@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}, } @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}, } @inproceedings{22119, author = {Muñoz Hermosilla, José M and Miles, Evan and McCarthy, Michael and Melo Velasco, Juan Vicente and Hardmeier, Florian and GANTAYAT, PRATEEK and Fontrodona-Bach, Adrià and Jouvet, Guillaume and Pellicciotti, Francesca}, booktitle = {EGU General Assembly 2026}, location = {Vienna, Austria & Virtual}, publisher = {European Geosciences Union}, title = {{Constraining debris input to Oberaletsch Glacier using ensemble-based Lagrangian modelling}}, doi = {10.5194/egusphere-egu26-19367}, year = {2026}, } @inproceedings{22245, abstract = {A single-commodity congestion approximator for a graph is a compact data structure that approximately predicts the edge congestion required to route any set of single-commodity flow demands in a network. A hierarchical congestion approximator (HCA) consists of a laminar family of cuts in the graph and has numerous applications in approximating cut and flow problems in graphs, designing efficient routing schemes, and managing distributed networks. There is a tradeoff between the running time for computing an HCA and its approximation quality. The best polynomial-time construction in an n-node graph gives an HCA with approximation quality O(log1.5n loglogn). Among near-linear time algorithms, the best previous result achieves approximation quality O(log4 n). We improve upon the latter result by giving the first near-linear time algorithm for computing an HCA with approximation quality O(log2 n loglogn). Additionally, our algorithm can be implemented in the parallel setting with polylogarithmic span and near-linear work, achieving the same approximation quality. This improves upon the best previous such algorithm, which has an O(log9n) approximation quality. We also present a lower bound of Ω(logn) for the approximation guarantee of hierarchical congestion approximators. Crucial for achieving a near-linear running time is a new partitioning routine that, unlike previous such routines, manages to avoid recursing on large subgraphs. To achieve the improved approximation quality, we introduce the new concept of border routability of a cut and provide an improved sparsest cut oracle for general vertex weights.}, author = {Henzinger, Monika H and Münk, Robin and Räcke, Harald}, booktitle = {58th Annual ACM Symposium on Theory of Computing}, isbn = {9798400725364}, issn = {0737-8017}, keywords = {Congestion Approximators, Hierarchical Graph Decompositions}, location = {Salt Lake City, UT, United States}, pages = {1417--1428}, publisher = {Association for Computing Machinery}, title = {{An improved quality hierarchical congestion approximator in near-linear time}}, doi = {10.1145/3798129.3800851}, year = {2026}, } @article{22241, abstract = {We revisit the computation of 3D generalized winding numbers, a useful measure for inside-outside classification on triangle meshes with gaps, self-intersections, and open boundaries. At the core of our new method is an analytical reduction of the surface integral that defines the winding number, resulting in a single ray-mesh intersection test and an elementary sum over boundary edges per evaluation. This construction is orders of magnitude more efficient than the state of the art in practice, which we show in an extensive performance benchmark. Conveniently, the method also reduces to the best-available asymptotic complexity in the worst case, and it introduces no approximations apart from floating-point errors. Our algorithm is conceptually simple to understand, straightforward to implement and debug, and it works reliably even on extremely noisy and corrupt input geometry.}, author = {Xie, Peiyuan and Hafner, Christian and Wojtan, Christopher J}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Fast and exact winding numbers for triangle meshes}}, doi = {10.1145/3811339}, volume = {45}, year = {2026}, } @article{22248, abstract = {Many living and artificial systems improve their fitness or performance by adapting to changing environments or diverse training data. However, it remains unclear how environmental variation shapes adaptation, what is learned, and when memory of past conditions is retained. Here we show how cyclic environmental change can produce robust memory. Using a model athermal disordered solid trained by inverse design to attain target elastic properties over a prescribed range, we find that the system evolves toward a marginally absorbing manifold (MAM), meaning that training is reversible within the training range but not beyond it, which encodes a memory of that range. We further propose a general mechanism for MAM formation and memory encoding based on discontinuities in the gradient of the trained quantity. These results provide a simple, broadly applicable physical framework for how adaptive systems learn under changing environments and retain memory of past conditions.}, author = {Zu, Mengjie and Goodrich, Carl Peter}, issn = {2835-8279}, journal = {PRX Life}, number = {2}, publisher = {American Physical Society}, title = {{Learning by Training: Emergent physical memory from cyclically tuning disordered sphere packings}}, doi = {10.1103/48k2-cw3b}, volume = {4}, year = {2026}, } @article{22244, abstract = {The sensitivity of a mechanical transducer is ultimately limited by its inherent quantum fluctuations. Here, we use an optically levitated nanoparticle to measure impulsive forces smaller than the particle’s zero-point momentum uncertainty. Our approach relies on reversibly squeezing the levitated particle’s center-of-mass motion to coherently amplify the perturbation. We demonstrate an impulsive-force resolution as small as 6.9  keV/c, a value 0.6 dB below the sensor’s zero-point value.}, author = {Skrabulis, Martynas and Sosa, Martin Colombano and Zambon, Nicola Carlon and Militaru, Andrei and Rossi, Massimiliano and Frimmer, Martin and Novotny, Lukas}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {23}, publisher = {American Physical Society}, title = {{Nanomechanical sensor resolving impulsive forces below its zero-point fluctuations}}, doi = {10.1103/9wzm-3qyb}, volume = {136}, year = {2026}, } @article{22247, abstract = {A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its vertices with colours 1, …, k such that each edge contains a unique maximal colour. Deciding whether an input hypergraph admits LO k-colouring with a fixed number of colours is NP-complete (and in the special case of graphs, LO colouring coincides with the usual graph colouring). Here, we investigate the complexity of approximating the “linearly ordered chromatic number” of a hypergraph. We prove that the following promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between the case that it is LO 3-colourable, and the case that it is not even LO 4-colourable. We prove this result by a combination of algebraic, topological, and combinatorial methods, building on and extending a topological approach for studying approximate graph colouring introduced by Krokhin, Opršal, Wrochna, and Živný (2023).}, author = {Filakovský, Marek and Nakajima, Tamio Vesa and Opršal, Jakub and Tasinato, Gianluca and Wagner, Uli}, issn = {1942-3462}, journal = {ACM Transactions on Computation Theory}, keywords = {Constraint satisfaction problem, hypergraph colouring, promise problem, topological methods}, number = {2}, publisher = {Association for Computing Machinery}, title = {{Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs}}, doi = {10.1145/3779121}, volume = {18}, year = {2026}, } @inproceedings{22246, abstract = {In this paper we construct distance sketches for intersection graphs of arbitrary path-connected regions in the plane (known as the string graphs) in the constant and 1+ε distortion regimes. Furthermore, the distance sketches themselves are planar graphs. First, we show that every unweighted string graph G has an O(1)-distortion planar emulator: that is, there exists an edge-weighted planar graph H containing every vertex in G, such that every pair of vertices (u,v) satisfies δG(u,v) ≤ δH(u,v) ≤ O(1) · δG(u,v). Furthermore, we show that for any constant ε > 0, there is an edge-weighted planar graph H′ such that every pair of vertices (u,v) satisfies δG(u,v) ≤ δH′(u,v) ≤ (1+ε) · δG(u,v) + O(ε−4polylogn). No previous constructions of sparse distance sketches were known even for intersection graphs of simple shapes like axis-parallel rectangles or fat convex polygons. As applications, we construct the first (1+ε, +O(1)) mixed-distortion tree cover and distance oracle for arbitrary string graphs, as well as the first additive +(εΔ+O(1))-distortion embedding of string graphs G with diameter Δ into graphs of constant treewidth O(ε−4).}, author = {Chang, Hsien Chih and Conroy, Jonathan and Tan, Zihan and Zheng, Da Wei}, booktitle = {58th Annual ACM Symposium on Theory of Computing}, isbn = {9798400725364}, issn = {0737-8017}, location = {Salt Lake City, UT, United States}, pages = {2140--2151}, publisher = {Association for Computing Machinery}, title = {{Cutting planarians: Planar emulators for string graphs}}, doi = {10.1145/3798129.3800917}, year = {2026}, }