Transcendental function

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Memoryless Worker-Task Assignment with Polylogarithmic Switching Cost

Adam Teodor Polak

We study the basic problem of assigning memoryless workers to tasks with dynamically changing demands. Given a set of w workers and a multiset T ⊆ [t] of |T| = w tasks, a memoryless worker-task assignment function is any function ϕ that assigns the workers ...

Schloss Dagstuhl -- Leibniz-Zentrum fur Informatik2022

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Martin Peter Stoller, Joao Pedro Gonçalves Ramos

We obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Fourier uniqueness and interpolation in Euclidean space

Martin Peter Stoller

We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...

EPFL2022

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Andreas Loukas, Nikolaos Karalias

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep lear ...

2022

The neocortical column as a universal template for perception and world-model learning

Mackenzie Mathis

Mackenzie Mathis highlights an essay by Vernon Mountcastle that shaped our understanding of the organization and function of the neocortex. ...

NATURE PORTFOLIO2022

A New Channel-Base Lightning Current Formula With Analytically Adjustable Parameters

Farhad Rachidi-Haeri

The article provides a new channel-based current function, which aims at faithfully reproducing the salient parameters of lightning currents. All the model parameters can be set in a fully analytical way, guaranteeing the possibility of changing them (acco ...

2021

Proving and Disproving Equivalence of Functional Programming Assignments

Viktor Kuncak, Dragana Milovancevic

We present an automated approach to verify the correctness of programming assignments, such as the ones that arise in a functional programming course. Our approach takes as input student submissions and reference solutions, and uses equivalence checking to ...

2023

Une approche computationnelle du cadastre napoléonien de Venise

Frédéric Kaplan, Isabella Di Lenardo, Raphaël Barman, Federica Pardini

At the beginning of the 19th century, the Napoleonic administration introduced a new standardised description system to give an objective account of the form and functions of the city of Venice. The cadastre, deployed on a European scale, was offering for ...

2021

Covers Of Rational Double Points In Mixed Characteristic

Javier Alonso Carvajal Rojas

We further the classification of rational surface singularities. Suppose (S, n, k) is a 3-dimensional strictly Henselian regular local ring of mixed characteristic (0, p > 5). We classify functions f for which S/(f) has an isolated rational singularity at ...

2021

Deterministic error bounds for kernel-based learning techniques under bounded noise

Colin Neil Jones, Paul Scharnhorst, Emilio Maddalena

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and epsilon-support vector regression. By assuming the ground-truth function belongs to th ...

2021

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NATURE PORTFOLIO2022