Graph isomorphism and volumes of convex bodies (2009)
We show that a nontrivial graph isomorphism problem of two undirected graphs, and more generally, the permutation similarity of two given $n\times n$ matrices, is equivalent to equalities of volumes...
A note on the nonzero spectrum of irreducible matrices (2009)
In this note we extend the necessary and sufficient conditions of Boyle-Handleman 1991 and Kim-Ormes-Roush 2000 for a nonzero eigenvalue multiset of primitive matrices over $\R_+$ and $\Z_+$,...
Positive diagonal scaling of a nonnegative tensor to one with prescribed slice sums (2009)
In this paper we give necessary and sufficient conditions on a nonnegative tensor to be diagonally equivalent to a tensor with prescribed slice sums. For matrices these conditions reduce to Menon's...
Friedland, Shmuel, Peled, Uri N.
We study theoretical and computational properties of the pressure function for subshifts of finite type on the integer lattice $\Z^d$, multidimensional SOFT, which are called Potts models in...
Asymptotic Positivity of Hurwitz Product Traces: Two Proofs (2008)
Fleischhack, Christian, Friedland, Shmuel
Consider the polynomial $tr (A + tB)^m$ in $t$ for positive hermitian matrices $A$ and $B$ with $m \in \N$. The Bessis-Moussa-Villani conjecture (in the equivalent form of Lieb and Seiringer) states...
On the First Eigenvalue of Bipartite Graphs (2008)
Bhattacharya, Amitava, Friedland, Shmuel, Peled, Uri N.
In this paper we study the maximum value of the largest eigenvalue for simple bipartite graphs, where the number of edges is given and the number of vertices on each side of the bipartition is given....
Additive invariants on quantum channels and applications to regularized minimum entropy (2008)
We introduce two additive invariants of output quantum channels. If the value of one these invariants is less than 1 then the logarithm of the inverse of its value is a positive lower bound for the...
Maximizing Sum Rates in Gaussian Interference-limited Channels (2008)
Friedland, Shmuel, Tan, Chee Wei
We study the problem of maximizing sum rates in a Gaussian interference-limited channel that models multiuser communication in a CDMA wireless network or DSL cable binder. Using tools from...
On the generic rank of 3-tensors (2008)
We study the generic rank of 3-tensors using results from matrices and algebraic geometry. We state a conjecture about the exact values of the generic rank of 3-tensors over the complex numbers. We...
Remarks on BMV conjecture (2008)
We show that for fixed $A,B$, hermitian nonnegative definite matrices, and fixed $k$ the coefficients of the $t^k$ in the polynomial $\tr (A+tB)^m$ is positive if $\tr AB >0$ and $m>N(A,B,k)$.
The maximum number of perfect matchings in graphs with a given degree sequence (2008)
We show that the number of perfect matching in a simple graph $G$ with an even number of vertices and degree sequence $d_1,d_2, ..., d_n$ is at most $\prod_{i=1}^n (d_i !)^{\frac{1}{2d_i}}$. This...
An upper bound for the number of perfect matchings in graphs (2008)
We give an upper bound on the number of perfect matchings in an undirected simple graph $G$ with an even number of vertices, in terms of the degrees of all the vertices in $G$. This bound is sharp if...
On the graph isomorphism problem (2008)
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
Properly Discontinuous Groups Acting on Certain Matrix Homogeneous Spaces (2007)
. We characterize discrete groups \Gamma ae GL(n; R) which act properly discontinuously on the homogeneous space GL(m;R)nGL(n;R). x1. Introduction A manifold M is called a complete locally...
Concentration Of Permanent Estimators For Certain Large Matrices (2007)
Shmuel Friedland, B. Rider, Ofer Zeitouni
Let A n = (a ij ) i;j=1 be an n n positive matrix with entries in [a; b]; 0 < a b. Let X n = ( i;j=1 be a random matrix where fx ij g are i.i.d. N(0; 1) random variables. We show that for large n,...
FPRAS for computing a lower bound for weighted matching polynomial of graphs (2007)
We give a fully polynomial randomized approximation scheme to compute a lower bound for the matching polynomial of any weighted graph at a positive argument. For the matching polynomial of complete...
The Polytope of Dual Degree Partitions (2006)
Bhattacharya, Amitava, Friedland, Shmuel, Peled, Uri N.
We determine the extreme points and facets of the convex hull of all dual degree partitions of simple graphs on $n$ vertices.
A polynomial-time approximation algorithm for the number of k-matchings in bipartite graphs (2006)
Friedland, Shmuel, Levy, Daniel
We show that the number of $k$-matching in a given undirected graph $G$ is equal to the number of perfect matching of the corresponding graph $G_k$ on an even number of vertices divided by a suitable...
Entropy of holomorphic and rational maps: a survey (2006)
We give a brief survey on the entropy of holomorphic self maps $f$ of compact K\"ahler manifolds, and rational dominating self maps $f$ of smooth projective varieties. We emphasize the connection...
Generalized rank-constrained matrix approximations (2006)
Friedland, Shmuel, Torokhti, Anatoli
In this paper we give an explicit solution to the rank constrained matrix approximation in Frobenius norm, which is a generalization of the classical approximation of an m by n matrix A by a matrix...
Generalized Friedland-Tverberg inequality: applications and extensions (2006)
Friedland, Shmuel, Gurvits, Leonid
We derive here the Friedland-Tverberg inequality for positive hyperbolic polynomials. This inequality is applied to give lower bounds for the number of matchings in $r$-regular bipartite graphs. It...
Theoretical and computational aspects of 1-vertex transfer matrices (2006)
Friedland, Shmuel, Lundow, Per Hakan, Markstrom, Klas
We introduce the notion of 1-vertex transfer matrix for near neighbor Potts models with $k$ kinds of particles. We show that the topological entropy (free energy) of this model can be expressed as...
Validations of the Asymptotic Matching Conjectures (2006)
Friedland, Shmuel, Krop, Elliot, Lundow, Per Hakan, Markström, Klas
In this paper we review the asymptotic matching conjectures for $r$-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in $d$-dimensional integer lattice and...
Exact conditions for countable inclusion-exclusion identity and extensions (2006)
Friedland, Shmuel, Krop, Elliot
We give simple necessary and sufficient conditions for the inclusion-exclusion identity to hold for an infinite countable number of sets. In terms of a random variable, whose range are nonnegative...
Data is presented in terms of a matrix (2006)
Shmuel Friedland, A. Niknejad, H. Zare
a11 a12... a1n a21 a22... a2n am1 am2... amn 1. digital picture: 512 × 512 matrix of pixels 2. DNA-microarrays: 60, 000 × 30 (rows are genes and columns are experiments) 3. web pages activities:...
Fast Monte-Carlo Low Rank Approximations for Matrices (2005)
Friedland, Shmuel, Kaveh, Mostafa, Niknejad, Amir, Zare, Hossein
In many applications, it is of interest to approximate data, given by mxn matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular...
An Algorithm for Missing Value Estimation for DNA Microarray Data (2005)
Friedland, Shmuel, Kaveh, Mostafa, Niknejad, Amir, Zare, Hossein
Gene expression data matrices often contain missing expression values. In this paper, we describe a new algorithm, named improved fixed rank approximation algorithm (IFRAA), for missing values...
2-adic valuations of certain ratios of products of factorials and applications (2005)
Friedland, Shmuel, Krattenthaler, Christian
We prove the conjecture of Falikman--Friedland--Loewy on the parity of the degrees of projective varieties of $n\times n$ complex symmetric matrices of rank at most $k$. We also characterize the...
Concentration of permanent estimators for certain large matrices (2004)
Friedland, Shmuel, Rider, Brian, Zeitouni, Ofer
Let An=(aij)i,j=1n be an n×n positive matrix with entries in [a,b], 0
Concentration of permanent estimators for certain large matrices (2004)
Friedland, Shmuel, Rider, Brian, Zeitouni, Ofer
Let A_n=(a_{ij})_{i,j=1}^n be an n\times n positive matrix with entries in [a,b], 0
Friedland, Shmuel, Peled, Uri N.
We outline the most recent theory for the computation of the exponential growth rate of the number of configurations on a multi-dimensional grid. As an application we compute the monomer-dimer...
Convergence of Products of Matrices in Projective Spaces (2004)
Ima Preprint Series, Shmuel Friedland
Let A k , k N be a sequence of n n matrices which converge to a matrix A. If A and each A k is positive then the product ||Ak Ak-1 ...A2 A1 converges to a rank one matrix positive matrix uw , where u...
Shmuel Friedland, Uri N. Peled
We outline the most recent theory for the computation of the exponential growth rate of the number of configurations on a multi-dimensional grid. As an application we compute the monomer-dimer...
Shmuel Friedland, Brian Rider, Ofer Zeitouni
Let An = (aij) n i,j=1 be an n × n positive matrix with entries in [a,b], 0<a ≤ b. LetXn = ( √ aij xij) n i,j=1 be a random matrix, where {xij} are i.i.d. N(0, 1) random variables. We show...
Concentration of Permanent Estimators for Certain Large Matrices (2003)
Shmuel Friedland, Brian Rider, Ofer Zeitouni
Let An = (a ij ) i;j=1 be an n n positive matrix with entries in [a; b]; 0 < a b. Let Xn = ( i;j=1 be a random matrix where fx ij g are i.i.d. N(0; 1) random variables. We show that for large n,...
A Characterization of Normal Operators. (2002)
Friedland,Shmuel, Tartar,Luc C.
Let A be a bounded linear operator in a Hilbert space. If A is normal then log(absolute value of ((e to the At)u)) and log(absolute value of ((e to the A prime t)u)) are convex functions for all u...
Discrete Lyapunov exponents and Hausdorff dimension (1997)
this paper we generalize these results to a discrete setting as follows. Let ! n ?= f1; :::; ng be an alphabet on n symbols. Denote by N;! n ?
On the second real eigenvalue of nonnegative and Z-matrices (1997)
Shmuel Friedland, Reinhard Nabben, Fakultat Fur Mathematik
We give bounds for the second real eigenvalue of nonnegative matrices and Z--matrices. Furthermore, we establish upper bounds for the maximal spectral radii of principal submatrices of nonnegative...
The Maximal Orders Of Finite Subgroups In GL n (Q) (1997)
We give a relatively simple proof that the orthogonal group over the integers is the unique finite subgroup (up to a conjugation) in GLn (Z) of the maximal order for n ?? 1. x0. Introduction In our...
The Sparse Basis Problem And Multilinear Algebra (1995)
Richard A. Brualdi, Shmuel Friedland, Alex Pothen
. Let A be a k by n underdetermined matrix. The sparse basis problem for the row space W of A is to find a basis of W with the fewest number of nonzeros. Suppose that all the entries of A are...
Limit sets of free groups, Hausdorff dimension and subshifts of finite type (1995)
Let X be a locally compact separable metric space which has an infinite diameter. Assume that X has a natural compact boundary @X with a corresponding induced (cordal) metric. Suppose that G is a...
Properly Discontinuous Groups on Certain Matrix Homogeneous Spaces (1994)
. We characterize discrete groups \Gamma ae GL(n;R) which act properly discontinuously on the homogeneous space GL(m;R)nGL(n;R). x1. Introduction A manifold M is called a complete locally homogeneous...
Towards theory of generic Principal Component Analysis
Torokhti, Anatoli, Friedland, Shmuel
In this paper, we consider a technique called the generic Principal Component Analysis (PCA) which is based on an extension and rigorous justification of the standard PCA. The generic PCA is treated...
On Cheeger-type inequalities for weighted graphs
Shmuel Friedland, Reinhard Nabben, Fakultat Fur Mathematik
We give several bounds on the second smallest eigenvalue of the weighted Laplacian matrix of a finite graph and on the second largest eigenvalue of its weighted adjacency matrix. We establish...