We give formulas, in terms of graph theoretical invariants, for the minimum distance and the generalized Hamming weights of the linear code generated by the rows of the incidence matrix of a signed graph over a finite field, and for those of its dual...
This paper studies the limiting behavior of Tyler's M-estimator for the scatter matrix, in the regime that the number of samples $n$ and their dimension $p$ both go to infinity, and $p/n$ converges to a constant $y$ with $0<y<1$. We prove that when t...
A fundamental problem in statistics is estimating the shape matrix of an Elliptical distribution. This generalizes the familiar problem of Gaussian covariance estimation, for which the sample covariance achieves optimal estimation error. For Elliptic...
Fiber-reinforced plastic is a composite made of a polymer matrix reinforced with fibers. A composite is a mixture of two materials, one of which makes the other stronger.
If $E=\{e_i\}$ and $F=\{f_i\}$ are two 1-unconditional basic sequences in $L_1$ with $E$ $r$-concave and $F$ $p$-convex, for some $1\le r<p\le 2$, then the space of matrices $\{a_{i,j}\}$ with norm $\|\{a_{i,j}\}\|_{E(F)}=\big\|\sum_k \|\sum_l a_{k...
A Heffter array $H(n;k)$ is an $n\times n$ matrix such that each row and column contains $k$ filled cells, each row and column sum is divisible by $2nk+1$ and either $x$ or $-x$ appears in the array for each integer $1\leq x\leq nk$. Heffter arrays a...
Online scientific calculator from MathDA: perform calculations with basic math to equation solver, integral, derivative, matrix, vector, statistics...
Blackbox algorithms for linear algebra problems start with projection of the sequence of powers of a matrix to a sequence of vectors (Lanczos), a sequence of scalars (Wiedemann) or a sequence of smaller matrices (block methods). Such algorithms usual...
Recently, Macharete, Del-Vecchio, Teixeira and de Lima showed that a star and any threshold graph on the same number of vertices share the same eigenbasis relative to the Laplacian matrix. We use this fact to establish two main results in this paper....
A novel methodology is proposed for clustering multivariate time series data using energy distance defined in Székely and Rizzo (2013). Specifically, a dissimilarity matrix is formed using the energy distance statistic to measure separation between...
Fiber-reinforced plastic is a composite made of a polymer matrix reinforced with fibers. A composite is a mixture of two materials, one of which makes the other stronger.
Rapid, efficient deactivation of the photoexcited PAH cations accounts for their remarkable photostability and have important implications for astrochemistry, as these cations are the leading candidates for the species responsible for the diffuse i...
A sign pattern is an array with entries in $\{+,-,0\}$. A matrix $Q$ is row orthogonal if $QQ^T = I$. The Strong Inner Product Property (SIPP), introduced in [B.A.~Curtis and B.L.~Shader, Sign patterns of orthogonal matrices and the strong inner prod...
The family of cycle completable graphs has several cryptomorphic descriptions, the equivalence of which has heretofore been proven by a laborious implication-cycle that detours through a motivating matrix completion problem. We give a concise proof,...
We present a new cryptomorphic definition of orthogonal matroids with coefficients using Grassmann--Plücker functions. The equivalence is motivated by Cayley's identities expressing principal and almost-principal minors of a skew-symmetric matrix in...
Fiber-reinforced plastic is a composite made of a polymer matrix reinforced with fibers. A composite is a mixture of two materials, one of which makes the other stronger.
A three-dimensional multi-scale computational homogenisation framework is developed for the prediction of nonlinear micro/meso-mechanical response of the fibre-reinforced polymer (FRP) composites. Two dominant damage mechanisms, i.e. matrix elasto-pl...
Fiber-reinforced plastic is a composite made of a polymer matrix reinforced with fibers. A composite is a mixture of two materials, one of which makes the other stronger.
It arose from watching this video: https://www.youtube.com/watch?v=chpc1nvpOZI I think the one cig, and the one cookie represents the 1's and 0's of binary technology. She's giving him "the one" coo...
Fiber-reinforced plastic is a composite made of a polymer matrix reinforced with fibers. A composite is a mixture of two materials, one of which makes the other stronger.