Related papers: On a "replicating character string" model
In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…
Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size…
The goal of this paper is to outline a scenario of emerging stochasticity in high-dimensional highly nonlinear systems, such as genetic regulatory networks (GRN). We focus attention on the fact that in such systems confluence of all the…
In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…
The entropy rate of printed English is famously estimated to be about one bit per character, a benchmark that modern large language models (LLMs) have only recently approached. This entropy rate implies that English contains nearly 80…
DNA stretching experiments are usually interpreted using the worm-like chain model; the persistence length A appearing in the model is then interpreted as the elastic stiffness of the double helix. In fact the persistence length obtained by…
In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in Ayache, Roueff and Xiao (2007). By using this representation, in the case where the sample…
We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…
In this paper, we are interested in the combinatorial analysis of the whole genome duplication - random loss model of genome rearrangement initiated in a paper of Chaudhuri, Chen, Mihaescu, and Rao in SODA 2006 and continued by Bouvel and…
Extropy, a complementary dual of entropy, (proposed by Lad et al. \cite{lad2015extropy} in 2015) has attracted considerable interest from the research community. In this study, we focus on discrete random variables and define conditional…
We propose to homogenize a periodic (along one direction) structure, first in order to verify the quasi-static prediction of its response to an acoustic wave arising from mixing theory, then to address the question of what becomes of this…
Stability is a central property in learning and statistics promising the output of an algorithm $A$ does not change substantially when applied to similar datasets $S$ and $S'$. It is an elementary fact that any sufficiently stable algorithm…
Persistent homology was shown by Carlsson and Zomorodian to be homology of graded chain complexes with coefficients in the graded ring $\kk[t]$. As such, the behavior of persistence modules -- graded modules over $\kk[t]$ is an important…
We study a genetic regulatory network model developed to demonstrate that genetic robustness can evolve through stabilizing selection for optimal phenotypes. We report preliminary results on whether such selection could result in a…
Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions, and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems…
Mixtures of regression are a powerful class of models for regression learning with respect to a highly uncertain and heterogeneous response variable of interest. In addition to being a rich predictive model for the response given some…
We propose a general technique for extracting a larger set of stable information from persistent homology computations than is currently done. The persistent homology algorithm is usually viewed as a procedure which starts with a filtered…
Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector. This necessitates that each component satisfies a marginal domain of attraction condition. An approximation of…
Assuming the existence of a monster model, tameness and continuity of nonsplitting in an abstract elementary class (AEC), we extend known superstability results: let $\mu>LS({\bf K})$ be a regular stability cardinal and let $\chi$ be the…
Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive…