valley coherent states. Here, the control of layer–valley coherence via strong coupling of valley excitons in bilayer WS2 to microcavity photons is demonstrated by exploiting the pseudomagnetic field arising in optical cavities owing to the transverse electric–transverse magnetic (TE–TM)mode splitting. The use of photonic structures to generate pseudomagnetic fields which can be used to manipulate exciton-polaritons presents an attractive approach to control optical responses without the need for large magnets or high-intensity optical pump powers.}, author = {Khatoniar, Mandeep and Yama, Nicholas and Ghazaryan, Areg and Guddala, Sriram and Ghaemi, Pouyan and Majumdar, Kausik and Menon, Vinod}, issn = {2195-1071}, journal = {Advanced Optical Materials}, number = {13}, publisher = {Wiley}, title = {{Optical manipulation of Layer–Valley coherence via strong exciton–photon coupling in microcavities}}, doi = {10.1002/adom.202202631}, volume = {11}, year = {2023}, } @article{12959, abstract = {This paper deals with the large-scale behaviour of dynamical optimal transport on Zd -periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes the effective behaviour of the discrete problems in terms of a continuous optimal transport problem. The effective energy density can be explicitly expressed in terms of a cell formula, which is a finite-dimensional convex programming problem that depends non-trivially on the local geometry of the discrete graph and the discrete energy density. Our homogenisation result is derived from a Γ -convergence result for action functionals on curves of measures, which we prove under very mild growth conditions on the energy density. We investigate the cell formula in several cases of interest, including finite-volume discretisations of the Wasserstein distance, where non-trivial limiting behaviour occurs.}, author = {Gladbach, Peter and Kopfer, Eva and Maas, Jan and Portinale, Lorenzo}, issn = {1432-0835}, journal = {Calculus of Variations and Partial Differential Equations}, number = {5}, publisher = {Springer Nature}, title = {{Homogenisation of dynamical optimal transport on periodic graphs}}, doi = {10.1007/s00526-023-02472-z}, volume = {62}, year = {2023}, } @article{12877, abstract = {We consider billiards obtained by removing from the plane finitely many strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift, which provides a natural labeling of periodic orbits. We show that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of the billiard table.}, author = {De Simoi, Jacopo and Kaloshin, Vadim and Leguil, Martin}, issn = {1432-1297}, journal = {Inventiones Mathematicae}, pages = {829--901}, publisher = {Springer Nature}, title = {{Marked Length Spectral determination of analytic chaotic billiards with axial symmetries}}, doi = {10.1007/s00222-023-01191-8}, volume = {233}, year = {2023}, } @article{12349, abstract = {Statistics of natural scenes are not uniform - their structure varies dramatically from ground to sky. It remains unknown whether these non-uniformities are reflected in the large-scale organization of the early visual system and what benefits such adaptations would confer. Here, by relying on the efficient coding hypothesis, we predict that changes in the structure of receptive fields across visual space increase the efficiency of sensory coding. We show experimentally that, in agreement with our predictions, receptive fields of retinal ganglion cells change their shape along the dorsoventral retinal axis, with a marked surround asymmetry at the visual horizon. Our work demonstrates that, according to principles of efficient coding, the panoramic structure of natural scenes is exploited by the retina across space and cell-types.}, author = {Gupta, Divyansh and Mlynarski, Wiktor F and Sumser, Anton L and Symonova, Olga and Svaton, Jan and Jösch, Maximilian A}, issn = {1546-1726}, journal = {Nature Neuroscience}, pages = {606--614}, publisher = {Springer Nature}, title = {{Panoramic visual statistics shape retina-wide organization of receptive fields}}, doi = {10.1038/s41593-023-01280-0}, volume = {26}, year = {2023}, } @misc{12370, abstract = {Statistics of natural scenes are not uniform - their structure varies dramatically from ground to sky. It remains unknown whether these non-uniformities are reflected in the large-scale organization of the early visual system and what benefits such adaptations would confer. Here, by relying on the efficient coding hypothesis, we predict that changes in the structure of receptive fields across visual space increase the efficiency of sensory coding. We show experimentally that, in agreement with our predictions, receptive fields of retinal ganglion cells change their shape along the dorsoventral retinal axis, with a marked surround asymmetry at the visual horizon. Our work demonstrates that, according to principles of efficient coding, the panoramic structure of natural scenes is exploited by the retina across space and cell-types. }, author = {Gupta, Divyansh and Sumser, Anton L and Jösch, Maximilian A}, publisher = {Institute of Science and Technology Austria}, title = {{Research Data for: Panoramic visual statistics shape retina-wide organization of receptive fields}}, doi = {10.15479/AT:ISTA:12370}, year = {2023}, } @article{12764, abstract = {We study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi cell corresponding to the singularity. We divide polyhedral surfaces into discrete conformal classes using a generalization of discrete conformal equivalence pioneered by Feng Luo. We subsequently show that, in every discrete conformal class, there exists a polyhedral surface with constant discrete Gaussian curvature. We also provide explicit examples to demonstrate that this surface is in general not unique.}, author = {Kourimska, Hana}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {123--153}, publisher = {Springer Nature}, title = {{Discrete yamabe problem for polyhedral surfaces}}, doi = {10.1007/s00454-023-00484-2}, volume = {70}, year = {2023}, } @phdthesis{13331, abstract = {The extension of extremal combinatorics to the setting of exterior algebra is a work in progress that gained attention recently. In this thesis, we study the combinatorial structure of exterior algebra by introducing a dictionary that translates the notions from the set systems into the framework of exterior algebra. We show both generalizations of celebrated Erdös--Ko--Rado theorem and Hilton--Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms. }, author = {Köse, Seyda}, issn = {2791-4585}, pages = {26}, publisher = {Institute of Science and Technology Austria}, title = {{Exterior algebra and combinatorics}}, doi = {10.15479/at:ista:13331}, year = {2023}, } @article{12680, abstract = {The celebrated Erdős–Ko–Rado theorem about the maximal size of an intersecting family of r-element subsets of was extended to the setting of exterior algebra in [5, Theorem 2.3] and in [6, Theorem 1.4]. However, the equality case has not been settled yet. In this short note, we show that the extension of the Erdős–Ko–Rado theorem and the characterization of the equality case therein, as well as those of the Hilton–Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms follow from a folklore puzzle about possible arrangements of an intersecting family of lines.}, author = {Ivanov, Grigory and Köse, Seyda}, issn = {0012-365X}, journal = {Discrete Mathematics}, number = {6}, publisher = {Elsevier}, title = {{Erdős-Ko-Rado and Hilton-Milner theorems for two-forms}}, doi = {10.1016/j.disc.2023.113363}, volume = {346}, year = {2023}, } @article{12792, abstract = {In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys 387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner–Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics.}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, pages = {1665--1700}, publisher = {Springer Nature}, title = {{On the spectral form factor for random matrices}}, doi = {10.1007/s00220-023-04692-y}, volume = {401}, year = {2023}, } @article{12709, abstract = {Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness.}, author = {Corbet, René and Kerber, Michael and Lesnick, Michael and Osang, Georg F}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {376--405}, publisher = {Springer Nature}, title = {{Computing the multicover bifiltration}}, doi = {10.1007/s00454-022-00476-8}, volume = {70}, year = {2023}, } @article{12763, abstract = {Kleinjohann (Archiv der Mathematik 35(1):574–582, 1980; Mathematische Zeitschrift 176(3), 327–344, 1981) and Bangert (Archiv der Mathematik 38(1):54–57, 1982) extended the reach rch(S) from subsets S of Euclidean space to the reach rchM(S) of subsets S of Riemannian manifolds M, where M is smooth (we’ll assume at least C3). Bangert showed that sets of positive reach in Euclidean space and Riemannian manifolds are very similar. In this paper we introduce a slight variant of Kleinjohann’s and Bangert’s extension and quantify the similarity between sets of positive reach in Euclidean space and Riemannian manifolds in a new way: Given p∈M and q∈S, we bound the local feature size (a local version of the reach) of its lifting to the tangent space via the inverse exponential map (exp−1p(S)) at q, assuming that rchM(S) and the geodesic distance dM(p,q) are bounded. These bounds are motivated by the importance of the reach and local feature size to manifold learning, topological inference, and triangulating manifolds and the fact that intrinsic approaches circumvent the curse of dimensionality.}, author = {Boissonnat, Jean Daniel and Wintraecken, Mathijs}, issn = {2367-1734}, journal = {Journal of Applied and Computational Topology}, pages = {619--641}, publisher = {Springer Nature}, title = {{The reach of subsets of manifolds}}, doi = {10.1007/s41468-023-00116-x}, volume = {7}, year = {2023}, } @inproceedings{13221, abstract = {The safety-liveness dichotomy is a fundamental concept in formal languages which plays a key role in verification. Recently, this dichotomy has been lifted to quantitative properties, which are arbitrary functions from infinite words to partially-ordered domains. We look into harnessing the dichotomy for the specific classes of quantitative properties expressed by quantitative automata. These automata contain finitely many states and rational-valued transition weights, and their common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum map infinite words into the totallyordered domain of real numbers. In this automata-theoretic setting, we establish a connection between quantitative safety and topological continuity and provide an alternative characterization of quantitative safety and liveness in terms of their boolean counterparts. For all common value functions, we show how the safety closure of a quantitative automaton can be constructed in PTime, and we provide PSpace-complete checks of whether a given quantitative automaton is safe or live, with the exception of LimInfAvg and LimSupAvg automata, for which the safety check is in ExpSpace. Moreover, for deterministic Sup, LimInf, and LimSup automata, we give PTime decompositions into safe and live automata. These decompositions enable the separation of techniques for safety and liveness verification for quantitative specifications.}, author = {Boker, Udi and Henzinger, Thomas A and Mazzocchi, Nicolas Adrien and Sarac, Naci E}, booktitle = {34th International Conference on Concurrency Theory}, isbn = {9783959772990}, issn = {1868-8969}, location = {Antwerp, Belgium}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Safety and liveness of quantitative automata}}, doi = {10.4230/LIPIcs.CONCUR.2023.17}, volume = {279}, year = {2023}, } @article{14406, abstract = {Recently, a concept of generalized multifractality, which characterizes fluctuations and correlations of critical eigenstates, was introduced and explored for all 10 symmetry classes of disordered systems. Here, by using the nonlinear sigma-model ( NL σ M ) field theory, we extend the theory of generalized multifractality to boundaries of systems at criticality. Our numerical simulations on two-dimensional systems of symmetry classes A, C, and AII fully confirm the analytical predictions of pure-scaling observables and Weyl symmetry relations between critical exponents of surface generalized multifractality. This demonstrates the validity of the NL σ M for the description of Anderson-localization critical phenomena, not only in the bulk but also on the boundary. The critical exponents strongly violate generalized parabolicity, in analogy with earlier results for the bulk, corroborating the conclusion that the considered Anderson-localization critical points are not described by conformal field theories. We further derive relations between generalized surface multifractal spectra and linear combinations of Lyapunov exponents of a strip in quasi-one-dimensional geometry, which hold under the assumption of invariance with respect to a logarithmic conformal map. Our numerics demonstrate that these relations hold with an excellent accuracy. Taken together, our results indicate an intriguing situation: the conformal invariance is broken but holds partially at critical points of Anderson localization.}, author = {Babkin, Serafim and Karcher, Jonas F. and Burmistrov, Igor S. and Mirlin, Alexander D.}, issn = {2469-9969}, journal = {Physical Review B}, number = {10}, publisher = {American Physical Society}, title = {{Generalized surface multifractality in two-dimensional disordered systems}}, doi = {10.1103/PhysRevB.108.104205}, volume = {108}, year = {2023}, } @inproceedings{14405, abstract = {We introduce hypernode automata as a new specification formalism for hyperproperties of concurrent systems. They are finite automata with nodes labeled with hypernode logic formulas and transitions labeled with actions. A hypernode logic formula specifies relations between sequences of variable values in different system executions. Unlike HyperLTL, hypernode logic takes an asynchronous view on execution traces by constraining the values and the order of value changes of each variable without correlating the timing of the changes. Different execution traces are synchronized solely through the transitions of hypernode automata. Hypernode automata naturally combine asynchronicity at the node level with synchronicity at the transition level. We show that the model-checking problem for hypernode automata is decidable over action-labeled Kripke structures, whose actions induce transitions of the specification automata. For this reason, hypernode automaton is a suitable formalism for specifying and verifying asynchronous hyperproperties, such as declassifying observational determinism in multi-threaded programs.}, author = {Bartocci, Ezio and Henzinger, Thomas A and Nickovic, Dejan and Oliveira da Costa, Ana}, booktitle = {34th International Conference on Concurrency Theory}, isbn = {9783959772990}, issn = {18688969}, location = {Antwerp, Belgium}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Hypernode automata}}, doi = {10.4230/LIPIcs.CONCUR.2023.21}, volume = {279}, year = {2023}, } @article{14408, abstract = {We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 01+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices.}, author = {Dubach, Guillaume and Erdös, László}, issn = {1083-589X}, journal = {Electronic Communications in Probability}, pages = {1--13}, publisher = {Institute of Mathematical Statistics}, title = {{Dynamics of a rank-one perturbation of a Hermitian matrix}}, doi = {10.1214/23-ECP516}, volume = {28}, year = {2023}, } @article{12761, abstract = {We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f (W). Going beyond the well-studied tracial mode, Trf (W), which is equivalent to the customary linear statistics of eigenvalues, we show that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find that the off-diagonal modes fluctuate on a much smaller scale than the tracial mode. As a main motivation to study CLT in such generality on small mesoscopic scales, we determine the fluctuations in the eigenstate thermalization hypothesis (Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps with any deterministic matrix are asymptotically Gaussian after a small spectral averaging. Finally, in the macroscopic regime our result also generalizes (Zh. Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover ensembles in between. The main technical inputs are the recent multiresolvent local laws with traceless deterministic matrices from the companion paper (Comm. Math. Phys. 388 (2021) 1005–1048).}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {1050-5164}, journal = {Annals of Applied Probability}, number = {1}, pages = {447--489}, publisher = {Institute of Mathematical Statistics}, title = {{Functional central limit theorems for Wigner matrices}}, doi = {10.1214/22-AAP1820}, volume = {33}, year = {2023}, } @article{8682, abstract = {It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover, for such varieties it follows from a general conjecture of Colliot-Thélène that the Brauer--Manin obstruction to the Hasse principle should be the only one, so that the Hasse principle is expected to hold. Working over the field of rational numbers and ordering Fano hypersurfaces of fixed degree and dimension by height, we prove that almost every such hypersurface satisfies the Hasse principle provided that the dimension is at least 3. This proves a conjecture of Poonen and Voloch in every case except for cubic surfaces.}, author = {Browning, Timothy D and Boudec, Pierre Le and Sawin, Will}, issn = {0003-486X}, journal = {Annals of Mathematics}, number = {3}, pages = {1115--1203}, publisher = {Princeton University}, title = {{The Hasse principle for random Fano hypersurfaces}}, doi = {10.4007/annals.2023.197.3.3}, volume = {197}, year = {2023}, } @article{12706, abstract = {Allometric settings of population dynamics models are appealing due to their parsimonious nature and broad utility when studying system level effects. Here, we parameterise the size-scaled Rosenzweig-MacArthur differential equations to eliminate prey-mass dependency, facilitating an in depth analytic study of the equations which incorporates scaling parameters’ contributions to coexistence. We define the functional response term to match empirical findings, and examine situations where metabolic theory derivations and observation diverge. The dynamical properties of the Rosenzweig-MacArthur system, encompassing the distribution of size-abundance equilibria, the scaling of period and amplitude of population cycling, and relationships between predator and prey abundances, are consistent with empirical observation. Our parameterisation is an accurate minimal model across 15+ orders of mass magnitude.}, author = {Mckerral, Jody C. and Kleshnina, Maria and Ejov, Vladimir and Bartle, Louise and Mitchell, James G. and Filar, Jerzy A.}, issn = {1932-6203}, journal = {PLoS One}, number = {2}, pages = {e0279838}, publisher = {Public Library of Science}, title = {{Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations}}, doi = {10.1371/journal.pone.0279838}, volume = {18}, year = {2023}, } @article{13202, abstract = {Phosphatidylinositol-4,5-bisphosphate (PI(4,5)P2) plays an essential role in neuronal activities through interaction with various proteins involved in signaling at membranes. However, the distribution pattern of PI(4,5)P2 and the association with these proteins on the neuronal cell membranes remain elusive. In this study, we established a method for visualizing PI(4,5)P2 by SDS-digested freeze-fracture replica labeling (SDS-FRL) to investigate the quantitative nanoscale distribution of PI(4,5)P2 in cryo-fixed brain. We demonstrate that PI(4,5)P2 forms tiny clusters with a mean size of ∼1000 nm2 rather than randomly distributed in cerebellar neuronal membranes in male C57BL/6J mice. These clusters show preferential accumulation in specific membrane compartments of different cell types, in particular, in Purkinje cell (PC) spines and granule cell (GC) presynaptic active zones. Furthermore, we revealed extensive association of PI(4,5)P2 with CaV2.1 and GIRK3 across different membrane compartments, whereas its association with mGluR1α was compartment specific. These results suggest that our SDS-FRL method provides valuable insights into the physiological functions of PI(4,5)P2 in neurons.}, author = {Eguchi, Kohgaku and Le Monnier, Elodie and Shigemoto, Ryuichi}, issn = {1529-2401}, journal = {The Journal of Neuroscience}, number = {23}, pages = {4197--4216}, publisher = {Society for Neuroscience}, title = {{Nanoscale phosphoinositide distribution on cell membranes of mouse cerebellar neurons}}, doi = {10.1523/JNEUROSCI.1514-22.2023}, volume = {43}, year = {2023}, } @article{12916, abstract = {We apply a variant of the square-sieve to produce an upper bound for the number of rational points of bounded height on a family of surfaces that admit a fibration over P1 whose general fibre is a hyperelliptic curve. The implied constant does not depend on the coefficients of the polynomial defining the surface. }, author = {Bonolis, Dante and Browning, Timothy D}, issn = {2036-2145}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, number = {1}, pages = {173--204}, publisher = {Scuola Normale Superiore - Edizioni della Normale}, title = {{Uniform bounds for rational points on hyperelliptic fibrations}}, doi = {10.2422/2036-2145.202010_018}, volume = {24}, year = {2023}, } @phdthesis{14374, abstract = {Superconductivity has many important applications ranging from levitating trains over qubits to MRI scanners. The phenomenon is successfully modeled by Bardeen-Cooper-Schrieffer (BCS) theory. From a mathematical perspective, BCS theory has been studied extensively for systems without boundary. However, little is known in the presence of boundaries. With the help of numerical methods physicists observed that the critical temperature may increase in the presence of a boundary. The goal of this thesis is to understand the influence of boundaries on the critical temperature in BCS theory and to give a first rigorous justification of these observations. On the way, we also study two-body Schrödinger operators on domains with boundaries and prove additional results for superconductors without boundary. BCS theory is based on a non-linear functional, where the minimizer indicates whether the system is superconducting or in the normal, non-superconducting state. By considering the Hessian of the BCS functional at the normal state, one can analyze whether the normal state is possibly a minimum of the BCS functional and estimate the critical temperature. The Hessian turns out to be a linear operator resembling a Schrödinger operator for two interacting particles, but with more complicated kinetic energy. As a first step, we study the two-body Schrödinger operator in the presence of boundaries. For Neumann boundary conditions, we prove that the addition of a boundary can create new eigenvalues, which correspond to the two particles forming a bound state close to the boundary. Second, we need to understand superconductivity in the translation invariant setting. While in three dimensions this has been extensively studied, there is no mathematical literature for the one and two dimensional cases. In dimensions one and two, we compute the weak coupling asymptotics of the critical temperature and the energy gap in the translation invariant setting. We also prove that their ratio is independent of the microscopic details of the model in the weak coupling limit; this property is referred to as universality. In the third part, we study the critical temperature of superconductors in the presence of boundaries. We start by considering the one-dimensional case of a half-line with contact interaction. Then, we generalize the results to generic interactions and half-spaces in one, two and three dimensions. Finally, we compare the critical temperature of a quarter space in two dimensions to the critical temperatures of a half-space and of the full space.}, author = {Roos, Barbara}, issn = {2663 - 337X}, pages = {206}, publisher = {Institute of Science and Technology Austria}, title = {{Boundary superconductivity in BCS theory}}, doi = {10.15479/at:ista:14374}, year = {2023}, } @article{13207, abstract = {We consider the linear BCS equation, determining the BCS critical temperature, in the presence of a boundary, where Dirichlet boundary conditions are imposed. In the one-dimensional case with point interactions, we prove that the critical temperature is strictly larger than the bulk value, at least at weak coupling. In particular, the Cooper-pair wave function localizes near the boundary, an effect that cannot be modeled by effective Neumann boundary conditions on the order parameter as often imposed in Ginzburg–Landau theory. We also show that the relative shift in critical temperature vanishes if the coupling constant either goes to zero or to infinity.}, author = {Hainzl, Christian and Roos, Barbara and Seiringer, Robert}, issn = {1664-0403}, journal = {Journal of Spectral Theory}, number = {4}, pages = {1507–1540}, publisher = {EMS Press}, title = {{Boundary superconductivity in the BCS model}}, doi = {10.4171/JST/439}, volume = {12}, year = {2023}, } @article{14452, abstract = {The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and an environmental component, and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents’ trait values, and has a variance that is independent of the parental traits. In previous work, we showed that when trait values are determined by the sum of a large number of additive Mendelian factors, each of small effect, one can justify the infinitesimal model as a limit of Mendelian inheritance. In this paper, we show that this result extends to include dominance. We define the model in terms of classical quantities of quantitative genetics, before justifying it as a limit of Mendelian inheritance as the number, M, of underlying loci tends to infinity. As in the additive case, the multivariate normal distribution of trait values across the pedigree can be expressed in terms of variance components in an ancestral population and probabilities of identity by descent determined by the pedigree. Now, with just first-order dominance effects, we require two-, three-, and four-way identities. We also show that, even if we condition on parental trait values, the “shared” and “residual” components of trait values within each family will be asymptotically normally distributed as the number of loci tends to infinity, with an error of order 1/M−−√⁠. We illustrate our results with some numerical examples.}, author = {Barton, Nicholas H and Etheridge, Alison M. and Véber, Amandine}, issn = {1943-2631}, journal = {Genetics}, number = {2}, publisher = {Oxford Academic}, title = {{The infinitesimal model with dominance}}, doi = {10.1093/genetics/iyad133}, volume = {225}, year = {2023}, } @misc{12949, abstract = {The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and a non-genetic (environmental) component and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents’ trait values, and has a variance that is independent of the trait values of the parents. Although the trait distribution across the whole population can be far from normal, the trait distributions within families are normally distributed with a variance-covariance matrix that is determined entirely by that in the ancestral population and the probabilities of identity determined by the pedigree. Moreover, conditioning on some of the trait values within the pedigree has predictable effects on the mean and variance within and between families. In previous work, Barton et al. (2017), we showed that when trait values are determined by the sum of a large number of Mendelian factors, each of small effect, one can justify the infinitesimal model as limit of Mendelian inheritance. It was also shown that under some forms of epistasis, trait values within a family are still normally distributed.}, author = {Barton, Nicholas H}, keywords = {Quantitative genetics, infinitesimal model}, publisher = {Institute of Science and Technology Austria}, title = {{The infinitesimal model with dominance}}, doi = {10.15479/AT:ISTA:12949}, year = {2023}, } @inproceedings{14461, abstract = {Communication-reduction techniques are a popular way to improve scalability in data-parallel training of deep neural networks (DNNs). The recent emergence of large language models such as GPT has created the need for new approaches to exploit data-parallelism. Among these, fully-sharded data parallel (FSDP) training is highly popular, yet it still encounters scalability bottlenecks. One reason is that applying compression techniques to FSDP is challenging: as the vast majority of the communication involves the model’s weights, direct compression alters convergence and leads to accuracy loss. We present QSDP, a variant of FSDP which supports both gradient and weight quantization with theoretical guarantees, is simple to implement and has essentially no overheads. To derive QSDP we prove that a natural modification of SGD achieves convergence even when we only maintain quantized weights, and thus the domain over which we train consists of quantized points and is, therefore, highly non-convex. We validate this approach by training GPT-family models with up to 1.3 billion parameters on a multi-node cluster. Experiments show that QSDP preserves model accuracy, while completely removing the communication bottlenecks of FSDP, providing end-to-end speedups of up to 2.2x.}, author = {Markov, Ilia and Vladu, Adrian and Guo, Qi and Alistarh, Dan-Adrian}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, issn = {2640-3498}, location = {Honolulu, Hawaii, HI, United States}, pages = {24020--24044}, publisher = {ML Research Press}, title = {{Quantized distributed training of large models with convergence guarantees}}, volume = {202}, year = {2023}, } @inproceedings{14462, abstract = {We study fine-grained error bounds for differentially private algorithms for counting under continual observation. Our main insight is that the matrix mechanism when using lower-triangular matrices can be used in the continual observation model. More specifically, we give an explicit factorization for the counting matrix Mcount and upper bound the error explicitly. We also give a fine-grained analysis, specifying the exact constant in the upper bound. Our analysis is based on upper and lower bounds of the completely bounded norm (cb-norm) of Mcount . Along the way, we improve the best-known bound of 28 years by Mathias (SIAM Journal on Matrix Analysis and Applications, 1993) on the cb-norm of Mcount for a large range of the dimension of Mcount. Furthermore, we are the first to give concrete error bounds for various problems under continual observation such as binary counting, maintaining a histogram, releasing an approximately cut-preserving synthetic graph, many graph-based statistics, and substring and episode counting. Finally, we note that our result can be used to get a fine-grained error bound for non-interactive local learning and the first lower bounds on the additive error for (ϵ,δ)-differentially-private counting under continual observation. Subsequent to this work, Henzinger et al. (SODA, 2023) showed that our factorization also achieves fine-grained mean-squared error.}, author = {Fichtenberger, Hendrik and Henzinger, Monika H and Upadhyay, Jalaj}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, issn = {2640-3498}, location = {Honolulu, Hawaii, HI, United States}, pages = {10072--10092}, publisher = {ML Research Press}, title = {{Constant matters: Fine-grained error bound on differentially private continual observation}}, volume = {202}, year = {2023}, } @inproceedings{14459, abstract = {Autoencoders are a popular model in many branches of machine learning and lossy data compression. However, their fundamental limits, the performance of gradient methods and the features learnt during optimization remain poorly understood, even in the two-layer setting. In fact, earlier work has considered either linear autoencoders or specific training regimes (leading to vanishing or diverging compression rates). Our paper addresses this gap by focusing on non-linear two-layer autoencoders trained in the challenging proportional regime in which the input dimension scales linearly with the size of the representation. Our results characterize the minimizers of the population risk, and show that such minimizers are achieved by gradient methods; their structure is also unveiled, thus leading to a concise description of the features obtained via training. For the special case of a sign activation function, our analysis establishes the fundamental limits for the lossy compression of Gaussian sources via (shallow) autoencoders. Finally, while the results are proved for Gaussian data, numerical simulations on standard datasets display the universality of the theoretical predictions.}, author = {Shevchenko, Aleksandr and Kögler, Kevin and Hassani, Hamed and Mondelli, Marco}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, issn = {2640-3498}, location = {Honolulu, Hawaii, HI, United States}, pages = {31151--31209}, publisher = {ML Research Press}, title = {{Fundamental limits of two-layer autoencoders, and achieving them with gradient methods}}, volume = {202}, year = {2023}, } @inproceedings{14460, abstract = {We provide an efficient implementation of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and common layer types (e.g., convolutional or linear). We provide a fast vectorized implementation on commodity CPUs, and show that it can yield speedups in end-to-end runtime experiments, both in transfer learning using already-sparsified networks, and in training sparse networks from scratch. Thus, our results provide the first support for sparse training on commodity hardware.}, author = {Nikdan, Mahdi and Pegolotti, Tommaso and Iofinova, Eugenia B and Kurtic, Eldar and Alistarh, Dan-Adrian}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, issn = {2640-3498}, location = {Honolulu, Hawaii, HI, United States}, pages = {26215--26227}, publisher = {ML Research Press}, title = {{SparseProp: Efficient sparse backpropagation for faster training of neural networks at the edge}}, volume = {202}, year = {2023}, } @inproceedings{14457, abstract = {Threshold secret sharing allows a dealer to split a secret s into n shares, such that any t shares allow for reconstructing s, but no t-1 shares reveal any information about s. Leakage-resilient secret sharing requires that the secret remains hidden, even when an adversary additionally obtains a limited amount of leakage from every share. Benhamouda et al. (CRYPTO’18) proved that Shamir’s secret sharing scheme is one bit leakage-resilient for reconstruction threshold t≥0.85n and conjectured that the same holds for t = c.n for any constant 0≤c≤1. Nielsen and Simkin (EUROCRYPT’20) showed that this is the best one can hope for by proving that Shamir’s scheme is not secure against one-bit leakage when t0c.n/log(n). In this work, we strengthen the lower bound of Nielsen and Simkin. We consider noisy leakage-resilience, where a random subset of leakages is replaced by uniformly random noise. We prove a lower bound for Shamir’s secret sharing, similar to that of Nielsen and Simkin, which holds even when a constant fraction of leakages is replaced by random noise. To this end, we first prove a lower bound on the share size of any noisy-leakage-resilient sharing scheme. We then use this lower bound to show that there exist universal constants c1, c2, such that for sufficiently large n it holds that Shamir’s secret sharing scheme is not noisy-leakage-resilient for t≤c1.n/log(n), even when a c2 fraction of leakages are replaced by random noise. }, author = {Hoffmann, Charlotte and Simkin, Mark}, booktitle = {8th International Conference on Cryptology and Information Security in Latin America}, isbn = {9783031444685}, issn = {1611-3349}, location = {Quito, Ecuador}, pages = {215--228}, publisher = {Springer Nature}, title = {{Stronger lower bounds for leakage-resilient secret sharing}}, doi = {10.1007/978-3-031-44469-2_11}, volume = {14168}, year = {2023}, } @inproceedings{14458, abstract = {We show for the first time that large-scale generative pretrained transformer (GPT) family models can be pruned to at least 50% sparsity in one-shot, without any retraining, at minimal loss of accuracy. This is achieved via a new pruning method called SparseGPT, specifically designed to work efficiently and accurately on massive GPT-family models. We can execute SparseGPT on the largest available open-source models, OPT-175B and BLOOM-176B, in under 4.5 hours, and can reach 60% unstructured sparsity with negligible increase in perplexity: remarkably, more than 100 billion weights from these models can be ignored at inference time. SparseGPT generalizes to semi-structured (2:4 and 4:8) patterns, and is compatible with weight quantization approaches. The code is available at: https://github.com/IST-DASLab/sparsegpt.}, author = {Frantar, Elias and Alistarh, Dan-Adrian}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, issn = {2640-3498}, location = {Honolulu, Hawaii, HI, United States}, pages = {10323--10337}, publisher = {ML Research Press}, title = {{SparseGPT: Massive language models can be accurately pruned in one-shot}}, volume = {202}, year = {2023}, } @article{14451, abstract = {We investigate the potential of Multi-Objective, Deep Reinforcement Learning for stock and cryptocurrency single-asset trading: in particular, we consider a Multi-Objective algorithm which generalizes the reward functions and discount factor (i.e., these components are not specified a priori, but incorporated in the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT, XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of the proposed Multi-Objective algorithm, and provide preliminary statistical evidence showing increased predictive stability over the corresponding Single-Objective strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge over the corresponding Single-Objective strategy when the reward mechanism is sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss the generalization properties with respect to the discount factor. The entirety of our code is provided in open-source format.}, author = {Cornalba, Federico and Disselkamp, Constantin and Scassola, Davide and Helf, Christopher}, issn = {1433-3058}, journal = {Neural Computing and Applications}, publisher = {Springer Nature}, title = {{Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading}}, doi = {10.1007/s00521-023-09033-7}, year = {2023}, }