Related papers: Simple proofs for lattice coverings and sparse ten…
We propose a rescaled LASSO, by premultipying the LASSO with a matrix term, namely linear unified LASSO (LLASSO) for multicollinear situations. Our numerical study has shown that the LLASSO is comparable with other sparse modeling…
Box splines provide smooth spline spaces as shifts of a single generating function on a lattice and so generalize tensor-product splines. Their elegant theory is laid out in classical papers and a summarizing book. This compendium aims to…
Motivated by questions arising in signal processing, computational complexity, and other areas, we study the ranks and border ranks of symmetric tensors using geometric methods. We provide improved lower bounds for the rank of a symmetric…
A recent result of G. Cz\'edli relates the ordered set of principal congruences of a bounded lattice $L$ with the ordered set of principal congruences of a~bounded sublattice $K$ of $L$. In this note, I sketch a new proof.
In a 1998 paper with H. Lakser, the authors proved that every finite distributive lattice $D$ can be represented as the congruence lattice of a finite \emph{semimodular lattice}. Some ten years later, the first author and E. Knapp proved a…
This note corrects the paper \cite{ex}, where lattice sequences having exponentially large kissing numbers were constructed. However it was noted in \cite{dif} that the arguments in that paper are not sufficient. Here we correct the…
We investigate the structure of join tensors, which may be regarded as the multivariable extension of lattice-theoretic join matrices. Explicit formulae for a polyadic decomposition (i.e., a linear combination of rank-1 tensors) and a…
We propose a unified mathematical framework for classifying phases of matter. The framework is based on different types of combinatorial structures with a notion of locality called lattices. A tensor lattice is a local prescription that…
We prove that the poset of $q$-decreasing words equipped with the componentwise order forms a lattice. We enumerate the join-irreducible elements for arbitrary $q>0$, and for any positive rational number $q$, we determine the number of…
Recent lattice calculations of hadron structure functions are described.
In this paper the number and lengths of minimal length lattice knots confined to slabs of width $L$, is determined. Our data on minimal length verify the results by Sharein et.al. (2011) for the similar problem, expect in a single case,…
Two approximation algorithms are proposed for $\ell_1$-regularized sparse rank-1 approximation to higher-order tensors. The algorithms are based on multilinear relaxation and sparsification, which are easily implemented and well scalable.…
We produce an explicit parameterization of well-rounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest…
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey…
This paper establishes some equivalent conditions of a uninorm, extending an arbitrary triangular norm on [0, e] or an arbitrary triangular conorm on [e, 1] to the whole lattice.
Given k sets such that no one is contained in another, there is an associated lattice on the power set P([k]) corresponding to inclusion relations among unions of the sets. Two lattices on P([k]) are equivalent if there is a permutation of…
We present several conditions for generic uniqueness of tensor decompositions of multilinear rank (1,L_{1}, L_{1}),..., (1, L_{R}, L_{R}) terms. In geometric language, we prove that the joins of relevant subspace varieties are not…
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by…