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Separating OR, SUM, and XOR Circuits
Given a boolean n by n matrix A we consider arithmetic circuits for computing the transformation x->Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative integers), a...
Cancellation-free circuits: An approach for proving superlinear lower bounds for linear Bo…
We continue to study the notion of cancellation-free linear circuits. We show that every matrix can be computed by a cancellation- free circuit, and almost all of these are at most a constant factor larger than the optimum linear circuit that compute...
dougkelly/TopicModeling_HilaryClintonEmails
GalvanizeU Machine Learning & Natural Language Processing Final Project. Explored topic modeling approaches in Python to summarize emails by latent foreign policy topics using Non-Negative Matrix Factorization and LDA approaches in Sklearn (⭐ 13)
Largest eigenvalues of sparse inhomogeneous Erdős-Rényi graphs
We consider inhomogeneous Erdős-Rényi graphs. We suppose that the maximal mean degree $d$ satisfies $d \ll \log n$. We characterize the asymptotic behavior of the $n^{1 - o(1)}$ largest eigenvalues of the adjacency matrix and its centred version. W...
Element (Matrix chat app) suspended from the Google Play Store
Points: 2009 | Comments: 940 | Author: redsolver
Investigating the inner structure of focal adhesions with single-molecule localization mic…
Cells rely on focal adhesions (FAs) to carry out a variety of important tasks, including motion, environmental sensing, and adhesion to the extracellular matrix. Although attaining a fundamental characterization of FAs is a compelling goal, their ext...
Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials
We express the averages of products of characteristic polynomials for random matrix ensembles associated with compact symmetric spaces in terms of Jack polynomials or Heckman and Opdam's Jacobi polynomials depending on the root system of the space....
Blind source separation methods for deconvolution of complex signals in cancer biology
Two blind source separation methods (Independent Component Analysis and Non-negative Matrix Factorization), developed initially for signal processing in engineering, found recently a number of applications in analysis of large-scale data in molecular...
Matrix Star Carrie-Anne Moss Says She Was Offered a 'Grandmother' Role After Her 40th Birt…
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A generalization of carries process and riffle shuffles
As a continuation to our previous work, we consider a generalization of carries process. Our results are : (i) right eigenvectors of the transition probability matrix, (ii) correlation of carries between different steps, and (iii) generalized riffle...
Winding number criterion for the origin to belong to the numerical range of a matrix on a…
Let $A:[0,1]\to GL(n,\mathbb{C})$ be continuous with $A(0)=A(1)$, thus the winding number of $\det A$ is well-defined. If the winding number is not divisible by $n$, then the origin belongs to the numerical range of $A(φ)$ for some $φ\in [0,1]$....
LED Matrix Earrings
Points: 615 | Comments: 84 | Author: nrabulinski
FEM modeling and simulation of broadband ultrasonic transducers with randomized inhomogene…
A FEM application for the accurate design of composite backing of ultrasonic transducers is presented. The idea is to obtain the dependence between the volume ratio of the tungsten powder in an epoxy matrix used as a backing and the final pulsed RF s...
P-Tensors, P$_0$-Tensors, and Tensor Complementarity Problem
The concepts of P- and P$_0$-matrices are generalized to P- and P$_0$-tensors of even and odd orders via homogeneous formulae. Analog to the matrix case, our P-tensor definition encompasses many important classes of tensors such as the positive defin...
Commuting Magic Square Matrices
We review a known method of compounding two magic square matrices of order m and n with the all-ones matrix to form two magic square matrices of order mn. We show that these compounded matrices commute. Simple formulas are derived for their Jordan fo...
Families of skew-symmetric matrices of even size
The main result of the paper is a classification of singularities of complex skew-symmetric matrix families of even size which are simple under a natural equivalence relation. The classification is obtained by appropriate suspensions of simple famili...
Kendall Correlation Coefficients for Portfolio Optimization
Markowitz's optimal portfolio relies on the accurate estimation of correlations between asset returns, a difficult problem when the number of observations is not much larger than the number of assets. Using powerful results from random matrix theory,...
The Characteristic Polynomial of a Random Permutation Matrix at Different Points
We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show that the beha...