Aligator: A mathematica package for invariant generation

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We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...

In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...

We discuss two extensions to a recently introduced theory of arrays, which are based on considerations coming from the model theory of power structures. First, we discuss how the ordering relation on the index set can be expressed succinctly by referring t ...

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

Image information about the state of a building after an earthquake, which can be collected without endangering the post-earthquake reconnaissance activities, can be used to reduce uncertainties in response predictions for future seismic events. This paper ...

Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...

It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

We prove that the set of-y-thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all-y =6 0. Our proof relies on the coupling between a GFF and the nested CLE4. In particular, we show that th ...

Witness encryption is a cryptographic primitive which encrypts a message under an instance of an NP language and decrypts the ciphertext using a witness associated with that instance. In the current state of the art, most of the witness encryption construc ...

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...

In the ITER Tokamak, four Electron Cyclotron Heating Upper Launchers (ECHUL) are needed to control plasma instabilities at the rational surfaces, most importantly the q = 3/2 and q = 2/1 neoclassical tearing modes (NTMs). Each ECHUL is equipped with a set ...

In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...

We study the computational complexity of the optimal transport problem that evaluates the Wasser- stein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in th ...

3D reconstruction of deformable (or non-rigid) scenes from a set of monocular 2D image observations is a long-standing and actively researched area of computer vision and graphics. It is an ill-posed inverse problem, since-without additional prior assumpti ...

Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in an environment wi ...

Self-attention mechanisms and non-local blocks have become crucial building blocks for state-of-the-art neural architectures thanks to their unparalleled ability in capturing long-range dependencies in the input. However their cost is quadratic with the nu ...

We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...

We address for the first time the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem analy ...

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

Aligator: A mathematica package for invariant generation

Chat with Graph Search

Hitting with Probability One for Stochastic Heat Equations with Additive Noise

Dynamical system approach to navigation around obstacles

Succinct ordering and aggregation constraints in algebraic array theories

Reliable data-driven decision-making through optimal transport

Reducing uncertainties in response predictions of earthquake-damaged masonry buildings using data from image-based inspection

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

The multivariate Serre conjecture ring

Thick points of the planar GFF are totally disconnected for all & gamma;=6 0*

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

Results on Sparse Integer Programming and Geometric Independent Sets

The first Grushin eigenvalue on cartesian product domains

Present design of the Steering Mirror Assembly (SMA) for ITER ECHUL

Approximation Algorithms for Allocation and Network Design

Discrete Optimal Transport with Independent Marginals is #P-Hard

State of the Art in Dense Monocular Non-Rigid 3D Reconstruction

Certification of Bottleneck Task Assignment With Shortest Path Criteria

Linear Complexity Self-Attention With 3rd Order Polynomials

Formula Normalizations in Verification

Removing Algorithmic Discrimination (With Minimal Individual Error)

Stable high-order randomized cubature formulae in arbitrary dimension