• 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

• Compressive sensing of sparse tensors, #
  
• Generalized tensor compressive sensing, Multimedia and Expo (ICME), 2013, IEEE International Conference, 15-19 July 2013, ISSN: 1945-7871.
  
• On best rank one approximation of tensors, Journal of Numerical Linear Algebra with Applications 20 (2013), 942-955 #
  
• 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 on the number of perfect matchings and directed 2-factors in graphs with given number of vertices and edges,  #
  
• Upper bounds for perfect matchings in pfaffian and planar graphs,  The Electronic Journal of Combinatorics, 20 (2013) Paper 64 #
  
• 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

• On convex optimization problems in quantum information theory, #
  
• Best approximation on semi-algebraic sets and k-border rank approximation of symmetric tensors, #
  
• Universal uncertainty relations, Physical Review Letters 111, 230401 (2013), 5pp, #
  
• On the extreme points of quantum channels, #
  
• Nonnegative definite hermitian matrices with increasing principal minors, Special Matrices, 1 (2013), 1-2, #
  
• The number of singular vector tuples and uniqueness of best rank one approximation of tensors, Foundation of Computational Mathematics (to appear) #
  
• 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
• 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, 436 (2012), 478--497, 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----------------------

• Best approximation by algebraic and semi-algebraic sets, Colloquium, NYU, Courant, May 12, 2014 (second part)#
  
• Computational Problems in Tensors, Numerical analysis & scientific computing seminar, NYU, Courant Institute, May 14, 2014 #
• A proof of the set-theoretical version of the salmon conjecture, LAA Madison conference, October 11, 2012 #
  
• 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