@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}, } @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{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}, } @article{12662, abstract = {Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their combinations. Multi-objective learning offers a natural framework for handling such problems without having to commit to early trade-offs. Surprisingly, statistical learning theory so far offers almost no insight into the generalization properties of multi-objective learning. In this work, we make first steps to fill this gap: We establish foundational generalization bounds for the multi-objective setting as well as generalization and excess bounds for learning with scalarizations. We also provide the first theoretical analysis of the relation between the Pareto-optimal sets of the true objectives and the Pareto-optimal sets of their empirical approximations from training data. In particular, we show a surprising asymmetry: All Pareto-optimal solutions can be approximated by empirically Pareto-optimal ones, but not vice versa.}, author = {Súkeník, Peter and Lampert, Christoph}, issn = {1433-3058}, journal = {Neural Computing and Applications}, pages = {24669–24683}, publisher = {Springer Nature}, title = {{Generalization in multi-objective machine learning}}, doi = {10.1007/s00521-024-10616-1}, volume = {37}, year = {2025}, } @inproceedings{20820, abstract = {The high computational costs of large language models (LLMs) have led to a flurry of research on LLM compression, via methods such as quantization, sparsification, or structured pruning. A new frontier in this area is given by dynamic, non-uniform compression methods, which adjust the compression levels (e.g., sparsity) per-block or even per-layer in order to minimize accuracy loss, while guaranteeing a global compression threshold. Yet, current methods rely on estimating the "importance" of a given layer, implicitly assuming that layers contribute independently to the overall compression error. We begin from the motivating observation that this independence assumption does not generally hold for LLM compression: pruning a model further may even significantly recover performance. To address this, we propose EvoPress, a novel evolutionary framework for dynamic LLM compression. By formulating dynamic compression as a general optimization problem, EvoPress identifies optimal compression profiles in a highly efficient manner, and generalizes across diverse models and compression techniques. Via EvoPress, we achieve state-of-the-art performance for dynamic compression of Llama, Mistral, and Phi models, setting new benchmarks for structural pruning (block/layer dropping), unstructured sparsity, and quantization with dynamic bitwidths.}, author = {Sieberling, Oliver and Kuznedelev, Denis and Kurtic, Eldar and Alistarh, Dan-Adrian}, booktitle = {42nd International Conference on Machine Learning}, issn = {2640-3498}, location = {Vancouver, Canada}, pages = {55556--55590}, publisher = {ML Research Press}, title = {{EvoPress: Accurate dynamic model compression via evolutionary search}}, volume = {267}, year = {2025}, } @inproceedings{20821, abstract = {Modern deep neural networks exhibit heterogeneity across numerous layers of various types such as residuals, multi-head attention, etc., due to varying structures (dimensions, activation functions, etc.), distinct representation characteristics, which impact predictions. We develop a general layer-wise quantization framework with tight variance and code-length bounds, adapting to the heterogeneities over the course of training. We then apply a new layer-wise quantization technique within distributed variational inequalities (VIs), proposing a novel Quantized Optimistic Dual Averaging (QODA) algorithm with adaptive learning rates, which achieves competitive convergence rates for monotone VIs. We empirically show that QODA achieves up to a 150% speedup over the baselines in end-to-end training time for training Wasserstein GAN on 12+GPUs.}, author = {Nguyen, Anh Duc and Markov, Ilia and Wu, Frank Zhengqing and Ramezani-Kebrya, Ali and Antonakopoulos, Kimon and Alistarh, Dan-Adrian and Cevher, Volkan}, booktitle = {42nd International Conference on Machine Learning}, issn = {2640-3498}, location = {Vancouver, Canada}, pages = {46026--46072}, publisher = {ML Research Press}, title = {{Layer-wise quantization for quantized optimistic dual averaging}}, volume = {267}, year = {2025}, } @article{20839, abstract = {For every couple of Hausdorff functions ψ and φ verifying some mild assumptions, there exists a compact subset K of the Baire space such that the φ-Hausdorff measure and the ψ-packing measure on K are both finite and positive. Such examples are then embedded in any infinite dimensional Banach space to answer positively a question of Fan on the existence of metric spaces with arbitrary scales.}, author = {Helfter, Mathieu}, issn = {2308-1317}, journal = {Journal of Fractal Geometry}, publisher = {EMS Press}, title = {{Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces}}, doi = {10.4171/jfg/177}, year = {2025}, } @misc{20842, abstract = {Probing the possibility of entanglement generation through gravity offers a path to tackle the question of whether gravitational fields possess a quantum mechanical nature. A potential realization necessitates systems with low-frequency dynamics at an optimal mass scale, for which the microgram-to-milligram range is a strong contender. Here, after refining a figure-of-merit for the problem, we present a 1-milligram torsional pendulum operating at 18 Hz. We demonstrate laser cooling its motion from room temperature to 240~microkelvins, surpassing by over 20-fold the coldest motions attained for oscillators ranging from micrograms to kilograms. We quantify and contrast the utility of the current approach with other platforms. The achieved performance and large improvement potential highlight milligram-scale torsional pendulums as a powerful platform for precision measurements relevant to future studies at the quantum-gravity interface.}, author = {Agafonova, Sofya}, publisher = {Institute of Science and Technology Austria}, title = {{Research Data for: 'One-milligram torsional pendulum toward experiments at the quantum-gravity interface'}}, doi = {10.15479/AT-ISTA-20842}, year = {2025}, } @inproceedings{20844, abstract = {We introduce and construct a new proof system called Non-interactive Arguments of Knowledge or Space (NArKoS), where a space-bounded prover can convince a verifier they know a secret, while having access to sufficient space allows one to forge indistinguishable proofs without the secret. An application of NArKoS are space-deniable proofs, which are proofs of knowledge (say for authentication in access control) that are sound when executed by a lightweight device like a smart-card or an RFID chip that cannot have much storage, but are deniable (in the strong sense of online deniability) as the verifier, like a card reader, can efficiently forge such proofs. We construct NArKoS in the random oracle model using an OR-proof combining a sigma protocol (for the proof of knowledge of the secret) with a new proof system called simulatable Proof of Transient Space (simPoTS). We give two different constructions of simPoTS, one based on labelling graphs with high pebbling complexity, a technique used in the construction of memory-hard functions and proofs of space, and a more practical construction based on the verifiable space-hard functions from TCC’24 where a prover must compute a root of a sparse polynomial. In both cases, the main challenge is making the proofs efficiently simulatable.}, author = {Dujmovic, Jesko and Günther, Christoph Ullrich and Pietrzak, Krzysztof Z}, booktitle = {23rd International Conference on Theory of Cryptography}, isbn = {9783032122896}, issn = {1611-3349}, location = {Aarhus, Denmark}, pages = {171--202}, publisher = {Springer Nature}, title = {{Space-deniable proofs}}, doi = {10.1007/978-3-032-12290-2_6}, volume = {16271}, year = {2025}, } @inproceedings{20845, abstract = {We develop new attacks against the Evasive LWE family of assumptions, in both the public and private-coin regime. To the best of our knowledge, ours are the first attacks against Evasive LWE in the public-coin regime, for any instantiation from the family. Our attacks are summarized below. Public-Coin Attacks. 1.The recent work by Hseih, Lin and Luo [17] constructed the first Attribute Based Encryption (ABE) for unbounded depth circuits by relying on the “circular” evasive LWE assumption. This assumption has been popularly considered as a safe, public-coin instance of Evasive LWE in contrast to its “private-coin” cousins (for instance, see [10, 11]). We provide the first attack against this assumption, challenging the widely held belief that this is a public-coin assumption. 2. We demonstrate a counter-example against vanilla public-coin evasive LWE by Wee [26] in an unnatural parameter regime. Our attack crucially relies on the error in the pre-condition being larger than the error in the post-condition, necessitating a refinement of the assumption. Private-Coin Attacks. 1. The recent work by Agrawal, Kumari and Yamada [2] constructed the first functional encryption scheme for pseudorandom functionalities (PRFE) and extended this to obfuscation for pseudorandom functionalities (PRIO) [4] by relying on private-coin evasive LWE. We provide a new attack against the assumption stated in the first posting of their work (subsequently refined to avoid these attacks). 2. The recent work by Branco et al. [8] (concurrently to [4]) provides a construction of obfuscation for pseudorandom functionalities by relying on private-coin evasive LWE. We provide a new attack against their stated assumption. 3. Branco et al. [8] showed that there exist contrived, “self-referential” classes of pseudorandom functionalities for which pseudorandom obfuscation cannot exist. We extend their techniques to develop an analogous result for pseudorandom functional encryption. While Evasive LWE was developed to specifically avoid “zeroizing attacks”, our work shows that in certain settings, such attacks can still apply.}, author = {Agrawal, Shweta and Modi, Anuja and Yadav, Anshu and Yamada, Shota}, booktitle = {23rd International Conference on Theory of Cryptography}, isbn = {9783032122926}, issn = {1611-3349}, location = {Aarhus, Denmark}, pages = {259--290}, publisher = {Springer Nature}, title = {{Zeroizing attacks against evasive and circular evasive LWE}}, doi = {10.1007/978-3-032-12293-3_9}, volume = {16269}, year = {2025}, } @inproceedings{20846, abstract = {CVRFs are PRFs that unify the properties of verifiable and constrained PRFs. Since they were introduced concurrently by Fuchsbauer and Chandran-Raghuraman-Vinayagamurthy in 2014, it has been an open problem to construct CVRFs without using heavy machinery such as multilinear maps, obfuscation or functional encryption. We solve this problem by constructing a prefix-constrained verifiable PRF that does not rely on the aforementioned assumptions. Essentially, our construction is a verifiable version of the Goldreich-Goldwasser-Micali PRF. To achieve verifiability we leverage degree-2 algebraic PRGs and bilinear groups. In short, proofs consist of intermediate values of the Goldreich-Goldwasser-Micali PRF raised to the exponents of group elements. These outputs can be verified using pairings since the underlying PRG is of degree 2. We prove the selective security of our construction under the Decisional Square Diffie-Hellman (DSDH) assumption and a new assumption, which we dub recursive Decisional Diffie-Hellman (recursive DDH). We prove the soundness of recursive DDH in the generic group model assuming the hardness of the Multivariate Quadratic (MQ) problem and a new variant thereof, which we call MQ+. Last, in terms of applications, we observe that our CVRF is also an exponent (C)VRF in the plain model. Exponent VRFs were recently introduced by Boneh et al. (Eurocrypt’25) with various applications to threshold cryptography in mind. In addition to that, we give further applications for prefix-CVRFs in the blockchain setting, namely, stake-pooling and compressible randomness beacons.}, author = {Brandt, Nicholas and Cueto Noval, Miguel and Günther, Christoph Ullrich and Ünal, Akin and Wohnig, Stella}, booktitle = {23rd International Conference on Theory of Cryptography}, isbn = {9783032122896}, issn = {1611-3349}, location = {Aarhus, Denmark}, pages = {478--511}, publisher = {Springer Nature}, title = {{Constrained verifiable random functions without obfuscation and friends}}, doi = {10.1007/978-3-032-12290-2_16}, volume = {16271}, year = {2025}, } @article{20847, abstract = {We report on an experimental active matter system with motion restricted to four cardinal directions. Our particles are magnetite-doped colloidal spheres driven by the Quincke electrorotational instability. The absence of a magnetic field (|𝑩|=0) leads to circular trajectories interspersed with short spontaneous runs. Intermediate fields (|𝑩|≲20mT) linearize the motion along the axis perpendicular to 𝑩. At high magnetic fields, we observe the surprising emergence of a second, distinct linearization along the axis parallel to 𝑩. With numerical simulations, we show that this behavior can be explained by anisotropic magnetic susceptibility.}, author = {Fitzgerald, Eavan and Clavaud, Cécile and Das, Debasish and Lenton, Isaac C and Waitukaitis, Scott R}, issn = {2470-0053}, journal = {Physical Review E}, number = {6}, publisher = {American Physical Society}, title = {{Rolling at right angles: Magnetic anisotropy enables dual-anisotropic active matter}}, doi = {10.1103/1ss8-31rb}, volume = {112}, year = {2025}, } @article{20848, abstract = {Genetic variation that influences complex disease susceptibility is introduced into the population by mutation and removed by natural selection and genetic drift. This mutation–selection–drift balance (MSDB) shapes the prevalence of a disease and its genetic architecture. To date, however, MSDB has been modeled only for monogenic (Mendelian) diseases. Here, we develop an MSDB model for complex disease susceptibility: we assume that genotype relates to disease risk according to the canonical liability threshold model and that the selection on variants affecting risk stems from the fitness cost of the disease. We focus on diseases that are highly polygenic, entail a substantial fitness cost, and are neither extremely common in the population nor exceedingly rare. The comparison of model predictions with genome-wide association studies and other observations in humans indicates that common genetic variation affecting complex disease susceptibility is little affected by directional selection and instead shaped by pleiotropic stabilizing selection on other traits. In turn, directional selection may exert a more substantial effect on rare, large-effect variants. Our results also suggest that current estimates of disease heritability are likely biased. The model thus provides a better understanding of the evolutionary processes that shape the architecture and prevalence of complex diseases.}, author = {Berg, Jeremy J. and Li, Xinyi and Riall, Kellen and Hayward, Laura and Sella, Guy}, issn = {1943-2631}, journal = {Genetics}, number = {4}, publisher = {Oxford University Press}, title = {{Mutation–selection–drift balance models of complex diseases}}, doi = {10.1093/genetics/iyaf220}, volume = {231}, year = {2025}, }