@unpublished{21968, abstract = {Balancing selection, a form of selection that maintains genetic diversity, is difficult to detect, and the importance of balancing selection for the maintenance of genetic variation may be larger than often assumed. We model the possibility that the diversity-promoting effects of balancing selection extend to other loci that show sign epistasis with a locus under balancing selection. Rather than focusing on overdominance, as was done in previous efforts, we explore the effects of negative frequency dependence and show that this has important effects on the conditions under which the diversity-promoting effect of epistasis can occur in diploids. Our results show that not only recombination rate but also the dominance of sign epistasis are key parameters that determine the maintenance of polymorphism beyond the locus under direct balancing selection. We suggest that the effect we explore may play a significant role, especially when balancing selection acts on major effect loci.}, author = {Khudiakova, Kseniia and Barton, Nicholas H and Arnqvist, Goran}, booktitle = {bioRxiv}, title = {{Sign epistasis extends the effects of balancing selection on genetic diversity}}, doi = {10.1101/2025.04.09.647826}, year = {2026}, } @misc{21971, abstract = {A Rust library for analyzing dendritic structures using quadric matrices. This project provides efficient tools for representing dendritic trees, computing quadric error metrics, and visualizing eigenvalue distributions on hexagonal plots. This library implements quadric-based geometric analysis of dendritic structures, commonly found in neuroscience applications. Key features include: Tree data structures: Hierarchical vertex and edge representations for dendritic trees Quadric matrices: Computation of quadric error metrics for edges and vertices Visualisation: Hexagonal plot generation using NormPolar transformations Interactive tools: Desktop application with plotting capabilities}, author = {Bleile, Yossi and Cortinovis, Emanuele}, keywords = {quadratics, mathematics, dendrites, geometry, topology}, publisher = {Institute of Science and Technology Austria}, title = {{Quadrix}}, doi = {10.15479/AT-ISTA-21971}, year = {2026}, } @article{21981, abstract = {For Hamiltonian actions of semidirect products G = FxH, we study 2-cocycles arising from residual Hamiltonian actions of F on Hamiltonian reductions for H. The motivation comes from the study of Teichmüller spaces for surfaces with boundary, which carry Hamiltonian actions of the Virasoro algebra. In this paper, we give a general setup for the problem, and we suggest an easier way to obtain the Gelfand-Fuchs 2-cocycles for Hamiltonian actions on Teichmüller spaces.}, author = {Goncharov, Viacheslav}, issn = {1879-1662}, journal = {Journal of Geometry and Physics}, publisher = {Elsevier}, title = {{An easier way to compute 2-cocycles coming from a reduction for semidirect products}}, doi = {10.1016/j.geomphys.2026.105878}, volume = {227}, year = {2026}, } @article{20328, abstract = {We consider the standard overlap (math formular) of any bi-orthogonal family of left and right eigenvectors of a large random matrix X with centred i.i.d. entries and we prove that it decays as an inverse second power of the distance between the corresponding eigenvalues. This extends similar results for the complex Gaussian ensemble from Bourgade and Dubach [15], as well as Benaych-Georges and Zeitouni [13], to any i.i.d. matrix ensemble in both symmetry classes. As a main tool, we prove a two-resolvent local law for the Hermitisation of X uniformly in the spectrum with optimal decay rate and optimal dependence on the density near the spectral edge.}, author = {Cipolloni, Giorgio and Erdös, László and Xu, Yuanyuan}, issn = {0022-1236}, journal = {Journal of Functional Analysis}, number = {1}, publisher = {Elsevier}, title = {{Optimal decay of eigenvector overlap for non-Hermitian random matrices}}, doi = {10.1016/j.jfa.2025.111180}, volume = {290}, year = {2026}, } @article{20422, abstract = {We show that if n is odd and p>=Clog n/n, then with high probability Hamilton cycles in G(n,p) span its cycle space. More generally, we show this holds for a class of graphs satisfying certain natural pseudorandom properties. The proof is based on a novel idea of parity-switchers, which can be thought of as analogues of absorbers in the context of cycle spaces. As another application of our method, we show that Hamilton cycles in a near-Dirac graph G, that is, a graph G with odd n vertices and minimum degree n/2+C for sufficiently large constant C, span its cycle space. }, author = {Christoph, Micha and Nenadov, Rajko and Petrova, Kalina H}, issn = {1096-0902}, journal = {Journal of Combinatorial Theory Series B}, pages = {254--267}, publisher = {Elsevier}, title = {{The Hamilton space of pseudorandom graphs}}, doi = {10.1016/j.jctb.2025.09.002}, volume = {176}, year = {2026}, } @article{20456, abstract = {Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications.}, author = {Biswas, Ranita and Cultrera di Montesano, Sebastiano and Draganov, Ondrej and Edelsbrunner, Herbert and Saghafian, Morteza}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {24--47}, publisher = {Springer Nature}, title = {{On the size of chromatic Delaunay mosaics}}, doi = {10.1007/s00454-025-00778-7}, volume = {75}, year = {2026}, } @article{20482, abstract = {In his study of graph codes, Alon introduced the concept of the odd-Ramsey number of a family of graphs H in Kn, defined as the minimum number of colours needed to colour the edges of K so that every copy of a graph H E H intersects some colour class in an odd number of edges. In this paper, we focus on complete bipartite graphs. First, we completely resolve the problem when H is the family of all spanning complete bipartite graphs on n vertices. We then focus on its subfamilies, that is, {Kt,n-t : t E T} for a fixed set of integers T c [[n/2]]. We prove that the odd-Ramsey problem is equivalent to determining the maximum dimension of a linear binary code avoiding codewords of given weights, and leverage known results from coding theory to deduce asymptotically tight bounds in our setting. We conclude with bounds for the odd-Ramsey numbers of fixed (that is, non-spanning) complete bipartite subgraphs.}, author = {Boyadzhiyska, Simona and Das, Shagnik and Lesgourgues, Thomas and Petrova, Kalina H}, issn = {0195-6698}, journal = {European Journal of Combinatorics}, publisher = {Elsevier}, title = {{Odd-Ramsey numbers of complete bipartite graphs}}, doi = {10.1016/j.ejc.2025.104235}, volume = {131}, year = {2026}, } @inproceedings{22103, abstract = {Modern AI systems increasingly rely on opaque, highly complex models whose inner workings remain inaccessible even to experts. This opacity creates challenges for trust, accountability, and compliance with emerging regulatory expectations such as the “right to an explanation”. While traditional explainability methods—feature attributions, counterfactuals, surrogate models—and interpretable model classes provide valuable insights for engineers, they often fall short of delivering the contextual, conversational explanations that real users expect. Large Language Models (LLMs) offer a promising new avenue for explanation due to their ability to engage interactively, adapt to user needs, and translate technical outputs into more accessible reasoning. However, their tendencies toward hallucination, conflict avoidance, and oversimplification introduce serious risks when used as explanatory agents. This paper analyzes these opportunities and limitations, examines verification strategies for ensuring explanation fidelity, and situates LLM-generated explanations within broader concerns about public trust. The paper concludes by outlining best practices and future research directions for building robust, verifiable, and human-aligned explanation systems.}, author = {Cano Cordoba, Filip}, booktitle = {Proceedings of the 18th International Conference on Agents and Artificial Intelligence}, isbn = {9789897587962}, issn = {2184-433X}, keywords = {Explainable AI, Large Language Models, Trust in AI}, location = {Marbella, Spain}, pages = {4689--4696}, publisher = {Science and Technology Publications}, title = {{Explaining decisions one conversation at a time: Opportunities and risks of LLMs as explainability assistants}}, doi = {10.5220/0014483200004052}, volume = {5}, year = {2026}, } @article{22116, abstract = {Magnets with isotropic easy-plane symmetry host Goldstone modes that can be leveraged for efficient spin transport. Here, we present a time-resolved optical polarimetry technique that allows us to detect and characterize such low-frequency modes, and use it to observe the Goldstone mode in the multi-Q broken helix phase of EuIn2As2. The strength of our technique comes from the ability to distinguish between nematic and magnetization dynamics in order to yield information about the mode structure, in addition to its frequency. We find that the nearly uniform spin precession characteristic of a Goldstone mode is realized only when a small magnetic field is used to unpin the broken helix from local strain generated during crystal growth. In this regime, the mode frequency scales linearly with the applied field due to the ground state C2z symmetry of the broken helix. Our work shows how optical polarimetry can be used to study the Goldstone modes of complex magnets.}, author = {Liebman-Peláez, A. and Garratt, S. J. and Sunko, Veronika and Sun, Y. and Soh, J. R. and Prabhakaran, D. and Boothroyd, A. T. and Orenstein, J.}, issn = {2469-9969}, journal = {Physical Review B}, number = {22}, publisher = {American Physical Society}, title = {{Observation of a Goldstone mode in the broken helix by time-resolved optical polarimetry}}, doi = {10.1103/b48p-kw5l}, volume = {113}, year = {2026}, } @article{21437, abstract = {Altermagnets are a class of collinear magnets that exhibit non-relativistic spin splitting (NRSS) of electronic bands in the absence of net magnetization. Their potential to generate large spin polarization without spin-orbit coupling has created strong interest in probes that access the underlying order parameter directly. In this Perspective, we show that linear magneto-birefringence (LMB) provides a natural and broadly applicable route to detecting altermagnetic order. Building on the correspondence between the momentum-space structure of NRSS and the ferroic ordering of magnetic multipoles in real space, we demonstrate how $d$-wave and $g$-wave NRSS textures yield distinct LMB responses. We present a symmetry-based framework that identifies the optical geometries and field configurations required to isolate specific multipole components, enabling domain imaging and providing benchmarks for theoretical models of LMB.}, author = {Sunko, Veronika and Orenstein, J.}, issn = {2397-4648}, journal = {npj Quantum Materials}, publisher = {Springer Nature}, title = {{Linear magneto-birefringence as a probe of altermagnetism}}, doi = {10.1038/s41535-026-00901-8}, year = {2026}, } @inproceedings{22146, abstract = {We study differentially private model training with stochastic gradient descent under learning rate scheduling and correlated noise. Although correlated noise, in particular via matrix factorizations, has been shown to improve accuracy, prior theoretical work focused primarily on the prefix-sum workload. That workload assumes a constant learning rate, whereas in practice learning rate schedules are widely used to accelerate training and improve convergence. We close this gap by deriving general upper and lower bounds for a broad class of learning rate schedules in both single- and multi-epoch settings. Building on these results, we propose a learning-rate-aware factorization that achieves improvements over prefix-sum factorizations under both MaxSE and MeanSE error metrics. Our theoretical analysis yields memory-efficient constructions suitable for practical deployment, and experiments on CIFAR-10 and IMDB datasets confirm that schedule-aware factorizations improve accuracy in private training.}, author = {Kalinin, Nikita and Andersson, Joel D}, booktitle = {7th Symposium on Foundations of Responsible Computing}, isbn = {9783959774192}, issn = {1868-8969}, keywords = {differential privacy, machine learning, matrix factorization}, location = {Cambridge, MA; United States}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Learning rate scheduling with matrix factorization for private training}}, doi = {10.4230/LIPIcs.FORC.2026.2}, volume = {368}, year = {2026}, } @article{22145, abstract = {An in-operando electro-intercalation method for the on-chip synthesis of alkali-metal-intercalated materials and their Raman spectroscopic and transport characterization in ultrahigh vacuum (UHV) is developed. We apply this method to synthesize fulleride superconductors via Rb+ intercalation into a C60 film. During the intercalation, we monitor the stoichiometry via UHV-Raman spectroscopy and probe superconductivity via transport measurements. An increase of the superconducting transition temperature from 7.0 K to 14.5 K is observed when the stoichiometry is tuned from Rb2.7C60 to Rb3C60. In our experiment, an ionic Rb+ flux into the host material is induced by an applied electronic current via a Butler–Volmer-type mechanism. Electro-intercalation captivates through improved stoichiometric precision, the ability to smoothly vary stoichiometry via duration of current application, and the absence of a lower limit of the volume of the host material. It represents a powerful concept for the on-chip synthesis of intercalated materials, battery research, and beyond.}, author = {Shchukin, Konstantin P. and Gallego Lacey, Oliver N. and Coquinot, Baptiste and Jakowski, Jacek and Huang, Jingsong and Staudenmayer, Patrik and Falke, Yannic and Pandeya, Ram Prakash and Grüneis, Alexander}, issn = {1936-086X}, journal = {ACS Nano}, keywords = {fulleride, intercalation, alkali metal, superconductivity, Raman}, number = {24}, pages = {17360--17372}, publisher = {American Chemical Society}, title = {{On-chip tuning of superconductivity in fullerides via current-driven Rb+ intercalation}}, doi = {10.1021/acsnano.6c02466}, volume = {20}, year = {2026}, } @article{22141, abstract = {Molecular electrocatalysis is commonly interpreted through electronic descriptors, implicitly treating catalysts as mechanically passive during redox cycling. Yet, electron transfer often imposes structural demands on molecular scaffolds, raising the question of whether internal mechanical constraints can directly regulate access to reactive states and, in turn, catalytic outcomes. Addressing this question has remained challenging because mechanical effects are typically inseparable from changes in composition or electronic structure. Here, we achieve this separation by exploiting two constitutionally identical molecular catalysts whose only distinction is ligand geometry. This minimal geometric variation enables or suppresses intramolecular hydrogen bonding, thereby encoding distinct mechanical constraints that isolate molecular mechanics as a variable in redox accessibility. In the α isomer, molecular constraints impose a mechanically enforced barrier that severely limits access to the reactive redox state. This disrupts the temporal ordering of elementary steps, and diverts reactivity toward competing hydrogen evolution, eroding both selectivity and stability. In contrast, mechanical compliance in the β isomer enables facile access to the redox-active state, allowing CO2 activation to intrinsically outpace water activation and yielding CO selectivities exceeding 92%. Operando spectroscopy and real-time mass spectrometry, combined with computational simulation, directly resolve this mechanically gated reaction sequence as it unfolds. Molecular mechanics thus emerge as determinants that link electron flow to reaction sequencing and catalytic selectivity, revealing that constitutionally similar catalysts can be mechanically, and therefore catalytically, distinct.}, author = {Mendhe, Rahul Mahadeo and Christudas Dargily, Neethu and Kottaichamy, Alagar Raja and Dutt, Shifali and Sk, Mukaddar and Makri Nimbegondi Kotresh, Harish and Ottakam Thotiyl, Musthafa}, issn = {1520-5126}, journal = {Journal of the American Chemical Society}, publisher = {American Chemical Society}, title = {{Mechanical gating of redox access in molecular electrocatalysis}}, doi = {10.1021/jacs.6c02632}, year = {2026}, } @article{22144, abstract = {Most cells polarize and migrate in response to electrical fields. In this issue of Cell, Belliveau et al. identify TMEM154/Galvanin, a receptor that serves as a cellular antenna to sense electrical gradients and guide migration toward the cathode.}, author = {Riedl, Michael and Sixt, Michael K}, issn = {1097-4172}, journal = {Cell}, number = {13}, pages = {3845--3846}, publisher = {Elsevier}, title = {{A new sense for electrical fields}}, doi = {10.1016/j.cell.2026.05.038}, volume = {189}, year = {2026}, } @article{22147, abstract = {Let 1 ≤ k ≤ n and M be a random n × n matrix with independent uniformly random {±1}-entries. We show that there exists an absolute constant c > 0 such that P[rank(M) ≤ n − k] ≤ exp(−cnk). This confirms a well-known prediction in the area, extending a result of Rudelson (who previously proved this same result under the restriction k ≤ √n, via different methods).}, author = {Hunter, Zach and Kwan, Matthew Alan and Sauermann, Lisa and Sawhney, Mehtaab}, issn = {1687-0247}, journal = {International Mathematics Research Notices}, number = {12}, publisher = {Oxford University Press}, title = {{On random matrices with large corank}}, doi = {10.1093/imrn/rnag126}, volume = {2026}, year = {2026}, } @article{22097, abstract = {We consider the cubic defocusing nonlinear Schrödinger equation in one dimension with the nonlinearity concentrated at a single point. We prove global well-posedness in the scaling-critical space L^2(R) and scattering for all such solutions. Moreover, we demonstrate that the same phenomenology holds whenever nonlinear effects are sufficiently concentrated in space.}, author = {Harrop-Griffiths, Benjamin and Killip, Rowan and Visan, Monica}, issn = {1088-6826}, journal = {Proceedings of the American Mathematical Society}, publisher = {American Mathematical Society}, title = {{Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity}}, doi = {10.1090/proc/17760}, year = {2026}, } @article{22229, abstract = {Hippocampal CA3 pyramidal neurons (PNs) form the largest autoassociative network in the mammalian brain. Whether CA3–CA3 recurrent connectivity is genetically preconfigured or environmentally shaped during ongoing memory storage is currently unknown. To address this question, we performed multicellular patch-clamp-based circuit mapping of up to eight CA3 PNs in the mouse hippocampus at multiple postnatal time points (P7–8, P18–25, and P45–50). Here, we show that the hippocampal CA3 network undergoes a developmental transformation from local, dense, and random connectivity to a distributed, sparse, and structured configuration. Thus, sparse and structured connectivity may emerge via experience-dependent mechanisms. In parallel, the strength of single synapses is downregulated; single synaptic events are sufficient to trigger postsynaptic spiking early in development, whereas spatial summation of several inputs is required at later time points. Biologically inspired models of memory storage by Hebbian synaptic plasticity and retrieval via pattern completion suggest that developmental changes improve specific aspects of memory storage and retrieval. Our results imply a developmental transformation of the neuronal code and the memory functions in the hippocampal CA3 network.}, author = {Vargas Barroso, Victor M and Watson, Jake and Navas Olivé, Andrea C and Schlögl, Alois and Jonas, Peter M}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Developmental emergence of sparse and structured synaptic connectivity in the hippocampal CA3 memory circuit}}, doi = {10.1038/s41467-026-71914-x}, volume = {17}, year = {2026}, } @article{22228, abstract = {In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two statistically independent signals in a mixed generalized linear model with Gaussian covariates. Spectral methods are a popular class of estimators which output the top two eigenvectors of a suitable data-dependent matrix. However, despite the wide applicability, their design is still obtained via heuristic considerations, and the number of samples 𝑛 needed to guarantee recovery is superlinear in the signal dimension 𝑑. In this paper, we develop exact asymptotics on spectral methods in the challenging proportional regime in which 𝑛,𝑑 grow large and their ratio converges to a finite constant. This allows us optimize the design of the spectral method, and combine it with a simple linear estimator, to minimize the estimation error. Our characterization exploits a mix of tools from random matrices, free probability, and the theory of approximate message passing algorithms. Numerical simulations for mixed linear regression and phase retrieval demonstrate the advantage enabled by our analysis over existing designs of spectral methods.}, author = {Zhang, Yihan and Mondelli, Marco and Venkataramanan, Ramji}, issn = {2577-0187}, journal = {SIAM Journal on Mathematics of Data Science}, keywords = {spectral estimator, generalized linear models, mixed regression, high-dimensional asymptotics, random matrix theory, approximate message passing (AMP)}, number = {2}, pages = {411--439}, publisher = {Society for Industrial & Applied Mathematics}, title = {{Precise asymptotics for spectral methods in mixed generalized linear models}}, doi = {10.1137/24m1702854}, volume = {8}, year = {2026}, } @misc{21442, author = {Schlögl, Alois}, keywords = {hypocampus, ca3 simulations, modelling}, publisher = {Institute of Science and Technology Austria}, title = {{CA3Simu v1.06 (vargas2026v1)}}, doi = {10.15479/AT-ISTA-21442}, year = {2026}, } @article{22096, abstract = {We prove uniform-in-time a priori Hs bounds for solutions to the intermediate longwave equation posed both on the line and on the circle, covering the range −1 2 < s ≤ 0. Additionally, we prove that the set of orbits emanating from a bounded and equicontinuous set in Hs is also bounded and equicontinuous in Hs . Our proof is based on the identification of a suitable Lax pair formulation for the intermediate long wave equation.}, author = {Harrop-Griffiths, B. and Killip, R. and Visan, Monica}, issn = {1424-3202}, journal = {Journal of Evolution Equations}, number = {3}, publisher = {Springer Nature}, title = {{A priori bounds and equicontinuity of orbits for the intermediate long wave equation}}, doi = {10.1007/s00028-026-01228-4}, volume = {26}, year = {2026}, }