Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models. Compared to othe
We present a systematic evaluation framework - thirty-seven analyses, 153 statistical tests, four cell types, two perturbation modalities - for assessing mechanistic interpretability in single-cell foundation models. Applying this framework to scGPT
We classify projective terminalizations of quotients of Fano varieties of lines on smooth cubic fourfolds by finite groups of symplectic automorphisms of the underlying cubic. We compute the second Betti number and the fundamental group of the regula
In this paper we combine topological and functional analysis methods to prove that a non-locally trivial quasi-linear map defined on a C(K) must be nontrivial on a subspace isomorphic to c_0 . We conclude the paper with a few examples showing that
We prove that the point process of the eigenvalues of real or complex non-Hermitian matrices X with independent, identically distributed entries is hyperuniform: the variance of the number of eigenvalues in a subdomain Ω of the spectrum is much s
The Ep,i - Eiso correlation is one of the most intriguing properties of GRBs, with significant implications for the understanding of the physics and geometry of the prompt emission, the identification and investigation of different classes of GRBs, t
We investigate the Fermat-Torricelli problem in d-dimensional real normed spaces or Minkowski spaces, mainly for d=2. Our approach is to study the Fermat-Torricelli locus in a geometric way. We present many new results, as well as give an exposition
The results of J. F. Qiann et al. [4] on (1-gamma) -cyclic codes over finite chain rings of nilpotency index 2 are extended to (1-gamma^e) -cyclic codes over finite chain rings of arbitrary nilpotency index e+1 . The Gray map is introduced for thi
A new variant of the pencil-beam (PB) algorithm for dose distribution calculation for radiotherapy with protons and heavier ions, the grid-dose spreading (GDS) algorithm, is proposed. The GDS algorithm is intrinsically faster than conventional PB alg
The economic crisis in Argentina around year 2002 provides a unique opportunity for Econophysics studies. The available data on individual income are analyzed to show that they correspond to non stationary states. However, the rather restricted size
This paper concerns the question of how AI systems encode semantic structure into the geometric structure of their representation spaces. The motivating observation of this paper is that the natural geometry of these representation spaces should refl
We prove dimension bounds on the jet schemes of the variety of nilpotent matrices (and of related varieties) in positive characteristic. This result has applications to the analytic properties of the Chevalley map that sends a matrix to its charact
We resolve a folklore problem for the optimal hypercontractive constant of the cyclic group mathbb{Z}_3 for all 1 < p < q < infty . Precisely, the optimal hypercontractive constant is given by [ r_{p,q}(mathbb{Z}_3) = frac{(1 + 2x)(1 - y)}{(1 + 2y
We introduce the non-self OU sequence and the OU number for link diagrams. Using these, we give a lower bound for the number of necessary Reidemeister moves of type III between two diagrams of the same link.
Usually, mathematical objects have highly parallel interpretations. In this paper, we consider them as sequential constructors of other objects. In particular, we prove that every reflexive directed graph can be interpreted as a program that builds a
The physics of randomness and regularities for languages (mother tongues) and their lifetimes and family trees and for the second languages are studied in terms of two opposite processes; random multiplicative noise [1], and fragmentation [2], where
The quantum symmetric simple exclusion process (QSSEP) is a recent extension of the symmetric simple exclusion process, designed to model quantum coherent fluctuating effects in noisy diffusive systems. It models stochastic nearest-neighbor fermionic
Clique-width is a complexity measure of directed as well as undirected graphs. Rank-width is an equivalent complexity measure for undirected graphs and has good algorithmic and structural properties. It is in particular related to the vertex-minor re
This paper I assume that in humans the creation of knowledge depends on a discrete time, or stage, sequential decision-making process subjected to a stochastic, information transmitting environment. For each time-stage, this environment randomly tran
By assuming that a particle of energy hbar.omega is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy (heat flow), the exact Schroedinger equation is derived, both for conservative and noncon
The research area 'Virtual Manufacturing (VM)'' is the use of information technology and computer simulation to model real world manufacturing processes for the purpose of analysing and understanding them. As automation technologies such as CAD/CAM h
Temperature scaling is a simple method that allows to control the uncertainty of probabilistic models. It is mostly used in two contexts: improving the calibration of classifiers and tuning the stochasticity of large language models (LLMs). In both c
We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii energy functi
The recent demonstrations of cascaded PDC (CPDC) and the hopeful prospects of realizing third-order PDC (TOPDC) for the generation of three-photon entangled states are paving the way for experimental studies on genuine three-photon interference. In t
Despite significant advances in lead-free perovskite photovoltaics, achieving a balance among environmental safety and high optoelectronic performance remains challenging. The inorganic double perovskite Cs2AgBiBr6 has emerged as a promising candidat
Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic population model wh
A network of n communication links, operating over a shared wireless channel, is considered. Fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. It is assumed that each link c
The debate surrounding the hot hand in the NBA has been ongoing for many years. However, many of the previous works on this theme has focused on only the very next sequential shot attempt, often on very select players. This work looks in more detail
Motivated by recent developments in the theory of gravitation, we revisit the idea of topological variations, originally introduced by Wheeler and Hawking, from a rigorous perspective. Starting from a localized version of the Einstein-Hilbert variati
The technique of symmetric extensions is derived from forcing and it is one of the most important tools for studying models without the Axiom of Choice. Despite being incredibly successful since the 1960s, our understanding of the technique remained
We outline an approach to obtain direct L^2 estimates not requiring interpolation for so-called linearized partial sums operators associated with expansions in Walsh functions. We focus specifically on a simpler case of dyadic partial sums but also
Introduction: While the origin and evolution of proteins remain mysterious, advances in evolutionary genomics and systems biology are facilitating the historical exploration of the structure, function and organization of proteins and proteomes. Molec
One of the most important aspects of detector development for the ILC is a good jet energy resolution sigma_E/E. To achieve the goal of high precision measurements sigma_E/E = 0.30/sqrt(E(GeV)} is proposed. The particle flow approach together with hi
Small single-domain proteins often exhibit only a single free-energy barrier, or transition state, between the denatured and the native state. The folding kinetics of these proteins is usually explored via mutational analysis. A central question is w
Microwave synthesizers are central to test and measurement systems across applications including wireless communications, radar, spectroscopy, and time and frequency metrology. State-of-the-art microwave sources, however, are fundamentally constraine
We describe a new model for studying intermittently connected mobile networks, based on Markovian random temporal graphs, that captures the influence of message size, maximum tolerated delay and link stability on the delivery ratio.
It is known that the moments of the maximum value of a one-dimensional conditional Brownian motion, the three-dimensional Bessel bridge with duration 1 started from the origin, are expressed using the Riemann zeta function. We consider a system of tw
Most cold atoms experiments in microgravity platforms or in Space are achieved using atom chips, leading to limitations in terms of optical access and inhomogeneous magnetic fields. Optical dipole traps do not have these drawbacks but have difficulti
We propose Deep Neural Coregionalization, a scalable framework for uncertainty-aware multivariate geostatistics. DNC models multivariate spatial effects through spatially varying latent factors and loadings, assigning deep Gaussian process (DGP) prio
Accelerator design languages (ADLs), high-level languages that compile to hardware units, help domain experts quickly design efficient application-specific hardware. ADL compilers optimize datapaths and convert software-like control flow constructs i
Twinning is a primary deformation mechanism in Mg alloys. This study focuses on tension twins during uniaxial compression of Mg-Y alloys, with three key aspects: the orientation specificity of twin grains, the relative evolution of CRSS with increasi
Spatiotemporal flows govern diverse phenomena across physics, biology, and engineering, yet modelling their multiscale dynamics remains a central challenge. Despite major advances in physics-informed machine learning, existing approaches struggle to
Universal approximation theorems establish the expressive capacity of neural network architectures. For dynamical systems, existing results are limited to finite time horizons or systems with a globally stable equilibrium, leaving multistability and
Crystal structure prediction (CSP), which aims to predict the three-dimensional atomic arrangement of a crystal from its composition, is central to materials discovery and mechanistic understanding. Existing deep learning models often treat crystallo
We theoretically justify the recent empirical finding of [Teh et al., 2025] that a transformer pretrained on synthetically generated data achieves strong performance on empirical Bayes (EB) problems. We take an indirect approach to this question: rat
We review the evidence for the argument that Rudolf Wolf's calibration of the Sunspot Number is likely to be correct and that Max Waldmeier introduced an upwards jump in the sunspot number in 1945. The combined effect of these adjustments suggests th
Family planning is a global development priority and a key indicator of reproductive health. Monitoring progress is challenged by gaps in survey data across countries. The United Nations Population Division addresses this with the Family Planning Est
We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or flexibly. Wh
In variational inference (VI), the practitioner approximates a high-dimensional distribution π with a simple surrogate one, often a (product) Gaussian distribution. However, in many cases of practical interest, Gaussian distributions might not capt
Processing sensory data close to the data source, often involving Edge devices, promises low latency for pervasive applications, like smart cities. This commonly involves a multitude of processing services, executed with limited resources; this setup
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