Concept

Least-upper-bound property

Related publications (102)

Improving SAM Requires Rethinking its Optimization Formulation

Volkan Cevher, Kimon Antonakopoulos, Thomas Michaelsen Pethick, Wanyun Xie, Fabian Ricardo Latorre Gomez

This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. We argue that SAM shou ...

2024

Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures

Matteo Raphael Tacchi

This paper proposes an algorithm to upper-bound maximal quantile statistics of a state function over the course of a Stochastic Differential Equation (SDE) system execution. This chance-peak problem is posed as a nonconvex program aiming to maximize the Va ...

New York2023

Upper bounds on technoemission rates from 60 years of "silence"

Claudio Grimaldi

The lack of detection to date of electromagnetic technosignatures implies either that we have been unable to detect them due to incomplete sampling of the search space or that we cannot detect them because the Earth has been located during the entire histo ...

PERGAMON-ELSEVIER SCIENCE LTD2023

Near-Optimal Communication Lower Bounds for Approximate Nash Equilibria

Mika Tapani Göös

We prove an N2-o(1) lower bound on the randomized communication complexity of finding an epsilon-approximate Nash equilibrium (for constant epsilon > 0) in a two-player N x N game. ...

Philadelphia2023

Intrinsic area near the origin for self-similar growth-fragmentations and related random surfaces

We study the behaviour of a natural measure defined on the leaves of the genealogical tree of some branching processes, namely self-similar growth-fragmentation processes. Each particle, or cell, is attributed a positive mass that evolves in continuous tim ...

2022

Explaining multiple patches of aquatic vegetation through linear stability analysis

Giulio Calvani

Aquatic vegetation is ubiquitous in lowland rivers, and it is typically present in the shape of spatial self-organized patches of biomass. In this work, we mathematically define the threshold conditions for the incipient formation of self-organized vegetat ...

2022

IR side of positivity bounds

Francesco Riva, Brando Bellazzini, Marc Riembau Saperas

We show how calculable IR loop effects impact positivity bounds in effective field theories with causal and unitary UV completions. We identify infrared singularities that appear in dispersion relations at |t| less than or similar to m(2). In the massless ...

AMER PHYSICAL SOC2022

Thermalization and hydrodynamics of two-dimensional quantum field theories

Matthew Thomas Walters

We consider 2d QFTs as relevant deformations of CFTs in the thermodynamic limit. Using causality and KPZ universality, we place a lower bound on the timescale characterizing the onset of hydrodynamics. The bound is determined parametrically in terms of the ...

2022

On Semi-Algebraic Proofs and Algorithms

Mika Tapani Göös

We give a new characterization of the Sherali-Adams proof system, showing that there is a degree-d Sherali-Adams refutation of an unsatisfiable CNF formula C if and only if there is an ε > 0 and a degree-d conical junta J such that viol_C(x) - ε = J, where ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2022

The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...

2021

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