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Concept

Rank–nullity theorem

Related publications (13)

NORM TORI OF ETALE ALGEBRAS AND UNRAMIFIED BRAUER GROUPS

Eva Bayer Fluckiger, Ting-Yu Lee

Let k be a field, and let L be an etale k-algebra of finite rank. If a is an element of k(x), let X-a be the affine variety defined by N-L/k(x) = a. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial desc ...

Hebrew Univ Magnes Press2023

Sampling Geometry and Colour

Michalina Wanda Pacholska

In this thesis, we take a signal-processing approach to two research areas outside of the core of the signal processing research: geometry reconstruction and light propagation through non-uniform media. In the first area, we consider new sampling schemes ...

EPFL2021

Mutual information for low-rank even-order symmetric tensor estimation

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method orig ...

Oxford University Press2021

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

Friedrich Eisenbrand

We consider integer programming problems in standard form max{c(T)x : Ax = b, x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m), and c is an element of Z(n). We show that such an integer program can be solved in time ...

ASSOC COMPUTING MACHINERY2020

Faster Algorithms for Integer Programs with Block Structure

Friedrich Eisenbrand, Kim-Manuel Klein, Christoph Hunkenschröder

We consider integer programming problems max {c^Tx : A x = b, l

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik2018

Proximity results and faster algorithms for Integer Programming using the Steinitz Lemma

Friedrich Eisenbrand

We consider integer programming problems in standard form max{c(T)x : Ax = b; x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m) and c is an element of Z(n). We show that such an integer program can be solved in time ...

ASSOC COMPUTING MACHINERY2018

The Truncated Tracial Moment Problem

Sabine Burgdorf

We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in noncommuting variables with values invariant under cyclic permutations of the indexes, is called a tracial sequence. ...

Theta Foundation2012

Light Field Tensor Recovery

Pierre Vandergheynst, Mahdad Hosseini Kamal

This paper presents a novel approach to capture light field in camera arrays based on the tensor recovery framework. Light fields are acquired by a linear array of cameras with overlapping field of view. We represent the light fields in shape of a tensor t ...

2012

Vectors in a box

Doemoetoer Palvoelgyi

For an integer d a parts per thousand yen 1, let tau(d) be the smallest integer with the following property: if v (1), v (2), . . . , v (t) is a sequence of t a parts per thousand yen 2 vectors in [-1, 1] (d) with , then there is a set of indices, 2 a part ...

Springer2012

Rank-Deficient Quadratic-Form Maximization Over M-Phase Alphabet: Polynomial-Complexity Solvability And Algorithmic Developments

Anastasios Kyrillidis

The maximization of a positive (semi) definite complex quadratic form over a finite alphabet is NP-hard and achieved through exhaustive search when the form has full rank. However, if the form is rank-deficient, the optimal solution can be computed with on ...

IEEE2011

Subspace properties of randomized network coding

Christina Fragouli, Suhas Diggavi, Mahdi Jafari Siavoshani

Randomized network coding has network nodes randomly combine and exchange linear combinations of the source packets. A header appended to the packet, called coding vector, specifies the exact linear combination that each packet carries. The main contributi ...

2007

Network Loss Inference with Second Order Statistics of End-to-End Flows

Patrick Thiran, Xuan Hung Nguyen

We address the problem of calculating link loss rates from end-to-end measurements. Contrary to existing works that use only the average end-to-end loss rates or strict temporal correlations between probes, we exploit second-order moments of end-to-end flo ...

2007

Bottleneck Discovery and Overlay Management in Network Coded Peer-to-Peer Systems

Christina Fragouli, Suhas Diggavi, Mahdi Jafari Siavoshani

The performance of peer-to-peer (P2P) networks depends critically on the good connectivity of the overlay topology. In this paper we study P2P networks for content distribution (such as Avalanche) that use randomized network coding techniques. The basic id ...

2007