@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}, } @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}, } @article{22101, abstract = {Evolutionary biology examines how the genetic and phenotypic composition of populations changes over time. An important goal is to determine the fixation probability of a single advantageous mutant that arises in a homogeneous population of N residents. Many real populations experience environmental gradients that cause mutations to be beneficial in some spatial regions but harmful in others. Here, we study the fixation probability of a mutant placed on a simple one-dimensional spatial structure that experiences such a gradient. The mutant’s fitness varies linearly from1 − s to 1 + s, whereas the resident fitness is constant and equal to 1. The existing literature suggests that such heterogeneity in the mutant’s fitness should lead to a decrease in its fixation probability. However, in this work, we find that small, non-negligible gradients (s < 1=√N) substantially increase the fixation probability,while larger gradients (s > (log N)/√N) substantially decrease it.Moreover, we quantify the strength of this phenomenon analytically and we precisely delimit the range of the gradients for which it occurs. Our computer simulations closely match those findings. Altogether, our results indicate that subjecting a simple population structure to natural environmental conditions can produce strong counterintuitive effects.}, author = {Svoboda, Jakub and Nemati, Hossein and Tkadlec, Josef and Kaveh, Kamran and Chatterjee, Krishnendu}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{The effect of the fitness gradient on fixation probability}}, doi = {10.1038/s41467-026-71777-2}, volume = {17}, 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{22105, abstract = {Protein conformational energy landscapes are shaped not only by intramolecular interactions but also by their environment. In protein crystals and protein–protein complexes, intermolecular contacts alter this energy landscape, but the exact nature of this alteration is difficult to decipher. Understanding how the crystal lattice affects protein dynamics is crucial for crystallography-based studies of motion, yet its influence on collective motions remains unclear. Aromatic ring flips in the hydrophobic core represent sensitive probes of such dynamics. Here, we compare the kinetics of aromatic ring flips in the protein GB1 in crystals, in complex with its binding partner IgG, and in solution, combining advanced isotope labelling with quantitative NMR methods. We show that rings in the core flip nearly a thousand times less frequently in crystals than in solution. Enhanced-sampling molecular dynamics simulations, based on a crystal structure of a GB1 variant reported in this work, reproduce these elevated barriers and reveal how the crystal restrains motions.}, author = {Becker, Lea Marie and Fu, Haohao and Tatman, Benjamin and Dreydoppel, Matthias and Kapitonova, Anna and Balazs, Daniel and Weininger, Ulrich and Engilberge, Sylvain and Chipot, Christophe and Schanda, Paul}, issn = {17554349}, journal = {Nature Chemistry}, publisher = {Springer Nature}, title = {{Aromatic ring flips reveal reshaping of protein dynamics in crystals and complexes}}, doi = {10.1038/s41557-026-02155-0}, year = {2026}, } @misc{21145, abstract = {Protein conformational energy landscapes are shaped not only by intramolecular interactions but also by their environment. In protein crystals and protein-protein complexes, intermolecular contacts alter this energy landscape, but the exact nature of this alteration is difficult to decipher. Understanding how the crystal lattice affects protein dynamics is crucial for crystallography-based studies of motion, yet its influence on collective motions remains unclear. Aromatic ring flips in the hydrophobic core represent sensitive probes of such dynamics. Here, we compare the kinetics of aromatic ring flips in the protein GB1 in crystals, in complex with its binding partner IgG, and in solution, combining advanced isotope labeling with quantitative NMR methods. We show that rings in the core flip nearly a thousand times less frequently in crystals than in solution. Enhanced-sampling molecular dynamics simulations, based on a new crystal structure, reproduce these elevated barriers and reveal how the crystal restrains motions. }, author = {Becker, Lea Marie and Schanda, Paul and Chipot, Christophe}, publisher = {Institute of Science and Technology Austria}, title = {{Additional Data for "Aromatic Ring Flips Reveal Reshaping of Protein Dynamics in Crystals and Complexes"}}, doi = {10.15479/AT-ISTA-21145}, 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{22148, abstract = {How the twin-arginine translocase (Tat) system transports fully folded substrate proteins across cellular membranes without disrupting membrane integrity has been a fundamental question in cell biology for decades. The Tat system, found in prokaryotes and plant organelles, recognizes a cargo signal peptide via a conserved twin-arginine motif. The multi-subunit Tat complex facilitates the proton-motive-force-dependent translocation process, yet its overall architecture has remained unknown. Here, we present the cryo-electron microscopy (cryo-EM) structure of the Escherichia coli (E. coli) trimeric TatB₃C₃ complex with bound substrate SufI, assembled in vivo. The complex adopts an unusual, wide-open, bowl-shaped architecture with a polar inner cavity. Unexpectedly, the cargo is engaged in a dual-contact mode: while the signal peptide binds inside one TatBC unit, the folded domain docks tightly onto an adjacent unit, possibly performing a proofreading function. This structure provides a mechanistic framework for substrate engagement and suggests the direct involvement of the entire Tat complex in substrate translocation.}, author = {Zhao, Ziyu and Sazanov, Leonid A}, issn = {1097-4164}, journal = {Molecular Cell}, publisher = {Elsevier}, title = {{Structure of E. Coli twin-arginine translocase (Tat) complex with bound cargo}}, doi = {10.1016/j.molcel.2026.05.026}, year = {2026}, } @inproceedings{22007, abstract = {Truncation of cryptographic outputs is a technique that was recently introduced in Baldimtsi et al. [Foteini Baldimtsi et al., 2022]. The general idea is to try out many inputs to some cryptographic algorithm until the output (e.g. a public-key or some hash value) falls into some sparse set and thus can be compressed: by trying out an expected 2^k different inputs one will find an output that starts with k zeros. Using such truncation one can for example save substantial gas fees on Blockchains where storing values is very expensive. While [Foteini Baldimtsi et al., 2022] show that truncation preserves the security of the underlying primitive, they only consider a setting without preprocessing. In this work we show that lower bounds on the time-space tradeoff for inverting random functions and permutations also hold with truncation, except for parameters ranges where the bound fails to hold for "trivial" reasons. Concretely, it’s known that any algorithm that inverts a random function or permutation with range N making T queries and using S bits of auxiliary input must satisfy S⋅ T ≥ Nlog N. This lower bound no longer holds in the truncated setting where one must only invert a challenge from a range of size N/2^k, as now one can simply save the replies to all N/2^k challenges, which requires S = log N⋅ N /2^k bits and allows to invert with T = 1 query. We show that with truncation, whenever S is somewhat smaller than the log N⋅ N /2^k bits required to store the entire truncated function table, the known S⋅ T ≥ Nlog N lower bound applies.}, author = {Pietrzak, Krzysztof Z and Wang, Pengxiang}, booktitle = {6th Conference on Information-Theoretic Cryptography}, isbn = {9783959773850}, issn = {1868-8969}, keywords = {Time-Space Lower Bounds, Blockchains}, location = {Santa Barbara, CA, United States}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Time-space tradeoffs of truncation with preprocessing}}, doi = {10.4230/LIPIcs.ITC.2025.4}, volume = {343}, year = {2025}, } @article{22032, abstract = {We prove that the focusing and defocusing continuum Calogero–Moser models are well-posed in the scaling-critical space L^2+(R). In the focusing case, this requires solutions to have mass less than that of the soliton.}, author = {Killip, Rowan and Laurens, Thierry and Visan, Monica}, issn = {2692-3688}, journal = {Communications of the American Mathematical Society}, number = {7}, pages = {284--320}, publisher = {American Mathematical Society}, title = {{Scaling-critical well-posedness for continuum Calogero–Moser models on the line}}, doi = {10.1090/cams/48}, volume = {5}, year = {2025}, } @article{22036, abstract = {We prove dispersive decay, pointwise in time, for solutions to the mass-critical nonlinear Schrödinger equation in spatial dimensions d= 1, 2, 3.}, author = {Fan, Chenjie and Killip, Rowan and Visan, Monica and Zhao, Zehua}, issn = {1432-1823}, journal = {Mathematische Zeitschrift}, publisher = {Springer Nature}, title = {{Dispersive decay for the mass-critical nonlinear Schrödinger equation}}, doi = {10.1007/s00209-025-03821-8}, volume = {311}, year = {2025}, } @article{12311, abstract = {In this note, we prove a formula for the cancellation exponent kv,n between division polynomials ψn and ϕn associated with a sequence {nP}n∈N of points on an elliptic curve E defined over a discrete valuation field K. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields.}, author = {Naskręcki, Bartosz and Verzobio, Matteo}, issn = {1473-7124}, journal = {Proceedings of the Royal Society of Edinburgh Section A: Mathematics}, keywords = {Elliptic curves, Néron models, division polynomials, height functions, discrete valuation rings}, number = {5}, pages = {1646--1660}, publisher = {Cambridge University Press}, title = {{Common valuations of division polynomials}}, doi = {10.1017/prm.2024.7}, volume = {155}, year = {2025}, }