Despite their impressive performance on a wide variety of tasks, modern language models remain susceptible to distribution shifts, exhibiting brittle behavior when evaluated on data that differs in distribution from their training data. In this paper
Epilepsy affects over 50 million people worldwide, and one-third of patients suffer drug-resistant seizures where surgery offers the best chance of seizure freedom. Accurate localization of the epileptogenic zone (EZ) relies on intracranial EEG (iEEG
This paper establishes a categorical equivalence between the category mathbb{COL} of complete orthomodular lattices and the category mathscr{T}mathbb{ODA} of mathscr{T} -based orthomodular dynamic algebras. Complete orthomodular lattices serve a
Let {ρ_λ:G_Krightarrow GL_n(overline E_λ)} be a semisimple E-rational compatible system of a number field K. In a first step, building upon the theory of pseudocharacters [Ro96],[Ch14], we attach to each ρ_λ an algebraic monodromy group G_λ def
In this paper, we present a detailed convergence analysis of a recently developed approximate Newton-type fully distributed optimization method for smooth, strongly convex local loss functions, called Network-GIANT, which has been empirically illustr
Let mathcal{E} be the class of finite-dimensional algebras isomorphic to endomorphism algebras of silting complexes over hereditary abelian categories. It is proved that the class mathcal{E} is closed under taking idempotent quotients, idempotent
A topological group G is {em extremely amenable} if every compact G -space has a G -fixed point. Let X be compact and Gsubset{mathrm{Homeo}} (X) . We prove that the following are equivalent: (1) G is extremely amenable; (2) every minimal clo
We demonstrate strong interference patterns in the photoionization cross-section of the subvalent subshells of noble gas (NG) endohedral atoms NG@F. This interference is a result of common action of three factors: the effect of neighboring atomic sub
We consider a class of optimization problems on the space of probability measures motivated by the mean-field approach to studying neural networks. Such problems can be solved by constructing continuous-time gradient flows that converge to the minimi
We consider hypothetical solutions of 3D Euler which blow up in finite time in a self-similar fashion. We prove that if the initial data has finite kinetic energy, then the similarity exponent γ which governs the rate of zooming in must be larger t
Let P be a set of n points in the plane, not all on a line, each colored emph{red} or emph{blue}. The classical Motzkin--Rabin theorem guarantees the existence of a emph{monochromatic} line. Motivated by the seminal work of Green and Tao (2013) o
Generalized Sliced Inverse Regression (GSIR) is one of the most important methods for nonlinear sufficient dimension reduction. As shown in Li and Song (2017), it enjoys a convergence rate that is independent of the dimension of the predictor, thus a
We derive the approximate pressure profiles, density profiles, and temperature profiles of an atmosphere, also called barometric formulas. Our variant of a derivation goes beyond the common standard exercise of a thermodynamics lecture, where commonl
The aim of this paper is threefold. First, it presents a multi-dimensional Markovian state transition model characterizing the behavior of the IEEE 802.11 protocol at the Medium Access Control layer which accounts for packet transmission failures due
We extend recent algebro-geometric results for coupled cluster theory of quantum many-body systems to the truncation varieties arising from the doubles approximation (CCD), focusing on the first genuinely nonlinear doubles regime of four electrons. S
Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier to extended
We examine when differentially flat nonlinear control systems with more than two inputs can be rendered static feedback linearizable by prolongations of suitably chosen inputs after applying a static input transformation. Building on the structure of
A run is a maximal occurrence of a repetition v with a period p such that 2p le v . The maximal number of runs in a string of length n was studied by several authors and it is known to be between 0.944 n and 1.029 n . We investigate highl
We present a comprehensive analysis of how two-layer neural networks learn features to solve the modular addition task. Our work provides a full mechanistic interpretation of the learned model and a theoretical explanation of its training dynamics. W
The advent of network coding presents promising opportunities in many areas of communication and networking. It has been recently shown that network coding technique can significantly increase the overall throughput of wireless networks by taking adv
Quillen's algebraic K-theory is reconstructed via Voevodsky's algebraic cobordism. More precisely, for a ground field k the algebraic cobordism P^1-spectrum MGL of Voevodsky is considered as a commutative P^1-ring spectrum. There is a unique ring mor
An odd meromorphic function f(s) is constructed from the Riemann zeta-function evaluated at one-half plus s. The partial fraction expansion, p(s), of f(s) is obtained using the conjunction of the Riemann hypothesis and hypotheses advanced by the auth
This paper investigates goal-oriented remote monitoring of an unobservable Markov source using energy-harvesting sensors that communicate with a mobile receiver, such as a Low Earth Orbit (LEO) satellite or Unmanned Aerial Vehicle (UAV). Unlike conve
How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present practical examples of a new way to address this problem. By giving an appro
Modern scientific instruments operate under increasingly extreme constraints on bandwidth, latency, and power. Inference at the sensor edge determines experimental data collection efficiency by deciding which information to save for further analysis.
We construct, assuming Jensen's principle diamond, a one-dimensional locally connected hereditarily separable continuum without convergent sequences. The construction is an inverse limit in omega_1 steps, and is patterned after the original Fedorchuk
The present paper considers multipartite graphs from the perspective of design theory and coding theory. A one-factor F of the complete multipartite graph K_{ntimes g} (with n parts of size g ) gives rise to a (g+1) -ary code {cal C} of len
We investigate the recently introduced model of learning with improvements, where agents are allowed to make small changes to their feature values to be warranted a more desirable label. We extensively extend previously published results by providing
Relativistic equilibrium is described by the inverse-temperature four-vector β^μ= u^μ/(k_B T_0) rather than by a frame-dependent scalar temperature. We show that β^μ can be reconstructed directly from electromagnetic fluctuations emitted by a dri
We introduce a compact operator-based technique that solves the paraxial wave equation for a broad class of structured light fields. Using the spatial evolution operator to propagate two families of physically apodized inputs, Gaussian apodized Whitt
Accurate estimation of the relative concentrations of chromophores in a spectroscopic photoacoustic (sPA) image can reveal immense structural, functional, and molecular information about physiological processes. However, due to nonlinearities and ill
In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in cite{nos} for the infinite horizon case to the finite horizon case. We prove an a priori bo
This research paper proposes an efficient methodology for the allocation of multiple photovoltaic (PV)-based distributed generation (DG) units in the radial distribution network (RDN), while considering the loading capacity of the network. The propos
Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth labels and the teacher's own predictions using the same architecture and training data. Although SD has been empirically shown to often improve generalization,
This paper investigates a specific class of nonsmooth nonconvex optimization problems in the face of data uncertainty, namely, robust optimization problems, where the given objective function can be expressed as a difference of two tangentially conve
p-spin glasses, characterized by frustrated many-body interactions beyond the conventional pairwise case (p>2), are prototypical disordered systems whose ground-state search is NP-hard and computationally prohibitive for large instances. Solving this
After a brief review of the electroweak radiative corrections to gauge-boson self-energies, otherwise known as the direct and oblique corrections, a tool for calculation of the oblique parameters is presented. This tool, named OPUCEM, brings together
Gene Regulatory Networks(GRNs) with feedback are essential components of many cellular processes and may exhibit oscillatory behavior. Analyzing such systems becomes increasingly complex as the number of components increases. Since gene regulation of
Redox proteomics generates bounded biochemical measurements that are categorically mismatched to conventional linear algebraic formalisms. This work introduces Oxi-Shapes, a tropical geometric framework for the measurement-native analysis of bounded
The present paper is devoted to foundations of p-adic modelling in genomics. Considering nucleotides, codons, DNA and RNA sequences, amino acids, and proteins as information systems, we have formulated the corresponding p-adic formalisms for their in
The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A particula
We seek to narrow the gap between parametric and nonparametric modelling of stationary time series processes. The approach is inspired by recent advances in focused inference and model selection techniques. The paper generalises and extends recent wo
We consider a class of optimal control problems, with finite or infinite horizon, for a continuous-time Markov chain with finite state space. In this case, the control process affects the transition rates. We suppose that the controlled process can n
We show that P2T - the problem of deciding whether the edge set of a simple graph can be partitioned into two trees or not - is NP-complete.
In 1909, Einstein derived a formula for the mean square energy fluctuation in black-body radiation. This formula is the sum of a wave term and a particle term. In a key contribution to the 1925 Dreimaennerarbeit with Born and Heisenberg, Jordan showe
It is known that waves generated by ambient noise sources and recorded by passive receivers can be used to image the reflectivities of an unknown medium. However, reconstructing the reflectivity of the medium from partial boundary measurements remain
While recent advances in humanoid locomotion have achieved stable walking on varied terrains, capturing the agility and adaptivity of highly dynamic human motions remains an open challenge. In particular, agile parkour in complex environments demands
We introduce millimeter-wave silicon photonic crystal cavities as a versatile platform for the perturbative sensing of nanoscale materials. This dielectric-based platform is compatible with strong magnetic fields, opening avenues for studying quantum
Quantum phase transition is interpreted as an evolution, at the end of which a parameter-dependent Hamiltonian H(g) loses its observability. In the language of mathematics, such a quantum catastrophe occurs at an exceptional point of order N (EPN
With the rise of artificial intelligence and machine learning, a new wave of private information is being flushed into applications. This development raises privacy concerns, as private datasets can be stolen or abused for non-authorized purposes. Se
Enter keywords to search articles