相关论文: L\'evy statistics in coding and non-coding nucleot…

Recent theories suggest that Neural Scaling Laws arise whenever the task is linearly decomposed into power-law distributed units. Alternatively, scaling laws also emerge when data exhibit a hierarchically compositional structure, as is…

In this paper we study general nonlinear stochastic differential equations, where the usual Brownian motion is replaced by a L\'evy process. We also suppose that the coefficient multiplying the increments of this process is merely Lipschitz…

We consider a class of real numbers, a subset of irrational numbers and certain mathematical constants, for which the elements in the simple continued fraction appears to be random. As an illustrative example, one can consider $\pi = \{x_0,…

We give a realization of the stable L\'evy forest of a given size conditioned by its mass from the path of the unconditioned forest. Then, we prove an invariance principle for this conditioned forest by considering $k$ independent…

Generative models of graphs are well-known, but many existing models are limited in scalability and expressivity. We present a novel sequential graphical variational autoencoder operating directly on graphical representations of data. In…

Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor is however the cubic scaling of the algorithms used. Building on previous work [F. R.…

We analyze time evolution of statistical distributions of citations to scientific papers published in one year. While these distributions can be fitted by a power-law dependence we find that they are nonstationary and the exponent of the…

The L\'evy hypothesis states that inverse square L\'evy walks are optimal search strategies because they maximise the encounter rate with sparse, randomly distributed, replenishable targets. It has served as a theoretical basis to interpret…

L\'evy noise influences diverse non-equilibrium systems across scales, including quantum devices, active biological matter, and financial markets. While such noise is pervasive, its overall impact on activated transitions between metastable…

Neural scaling laws--power-law relationships between generalization errors and characteristics of deep learning models--are vital tools for developing reliable models while managing limited resources. Although the success of large language…

We consider the testing and estimation of change-points -- locations where the distribution abruptly changes -- in a data sequence. A new approach, based on scan statistics utilizing graphs representing the similarity between observations,…

This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driven by Markovian additive jump noise with heavy-tailed jumps,…

Verifying multi-step reasoning in large language models is difficult due to imprecise error localization and high token costs. Existing methods either assess entire reasoning chains, suffering attention dilution, or rely on expensive…

In the course of evolution, proteins undergo important changes in their amino acid sequences, while their three-dimensional folded structure and their biological function remain remarkably conserved. Thanks to modern sequencing techniques,…

Stochastic models, based on random processes, may lead to power law distributions, which provide long range correlations. The observation of power law behavior and the presence of long range correlations in biological systems has been…

The time that waves spend inside 1D random media with the possibility of performing L\'evy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered…

Physics seeks to uncover the laws of Nature and express them through mathematical equations. Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical…

We consider the problem of storing and retrieving information from synthetic DNA media. The mathematical basis of the problem is the construction and design of sequences that may be discriminated based on their collection of substrings…

We consider a system in which two nodes take correlated measurements of a random source with time-varying and unknown statistics. The observations of the source at the first node are to be losslessly replicated with a given probability of…

In this paper we consider the use of variable length non prefix-free codes for coding constrained sequences of symbols. We suppose to have a Markov source where some state transitions are impossible, i.e. the stochastic matrix associated…