@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{10550, abstract = {The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy inequality. The difficulties in establishing global renormalised solutions caused by possibly degenerate diffusion are overcome by introducing a new class of weighted truncation functions. By means of the obtained global renormalised solutions, we study the large-time behaviour of complex balanced systems arising from chemical reaction network theory with non-linear diffusion. When the reaction network does not admit boundary equilibria, the complex balanced equilibrium is shown, by using the entropy method, to exponentially attract all renormalised solutions in the same compatibility class. This convergence extends even to a range of non-linear diffusion, where global existence is an open problem, yet we are able to show that solutions to approximate systems converge exponentially to equilibrium uniformly in the regularisation parameter.}, author = {Fellner, Klemens and Fischer, Julian L and Kniely, Michael and Tang, Bao Quoc}, issn = {1432-1467}, journal = {Journal of Nonlinear Science}, publisher = {Springer Nature}, title = {{Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion}}, doi = {10.1007/s00332-023-09926-w}, volume = {33}, year = {2023}, } @article{10551, abstract = {The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of fluctuating hydrodynamics; it has been proposed in the physics literature to describe the fluctuations of the density of N independent diffusing particles in the regime of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation presents a substantial challenge for both its analysis and its rigorous mathematical justification. Besides being non-renormalisable by the theory of regularity structures by Hairer et al., it has recently been shown to not even admit nontrivial martingale solutions. In the present work, we give a rigorous and fully quantitative justification of the Dean–Kawasaki equation by considering the natural regularisation provided by standard numerical discretisations: We show that structure-preserving discretisations of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting diffusing particles to arbitrary order in N−1 (in suitable weak metrics). In other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate and efficient numerical simulations of the density fluctuations of independent diffusing particles.}, author = {Cornalba, Federico and Fischer, Julian L}, issn = {1432-0673}, journal = {Archive for Rational Mechanics and Analysis}, number = {5}, publisher = {Springer Nature}, title = {{The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles}}, doi = {10.1007/s00205-023-01903-7}, volume = {247}, 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{9651, abstract = {We introduce a hierachy of equivalence relations on the set of separated nets of a given Euclidean space, indexed by concave increasing functions ϕ:(0,∞)→(0,∞). Two separated nets are called ϕ-displacement equivalent if, roughly speaking, there is a bijection between them which, for large radii R, displaces points of norm at most R by something of order at most ϕ(R). We show that the spectrum of ϕ-displacement equivalence spans from the established notion of bounded displacement equivalence, which corresponds to bounded ϕ, to the indiscrete equivalence relation, coresponding to ϕ(R)∈Ω(R), in which all separated nets are equivalent. In between the two ends of this spectrum, the notions of ϕ-displacement equivalence are shown to be pairwise distinct with respect to the asymptotic classes of ϕ(R) for R→∞. We further undertake a comparison of our notion of ϕ-displacement equivalence with previously studied relations on separated nets. Particular attention is given to the interaction of the notions of ϕ-displacement equivalence with that of bilipschitz equivalence.}, author = {Dymond, Michael and Kaluza, Vojtech}, issn = {1572-9168}, journal = {Geometriae Dedicata}, publisher = {Springer Nature}, title = {{Divergence of separated nets with respect to displacement equivalence}}, doi = {10.1007/s10711-023-00862-3}, year = {2023}, } @article{9652, abstract = {In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice. We study weaker notions of equivalence of separated nets and demonstrate that such notions also give rise to distinct equivalence classes. Put differently, we find occurrences of particularly strong divergence of separated nets from the integer lattice. Our approach generalises that of Burago and Kleiner and McMullen which takes place largely in a continuous setting. Existence of irregular separated nets is verified via the existence of non-realisable density functions ρ:[0,1]d→(0,∞). In the present work we obtain stronger types of non-realisable densities.}, author = {Dymond, Michael and Kaluza, Vojtech}, issn = {1565-8511}, journal = {Israel Journal of Mathematics}, keywords = {Lipschitz, bilipschitz, bounded displacement, modulus of continuity, separated net, non-realisable density, Burago--Kleiner construction}, pages = {501--554}, publisher = {Springer Nature}, title = {{Highly irregular separated nets}}, doi = {10.1007/s11856-022-2448-6}, volume = {253}, year = {2023}, } @article{11479, abstract = {Understanding population divergence that eventually leads to speciation is essential for evolutionary biology. High species diversity in the sea was regarded as a paradox when strict allopatry was considered necessary for most speciation events because geographical barriers seemed largely absent in the sea, and many marine species have high dispersal capacities. Combining genome-wide data with demographic modelling to infer the demographic history of divergence has introduced new ways to address this classical issue. These models assume an ancestral population that splits into two subpopulations diverging according to different scenarios that allow tests for periods of gene flow. Models can also test for heterogeneities in population sizes and migration rates along the genome to account, respectively, for background selection and selection against introgressed ancestry. To investigate how barriers to gene flow arise in the sea, we compiled studies modelling the demographic history of divergence in marine organisms and extracted preferred demographic scenarios together with estimates of demographic parameters. These studies show that geographical barriers to gene flow do exist in the sea but that divergence can also occur without strict isolation. Heterogeneity of gene flow was detected in most population pairs suggesting the predominance of semipermeable barriers during divergence. We found a weak positive relationship between the fraction of the genome experiencing reduced gene flow and levels of genome-wide differentiation. Furthermore, we found that the upper bound of the ‘grey zone of speciation’ for our dataset extended beyond that found before, implying that gene flow between diverging taxa is possible at higher levels of divergence than previously thought. Finally, we list recommendations for further strengthening the use of demographic modelling in speciation research. These include a more balanced representation of taxa, more consistent and comprehensive modelling, clear reporting of results and simulation studies to rule out nonbiological explanations for general results.}, author = {De Jode, Aurélien and Le Moan, Alan and Johannesson, Kerstin and Faria, Rui and Stankowski, Sean and Westram, Anja M and Butlin, Roger K. and Rafajlović, Marina and Fraisse, Christelle}, issn = {1752-4571}, journal = {Evolutionary Applications}, number = {2}, pages = {542--559}, publisher = {Wiley}, title = {{Ten years of demographic modelling of divergence and speciation in the sea}}, doi = {10.1111/eva.13428}, volume = {16}, 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{11741, abstract = {Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble.}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {1432-2064}, journal = {Probability Theory and Related Fields}, pages = {1183–1218}, publisher = {Springer Nature}, title = {{Quenched universality for deformed Wigner matrices}}, doi = {10.1007/s00440-022-01156-7}, volume = {185}, year = {2023}, } @article{11999, abstract = {A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G+e extending D(G). As a result of Levi’s Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP-complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment σ, it can be decided in polynomial time whether there exists a pseudocircle Φσ extending σ for which A∪{Φσ} is again an arrangement of pseudocircles.}, author = {Arroyo Guevara, Alan M and Klute, Fabian and Parada, Irene and Vogtenhuber, Birgit and Seidel, Raimund and Wiedera, Tilo}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {745–770}, publisher = {Springer Nature}, title = {{Inserting one edge into a simple drawing is hard}}, doi = {10.1007/s00454-022-00394-9}, volume = {69}, year = {2023}, } @article{12086, abstract = {We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets.}, author = {Edelsbrunner, Herbert and Osang, Georg F}, issn = {1432-0541}, journal = {Algorithmica}, pages = {277--295}, publisher = {Springer Nature}, title = {{A simple algorithm for higher-order Delaunay mosaics and alpha shapes}}, doi = {10.1007/s00453-022-01027-6}, volume = {85}, year = {2023}, } @article{12087, abstract = {Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups.}, author = {Wirth, Melchior and Zhang, Haonan}, issn = {1424-0637}, journal = {Annales Henri Poincare}, pages = {717--750}, publisher = {Springer Nature}, title = {{Curvature-dimension conditions for symmetric quantum Markov semigroups}}, doi = {10.1007/s00023-022-01220-x}, volume = {24}, year = {2023}, } @article{12104, abstract = {We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces.}, author = {Dello Schiavo, Lorenzo and Wirth, Melchior}, issn = {1424-3202}, journal = {Journal of Evolution Equations}, number = {1}, publisher = {Springer Nature}, title = {{Ergodic decompositions of Dirichlet forms under order isomorphisms}}, doi = {10.1007/s00028-022-00859-7}, volume = {23}, year = {2023}, } @article{12105, abstract = {Data-driven dimensionality reduction methods such as proper orthogonal decomposition and dynamic mode decomposition have proven to be useful for exploring complex phenomena within fluid dynamics and beyond. A well-known challenge for these techniques is posed by the continuous symmetries, e.g. translations and rotations, of the system under consideration, as drifts in the data dominate the modal expansions without providing an insight into the dynamics of the problem. In the present study, we address this issue for fluid flows in rectangular channels by formulating a continuous symmetry reduction method that eliminates the translations in the streamwise and spanwise directions simultaneously. We demonstrate our method by computing the symmetry-reduced dynamic mode decomposition (SRDMD) of sliding windows of data obtained from the transitional plane-Couette and turbulent plane-Poiseuille flow simulations. In the former setting, SRDMD captures the dynamics in the vicinity of the invariant solutions with translation symmetries, i.e. travelling waves and relative periodic orbits, whereas in the latter, our calculations reveal episodes of turbulent time evolution that can be approximated by a low-dimensional linear expansion.}, author = {Marensi, Elena and Yalniz, Gökhan and Hof, Björn and Budanur, Nazmi B}, issn = {1469-7645}, journal = {Journal of Fluid Mechanics}, publisher = {Cambridge University Press}, title = {{Symmetry-reduced dynamic mode decomposition of near-wall turbulence}}, doi = {10.1017/jfm.2022.1001}, volume = {954}, year = {2023}, } @article{12106, abstract = {Regulation of chromatin states involves the dynamic interplay between different histone modifications to control gene expression. Recent advances have enabled mapping of histone marks in single cells, but most methods are constrained to profile only one histone mark per cell. Here, we present an integrated experimental and computational framework, scChIX-seq (single-cell chromatin immunocleavage and unmixing sequencing), to map several histone marks in single cells. scChIX-seq multiplexes two histone marks together in single cells, then computationally deconvolves the signal using training data from respective histone mark profiles. This framework learns the cell-type-specific correlation structure between histone marks, and therefore does not require a priori assumptions of their genomic distributions. Using scChIX-seq, we demonstrate multimodal analysis of histone marks in single cells across a range of mark combinations. Modeling dynamics of in vitro macrophage differentiation enables integrated analysis of chromatin velocity. Overall, scChIX-seq unlocks systematic interrogation of the interplay between histone modifications in single cells.}, author = {Yeung, Jake and Florescu, Maria and Zeller, Peter and De Barbanson, Buys Anton and Wellenstein, Max D. and Van Oudenaarden, Alexander}, issn = {1546-1696}, journal = {Nature Biotechnology}, pages = {813–823}, publisher = {Springer Nature}, title = {{scChIX-seq infers dynamic relationships between histone modifications in single cells}}, doi = {10.1038/s41587-022-01560-3}, volume = {41}, year = {2023}, } @article{12114, abstract = {Probing the dynamics of aromatic side chains provides important insights into the behavior of a protein because flips of aromatic rings in a protein’s hydrophobic core report on breathing motion involving a large part of the protein. Inherently invisible to crystallography, aromatic motions have been primarily studied by solution NMR. The question how packing of proteins in crystals affects ring flips has, thus, remained largely unexplored. Here we apply magic-angle spinning NMR, advanced phenylalanine 1H-13C/2H isotope labeling and MD simulation to a protein in three different crystal packing environments to shed light onto possible impact of packing on ring flips. The flips of the two Phe residues in ubiquitin, both surface exposed, appear remarkably conserved in the different crystal forms, even though the intermolecular packing is quite different: Phe4 flips on a ca. 10–20 ns time scale, and Phe45 are broadened in all crystals, presumably due to µs motion. Our findings suggest that intramolecular influences are more important for ring flips than intermolecular (packing) effects.}, author = {Gauto, Diego F. and Lebedenko, Olga O. and Becker, Lea Marie and Ayala, Isabel and Lichtenecker, Roman and Skrynnikov, Nikolai R. and Schanda, Paul}, issn = {2590-1524}, journal = {Journal of Structural Biology: X}, keywords = {Structural Biology}, publisher = {Elsevier}, title = {{Aromatic ring flips in differently packed ubiquitin protein crystals from MAS NMR and MD}}, doi = {10.1016/j.yjsbx.2022.100079}, volume = {7}, year = {2023}, } @article{12115, author = {Glajzer, Jacek and Castillo-Tong, Dan Cacsire and Richter, Rolf and Vergote, Ignace and Kulbe, Hagen and Vanderstichele, Adriaan and Ruscito, Ilary and Trillsch, Fabian and Mustea, Alexander and Kreuzinger, Caroline and Gourley, Charlie and Gabra, Hani and Taube, Eliane T. and Dorigo, Oliver and Horst, David and Keunecke, Carlotta and Baum, Joanna and Angelotti, Timothy and Sehouli, Jalid and Braicu, Elena Ioana}, issn = {1534-4681}, journal = {Annals of Surgical Oncology}, keywords = {Oncology, Surgery}, pages = {46--47}, publisher = {Springer Nature}, title = {{ASO Visual Abstract: Impact of BRCA mutation status on tumor dissemination pattern, surgical outcome, and patient survival in primary and recurrent high-grade serous ovarian cancer (HGSOC). A multicenter, retrospective study of the ovarian cancer therapy—innovative models prolong survival (OCTIPS) consortium}}, doi = {10.1245/s10434-022-12681-z}, volume = {30}, year = {2023}, } @article{12430, abstract = {We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (with respect to the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of partial differential equations describing the time evolution of the first- and second-order approximations to the one-particle reduced density matrices of the particles and the quantum field, respectively.}, author = {Falconi, Marco and Leopold, Nikolai K and Mitrouskas, David Johannes and Petrat, Sören P}, issn = {0129-055X}, journal = {Reviews in Mathematical Physics}, number = {4}, publisher = {World Scientific Publishing}, title = {{Bogoliubov dynamics and higher-order corrections for the regularized Nelson model}}, doi = {10.1142/S0129055X2350006X}, volume = {35}, year = {2023}, } @article{12149, abstract = {Editorial on the Research Topic}, author = {Gambino, Giuditta and Bhik-Ghanie, Rebecca and Giglia, Giuseppe and Puig, M. Victoria and Ramirez Villegas, Juan F and Zaldivar, Daniel}, issn = {1662-5110}, journal = {Frontiers in Neural Circuits}, keywords = {Cellular and Molecular Neuroscience, Cognitive Neuroscience, Sensory Systems, Neuroscience (miscellaneous)}, publisher = {Frontiers Media}, title = {{Editorial: Neuromodulatory ascending systems: Their influence at the microscopic and macroscopic levels}}, doi = {10.3389/fncir.2022.1028154}, volume = {16}, year = {2022}, } @article{12150, abstract = {Methods inspired from machine learning have recently attracted great interest in the computational study of quantum many-particle systems. So far, however, it has proven challenging to deal with microscopic models in which the total number of particles is not conserved. To address this issue, we propose a variant of neural network states, which we term neural coherent states. Taking the Fröhlich impurity model as a case study, we show that neural coherent states can learn the ground state of nonadditive systems very well. In particular, we recover exact diagonalization in all regimes tested and observe substantial improvement over the standard coherent state estimates in the most challenging intermediate-coupling regime. Our approach is generic and does not assume specific details of the system, suggesting wide applications.}, author = {Rzadkowski, Wojciech and Lemeshko, Mikhail and Mentink, Johan H.}, issn = {2469-9969}, journal = {Physical Review B}, number = {15}, publisher = {American Physical Society}, title = {{Artificial neural network states for nonadditive systems}}, doi = {10.1103/physrevb.106.155127}, volume = {106}, year = {2022}, }