相关论文: Coverage of space in Boolean models
We develop an algorithm which, given a trained transformer model $\mathcal{M}$ as input, as well as a string of tokens $s$ of length $n_{fix}$ and an integer $n_{free}$, can generate a mathematical proof that $\mathcal{M}$ is…
The present paper mainly considers the representation type of the enveloping algebra of monomial algebra. Let $A$ be a monomial algebra and $A^e= A\otimes_{\mathrm{l}\!\mathrm{k}} A^{\mathrm{op}}$ its enveloping algebra. It is shown that…
An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been…
Full likelihood inference under Kingman's coalescent is a computationally challenging problem to which importance sampling (IS) and the product of approximate conditionals (PAC) method have been applied successfully. Both methods can be…
Given a complete noncompact Riemannian manifold $N^n$, we investigate whether the set of bounded Sobolev maps $(W^{1, p} \cap L^\infty) (Q^m; N^n)$ on the cube $Q^m$ is strongly dense in the Sobolev space $W^{1, p} (Q^m; N^n)$ for $1 \le p…
Let $\mathcal{I}$ be an ideal on $\mathbb{N}$. A mapping $f:X\to Y$ is called an $\mathcal{I}$-covering mapping provided a sequence $\{y_{n}\}_{n\in\mathbb N}$ is $\mathcal{I}$-converging to a point $y$ in $Y$, there is a sequence…
We introduce a stochastic model in which adjacent planar regions $A, B$ merge stochastically at some rate $\lambda(A,B)$, and observe analogies with the well-studied topics of mean-field coagulation and of bond percolation. Do infinite…
Point completion refers to completing the missing geometries of an object from incomplete observations. Main-stream methods predict the missing shapes by decoding a global feature learned from the input point cloud, which often leads to…
Shape completion is the problem of completing partial input shapes such as partial scans. This problem finds important applications in computer vision and robotics due to issues such as occlusion or sparsity in real-world data. However,…
Collider events with multi-stage cascade decays fill out the kinematically allowed region in phase space with a density that is enhanced at the boundary. The boundary encodes all available information about the spectrum and is well…
Uncertainty quantification for neural operators remains an open problem in the infinite-dimensional setting due to the lack of finite-sample coverage guarantees over functional outputs. While conformal prediction offers finite-sample…
We consider the convex subset $[A,B]$ of all elements between two levels $A$ and $B$ of a finite distributive lattice, as a union of (or covered by) intervals $[a,b]$. A 1988 result of Voigt and Wegener shows that for such convex subsets of…
We consider the Boolean model with random radii based on Cox point processes. Under a condition of stabilization for the random environment, we establish existence and non-existence of subcritical regimes for the size of the cluster at the…
Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…
Standard conformal prediction methods provide a marginal coverage guarantee, which means that for a random test point, the conformal prediction set contains the true label with a user-specified probability. In many classification problems,…
We explore "semibounded" expansions of arbitrary ordered groups; namely, expansions that do not define a field on the whole universe. We show that if $\mathcal R=\langle R, <, +, \dots\rangle$ is a semibounded o-minimal structure and…
We present a method to obtain upper bounds on covering numbers. As applications of this method, we reprove and generalize results of Rogers on economically covering Euclidean $n$-space with translates of a convex body, or more generally,…
In this paper we prove: Theorem 1. Let $\mathcal{K}$ be an abstract elementary class which satisfies the joint embedding and amalgamation properties. Suppose $\lambda>\mu\geq LS(\mathcal{K})$ and $\theta$ is a limit ordinal $<\lambda^+$. If…
Given S_1, a finite set of points in the plane, we define a sequence of point sets S_i as follows: With S_i already determined, let L_i be the set of all the line segments connecting pairs of points of the union of S_1,...,S_i, and let…
We show how Lasry-Lions's result on regularization of functions defined on $\mathbb{R}^n$ or on Hilbert spaces by sup-inf convolutions with squares of distances can be extended to (finite or infinite dimensional) Riemannian manifolds $M$ of…