Concept

Homogeneous polynomial

Related publications (76)

The multivariate Serre conjecture ring

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

San Diego2023

Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points

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 Part I [3] of this work we established that agents cluster around a network centroid and pr ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Structure of multicorrelation sequences with integer part polynomial iterates along primes

Florian Karl Richter

Let T be a measure-preserving Zℓ-action on the probability space (X,B,μ), let q1,…,qm:R→Rℓ be vector polynomials, and let f0,…,fm∈L∞⁡(X). For any ϵ>0 and multicorrelation sequences of the form α⁡(n)=∫Xf0⋅T⌊q1⁡(n)⌋⁢f1⋯T⌊qm⁡(n)⌋⁢fmd⁢μ we show that there exis ...

2021

Distributed Learning in Non-Convex Environments-Part I: Agreement at a Linear Rate

Ali H. Sayed, Stefan Vlaski

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available wor ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Markov cubature rules for polynomial processes

Damir Filipovic, Martin Larsson, Sergio Andres Pulido Nino

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rul ...

ELSEVIER2020

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...

SPRINGER HEIDELBERG2020

Metal-organic frameworks as kinetic modulators for branched selectivity in hydroformylation

Berend Smit, Gerald Bauer, Daniele Ongari, Davide Tiana, Mohamed Tarik

Finding heterogeneous catalysts that are superior to homogeneous ones for selective catalytic transformations is a major challenge in catalysis. Here, we show how micropores in metal-organic frameworks (MOFs) push homogeneous catalytic reactions into kinet ...

2020

An edge detector based on artificial neural network with application to hybrid Compact-WENO finite difference schemes

Jan Sickmann Hesthaven, Zhen Gao

A new approach is proposed to detect edges based on an artificial neural network (ANN). Some elementary continuous and discontinuous functions interpolated in the polynomial space and their continuity are used as the training sets to train a back propagati ...

Springer/Plenum2020

Polynomial Jump-Diffusion Models

Damir Filipovic, Martin Larsson

We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial trans ...

2020

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

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