Publications related to Proof theory

A combinatorial proof of a sumset conjecture of Furstenberg

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if

\log r / \log s

is irrational and

X

and

Y

are

\times r

- and

\times s

-invariant subsets of

[0,1]

, respectively, then $\dim_\text{ ...

2021

Interlacing families III: Sharper restricted invertibility estimates

Adam Wade Marcus

We use the method of interlacing families of polynomials to derive a simple proof of Bourgain and Tzafriri's Restricted Invertibility Principle, and then to sharpen the result in two ways. We show that the stable rank can be replaced by the Schatten 4-norm ...

HEBREW UNIV MAGNES PRESS2021

The First Passage Sets of the 2D Gaussian Free Field: Convergence and Isomorphisms

Juhan Aru, Titus Lupu

In a previous article, we introduced the first passage set (FPS) of constant level -aof the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set of points in the domain that can be connected to the bo ...

SPRINGER2020

Analysis and Remediation of Handwriting difficulties

Thibault Lucien Christian Asselborn

Even with correct training, up to 25% of children never master handwriting like their peers. While research shows a correlation between handwriting difficulties and school failure, these difficulties can also impact children in their self esteem and behavi ...

EPFL2020

Automated phenotyping of Caenorhabditis elegans embryos with a high-throughput-screening microfluidic platform

Martinus Gijs, Matteo Cornaglia, Raphaël Etienne Jean Trouillon, Hüseyin Baris Atakan, Tunç Alkanat

The nematode Caenorhabditis elegans has been extensively used as a model multicellular organism to study the influence of osmotic stress conditions and the toxicity of chemical compounds on developmental and motility-associated phenotypes. However, the sev ...

2020

Linear convergence of primal-dual gradient methods and their performance in distributed optimization

Ali H. Sayed, Sulaiman A S A E Alghunaim

In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear (exponential) conver ...

PERGAMON-ELSEVIER SCIENCE LTD2020

On subgraphs of C-2k-free graphs and a problem of Kuhn and Osthus

Abhishek Methuku

Let c denote the largest constant such that every C-6-free graph G contains a bipartite and C-4-free subgraph having a fraction c of edges of G. Gyori, Kensell and Tompkins showed that 3/8

2020

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

Design and fabrication of miniaturized shape memory alloy gripper prototype

Grippers, currently used in Industry, are not suited for clean room application. Thus, a novel type of smart gripper is being designed using Shape Memory Alloys (SMA). In the development of this Smart Gripper, the modelling of the material is quite critica ...

2019

Provable Robustness of ReLU networks via Maximization of Linear Regions

Maksym Andriushchenko, Francesco Croce

It has been shown that neural network classifiers are not robust. This raises concerns about their usage in safety-critical systems. We propose in this paper a regularization scheme for ReLU networks which provably improves the robustness of the classifier ...

2019

Proof theory

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A combinatorial proof of a sumset conjecture of Furstenberg

Interlacing families III: Sharper restricted invertibility estimates

The First Passage Sets of the 2D Gaussian Free Field: Convergence and Isomorphisms

Analysis and Remediation of Handwriting difficulties

Automated phenotyping of Caenorhabditis elegans embryos with a high-throughput-screening microfluidic platform

Linear convergence of primal-dual gradient methods and their performance in distributed optimization

On subgraphs of C-2k-free graphs and a problem of Kuhn and Osthus

A proof of a sumset conjecture of Erdős

Design and fabrication of miniaturized shape memory alloy gripper prototype

Provable Robustness of ReLU networks via Maximization of Linear Regions

Interlacing families III: Sharper restricted invertibility estimates

On subgraphs of C-2k-free graphs and a problem of Kuhn and Osthus

A combinatorial proof of a sumset conjecture of Furstenberg

Analysis and Remediation of Handwriting difficulties

Automated phenotyping of Caenorhabditis elegans embryos with a high-throughput-screening microfluidic platform

Linear convergence of primal-dual gradient methods and their performance in distributed optimization

The First Passage Sets of the 2D Gaussian Free Field: Convergence and Isomorphisms

A proof of a sumset conjecture of Erdős

Design and fabrication of miniaturized shape memory alloy gripper prototype

Provable Robustness of ReLU networks via Maximization of Linear Regions