Minimum-Error Classes for Matching Parts

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Information theory has allowed us to determine the fundamental limit of various communication and algorithmic problems, e.g., the channel coding problem, the compression problem, and the hypothesis testing problem. In this work, we revisit the assumptions ...

5G New Radio (NR) has stringent demands on both performance and complexity for the design of low-density parity-check (LDPC) decoding algorithms and corresponding VLSI implementations. Furthermore, decoders must fully support the wide range of all 5G NR bl ...

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...

In the last decade, DNA has been increasingly investigated as an alternative medium for cold data storage, presenting several advantages over standard hard drives such as a higher density, longer lifespan and lower energy consumption. However, such coding ...

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

Graph machine learning offers a powerful framework with natural applications in scientific fields such as chemistry, biology and material sciences. By representing data as a graph, we encode the prior knowledge that the data is composed of a set of entiti ...

Modern digital connectivity has necessitated the creation of robust methods for securely storing and transferring data. At the heart of all security infrastructure is the random number generator (RNG). While random numbers find use in a variety of applicat ...

Submodular functions are a widely studied topic in theoretical computer science. They have found several applications both theoretical and practical in the fields of economics, combinatorial optimization and machine learning. More recently, there have also ...

This paper examines the minimization of the cost for an expected random production output, given an assembly of finished goods from two random inputs, matched in two categories. We describe the optimal input portfolio, first using the standard normal appro ...

We approach the graph generation problem from a spectral perspective by first generating the dominant parts of the graph Laplacian spectrum and then building a graph matching these eigenvalues and eigenvectors. Spectral conditioning allows for direct model ...

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

Coconut tree plantations are one of the main sources of income in several South Pacific countries. Thus, keeping track of the location of coconut trees is important for monitoring and post-disaster assessment. Although deep learning based object detectors ...

The de-facto standard decoding algorithm for polar codes, successive cancellation list (SCL) decoding, is a breadth-first search algorithm. By keeping a list of candidate codewords, SCL decoding improves the performance as the list size L increases. Howeve ...

Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...

In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

Spectral-based graph neural networks (SGNNs) have been attracting increasing attention in graph representation learning. However, existing SGNNs are limited in implementing graph filters with rigid transforms and cannot adapt to signals residing on graphs ...

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

Minimum-Error Classes for Matching Parts

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On Speed and Advantage : Results in Information Velocity and Monitoring Problems

A Generalized Adjusted Min-Sum Decoder for 5G LDPC Codes: Algorithm and Implementation

Results on Sparse Integer Programming and Geometric Independent Sets

Approximation Algorithms for Allocation and Network Design

Analysis of the influence of errors in DNA-based image coding

An equilibrated flux a posteriori error estimator for defeaturing problems

Equivariant Neural Architectures for Representing and Generating Graphs

Modelling and design of CMOS SPAD sensors for quantum random number generation

Streaming and Matching Problems with Submodular Functions

Optimal Matching of Random Parts

SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Towards Efficient Correction of Coconut Tree Detection Errors

List Ordered Statistics Decoders for Polar Codes

Random walks and forbidden minors III: poly(d epsilon(-1))-time partition oracles for minor-free graph classes

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

A Functional Perspective on Information Measures

Graph Neural Networks With Lifting-Based Adaptive Graph Wavelets

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Dynamical low rank approximation for uncertainty quantification of time-dependent problems