Topics: Matrices&Applications, Statistical Mechanics, Math. Biology, Dynamical Systems SELECTED PUBLISHED PAPERS: 1990-2010 ENTROPY, DYNAMICS, ERGODIC THEORY The pressure, densities and first order phase transitions associated with multidimensional SOFT, notions of Positivity and the Geometry of Polynomials, Trends in Matheamtics, 179-220, 2011 Springer Basel AG #  Entropy of holomorphic and rational maps: a survey, Recent Progress in Dynamics, Edited by Boris Hasselblatt, Mathematical Science Research Institute Publications, vol. 54, Cambridge University Press, 2007, 113--128., # The $1$-vertex transfer matrix and accurate estimation of channel capacity, IEEE Transaction on Information Theory 56 (2010), 3692-3699, # Theory of Computation of Multidimensional Entropy with an Application to the Monomer-Dimer Problem, Advances of Applied Math. 34(2005), 486-522.#  Top cited paper 2005-2010# Generalized interval exchanges and the 2-3 conjecture, CEJM 3 (3), 2005, 412-429. pdf Computation of entropy in statistical mechanics and information theory,  Congr. Numer. 168 (2004), 207--213.  ps file  Multi-dimensional capacity, pressure and Hausdorff dimension, Mathematical Systems in Biology, Communications, Computations, and Finance, Editors: J. Rosenthal and D. Gilliam,  IMA vol. 134 (2003),  183-222 pdf Discrete Lyapunov exponents and Hausdorff dimension, J. Ergod. Th. & Dynam. Sys, 20 (2000), 145-172. Corrections: J. Ergod. Th. & Dynam. Sys, 20 (2000), 1551. pdf Hausdorff dimension, strong hyperbolicity and complex dynamics, Dis. Cont. Dynamical Systems, 4 (1998), 405-430. pdf On the entropy of Z-d subshifts of finite type, Linear Algebra Appl. 252 (1997), 199-220. pdf Entropy of graphs, semigroups and groups, Ergodic Theory of Z^d-Actions, London Math. Soc. Lecture Notes Ser. 228, 319-343, Cambridge Univ. Press, 1996.pdf Entropy of algebraic maps, J. Fourier Anal. Appl., Kahane's issue, (1995) 215-228. pdf Invariant measures of groups of homeomorphisms and Auslander's conjecture, J. Ergod. Th. & Dynam. Sys. 15 (1995), 1075-1089. pdf Entropy of rational self-maps of projective varieties, Advanced Series in Dynamical Systems, vol. 9, 128-140, World Sci. Publishing Co., Singapure 1991 pdf Dynamical properties of plane polynomial automorphisms, J. Ergod. Th. & Dynam. Sys. 9 (1989), 67-99. # MATRICES, TENSORS AND RELATED SUBJECTS: 1. Applied and computational aspects On best rank one approximation of tensors, to appear in Journal of Numerical Linear Algebra, # Upper bounds on the magnitude of solutions of certain linear systems with integer coefficients,  Electronic Journal of Linear Algebra, vol. 24, 113-125  #  arXiv:1108.4078 Numerical estimation of the relative entropy of entanglement,Physical Review A, 82(5). DOI: 10.1103/PhysRevA.82.052336, pdf Spectrum Management in Multiuser Cognitive Wireless Networks: Optimality and Algorithm, IEEE Journal on Selected Areas in Communications, Vol. 29, No. 2, pp. 421-430, Feb. 2011, pdf A note on the nonzero spectrum of irreducible matrices, Linear and Multilinear Algebra, to appear, arXiv:0910.3415 Positive diagonal scaling of a nonnegative tensor to one with prescribed slice sums,  Linear Algebra and its Applications 434 (2011), 1615-1619  arXiv:0908.2368  Nonnegative Matrix Inequalities and Their Application to Nonconvex Power Control Optimization, to appear in SIAM J. Matrix Anal. Appl pdf Best subspace tensor approximations, arXiv.0805.4220 pdf Towards theory of generic Principal Component Analysis, J. Multivariate Analysis, 100 (2009), 661-669, pdf. Nonnegativity of Schur complements of nonnegative idempotent matrices, Electronic Journal of Linear Algebra, 17 (2008), 426-435 #  Fast low rank approximations of matrices and tensors, to appear in Electronic Journal of Linear Algebra, 15 pp, 2008. pdf Generalized rank-constrained matrix approximations, SIAM J. Matrix Anal. Appl. 29 (2007), 656--659.# A simultaneous reconstruction of missing data in DNA microarrays, Linear Alg. Appl 416 (2006), 8-28. file An algorithm for missing value estimation for DNA microarray data, Proc. ICASSP, 2006 pdf  Fast Monte-Carlo low rank approximations for matrices, Proc. IEEE Conference SoSE, Los Angeles, 2006, 218-223. pdf  A New Approach to Generalized Singular Value Decomposition,  SIMAX 27 (2005), 434-444  pdf Normal matrices and the completion problem,  SIMAX  J. Matrix Anal. Appl. 23(2002), 896-902 normalm.ps  Some inequalities for the spectral radius of nonnegative matrices and applications, (with S. Karlin), Duke Math. J. 42 (1975), 459-490. pdf 2. Graphs and combinatorics Upper bounds for perfect matchings in pfaffian and planar graphs,  to appear in The Electronic Journal of Combinatorics, # Results and open problems in matchings in regular graphs,  Electronic Journal of Linear Algebra 24:18-33, 2012, # Analogs of the van der Waerden and Tverberg conjectures for haffnians, # An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem, Journal of Statistical Physics, 143(2):306-325, 2011 arXiv:1011.6579 On the minimum rank of a graph over finite fields, Linear Algebra and its Applications, to appear, arXiv:1006.0770 Graph isomorphism and volumes of convex bodies, arXiv:0911.1739 A note on fractal structure of cubic graphs in the mean-variance coordinates of graph resolvent, LAA 431 (2009), 1367-2379 , pdf On the First Eigenvalue of Bipartite Graphs, arXiv:0809.1615v1 , Electron. J. Combin., 15(1):Research Paper 144, 23, 2008. MR2465768 On the graph isomorphism problem, arXiv:0801.0398v3, pdf On the number of matchings in regular graphs, The Electronic Journal of Combinatorics, 15 (2008), #R110, 1-28. pdf An upper bound for the minimum rank of a graph, Linear Algebra Appl., 429(7):1629--1638, 2008. pdf The maximum number of perfect matchings in graphs with a given degree sequence, The Electronic Journal of Combinatorics, 15 (2008), #N13, 1-2. pdf Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers, The Electronic Journal of Combinatorics, 15 (2008), #R25, 1-19. pdf Lower bounds for partial matchings in regular bipartite graphs and applications to the monomer-dimer entropy, Combinatorics, Probability and Computing, 17 (2008), 347-361. pdf On the validations of the asymptotic matching conjectures, J. Stat. Phys., 133(3):513--533, 2008. pdf  FPRAS for computing a lower bound for weighted matching polynomial of graphs, arXiv:cs/0703029 pdf The Polytope of Dual Degree Partitions, Linear Alg.Appl., 426 (2007), 458-461. arXiv:math/0612061 pdf A polynomial-time approximation algorithm for the number of $k$-matchings in bipartite graphs, Mathematical papers in honour of Eduardo Marques de S\'a, Textos de Matem\'atica #39, Coimbra University, Portugal, 2006, 61-67. arXiv:cs/0607135 pdf Exact conditions for countable inclusion-exclusion identity and extensions, International Journal of Pure and Applied Mathematics, 29 (2006), 177-182. arXiv:math/0602035   pdf  Explicit constructions of families of LDPC codes with no 4-cycles, IEEE Trans. Inform. Theory 50 (2004), 1-12. pdf  Concentration of permanent estimators for certain large matrices, Annals of Applied Probability, 14(2004), 1559-1576. pdf On Cheeger-type inequalities,  J. Graph Theory 41 (2002), 1-17 ps file Spectra of expansion graphs, (with H. Schneider), Elec. Lin. Alg., 6 (1999/2000), 2-10. pdf 3. Geometry p-Metrics on GL(n,C)/U_n and their Busemann compactifications, Linear Algebra Appl. 376 (2004), 1-18.  pmetricm.pdf  Revisiting Siegel upper half plane I, Linear Algebra Appl. 376 (2004) 19-44, as PDF  Revisiting Siegel upper half lane II, Linear Algebra Appl. 376 (2004), 45-67, as PDF Properly discontinuous groups on certain matrix homogeneous spaces, Linear Multilin. Algebra 43 (1997), 151-167. pdf 4. Theoretical properties Nonnegative definite hermitian matrices with increasing principal minors,# The number of singular vector tuples and uniqueness of best rank one approximation of tensors, # Best rank one approximation of real symmetric tensors can be chosen symmetric, Front. Math. China 2013, 8(1), 19-40,# The minimum entropy output of a quantum channel is locally additive,  InformationTheory, IEEE Transactions,  vol. PP, issue 99, 2012  arXiv:1105.6122 publApr12. The automorphism group of separable states in quantum information theory, Journal of Mathematical Physics, 52(042203):042203-1 -- 042203-8, 2011 arXiv:1012.4221 A proof of the set-theoretic version of the salmon conjecture, arXiv:1104.1776 , slightly revised version #, Journal of Algebra 356 (2012), 374–379. An explicit expression for the relative entropy of entanglement in all dimensions,  Journal of Mathematical Physics 52, 052201 (2011), arXiv:1007.4544 Submodular spectral functions of principal submatrices of an hermitian matrix arXiv:1007.3478 , Linear Algebra and its Applications,  438 (2013), 3872-3884. On tensors of border rank $l$ in $\C^{m\times n\times l}$, Linear Algebra and its Applications 438 (2013), 713-737, arXiv:1003.1968 Received the salmon prize for solving the set-theoretic version of the challenge problem posed by Elizabeth Allman http://www.dms.uaf.edu/~eallman/ Salmon photo # On Asymptotic Ratio of a Sequence of Functions Obeying a Finite Recurrence Relation, J. d'Analyse Mathematique, 113 (2011) 197--225, arXiv:0909.1216, arXiv:0909.1216 Perron-Frobenius theorem for nonnegative multilinear forms and extensions, Linear Alg. Appl. 438 (2013), 738-749, arXiv:0905.1626 Additive invariants on quantum channels and regularized minimum entropy, Proceedings of IWOTA 2008,pdf , arXiv:0809.0078 On the generic rank of 3-tensors , Linear Algebra and its Applications, In Pres, 2011, arXiv:0805.3777 Asymptotic Positivity of Hurwitz Product Traces: Two Proofs, LAA 432 (2010), 1363-1383, pdf Remarks on BMV conjecture , arXiv:0804.3948 2-addic valuations of certain ratios of products of factorials and applications, Linear Alg.Appl., 426 (2007), 159-189. pdf Matrices over Integral Domains, Chapter 23, Handbook of Linear Algebra, Edited by Leslie Hogben, CRC Press, Boca Raton, 2006, 23-1 -- 23-11.   pdf  Similarities of Families of Matrices, Chapter 24, Handbook of Linear Algebra, Edited by Leslie Hogben, CRC Press, Boca Raton, 2006, 24-1 -- 24-12.  pdf  Convergence of products of matrices in projective spaces, Linear Alg. Appl 413(2006), 247-263. pdf On "The multiplicity of eigenvalues" by P. Lax, BAMS 6(1982), in Lax Selecta II, 588-590, 2005. pdf  Positive entries of stable matrices, ELA 12 (2005), 17-24 # pdf Generalizations of  the odd degree theorem and applications, Israel J. Math.136 (2003), 353-371. pdf On spaces of matrices containing a nonzero matrix of bounded rank,  Pacific J. Math. 207 (2002), 157-176 pdf 5. Functional Analysis Finite and infinite dimensional generalizations of Klyachko theorem, Linear Algebra Appl. 319 (2000), 3-22. pdf The limit of the product of the parametrized exponential of two operators,  J. Functional Analysis 210 (2004), 436-464.  pdf    --------------------------Slides of Lectures---------------------- Completion of missing entries in matrices and tensors, Statistics Seminar, UIC, January 11, 2012 Some open problems in matchings in graphs, Stability, hyperbolicity, and zero localization of functions, AIM workshop, Palo Alto, December 9, 2011 pdf The global and local additivity problems in quantum information theory, IQIS Seminar, University of Calgary 9 November, 2011, # Approximating, denoising and completing missing entries in 2 and 3 dimensional data, Department of Informatics, University Zurich Nord 19 October, 2011, pdf From nonnegative matrices to nonnegative tensors, Workshop on Linear Algebra \& Applications, 17 October, 2011, Hamilton Institute, National University of Ireland, pdf Completion of missing entries in matrices and tensors, Department of Statistics, The University of Chicago, September 12, 2011, pdf Topics in Tensors, A Summer School by Shmuel Friedland, July 6-8, 2011, University of Coimbra, Portugal, intro, Lec1, Lec2, Lec3 Theoretical and Numerical Results and Problems in Tensors, Householder Symposium XVIII, June 14, 2011, pdf Some open problems in matchings in graphs, Linear Algebraic Techniques in Combinatorics/Graph Theory , BIRS, January 30-Friday February 4, 2011, pdf Perron-Frobenius theorem for nonnegative multilinear forms and extensions, PolyTech Univ. Hong-Kong,18 December 2010, pdf The pressure, densities and first order phase transitions associated with multidimensional SOFT, Dynamics Seminar, College Park, October 28, 2010 pdf Tensors, Hong-Kong , 2010, pdf Phylogenetic invariants and\\tensors of border rank $4$ at most in $\C^{4\times 4\times 4}$, ILAS meeting in Pisa, 22 June, 2010 pdf Tensors and Matrices, Séminaire du CMAP, Ecole Polytechnique , Mardi 15 Juin 2010; West Canada Linear Algebra Meeting, May 8, 2010, pdf Matchings, permanents and their random approximations, Tutte seminar series, U. Michigan, Nov 13, 2009, U. Waterloo, Nov 20, 2009 pdf On the eigenvalues of graphs: results and conjectures, U-Waterloo Continuous Optimization Seminar, 19 November, 2009 pdf Fixed points theorems for nonnegative tensors and Newton method, SIAM LA09, Monterey, CA, October 29, 2009 pdf Theoretical and computational methods in statistical mechanics, U. Berkeley, October 26, 2009 pdf Results and problems for 3-tensors, NIU LA'09 pdf Results and problems for 3-tensors, Haifa Matrix Conference, May 2009 pdf Tensors: theory and applications, TTI-C, March 2, 2009 pdf Results and problems for 3-tensors, NSF TENSOR COMPUTATION WORKSHOP, Arlington, February 20-21, 2009 pdf Approximation of matrices and tensors, KU, December 11, 2008 pdf Eigenvalue inequalities, log-convexity and scaling: old results and new applications, a tribute to Sam Karlin, Honk-Kong 2010, pdf Maximizing Sum Rates in Gaussian Interference-limited Channels , Hamilton Instittute, August 5, 2008 pdf 3-Tensors, Geometry and Representation Theory of Tensors, MSRI, July 17, 2008, pdf Low Rank Approximations of Matrices and Tensors, 2008 SIAM Annual Meeting, July 11, 2008, pdf Counting matchings in graphs, with applications to the monomer-dimer models, Berlin 8.2.08, Vienna19.2.08, Umea 9.4.08, Stockholm 16.4.08 pdf "Fast low rank approximations of matrices and tensors", Gene Golub memorial meeting, Berlin, February 29, 2008. pdf "Analysis of Big Multidimensional Data", Google Tech Talks, June 1, 2007. link Pressure and phase transition in Potts models in Statistical Mechanics, Seminar Hebrew Univ., December 2006 pdf Matchings and Independent Sets: Problems, Conjectures and Results, Hamilton Institute, July 2006 pdf 3-Tensors: ranks and approximations, Stanford-Yahoo conference, June 2006 pdf Fast Monte-Carlo Low Rank Approximations for Matrices, IEEE SoSE, 2006 pdf Entropy of holomorphic and rational maps, 2006 pdf  Matchings and Positive Hyperbolic Polynomial, 2005 pdf  The Role of Singular Value Decomposition in Data Analysis, 2005   pdf  Multi-dimensional entropy and the monomer-dimer problem, HU, Technion, TAU, 2003 pdf Multi-dimensional capacity, MTNS 2002 lecture pdf -------- MY STUDENTS----------------- Amir Niknejad": Application of Singular Value Decompositions to DNA Microarrays", 2005 pdf  Amir's Lecture "The Role of Singular Value Decomposition in Gene Expression Microarrays "pdf Amir's Lecture "Fast low rank approximation of matrices using Monte-Carlo techniques" pdf --------------Lecture Notes------------------- Matrices - Fall 2005 pdf Probability on Graphs - Spring 2005 pdf Methods of algebraic geometry in matrix theory pdf -------------------------------------------- APPLICATIONS OF LINEAR ALGEBRA TO DNA MICROARRAYS, A. Niknejad and S. Friedland, VDM Verlag Dr M\"uller Aktiengesellschaft\&Co.KG, Germany, 2009, ISBN: 978-3-639-17994-1, book cover, contents of the book MATRICES- a book draft in preparation pdf -Last Updated: January 10, 2012