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Exponentially long orbits in Hopfield neural networks

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A proof of a sumset conjecture of Erdős

Florian Karl Richter

In this paper we show that every set A ⊂ ℕ with positive density contains B + C for some pair B, C of infinite subsets of ℕ , settling a conjecture of Erdős. The proof features two different decompositions of an arbitrary bounded sequence into a structured ...

2019

A 1,3,2-Diazaphospholene-Catalyzed Reductive Claisen Rearrangement

Nicolai Cramer, Pavel Alexandrovich Donets, John Henry Reed, Solène Florie Miaskiewicz

1,3,2-Diazaphospholenes (DAPs) are an emerging class of organic hydrides. In this work, we exploited them as efficient catalysts for very mild reductive Claisen rearrangements. The method is tolerant towards a wide variety of functional groups and operates ...

2019

Slow dynamics in structured neural network models

Samuel Pavio Muscinelli

Humans and some other animals are able to perform tasks that require coordination of movements across multiple temporal scales, ranging from hundreds of milliseconds to several seconds. The fast timescale at which neurons naturally operate, on the order of ...

EPFL2018

The Unfolding Argument: Why Recurrent Processing Cannot Explain Consciousness

Michael Herzog, Adrien Christophe Doerig, Aaron Schurger

Neuroscientific theories aim to explain paradigm cases of consciousness such as masking, binocular rivalry or the transition from dreamless sleep to wakefulness. The most popular theories are based on computational principles. Recurrent processing is a key ...

2018

Corpora Delicti

Alexandre Blanc, Marco Bakker

CORPORA DELICTI, The Significant Detail. The Corpus Delicti is the evidence of a crime. The term denotes the formation of a proof that allows the unmasking of a perpetrator. In the realm of interpretation and language, it could reveal matter on which an ac ...

MANSLAB2017

A Formally Verified NAT

George Candea, Solal Vincenzo Pirelli, Arseniy Zaostrovnykh, Luis David Figueiredo Mascarenhas Moreira Pedrosa

We present a Network Address Translator (NAT) written in C and proven to be semantically correct according to RFC 3022, as well as crash-free and memory-safe. There exists a lot of recent work on network verification, but it mostly assumes models of networ ...

Assoc Computing Machinery2017

Why our best theories of perception lead to Anti-reductionism

Michael Herzog, Adrien Christophe Doerig

Basic percepts and observation sentences, such as "the voltmeter is at 7A", provide the ground truth for realistic theories. Reduction is the second backbone of these theories linking, for example, neuroscience to physics. First, we will show, by mathemati ...

2016

Logarithmic estimates for continuity equations

Maria Colombo

The aim of this short note is twofold. First, we give a sketch of the proof of a recent result proved by the authors in the paper [7] concerning existence and uniqueness of renormalized solutions of continuity equations with unbounded damping coefficient. ...

2016

Cloaking using complementary media in the quasistatic regime

Hoài-Minh Nguyên

Cloaking using complementary media was suggested by Lai et al. in [8]. The study of this problem faces two difficulties. Firstly, this problem is unstable since the equations describing the phenomenon have sign changing coefficients, hence the ellipticity ...

2016

Superlensing using complementary media

Hoài-Minh Nguyên

This paper studies magnifying superlens using complementary media. Superlensing using complementary media was suggested by Veselago in [16] and innovated by Nicorovici et al. in [9] and Pendry in [10]. The study of this problem is difficult due to two fact ...

Gauthier-Villars/Editions Elsevier2015