In this paper we compute the minimum degree of a faithful representation by partial transformations of a finite semigroup admitting a faithful completely reducible matrix representation over the field of complex numbers. This includes all inverse sem...
Sea ice is highly complex due to the inhomogeneity of the physical properties (e.g. temperature and salinity) as well as the permeability and mixture of water and a matrix of sea ice and/or sea ice crystals. Such complexity has proven itself to be di...
The goal of this expository note is to give a short, self-contained proof of nearly optimal lower bounds for the second largest eigenvalue of the adjacency matrix of regular graphs....
transform to a surface it is often useful to derive normals for the resulting surface from the original normals. Specifically, given a 3×3 transformation matrix
We study the scattering of an electron from a one dimensional inverted Gaussian atomic potential in the presence of strong time periodic electric fields. Using Floquet theory, we construct the Floquet Scattering matrix in the Kramers-Henneberger fr...
In this paper we generalize the Weierstrass and Malgrange preparation theorems to the symmetric matrix valued case, proving symmetric preparation of analytic and smooth symmetric systems that vanish of finite order....
High-resolution label-free imaging of oocytes and embryos is essential for in vitro fertilization procedures. Yet conventional microscopy fails in this task because of aberrations and multiple scattering induced by refractive index heterogeneities in...
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We perform a systematic study of the one-loop renormalizability of all Poisson-Lie T-dualizable $\si$-models with two-dimensional targets. We show that whatever Drinfeld double and whatever matrix of coupling constants we consider the corresponding...
Raz's recent result \cite{Raz2010} has rekindled people's interest in the study of \emph{tensor rank}, the generalization of matrix rank to high dimensions, by showing its connections to arithmetic formulas. In this paper, we follow Raz's work and sh...
Having observed an $m\times n$ matrix $X$ whose rows are possibly correlated, we wish to test the hypothesis that the columns are independent of each other. Our motivation comes from microarray studies, where the rows of $X$ record expression level...
This chapter gives a self-contained review of the how standard open quantum system Hamiltonians can be mapped analytically onto representations in which the environments appear as one dimensional harmonic chains with nearest neighbour interactions. T...
The Canada Day Theorem is an identity involving sums of $k \times k$ minors of an arbitrary $n \times n$ symmetric matrix. It was discovered as a by-product of the work on so-called peakon solutions of an integrable nonlinear partial differential equ...
We give a self-contained randomized algorithm based on shifted inverse iteration which provably computes the eigenvalues of an arbitrary matrix $M\in\mathbb{C}^{n\times n}$ up to backward error $δ\|M\|$ in $O(n^4+n^3\log^2(n/δ)+\log(n/δ)^2\log\log...
In numerical analysis, an incomplete Cholesky factorization of a symmetric positive definite matrix is a sparse approximation of the Cholesky factorization
An approximate Spielman-Teng theorem for the least singular value $s_n(M_n)$ of a random $n\times n$ square matrix $M_n$ is a statement of the following form: there exist constants $C,c >0$ such that for all $η\geq 0$, $\Pr(s_n(M_n) \leq η) \lesssi...
Let $M$ be an $n\times n$ matrix with iid subgaussian entries with mean $0$ and variance $1$ and let $σ_n(M)$ denote the least singular value of $M$. We prove that \[\mathbb{P}\big( σ_{n}(M) \leq \varepsilon n^{-1/2} \big) = (1+o(1)) \varepsilon +...
Venue recommendation systems model the past interactions (i.e., check-ins) of the users and recommend venues. Traditional recommendation systems employ collaborative filtering, content-based filtering or matrix factorization. Recently, vector space e...
In a recent article, D. Kazhdan and A. Yom Din conjectured the validity of an asymptotic form of Schur's orthogonality for tempered irreducible unitary representations of semisimple groups defined over local fields. In the non-Archimedean case, they...
In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number
It is shown that Parisi-Sourlas supersymmetry of stochastic quantization is a Cartan model of equivariant cohomology. Equivariant cohomological structure of stochastic quantization of linear and non-linear sigma models are discussed. Witten's nonab...
We provide an example for the generating matrix $A$ of a two-dimensional lattice $Γ= A\mathbb{Z}^2$, such that the following holds: For any sufficiently smooth and localized mother wavelet $ψ$, there is a constant $β(A,ψ)>0$, such that $βΓ\cap...
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$10,000 in Nvidia just 2 years ago would of turned into $34,900 today ? source: The Market Matrix on the Blossom App. I’m still buying and holding my Nvidia. ...
In this work, we establish the connection between the study of free spectrahedra and the compatibility of quantum measurements with an arbitrary number of outcomes. This generalizes previous results by the authors for measurements with two outcomes....
The Monte Carlo model JEWEL 1.0 (Jet Evolution With Energy Loss) simulates parton shower evolution in the presence of a dense QCD medium. In its current form medium interactions are modelled as elastic scattering based on perturbative matrix elemen...
A mixed multigraph is obtained from an undirected multigraph by orienting a subset of its edges. In this paper, we study a new Hermitian matrix representation of mixed multigraphs, give an introduction to cospectral operations on mixed multigraphs, a...
Matrix WhitePaper (⭐ 86)
In this letter, a realistic coaxial feed is integrated into the design of cascaded cylindrical metasurfaces. This is in contrast to the fictitious current source that is often reported in literature. The S-matrix of the coaxial feed is obtained by wa...
Partitions of unity in ${\mathbf R}^d$ formed by (matrix) scales of a fixed function appear in many parts of harmonic analysis, e.g., wavelet analysis and the analysis of Triebel-Lizorkin spaces. We give a simple characterization of the functions and...
In finite entropy systems, real-time partition functions do not decay to zero at late time. Instead, assuming random matrix universality, suitable averages exhibit a growing "ramp" and "plateau" structure. Deriving this non-decaying behavior in a lar...
The CKM paradigm has been proven to be successful in explaining the flavour structure of the standard model and the non-trivial imaginary phase of the CKM matrix is the only know source of CP-violation. B-meson decays allow us to precisely determine...
Feb 5, 2015 · Tensor : Multidimensional array :: Linear transformation : Matrix. The short of it is, tensors and multidimensional arrays are different types of object; the first is a type of function, the second is a …
We consider questions about the much discussed "perfect lenses" made by left handed materials. The transmission and reflection from a slab of left handed materials are investigated and the coefficients are obtained by the standard transfer matrix m...
Matrix Trendings as well as Digests (⭐ 197)
This research introduce our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for single GPU and multiple GPUs are implemented. A HEC matrix format and a communic...
began research into natural language processing, machine learning and recommendation systems. In 2009, the proprietary machine learning algorithm MatrixNet
We consider the problem of recovering a structured signal $\mathbf{x} \in \mathbb{R}^{n}$ from noisy linear observations $\mathbf{y} =\mathbf{M} \mathbf{x}+\mathbf{w}$. The measurement matrix is modeled as $\mathbf{M} = \mathbf{B}\mathbf{A}$, where $...
Example implementation of the Bayesian neural network in "Structured and Efficient Variational Deep Learning with Matrix Gaussian Posteriors", Christos Louizos & Max Welling, ICML 2016 (⭐ 30)
Social contact studies, investigating social contact patterns in a population sample, have been an important contribution for epidemic models to better fit real life epidemics. A contact matrix $M$, having the \emph{mean} number of contacts between i...