@inproceedings{19010, abstract = {Causal representation learning aims at recovering latent causal variables from high-dimensional observations to solve causal downstream tasks, such as predicting the effect of new interventions or more robust classification. A plethora of methods have been developed, each tackling carefully crafted problem settings that lead to different types of identifiability. The folklore is that these different settings are important, as they are often linked to different rungs of Pearl's causal hierarchy, although not all neatly fit. Our main contribution is to show that many existing causal representation learning approaches methodologically align the representation to known data symmetries. Identification of the variables is guided by equivalence classes across different "data pockets" that are not necessarily causal. This result suggests important implications, allowing us to unify many existing approaches in a single method that can mix and match different assumptions, including non-causal ones, based on the invariances relevant to our application. It also significantly benefits applicability, which we demonstrate by improving treatment effect estimation on real-world high-dimensional ecological data. Overall, this paper clarifies the role of causality assumptions in the discovery of causal variables and shifts the focus to preserving data symmetries.}, author = {Yao, Dingling and Rancati, Dario and Cadei, Riccardo and Fumero, Marco and Locatello, Francesco}, booktitle = {13th International Conference on Learning Representations}, location = {Singapore}, publisher = {ICLR}, title = {{Unifying causal representation learning with the invariance principle}}, year = {2025}, } @article{19012, abstract = {False vacuum decay—the transition from a metastable quantum state to a true vacuum state—plays an important role in quantum field theory and non-equilibrium phenomena such as phase transitions and dynamical metastability. The non-perturbative nature of false vacuum decay and the limited experimental access to this process make it challenging to study, leaving several open questions regarding how true vacuum bubbles form, move and interact. Here we observe quantized bubble formation in real time, a key feature of false vacuum decay dynamics, using a quantum annealer with 5,564 superconducting flux qubits. We develop an effective model that captures both initial bubble creation and subsequent interactions, and remains accurate under dissipation. The annealer reveals coherent scaling laws in the driven many-body dynamics for more than 1,000 intrinsic qubit time units. This work provides a method for investigating false vacuum dynamics of large quantum systems in quantum annealers.}, author = {Vodeb, Jaka and Desaules, Jean-Yves Marc and Hallam, Andrew and Rava, Andrea and Humar, Gregor and Willsch, Dennis and Jin, Fengping and Willsch, Madita and Michielsen, Kristel and Papić, Zlatko}, issn = {1745-2481}, journal = {Nature Physics}, pages = {386--392}, publisher = {Springer Nature}, title = {{Stirring the false vacuum via interacting quantized bubbles on a 5,564-qubit quantum annealer}}, doi = {10.1038/s41567-024-02765-w}, volume = {21}, year = {2025}, } @article{19015, abstract = {When microplastics (MPs) enter water bodies, they undergo various transport processes, including sedimentation, which can be influenced by factors such as particle size, density, and interactions with other particles. Surface waters contain suspended natural particles (e.g., clay and silt), which may impact MP settling rates. Here, we investigated how the presence of suspended sediments (SS) influenced the deposition patterns and rates of MPs in turbid waters. We systematically analyzed the settling velocities of particles, including different MP sizes and SS concentrations, in a plexiglass column with a camera array. For each experimental variant, we collected data on thousands of individual MPs, strengthening the statistical analysis of the particles’ velocities. Simultaneous measurements of the SS flow and MPs trajectories revealed that the SS induced complex flow patterns, with MPs spending more time in downwelling flow regions, thereby accelerating MPs sedimentation. This effect was more pronounced when SS were aggregated. Additionally, we found that smaller MP fragments were more affected by the fluctuations than spheres or larger fragments. Collectively, our results provide valuable data for future MP fate models and help to understand the sedimentation processes of MPs in natural waters, which is crucial for assessing their environmental transport and impact.}, author = {Parrella, Francesco and Brizzolara, Stefano and Holzner, Markus and Mitrano, Denise M.}, issn = {1520-5851}, journal = {Environmental Science and Technology}, number = {4}, pages = {2257--2265}, publisher = {American Chemical Society}, title = {{Microplastics settling in turbid water: Impacts of sediments-induced flow patterns on particle deposition rates}}, doi = {10.1021/acs.est.4c10551}, volume = {59}, year = {2025}, } @article{19017, abstract = {Let f(r)(n;s,k) denote the maximum number of edges in an n-vertex r-uniform hypergraph containing no subgraph with k edges and at most s vertices. Brown, Erdős and Sós [New directions in the theory of graphs (Proc. Third Ann Arbor Conf., Univ. Michigan 1971), pp. 53--63, Academic Press 1973] conjectured that the limit limn→∞n−2f(3)(n;k+2,k) exists for all k. The value of the limit was previously determined for k=2 in the original paper of Brown, Erdős and Sós, for k=3 by Glock [Bull. Lond. Math. Soc. 51 (2019) 230--236] and for k=4 by Glock, Joos, Kim, Kühn, Lichev and Pikhurko [arXiv:2209.14177, accepted by Proc. Amer. Math. Soc.] while Delcourt and Postle [arXiv:2210.01105, accepted by Proc. Amer. Math. Soc.] proved the conjecture (without determining the limiting value). In this paper, we determine the value of the limit in the Brown-Erdős-Sós Problem for k∈{5,6,7}. More generally, we obtain the value of limn→∞n−2f(r)(n;rk−2k+2,k) for all r≥3 and k∈{5,6,7}. In addition, by combining these new values with recent results of Bennett, Cushman and Dudek [arXiv:2309.00182] we obtain new asymptotic values for several generalised Ramsey numbers.}, author = {Glock, Stefan and Kim, Jaehoon and Lichev, Lyuben and Pikhurko, Oleg and Sun, Shumin}, issn = {1496-4279}, journal = {Canadian Journal of Mathematics}, pages = {1--43}, publisher = {Cambridge University Press}, title = {{On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7}}, doi = {10.4153/s0008414x25000021}, year = {2025}, } @article{19018, abstract = {The online semi-random graph process is a one-player game which starts with the empty graph on n vertices. At every round, a player (called Builder) is presented with a vertex v chosen uniformly at random and independently from previous rounds, and constructs an edge of their choice that is incident to v. Inspired by recent advances on the semi-random graph process, we define a family of generalized online semi-random models. We analyse a particular instance that shares similar features with the original semi-random graph process and determine the hitting times of the classical graph properties minimum degree k,k-connectivity, containment of a perfect matching, a Hamiltonian cycle and an H-factor for a fixed graph H possessing an additional tree-like property. Along the way, we derive a few consequences of the famous Aldous-Broder algorithm that may be of independent interest.}, author = {Burova, Sofiya and Lichev, Lyuben}, issn = {0195-6698}, journal = {European Journal of Combinatorics}, publisher = {Elsevier}, title = {{The semi-random tree process}}, doi = {10.1016/j.ejc.2025.104120}, volume = {126}, year = {2025}, } @article{19023, abstract = {Alcohol consumption is an important risk factor for multiple diseases. It is typically assessed via self-report, which is open to measurement error through recall bias. Instead, molecular data such as blood-based DNA methylation (DNAm) could be used to derive a more objective measure of alcohol consumption by incorporating information from cytosine-phosphate-guanine (CpG) sites known to be linked to the trait. Here, we explore the epigenetic architecture of self-reported weekly units of alcohol consumption in the Generation Scotland study. We first create a blood-based epigenetic score (EpiScore) of alcohol consumption using elastic net penalized linear regression. We explore the effect of pre-filtering for CpG features ahead of elastic net, as well as differential patterns by sex and by units consumed in the last week relative to an average week. The final EpiScore was trained on 16,717 individuals and tested in four external cohorts: the Lothian Birth Cohorts (LBC) of 1921 and 1936, the Sister Study, and the Avon Longitudinal Study of Parents and Children (total N across studies > 10,000). The maximum Pearson correlation between the EpiScore and self-reported alcohol consumption within cohort ranged from 0.41 to 0.53. In LBC1936, higher EpiScore levels had significant associations with poorer global brain imaging metrics, whereas self-reported alcohol consumption did not. Finally, we identified two novel CpG loci via a Bayesian penalized regression epigenome-wide association study of alcohol consumption. Together, these findings show how DNAm can objectively characterize patterns of alcohol consumption that associate with brain health, unlike self-reported estimates.}, author = {Bernabeu, Elena and Chybowska, Aleksandra D. and Kresovich, Jacob K. and Suderman, Matthew and Mccartney, Daniel L. and Hillary, Robert F. and Corley, Janie and Valdés-Hernández, Maria Del C. and Maniega, Susana Muñoz and Bastin, Mark E. and Wardlaw, Joanna M. and Xu, Zongli and Sandler, Dale P. and Campbell, Archie and Harris, Sarah E. and Mcintosh, Andrew M. and Taylor, Jack A. and Yousefi, Paul and Cox, Simon R. and Evans, Kathryn L. and Robinson, Matthew Richard and Vallejos, Catalina A. and Marioni, Riccardo E.}, issn = {1868-7083}, journal = {Clinical Epigenetics}, publisher = {Springer Nature}, title = {{Blood-based epigenome-wide association study and prediction of alcohol consumption}}, doi = {10.1186/s13148-025-01818-y}, volume = {17}, year = {2025}, } @article{19024, abstract = {Aqueous two-phase systems (ATPSs), phase-separating solutions of water soluble but mutually immiscible molecular species, offer fascinating prospects for selective partitioning, purification, and extraction. Here, we formulate a general Brownian dynamics based coarse-grained simulation model for an ATPS of two water soluble but mutually immiscible polymer species. Including additional solute species into the model is straightforward, which enables capturing the assembly and partitioning response of, e.g., nanoparticles (NPs), additional macromolecular species, or impurities in the ATPS. We demonstrate that the simulation model captures satisfactorily the phase separation, partitioning, and interfacial properties of an actual ATPS using a model ATPS in which a polymer mixture of dextran and polyethylene glycol (PEG) phase separates, and magnetic NPs selectively partition into one of the two polymeric phases. Phase separation and NP partitioning are characterized both via the computational model and experimentally, under different conditions. The simulation model captures the trends observed in the experimental system and quantitatively links the partitioning behavior to the component species interactions. Finally, the simulation model reveals that the ATPS interface fluctuations in systems with magnetic NPs as a partitioned species can be controlled by the magnetic field at length scales much smaller than those probed experimentally to date.}, author = {Scacchi, Alberto and Rigoni, Carlo and Haataja, Mikko and Timonen, Jaakko V.I. and Sammalkorpi, Maria}, issn = {1095-7103}, journal = {Journal of Colloid and Interface Science}, pages = {1135--1146}, publisher = {Elsevier}, title = {{A coarse-grained model for aqueous two-phase systems: Application to ferrofluids}}, doi = {10.1016/j.jcis.2025.01.256}, volume = {686}, year = {2025}, } @article{19025, abstract = {A complete understanding of the central stars of planetary nebulae (CSPNe) remains elusive. Over the past several decades, time-series photometry of CSPNe has yielded significant results including, but not limited to, discoveries of nearly 100 binary systems, insights into pulsations and winds in young white dwarfs, and studies of stars undergoing very late thermal pulses. We have undertaken a systematic study of optical photometric variability of cataloged CSPNe, using the light curves from the Zwicky Transient Facility (ZTF). By applying appropriate variability metrics, we arrive at a list of 94 highly variable CSPN candidates. Based on the timescales of the light-curve activity, we classify the variables broadly into short- and long-timescale variables. In this first paper in this series, we focus on the former, which is the majority class comprising 83 objects. We report periods for six sources for the first time, and recover several known periodic variables. Among the aperiodic sources, most exhibit a jitter around a median flux with a stable amplitude, and a few show outbursts. We draw attention to WeSb 1, which shows a different kind of variability: prominent deep and aperiodic dips, resembling transits from a dust/debris disk. We find strong evidence for a binary nature of WeSb 1 (possibly an F-type subgiant companion). The compactness of the emission lines and inferred high electron densities make WeSb 1 a candidate for either an EGB 6-type planetary nucleus, or a symbiotic system inside an evolved planetary nebula, both of which are rare objects. To demonstrate further promise with ZTF, we report three additional newly identified periodic sources that do not appear in the list of highly variable sources. Finally, we also introduce a two-dimensional metric space defined by the von Neumann statistics and Pearson Skew and demonstrate its effectiveness in identifying unique variables of astrophysical interest, like WeSb 1.}, author = {Bhattacharjee, Soumyadeep and Kulkarni, S. R. and Kong, Albert K.H. and Tam, M. S. and Bond, Howard E. and El-Badry, Kareem and Caiazzo, Ilaria and Chornay, Nicholas and Graham, Matthew J. and Rodriguez, Antonio C. and Zeimann, Gregory R. and Fremling, Christoffer and Drake, Andrew J. and Werner, Klaus and Rodriguez, Hector and Prince, Thomas A. and Laher, Russ R. and Chen, Tracy X. and Riddle, Reed}, issn = {0004-6280}, journal = {Publications of the Astronomical Society of the Pacific}, number = {2}, publisher = {IOP Publishing}, title = {{Variability of central stars of planetary nebulae with the zwicky transient facility. I. Methods, short-timescale variables, and the unusual nucleus of WeSb 1}}, doi = {10.1088/1538-3873/ada702}, volume = {137}, year = {2025}, } @article{19026, abstract = {The back-action damping of mechanical motion by electromagnetic radiation is typically overwhelmed by internal loss channels unless demanding experimental ingredients such as superconducting resonators, high-quality optical cavities, or large magnetic fields are employed. Here we demonstrate the first room temperature, cavity-free, all-electric device where back-action damping exceeds internal loss, enabled by a mechanically compliant parallel-plate capacitor with a nanoscale plate separation and an aspect ratio exceeding 1,000. The device has 4 orders of magnitude lower insertion loss than a comparable commercial quartz crystal and achieves a position imprecision rivaling optical interferometers. With the help of a back-action isolation scheme, we observe radiative cooling of mechanical motion by a remote cryogenic load. This work provides a technologically accessible route to high-precision sensing, transduction, and signal processing.}, author = {Puglia, Denise and Odessey, Rachel H and Burns, Peter and Luhmann, Niklas and Schmid, Silvan and Higginbotham, Andrew P}, issn = {1530-6992}, journal = {Nano Letters}, number = {7}, pages = {2749--2755}, publisher = {American Chemical Society}, title = {{Room temperature, cavity-free capacitive strong coupling to mechanical motion}}, doi = {10.1021/acs.nanolett.4c05796}, volume = {25}, year = {2025}, } @article{19027, abstract = {Stochastic PDEs of fluctuating hydrodynamics are a powerful tool for the description of fluctuations in many-particle systems. In this paper, we develop and analyze a multilevel Monte Carlo (MLMC) scheme for the Dean–Kawasaki equation, a pivotal representative of this class of SPDEs. We prove analytically and demonstrate numerically that our MLMC scheme provides a significant reduction in computational cost (with respect to a standard Monte Carlo method) in the simulation of the Dean–Kawasaki equation. Specifically, we link this reduction in cost to having a sufficiently large average particle density and show that sizeable cost reductions can be obtained even when we have solutions with regions of low density. Numerical simulations are provided in the two-dimensional case, confirming our theoretical predictions. Our results are formulated entirely in terms of the law of distributions rather than in terms of strong spatial norms: this crucially allows for MLMC speed-ups altogether despite the Dean–Kawasaki equation being highly singular.}, author = {Cornalba, Federico and Fischer, Julian L}, issn = {1095-7170}, journal = {SIAM Journal on Numerical Analysis}, number = {1}, pages = {262--287}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating hydrodynamics}}, doi = {10.1137/23M1617345}, volume = {63}, year = {2025}, } @misc{19033, abstract = {This data set contains the simulation input files, scripts, and figures data belonging to the publication Alberto Scacchi, Carlo Rigoni, Mikko P. Haataja, Jakko V. I. Timonen, and Maria Sammalkorpi, "A Coarse-grained Model for Aqueous Two-phase Systems: Application to Ferrofluids", Journal of Colloids and Interface Science (2025). https://doi.org/10.1016/j.jcis.2025.01.256.}, author = {Scacchi, Alberto}, publisher = {Fairdata}, title = {{2025_SCACCHI_JCIS}}, doi = {10.23729/4fb80194-cdb2-4f49-94f4-f8a87b8e29c1}, year = {2025}, } @article{19035, abstract = {Lagrangian coherent structures (LCSs) are widely recognized as playing a significant role in turbulence dynamics since they can control the transport of mass, momentum or heat. However, the methods used to identify these structures are often based on ambiguous definitions and arbitrary thresholding. While LCSs theory provides precise and frame-indifferent mathematical definitions of coherent structures, some of the commonly used extraction algorithms employed in the literature are still case-specific and involve user-defined parameters. In this study, we present a new, unsupervised extraction algorithm that enables the extraction of rotational LCSs based on Lagrangian average vorticity deviation from an arbitrary 3D velocity field. The algorithm utilizes two alternative methods for the identification of the LCS core (ridge): an unsupervised clustering method and a streamline-based method. In a subsequent step, the ridge curve is parametrized through a pruning procedure of minimum spanning tree graphs. To assess the effectiveness of the algorithm, we test it on two cases: (i) direct numerical simulations of forced homogeneous and isotropic turbulence and (ii) three-dimensional Particle Tracking Velocimetry experiments of a turbulent gravity current.}, author = {Neamtu-Halic, Marius M. and Brizzolara, Stefano and Haller, George and Holzner, Markus}, issn = {0045-7930}, journal = {Computers & Fluids}, publisher = {Elsevier}, title = {{Unsupervised extraction of rotational Lagrangian coherent structures}}, doi = {10.1016/j.compfluid.2025.106558}, volume = {290}, year = {2025}, } @article{19036, abstract = {Neuronal processing of external sensory input is shaped by internally generated top–down information. In the neocortex, top–down projections primarily target layer 1, which contains NDNF (neuron-derived neurotrophic factor)-expressing interneurons and the dendrites of pyramidal cells. Here, we investigate the hypothesis that NDNF interneurons shape cortical computations in an unconventional, layer-specific way, by exerting presynaptic inhibition on synapses in layer 1 while leaving synapses in deeper layers unaffected. We first confirm experimentally that in the auditory cortex, synapses from somatostatin-expressing (SOM) onto NDNF neurons are indeed modulated by ambient Gamma-aminobutyric acid (GABA). Shifting to a computational model, we then show that this mechanism introduces a distinct mutual inhibition motif between NDNF interneurons and the synaptic outputs of SOM interneurons. This motif can control inhibition in a layer-specific way and introduces competition between NDNF and SOM interneurons for dendritic inhibition onto pyramidal cells on different timescales. NDNF interneurons can thereby control cortical information flow by redistributing dendritic inhibition from fast to slow timescales and by gating different sources of dendritic inhibition.}, author = {Naumann, Laura B and Hertäg, Loreen and Müller, Jennifer and Letzkus, Johannes J. and Sprekeler, Henning}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, number = {4}, publisher = {National Academy of Sciences}, title = {{Layer-specific control of inhibition by NDNF interneurons}}, doi = {10.1073/pnas.2408966122}, volume = {122}, year = {2025}, } @article{19037, abstract = {We present a novel, portable sensor platform that enables concurrent monitoring of surface mass and charge density variations at thin biointerfaces. This platform combines a coplanar-gated field-effect transistor (FET) architecture with grating-coupled surface plasmon resonance (SPR), yielding an integrated disposable sensor chip prepared by nanoimprint and maskless photolithography techniques. The sensor chip design is suitable for scalable production and relies on reduced graphene oxide (rGO), serving as the FET’s semiconductor material for the electronic readout, and a metallic gate electrode surface that is corrugated with a multi-diffractive structure for optical probing with resonantly excited surface plasmons. Together with its integration in a compact instrumentation this results in a form factor optimized solution for dual-mode investigations without compromising the optical or electronic sensor performance. A poly-L-lysine (PLL) – based thin linker layer was deployed at the sensor surface to covalently attach azide-conjugated biomolecules by using incorporated “clickable” dibenzocyclooctyne (DBCO) moieties. Interestingly, the dual-mode measurements allow elucidating the role of the globular nature of the PLL chains when increasing the density of DBCO attached to their backbone, leading to PLL folding and internalization of DBCO moieties, and thus reducing the coupling yield for the used DNA oligomers. We envision that this platform can be employed to studying a range of other biointerface architectures and biomolecular interaction phenomena, which are inherently tied to mass and charge density variations.}, author = {Hasler, Roger and Livio, Pietro A. and Bozdogan, Anil and Fossati, Stefan and Hageneder, Simone and Montes-García, Verónica and Movilli, Jacopo and Moazzenzade, Taghi and Loohuis, Luna and Reiner-Rozman, Ciril and Tamayo, Adrián and Fiedler, Christine and Ibáñez, Maria and Kleber, Christoph and Huskens, Jurriaan and Dostalek, Jakub and Samorì, Paolo and Knoll, Wolfgang}, issn = {1558-1748}, journal = {IEEE Sensors Journal}, number = {7}, pages = {10521--10529}, publisher = {IEEE}, title = {{Dual electronic and optical monitoring of biointerfaces by a grating-structured coplanar-gated field-effect transistor}}, doi = {10.1109/jsen.2025.3533113}, volume = {25}, year = {2025}, } @inproceedings{19038, abstract = {Differentially private weighted prefix sum under continual observation is a crucial component in the production-level deployment of private next-word prediction for Gboard, which, according to Google, has over a billion users. More specifically, Google uses a differentially private mechanism to sum weighted gradients in its private follow-the-regularized leader algorithm. Apart from efficiency, the additive error of the private mechanism is crucial as multiplied with the square root of the model’s dimension d (with d ranging up to 10 trillion, for example, Switch Transformers or M6-10T), it determines the accuracy of the learning system. So, any improvement in leading constant matters significantly in practice. In this paper, we show a novel connection between mechanisms for continual weighted prefix sum and a concept in representation theory known as the group matrix introduced in correspondence between Dedekind and Frobenius (Sitzungsber. Preuss. Akad. Wiss. Berlin, 1897) and generalized by Schur (Journal für die reine und angewandte Mathematik, 1904). To the best of our knowledge, this is the first application of group algebra in the analysis of differentially private algorithms. Using this connection, we analyze a class of matrix norms known as factorization norms that give upper and lower bounds for the additive error under general ℓp-norms of the matrix mechanism. This allows us to give 1. the first efficient factorization that matches the best-known non-constructive upper bound on the factorization norm by Mathias (SIAM Journal of Matrix Analysis and Applications, 1993) for the matrix used in Google’s deployment, and also improves on the previous best-known constructive bound of Fichtenberger, Henzinger, and Upadhyay (ICML 2023) and Henzinger, Upadhyay, and Upadhyay (SODA 2023); thereby, partially resolving an open question in operator theory, 2. the first upper bound on the additive error for a large class of weight functions for weighted prefix sum problems, including the sliding window matrix (Bolot, Fawaz, Muthukrishnan, Nikolov, and Taft (ICDT 2013). We also improve the bound on factorizing the striped matrix used for outputting a synthetic graph that approximates all cuts (Fichtenberger, Henzinger, and Upadhyay (ICML 2023)); 3. a general improved upper bound on the factorization norms that depend on algebraic properties of the weighted sum matrices and that applies to a more general class of weighting functions than the ones considered in Henzinger, Upadhyay, and Upadhyay (SODA 2024). Using the known connection between these factorization norms and the ℓp-error of continual weighted sum, we give an upper bound on the ℓp-error for the continual weighted sum problem for p ≥ 2.}, author = {Henzinger, Monika H and Upadhyay, Jalaj}, booktitle = {Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms}, isbn = {979-833131200-8}, issn = {1071-9040}, location = {New Orleans, LA, United States}, pages = {2951 -- 2970}, publisher = {Association for Computing Machinery}, title = {{Improved differentially private continual observation using group algebra}}, doi = {10.1137/1.9781611978322.95}, volume = {5}, year = {2025}, } @article{19039, abstract = {We consider fluctuations of the largest eigenvalues of the random matrix model A + UBU∗ where A and B are N × N deterministic Hermitian (or symmetric) matrices and U is a Haar-distributed unitary (or orthogonal) matrix. We prove that the largest eigenvalue weakly converges to the GUE (or GOE) Tracy–Widom distribution, under mild assumptions on A and B to guarantee that the density of states of the model decays as square root around the upper edge. Our proof is based on the comparison of the Green function along the Dyson Brownian motion starting from the matrix A + UBU∗ and ending at time N−1/3+o(1). As a byproduct of our proof, we also prove an optimal local law for the Dyson Brownian motion up to the constant time scale.}, author = {Ji, Hong Chang and Park, Jaewhi}, issn = {0091-1798}, journal = {The Annals of Probability}, number = {1}, pages = {239 -- 298}, publisher = {Institute of Mathematical Statistics}, title = {{Tracy-Widom limit for free sum of random matrices}}, doi = {10.1214/24-aop1705}, volume = {53}, year = {2025}, } @article{19054, abstract = {This work concerns asymptotical stabilisation phenomena occurring in the moduli space of sections of certain algebraic families over a smooth projective curve, whenever the generic fibre of the family is a smooth projective Fano variety, or not far from being Fano. We describe the expected behaviour of the class, in a ring of motivic integration, of the moduli space of sections of given numerical class. Up to an adequate normalisation, it should converge, when the class of the sections goes arbitrarily far from the boundary of the dual of the effective cone, to an effective element given by a motivic Euler product. Such a principle can be seen as an analogue for rational curves of the Batyrev-Manin-Peyre principle for rational points. The central tool of this article is the property of equidistribution of curves. We show that this notion does not depend on the choice of a model of the generic fibre, and that equidistribution of curves holds for smooth projective split toric varieties. As an application, we study the Batyrev-Manin-Peyre principle for curves on a certain kind of twisted products.}, author = {Faisant, Loïs}, issn = {1944-7833}, journal = {Algebra & Number Theory}, pages = {883--965}, publisher = {Mathematical Sciences Publishers}, title = {{Motivic distribution of rational curves and twisted products of toric varieties}}, doi = {10.2140/ant.2025.19.883}, volume = {19}, year = {2025}, } @unpublished{19055, abstract = {Using the formalism of Cox rings and universal torsors, we prove a decomposition of the Grothendieck motive of the moduli space of morphisms from an arbitrary smooth projective curve to a Mori Dream Space (MDS). For the simplest cases of MDS, that of toric varieties, we use this decomposition to prove an instance of the motivic Batyrev--Manin--Peyre principle for curves satisfying tangency conditions with respect to the boundary divisors, often called Campana curves.}, author = {Faisant, Loïs}, booktitle = {arXiv}, title = {{Motivic counting of rational curves with tangency conditions via universal torsors}}, doi = {10.48550/ARXIV.2502.11704}, year = {2025}, } @article{19065, abstract = {The identification of the parameters of a neural network from finite samples of input-output pairs is often referred to as the teacher-student model, and this model has represented a popular framework for understanding training and generalization. Even if the problem is NP-complete in the worst case, a rapidly growing literature – after adding suitable distributional assumptions – has established finite sample identification of two-layer networks with a number of neurons (math. formula), D being the input dimension. For the range (math. formula) the problem becomes harder, and truly little is known for networks parametrized by biases as well. This paper fills the gap by providing efficient algorithms and rigorous theoretical guarantees of finite sample identification for such wider shallow networks with biases. Our approach is based on a two-step pipeline: first, we recover the direction of the weights, by exploiting second order information; next, we identify the signs by suitable algebraic evaluations, and we recover the biases by empirical risk minimization via gradient descent. Numerical results demonstrate the effectiveness of our approach.}, author = {Fornasier, Massimo and Klock, Timo and Mondelli, Marco and Rauchensteiner, Michael}, issn = {1096-603X}, journal = {Applied and Computational Harmonic Analysis}, publisher = {Elsevier}, title = {{Efficient identification of wide shallow neural networks with biases}}, doi = {10.1016/j.acha.2025.101749}, volume = {77}, year = {2025}, } @article{19066, abstract = {We present a sample of 1956 individual stellar clumps at redshift 0.7 < z < 10, detected with JWST/NIRCam in 476 galaxies lensed by the galaxy cluster Abell2744. The lensed clumps present magnifications ranging between μ = 1.8 and μ = 300. We perform simultaneous size-photometry estimates in 20 JWST/NIRCam median and broad-band filters from 0.7 to 5 μm. Spectral energy distribution (SED) fitting analyses enable us to recover the physical properties of the clumps. The majority of the clumps are spatially resolved and have effective radii in the range Reff = 10–700 pc. We restrict this first study to the 1751 post-reionization era clumps with redshift < 5.5. We find a significant evolution of the average clump ages, star formation rates (SFRs), SFR surface densities, and metallicity with increasing redshift, while median stellar mass and stellar mass surface densities are similar in the probed redshift range. We observe a strong correlation between the clump properties and the properties of their host galaxies, with more massive galaxies hosting more massive and older clumps. We find that clumps closer to their host galactic centre are on average more massive, while their ages do not show clear sign of migration. We find that clumps at cosmic noon sample the upper-mass end of the mass function to higher masses than at z > 3, reflecting the rapid increase towards the peak of the cosmic star formation history. We conclude that the results achieved over the studied redshift range are in agreement with expectation of in situ clump formation scenario from large-scale disc fragmentation. }, author = {Claeyssens, Adélaïde and Adamo, Angela and Messa, Matteo and Dessauges-Zavadsky, Miroslava and Richard, Johan and Kramarenko, Ivan and Matthee, Jorryt J and Naidu, Rohan P.}, issn = {1365-2966}, journal = {Monthly Notices of the Royal Astronomical Society}, number = {3}, pages = {2535--2558}, publisher = {Oxford University Press}, title = {{Tracing star formation across cosmic time at tens of parsec-scales in the lensing cluster field Abell 2744}}, doi = {10.1093/mnras/staf058}, volume = {537}, year = {2025}, }