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Four-Variable Expanders Over The Prime Fields

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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

Development of a new method to determine the axial void velocity profile in BWRs from measurements of the in-core neutron noise

Mathieu Hursin

Determination of the local void fraction in BWRs from in-core neutron noise measurements requires the knowledge of the axial velocity of the void. The purpose of this paper is to revisit the problem of determining the axial void velocity profile from the t ...

PERGAMON-ELSEVIER SCIENCE LTD2021

A (2+epsilon)-Approximation Algorithm for Preemptive Weighted Flow Time on a Single Machine

Lars Rohwedder

Weighted flow time is a fundamental and very well-studied objective function in scheduling. In this paper, we study the setting of a single machine with preemptions. ...

ASSOC COMPUTING MACHINERY2021

Efficient Sequential and Parallel Algorithms for Multistage Stochastic Integer Programming Using Proximity

Friedrich Eisenbrand, Moritz Andreas Venzin, Jana Tabea Cslovjecsek

We consider the problem of solving integer programs of the form min {c^⊺ x : Ax = b, x ∈ ℤ_{⩾ 0}}, where A is a multistage stochastic matrix in the following sense: the primal treedepth of A is bounded by a parameter d, which means that the columns of A ca ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2021

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

Automorphisms of even unimodular lattices and equivariant Witt groups

Eva Bayer Fluckiger

We characterize the irreducible polynomials that occur as the characteristic polynomial of an automorphism of an even unimodular lattice of a given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion i ...

EUROPEAN MATHEMATICAL SOC2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)

Felix Schürmann, Francesco Cremonesi, Timothée Ewart, Fabien Jonathan Delalondre

The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. ...

2020

Multiquadratic Rings and Walsh-Hadamard Transforms for Oblivious Linear Function Evaluation

Juan Ramón Troncoso-Pastoriza

The Ring Learning with Errors (RLWE) problem has become one of the most widely used cryptographic assumptions for the construction of modern cryptographic primitives. Most of these solutions make use of power-of-two cyclotomic rings mainly due to its simpl ...

IEEE2020

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 ...