- 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
-
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, 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
-Last
Updated: April 14, 2014
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