Related papers: The Batyrev-Manin conjecture for DM stacks II

To study problems involving heights as, eg, Manin's conjecture on the number of points of bounded height on an algebraic variety defined over a number field, it is desirable to have a good normalization of these height functions. We show…

In this paper we propose a new, simple and explicit mechanism allowing to derive Stein operators for random variables whose characteristic function satisfies a simple ODE. We apply this to study random variables which can be represented as…

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC)…

By a heuristic argument, we relate two conjectures. One is a version of Manin's conjecture about the distribution of rational points on a Fano variety. We concern specific singular Fano varieties, namely quotients of projective spaces by…

We define a new canonical height pairing on the rational points of elliptic curves over global function fields which takes values in the multiplicative group of a completion of the function field. This height serves as an analogue of both…

We prove the existence of a gap around zero for canonical height functions associated to endomorphisms of projective spaces defined over complex function fields. We also prove that if the rational points of height zero are Zariski dense,…

Though remarkable progress has been achieved in various vision tasks, deep neural networks still suffer obvious performance degradation when tested in out-of-distribution scenarios. We argue that the feature statistics (mean and standard…

This is a survey paper on derived symplectic geometry, that will appear as a chapter contribution to the book "New Spaces for Mathematics and Physics", edited by Mathieu Anel and Gabriel Catren. Our goal is to explain how derived stacks can…

Motivated by a result of van der Poorten and Shparlinski for univariate power series, Bell and Chen prove that if a multivariate power series over a field of characteristic 0 is D-finite and its coefficients belong to a finite set then it…

In this article, we prove the Manin conjecture for Darmon points on vector group compactifications using ideas similar to those in [PSTVA21]. We also calculate the leading constants in some examples.

The representability theorem for stacks, due to Artin in the underived setting and Lurie in the derived setting, gives conditions under which a stack is representable by an $n$-geometric stack. In recent work of Ben-Bassat, Kelly, and…

Geometric Manin's conjecture for complex Fano varieties describes the structure of the moduli space of curves. We propose a version of this conjecture in characteristic $p$ and describe its connection to the Batyrev--Manin--Peyre--Tschinkel…

A new class of nonparametric prior distributions, termed Beta-Binomial stick-breaking process, is proposed. By allowing the underlying length random variables to be dependent through a Beta marginals Markov chain, an appealing discrete…

Semiparametric discrete choice models are widely used in a variety of practical applications. While these models are point identified in the presence of continuous covariates, they can become partially identified when covariates are…

A differential version of the classical Weil descent is established in all characteristics. It yields a theory of differential restriction of scalars for differential varieties over finite differential field extensions. This theory is then…

We consider hypersurfaces in $(\mathbb{P}^1)^n$ that contain a generic sequence of small dynamical height with respect to a split map and project onto $n-1$ coordinates. We show that these hypersurfaces satisfy strong coincidence relations…

Dempster-Shafer theory is widely applied in uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. A distance between two basic probability assignments(BPAs) presents a measure of performance…

In this article, we establish an analogue of the dimension growth conjecture, which is regarding the density of rational points on projective varieties, for compact submanifolds of $\mathbb{R}^n$ with non-vanishing curvature. We also…

General purpose intelligent learning agents cycle through (complex,non-MDP) sequences of observations, actions, and rewards. On the other hand, reinforcement learning is well-developed for small finite state Markov Decision Processes…

This paper proposes a probabilistic approach to investigate the shape of landscapes of multi-dimensional potential functions. Under a suitable coupling scheme, two copies of the overdamped Langevin dynamics associated with the potential…