 The pressure, densities and first
order phase transitions associated with
multidimensional SOFT, notions of
Positivity and the Geometry of
Polynomials, Trends in Matheamtics,
179220, 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, 113128., #
 The $1$vertex transfer matrix and
accurate estimation of channel capacity,
IEEE Transaction on Information Theory
56 (2010), 36923699, #
 Theory of Computation of
Multidimensional Entropy with an
Application to the MonomerDimer
Problem, Advances of Applied Math.
34(2005), 486522.#
Top cited paper 20052010#
 Generalized interval exchanges and the
23 conjecture, CEJM 3 (3), 2005,
412429. pdf
 Computation of entropy in statistical
mechanics and information theory,
Congr. Numer. 168 (2004),
207213. ps
file
 Multidimensional capacity, pressure
and Hausdorff dimension, Mathematical
Systems in Biology, Communications,
Computations, and Finance, Editors: J.
Rosenthal and D. Gilliam, IMA vol.
134 (2003), 183222 pdf
 Discrete Lyapunov exponents and
Hausdorff dimension, J. Ergod. Th. &
Dynam. Sys, 20 (2000), 145172.
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Sys, 20 (2000), 1551. pdf
 Hausdorff dimension, strong
hyperbolicity and complex dynamics, Dis.
Cont. Dynamical Systems, 4 (1998),
405430. pdf
 On the entropy of Zd subshifts of
finite type, Linear Algebra Appl. 252
(1997), 199220. pdf
 Entropy of graphs, semigroups and
groups, Ergodic Theory of Z^dActions,
London Math. Soc. Lecture Notes Ser.
228, 319343, Cambridge Univ. Press,
1996.pdf
 Entropy of algebraic maps, J. Fourier
Anal. Appl., Kahane's issue, (1995)
215228. pdf
 Invariant measures of groups of
homeomorphisms and Auslander's
conjecture, J. Ergod. Th. & Dynam.
Sys. 15 (1995), 10751089. pdf
 Entropy of rational selfmaps of
projective varieties, Advanced Series in
Dynamical Systems, vol. 9, 128140,
World Sci. Publishing Co., Singapure
1991 pdf
 Dynamical properties of plane
polynomial automorphisms, J. Ergod. Th.
& Dynam. Sys. 9 (1989), 6799. #
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,
1519 July 2013, ISSN: 19457871.
 On best rank one approximation of
tensors, Journal of Numerical Linear
Algebra with Applications 20 (2013),
942955 #
 Upper bounds on the magnitude of
solutions of certain linear systems with
integer coefficients, Electronic
Journal of Linear Algebra, vol. 24,
113125 #
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. 421430, 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),
16151619 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), 661669, pdf.
 Nonnegativity of Schur complements of
nonnegative idempotent matrices,
Electronic Journal of Linear Algebra, 17
(2008), 426435 #
 Fast low rank approximations of
matrices and tensors, to appear in
Electronic Journal of Linear Algebra, 15
pp, 2008. pdf
 Generalized rankconstrained matrix
approximations, SIAM J. Matrix Anal.
Appl. 29 (2007),
656659.#
 A simultaneous reconstruction of
missing data in DNA microarrays, Linear
Alg. Appl 416 (2006), 828. file
 An algorithm for missing value
estimation for DNA microarray data,
Proc. ICASSP, 2006 pdf
 Fast MonteCarlo low rank
approximations for matrices, Proc. IEEE
Conference SoSE, Los Angeles, 2006,
218223. pdf
 A New Approach to Generalized Singular
Value Decomposition, SIMAX 27
(2005), 434444 pdf
 Normal matrices and the completion
problem, SIMAX J. Matrix
Anal. Appl. 23(2002), 896902 normalm.ps
 Some inequalities for the spectral
radius of nonnegative matrices and
applications, (with S. Karlin), Duke
Math. J. 42 (1975), 459490. pdf
2. Graphs and combinatorics
 Upper bounds on the number of perfect
matchings and directed 2factors 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 24:1833,
2012, #
 Analogs of the van der Waerden and
Tverberg conjectures for haffnians, #
 An Asymptotic Expansion and Recursive
Inequalities for the MonomerDimer
Problem, Journal of Statistical Physics,
143(2):306325, 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 meanvariance coordinates
of graph resolvent,
 LAA 431 (2009), 13672379 , 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, 128. pdf
 An upper bound for the minimum rank of
a graph, Linear Algebra Appl.,
429(7):16291638, 2008. pdf
 The maximum number of perfect
matchings in graphs with a given degree
sequence, The Electronic Journal of
Combinatorics, 15 (2008), #N13, 12. 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, 119. pdf
 Lower bounds for partial matchings in
regular bipartite graphs and
applications to the monomerdimer
entropy, Combinatorics, Probability and
Computing, 17 (2008), 347361. pdf
 On the validations of the asymptotic
matching conjectures, J. Stat. Phys.,
133(3):513533, 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), 458461. arXiv:math/0612061
pdf
 A polynomialtime 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,
6167. arXiv:cs/0607135
pdf
 Exact conditions for countable
inclusionexclusion identity and
extensions, International Journal of
Pure and Applied Mathematics, 29 (2006),
177182. arXiv:math/0602035
pdf
 Explicit constructions of families of
LDPC codes with no 4cycles, IEEE Trans.
Inform. Theory 50 (2004), 112. pdf
 Concentration of permanent estimators
for certain large matrices, Annals of
Applied Probability, 14(2004),
15591576. pdf
 On Cheegertype inequalities, J.
Graph Theory 41 (2002), 117 ps
file
 Spectra of expansion graphs, (with H.
Schneider), Elec. Lin. Alg., 6
(1999/2000),
210. pdf
3. Geometry
 pMetrics on GL(n,C)/U_n and their
Busemann compactifications, Linear
Algebra Appl. 376 (2004), 118. pmetricm.pdf
 Revisiting Siegel upper half plane I,
Linear Algebra Appl. 376 (2004) 1944, as PDF
 Revisiting Siegel upper half lane II,
Linear Algebra Appl. 376 (2004), 4567,
as
PDF
 Properly discontinuous groups on
certain matrix homogeneous
spaces, Linear Multilin. Algebra 43
(1997), 151167. pdf
4. Theoretical properties
 On convex optimization problems in
quantum information theory, #
 Best approximation on semialgebraic
sets and kborder 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), 12,
#
 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), 1940,#
 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):0422031  0422038, 2011 arXiv:1012.4221
 A proof of the settheoretic 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),
38723884.
 On tensors of border rank $l$ in
$\C^{m\times n\times l}$, Linear Algebra
and its Applications 438 (2013),
713737, arXiv:1003.1968
Received the salmon prize for
solving the settheoretic 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) 197225, arXiv:0909.1216, arXiv:0909.1216
 PerronFrobenius theorem for
nonnegative multilinear forms and
extensions, Linear Alg. Appl. 438
(2013), 738749, 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 3tensors ,
Linear Algebra and its Applications, 436
(2012), 478497, arXiv:0805.3777
 Asymptotic Positivity of Hurwitz
Product Traces: Two Proofs, LAA 432
(2010), 13631383, pdf
 Remarks on BMV conjecture , arXiv:0804.3948
 2addic valuations of certain ratios
of products of factorials and
applications, Linear Alg.Appl., 426
(2007), 159189. pdf
 Matrices over Integral Domains,
Chapter 23, Handbook of Linear Algebra,
Edited by Leslie Hogben, CRC Press, Boca
Raton, 2006, 231  2311.
pdf
 Similarities of Families of Matrices,
Chapter 24, Handbook of Linear Algebra,
Edited by Leslie Hogben, CRC Press, Boca
Raton, 2006, 241  2412. pdf
 Convergence of products of matrices in
projective spaces, Linear Alg. Appl
413(2006), 247263. pdf
 On "The multiplicity of eigenvalues"
by P. Lax, BAMS 6(1982), in Lax Selecta
II, 588590, 2005. pdf
 Positive entries of stable matrices,
ELA 12 (2005), 1724 #
pdf
 Generalizations of the odd
degree theorem and applications, Israel
J. Math.136 (2003), 353371. pdf
 On spaces of matrices containing a
nonzero matrix of bounded rank,
Pacific J. Math. 207 (2002), 157176 pdf
5. Functional Analysis
 Finite and infinite dimensional
generalizations of Klyachko theorem,
Linear Algebra Appl. 319 (2000), 322. pdf
 The limit of the product of the
parametrized exponential of two
operators, J. Functional
 Analysis 210 (2004), 436464. pdf
Slides of
Lectures
 Best approximation by algebraic and
semialgebraic 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 settheoretical 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 68, 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 30Friday February 4, 2011, pdf
 PerronFrobenius theorem for
nonnegative multilinear forms and
extensions, PolyTech Univ. HongKong,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, HongKong , 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, UWaterloo 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 3tensors,
NIU LA'09 pdf
 Results and problems for 3tensors,
Haifa Matrix Conference, May 2009 pdf
 Tensors: theory and applications,
TTIC, March 2, 2009 pdf
 Results and problems for 3tensors,
NSF TENSOR COMPUTATION WORKSHOP,
Arlington, February 2021, 2009 pdf
 Approximation of matrices and tensors,
KU, December 11, 2008 pdf
 Eigenvalue inequalities, logconvexity
and scaling: old results and new
applications, a tribute to Sam Karlin,
HonkKong 2010, pdf
 Maximizing Sum Rates in Gaussian
Interferencelimited Channels , Hamilton
Instittute, August 5, 2008 pdf
 3Tensors, 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 monomerdimer
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
 3Tensors: ranks and approximations,
StanfordYahoo conference, June 2006 pdf
 Fast MonteCarlo 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
 Multidimensional entropy and the
monomerdimer problem, HU, Technion,
TAU, 2003 pdf
 Multidimensional 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
MonteCarlo
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: 9783639179941,
book
cover, contents
of the book
 MATRICES a book draft in preparation
pdf
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Updated: April 14, 2014
