Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

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Simple and projective correspondence functors

Jacques Thévenaz, Serge Bouc

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. We determine exactly which simple correspondence functors are projective. We also determine which simple ...

2021

Minimal Polynomials Of Unipotent Elements Of Non-Prime Order In Irreducible Representations Of The Exceptional Algebraic Groups In Some Good Characteristics

Donna Testerman

In a number of cases the minimal polynomials of the images of unipotent elements of non-prime order in irreducible representations of the exceptional algebraic groups in good characteristics are found. It is proved that if p > 5 for a group of type E-8 and ...

2019

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

Ali H. Sayed, Stefan Vlaski

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In this work we establish that agents cluster around a network centroid in the mean-fourth sen ...

IEEE2019

Dynamic Optimization of Reaction Systems via Exact Parsimonious Input Parameterization

Dominique Bonvin, Diogo Filipe Mateus Rodrigues

This paper discusses the use of parsimonious input parameterization for the dynamic optimization of reaction systems. This parameterization is able to represent the optimal inputs with only a few parameters. In the context of batch, semibatch, and continuo ...

AMER CHEMICAL SOC2019

Correspondence functors and lattices

Jacques Thévenaz, Serge Bouc

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. A main tool for this study is the construction of a correspondence functor associated to any finite latt ...

2019

Stable high-order randomized cubature formulae in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

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 ...

2022

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham, Seyed Hossein Nassajianmojarrad

Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

AMER MATHEMATICAL SOC2018

Two-term, asymptotically sharp estimates for eigenvalue means of the Laplacian

Joachim Stubbe

We present asymptotically sharp inequalities for the eigenvalues mu(k) of the Laplacian on a domain with Neumann boundary conditions, using the averaged variational principle introduced in [14]. For the Riesz mean R-1(z) of the eigenvalues we improve the k ...

EUROPEAN MATHEMATICAL SOC2018

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Simple and projective correspondence functors

Jacques Thévenaz, Serge Bouc

2021

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham, Seyed Hossein Nassajianmojarrad

AMER MATHEMATICAL SOC2018

Minimal Polynomials Of Unipotent Elements Of Non-Prime Order In Irreducible Representations Of The Exceptional Algebraic Groups In Some Good Characteristics

Donna Testerman

2019