Related papers: The Batyrev-Manin conjecture for DM stacks II
In recent years, a variety of novel measures of dependence have been introduced being capable of characterizing diverse types of directed dependence, hence diverse types of how a number of predictor variables $\mathbf{X} = (X_1, \dots,…
We establish the dynamical Northcott property for polarized endomorphisms of a projective variety over a function field $\mathbf{K}$ of characteristic zero, and we relate this property to the notion of stability in complex dynamics. This…
Representing probability distributions by the gradient of their density functions has proven effective in modeling a wide range of continuous data modalities. However, this representation is not applicable in discrete domains where the…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…
Diffusion Models (DMs), also referred to as score-based diffusion models, utilize neural networks to specify score functions. Unlike most other probabilistic models, DMs directly model the score functions, which makes them more flexible to…
We determine when the equidistribution property for possibly moving targets holds for a rational function of degree more than one on the projective line over an algebraically closed field of any characteristic and complete with respect to a…
Though deep neural networks have achieved impressive success on various vision tasks, obvious performance degradation still exists when models are tested in out-of-distribution scenarios. In addressing this limitation, we ponder that the…
Distributional transformations characterized by equations relating expectations of test functions weighted by a given biasing function on the original distribution to expectations of the test function's higher derivatives with respect to…
In this paper, we introduce and study different dissipativity notions and different turnpike properties for discrete-time stochastic nonlinear optimal control problems. The proposed stochastic dissipativity notions extend the classic notion…
We study a generalization of the D-dimensional Vasiliev theory to include a tower of partially massless fields. This theory is obtained by replacing the usual higher-spin algebra of Killing tensors on (A)dS with a generalization that…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
We generalize the toric Bertini theorem of Fuchs, Mantova, and Zannier to positive characteristic. A key part of the proof is a new algebraically closed field containing the field \kk(t_1,\dots,t_d) of rational functions over an…
Determinantal point processes (DPPs) are probabilistic models for repulsion. When used to represent the occurrence of random subsets of a finite base set, DPPs allow to model global negative associations in a mathematically elegant and…
Deng (arXiv:math/9812082) gave an asymptotic formula for the number of rational points on a weighted projective space over a number field with respect to a certain height function. We prove a generalization of Deng's result involving a…
We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the…
Stark-Heegner points, also known as Darmon points, were introduced by H. Darmon as certain local points on rational elliptic curves, conjecturally defined over abelian extensions of real quadratic fields. The rationality conjecture for…
We show that the dynamical degree of an (i.i.d) random sequence of dominant, rational self-maps on projective space is almost surely constant. We then apply this result to height growth and height counting problems in random orbits.
We survey recent results regarding the study of dynamical properties of the space of positive definite functions and characters of higher rank lattices. These results have several applications to ergodic theory, topological dynamics,…
Integrative analysis of data from multiple sources is critical to making generalizable discoveries. Associations that are consistently observed across multiple source populations are more likely to be generalized to target populations with…
The starting point of the current paper is a sequence of uncorrelated random variables. The distribution functions of these variables are assumed to be given but no assumptions on the types or the structure of these distributions are made.…