### Bio

I am interested in developing efficient algorithms to make sense of large amounts of noisy data, extract information from observations, estimate signals from measurements. This effort spans several disciplines including statistics, computer science, information theory, machine learning.
I am also working on applications of these techniques to healthcare data analytics.

### Professional Education

• PhD, Scuola Normale Superiore, Pisa, Italy (2001)

### Journal Articles

• Localization from Incomplete Noisy Distance Measurements FOUNDATIONS OF COMPUTATIONAL MATHEMATICS Javanmard, A., Montanari, A. 2013; 13 (3): 297-345
• The phase transition of matrix recovery from Gaussian measurements matches the minimax MSE of matrix denoising. Proceedings of the National Academy of Sciences of the United States of America Donoho, D. L., Gavish, M., Montanari, A. 2013; 110 (21): 8405-8410

#### Abstract

Let X(0) be an unknown M by N matrix. In matrix recovery, one takes n < MN linear measurements y(1),…,y(n) of X(0), where y(i) = Tr(A(T)iX(0)) and each A(i) is an M by N matrix. A popular approach for matrix recovery is nuclear norm minimization (NNM): solving the convex optimization problem min ||X||*subject to y(i) =Tr(A(T)(i)X) for all 1 ? i ? n, where || · ||* denotes the nuclear norm, namely, the sum of singular values. Empirical work reveals a phase transition curve, stated in terms of the undersampling fraction ?(n,M,N) = n/(MN), rank fraction ?=rank(X0)/min {M,N}, and aspect ratio ?=M/N. Specifically when the measurement matrices Ai have independent standard Gaussian random entries, a curve ?*(?) = ?*(?;?) exists such that, if ? > ?*(?), NNM typically succeeds for large M,N, whereas if ? < ?*(?), it typically fails. An apparently quite different problem is matrix denoising in Gaussian noise, in which an unknown M by N matrix X(0) is to be estimated based on direct noisy measurements Y =X(0) + Z, where the matrix Z has independent and identically distributed Gaussian entries. A popular matrix denoising scheme solves the unconstrained optimization problem min|| Y-X||(2)(F)/2+?||X||*. When optimally tuned, this scheme achieves the asymptotic minimax mean-squared error M(?;?) = lim(M,N ? ?)inf(?)sup(rank(X) ? ? · M)MSE(X,X(?)), where M/N ? . We report extensive experiments showing that the phase transition ?*(?) in the first problem, matrix recovery from Gaussian measurements, coincides with the minimax risk curve M(?)=M(?;?) in the second problem, matrix denoising in Gaussian noise: ?*(?)=M(?), for any rank fraction 0 < ? < 1 (at each common aspect ratio ?). Our experiments considered matrices belonging to two constraint classes: real M by N matrices, of various ranks and aspect ratios, and real symmetric positive-semidefinite N by N matrices, of various ranks.

View details for DOI 10.1073/pnas.1306110110

View details for PubMedID 23650360

• Iterative Coding for Network Coding IEEE TRANSACTIONS ON INFORMATION THEORY Montanari, A., Urbanke, R. L. 2013; 59 (3): 1563-1572
• Factor models on locally tree-like graphs Annals of Probability Dembo, A., Montanari, A., Sun, N. 2013
• Finding Hidden Cliques of Size in Nearly Linear Time Deshpande, Y., Montanari, A. 2013
• Hypothesis Testing in High-Dimensional Regression under the Gaussian Random Design Model: Asymptotic Theory Javanmard, A., Montanari, A. 2013
• Confidence Intervals and Hypothesis Testing for High-Dimensional Regression Javanmard, A., Montanari, A. 2013
• High Dimensional Robust M-Estimation: Asymptotic Variance via Approximate Message Passing Donoho, D., Montanari, A. 2013
• Lossy Compression of Discrete Sources via the Viterbi Algorithm IEEE TRANSACTIONS ON INFORMATION THEORY Jalali, S., Montanari, A., Weissman, T. 2012; 58 (4): 2475-2489
• The LASSO Risk for Gaussian Matrices IEEE TRANSACTIONS ON INFORMATION THEORY Bayati, M., Montanari, A. 2012; 58 (4): 1997-2017
• The weak limit of Ising models on locally tree-like graphs PROBABILITY THEORY AND RELATED FIELDS Montanari, A., Mossel, E., Sly, A. 2012; 152 (1-2): 31-51
• Universality in Polytope Phase Transitions and Iterative Algorithms 2012 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT) Bayati, M., Lelarge, M., Montanari, A. 2012
• Information-Theoretically Optimal Compressed Sensing via Spatial Coupling and Approximate Message Passing 2012 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT) Donoho, D. L., Javanmard, A., Montanari, A. 2012
• ACCELERATED TIME-OF-FLIGHT MASS SPECTROMETRY 2012 IEEE STATISTICAL SIGNAL PROCESSING WORKSHOP (SSP) Ibrahimi, M., Montanari, A., Moore, G. S. 2012: 432-435
• Subsampling at Information Theoretically Optimal Rates 2012 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT) Javanmard, A., Montanari, A. 2012
• Universality in Polytope Phase Transitions and Message Passing Algorithms Bayati, M., Lelarge, M., Montanari, A. 2012
• The noise sensitivity phase transition in compressed sensing IEEE Transactions on Information Theory Donoho, D., L., Maleki, A., Montanari, A. 2012
• The Noise-Sensitivity Phase Transition in Compressed Sensing IEEE TRANSACTIONS ON INFORMATION THEORY Donoho, D. L., Maleki, A., Montanari, A. 2011; 57 (10): 6920-6941
• MAJORITY DYNAMICS ON TREES AND THE DYNAMIC CAVITY METHOD ANNALS OF APPLIED PROBABILITY Kanoria, Y., Montanari, A. 2011; 21 (5): 1694-1748

View details for DOI 10.1214/10-AAP729

View details for Web of Science ID 000297027800003

• Applications of the Lindeberg Principle in Communications and Statistical Learning IEEE TRANSACTIONS ON INFORMATION THEORY Korada, S. B., Montanari, A. 2011; 57 (4): 2440-2450
• Subexponential convergence for information aggregation on regular trees 2011 50TH IEEE CONFERENCE ON DECISION AND CONTROL AND EUROPEAN CONTROL CONFERENCE (CDC-ECC) Kanoria, Y., Montanari, A. 2011: 5317-5322
• Fast Convergence of Natural Bargaining Dynamics in Exchange Networks PROCEEDINGS OF THE TWENTY-SECOND ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS Kanoria, Y., Bayati, M., Borgs, C., Chayes, J., Montanari, A. 2011: 1518-1537
• Localization from Incomplete Noisy Distance Measurements 2011 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT) Javanmard, A., Montanari, A. 2011: 1584-1588
• RECONSTRUCTION AND CLUSTERING IN RANDOM CONSTRAINT SATISFACTION PROBLEMS SIAM JOURNAL ON DISCRETE MATHEMATICS Montanari, A., Restrepo, R., Tetali, P. 2011; 25 (2): 771-808

View details for DOI 10.1137/090755862

View details for Web of Science ID 000292302000024

• Information Theoretic Limits on Learning Stochastic Differential Equations 2011 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT) Bento, J., Ibrahimi, M., Montanari, A. 2011: 855-859
• Factor models on locally tree-like graphs Dembo, A., Montanari, A., Sun, N. 2011
• Accurate Prediction of Phase Transitions in Compressed Sensing via a Connection to Minimax Denoising Donoho, D., Johnstone, I., Montanari, A. 2011
• Information-Theoretically Optimal Compressed Sensing via Spatial Coupling and Approximate Message Passing Donoho, D., Javanmard, A., Montanari, A. 2011
• The spread of innovations in social networks PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Montanari, A., Saberi, A. 2010; 107 (47): 20196-20201

#### Abstract

Which network structures favor the rapid spread of new ideas, behaviors, or technologies? This question has been studied extensively using epidemic models. Here we consider a complementary point of view and consider scenarios where the individuals' behavior is the result of a strategic choice among competing alternatives. In particular, we study models that are based on the dynamics of coordination games. Classical results in game theory studying this model provide a simple condition for a new action or innovation to become widespread in the network. The present paper characterizes the rate of convergence as a function of the structure of the interaction network. The resulting predictions differ strongly from the ones provided by epidemic models. In particular, it appears that innovation spreads much more slowly on well-connected network structures dominated by long-range links than in low-dimensional ones dominated, for example, by geographic proximity.

View details for DOI 10.1073/pnas.1004098107

View details for Web of Science ID 000284529000013

View details for PubMedID 21076030

• Matrix Completion from Noisy Entries JOURNAL OF MACHINE LEARNING RESEARCH Keshavan, R. H., Montanari, A., Oh, S. 2010; 11: 2057-2078
• Matrix Completion From a Few Entries IEEE TRANSACTIONS ON INFORMATION THEORY Keshavan, R. H., Montanari, A., Oh, S. 2010; 56 (6): 2980-2998
• ISING MODELS ON LOCALLY TREE-LIKE GRAPHS ANNALS OF APPLIED PROBABILITY Dembo, A., Montanari, A. 2010; 20 (2): 565-592

View details for DOI 10.1214/09-AAP627

View details for Web of Science ID 000283529500007

• Regularization for Matrix Completion 2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY Keshavan, R. H., Montanari, A. 2010: 1503-1507
• On the deletion channel with small deletion probability 2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY Kanoria, Y., Montanari, A. 2010: 1002-1006
• The dynamics of message passing on dense graphs, with applications to compressed sensing 2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY Bayati, M., Montanari, A. 2010: 1528-1532
• Tight Thresholds for Cuckoo Hashing via XORSAT AUTOMATA, LANGUAGES AND PROGRAMMING, PT I Dietzfelbinger, M., Goerdt, A., Mitzenmacher, M., Montanari, A., Pagh, R., Rink, M. 2010; 6198: 213-225
• An Empirical Scaling Law for Polar Codes 2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY Korada, S. B., Montanari, A., Telatar, E., Urbanke, R. 2010: 884-888
• Ising models on locally tree-like graphs Annals of Applied Probability Dembo, A., Montanari, A. 2010
• Majority dynamics on trees and the dynamic cavity method Annals of Applied Probability Kanoria, Y., Montanari, A. 2010
• Graphical Models Concepts in Compressed Sensing Montanari, A. 2010
• Message-passing algorithms for compressed sensing PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Donoho, D. L., Maleki, A., Montanari, A. 2009; 106 (45): 18914-18919

#### Abstract

Compressed sensing aims to undersample certain high-dimensional signals yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a known basis. Currently, the best known sparsity-undersampling tradeoff is achieved when reconstructing by convex optimization, which is expensive in important large-scale applications. Fast iterative thresholding algorithms have been intensively studied as alternatives to convex optimization for large-scale problems. Unfortunately known fast algorithms offer substantially worse sparsity-undersampling tradeoffs than convex optimization. We introduce a simple costless modification to iterative thresholding making the sparsity-undersampling tradeoff of the new algorithms equivalent to that of the corresponding convex optimization procedures. The new iterative-thresholding algorithms are inspired by belief propagation in graphical models. Our empirical measurements of the sparsity-undersampling tradeoff for the new algorithms agree with theoretical calculations. We show that a state evolution formalism correctly derives the true sparsity-undersampling tradeoff. There is a surprising agreement between earlier calculations based on random convex polytopes and this apparently very different theoretical formalism.

View details for DOI 10.1073/pnas.0909892106

View details for Web of Science ID 000271637500010

View details for PubMedID 19858495

• The Generalized Area Theorem and Some of its Consequences IEEE TRANSACTIONS ON INFORMATION THEORY Measson, C., Montanari, A., Richardson, T. J., Urbanke, R. 2009; 55 (11): 4793-4821
• Finite-Length Scaling for Iteratively Decoded LDPC Ensembles IEEE TRANSACTIONS ON INFORMATION THEORY Amraoui, A., Montanari, A., Richardson, T., Urbanke, R. 2009; 55 (2): 473-498
• Low-rank Matrix Completion with Noisy Observations: a Quantitative Comparison 2009 47TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING, VOLS 1 AND 2 Keshavan, R. H., Montanari, A., Oh, S. 2009: 1216-1222
• Matrix Completion from a Few Entries 2009 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1- 4 Keshavan, R. H., Oh, S., Montanari, A. 2009: 324-328
• Convergence to Equilibrium in Local Interaction Games 2009 50TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE: FOCS 2009, PROCEEDINGS Montanari, A., Saberi, A. 2009: 303-312
• An Iterative Scheme for Near Optimal and Universal Lossy Compression ITW: 2009 IEEE INFORMATION THEORY WORKSHOP ON NETWORKING AND INFORMATION THEORY Jalali, S., Montanari, A., Weissman, T. 2009: 231-235
• Generating random Tanner-graphs with large girth 2009 IEEE INFORMATION THEORY WORKSHOP (ITW 2009) Bayati, M., Keshavan, R., Montanari, A., Oh, S., Saberi, A. 2009: 154-157
• Generating Random Graphs with Large Girth PROCEEDINGS OF THE TWENTIETH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS Bayati, M., Montanari, A., Saberi, A. 2009: 566-575
• Maxwell Construction: The Hidden Bridge Between Iterative and Maximum a Posteriori Decoding IEEE TRANSACTIONS ON INFORMATION THEORY Measson, C., Montanari, A., Urbanke, R. 2008; 54 (12): 5277-5307
• Estimating random variables from random sparse observations EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS Montanari, A. 2008; 19 (4): 385-403

View details for DOI 10.1002/ett.1289

View details for Web of Science ID 000257012200005

• Clusters of solutions and replica symmetry breaking in random k-satisfi ability JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT Montanari, A., Ricci-Tersenghi, F., Semerjian, G. 2008
• Counter Braids 2008 IEEE INFORMATION THEORY WORKSHOP Lu, Y., Montanari, A., Prabhakar, B. 2008: 220-221
• Counter Braids: A Novel Counter Architecture for Per-Flow Measurement SIGMETRICS'08: PROCEEDINGS OF THE 2008 INTERNATIONAL CONFERENCE ON MEASUREMENT & MODELING OF COMPUTER SYSTEMS Lu, Y., Montanari, A., Prabhakar, B., Dharmapurikar, S., Kabbani, A. 2008; 36 (1): 121-132
• Counter Braids: Asymptotic Optimality of the Message Passing Decoding Algorithm 2008 46TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING, VOLS 1-3 Lu, Y., Montanari, A., Prabhakar, B. 2008: 209-216
• Learning Low Rank Matrices from O(n) Entries 2008 46TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING, VOLS 1-3 Keshavan, R. H., Montanari, A., Oh, S. 2008: 1365-1372
• Computing the threshold shift for general channels 2008 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-6 Ezri, J., Urbanke, R., Montanari, A., Oh, S. 2008: 1448-1452
• An Implementable Scheme for Universal Lossy Compression of Discrete Markov Sources DCC 2009: 2009 DATA COMPRESSION CONFERENCE, PROCEEDINGS Jalali, S., Montanari, A., Weissman, T. 2008: 292-301
• The Slope Scaling Parameter for General Channels, Decoders, and Ensembles 2008 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-6 Ezri, J., Montanari, A., Oh, S., Urbanke, R. 2008: 1443-1447
• Finite Size Scaling for the Core of Large Random Hypergraphs Annals of Applied Probability Dembo, A., Montanari, A. 2008
• Smooth compression, Gallager bound and Nonlinear sparse-graph codes 2008 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-6 Montanari, A., Mossel, E. 2008: 2474-2478
• A simple one dimensional glassy Kac model JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT Montanari, A., Sinton, A. 2007
• Gibbs states and the set of solutions of random constraint satisfaction problems PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Krzakala, F., Montanari, A., Ricci-Tersenghi, F., Semerjian, G., Zdeborova, L. 2007; 104 (25): 10318-10323

#### Abstract

An instance of a random constraint satisfaction problem defines a random subset (the set of solutions) of a large product space chiN (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and q-coloring of random regular graphs) and study the uniform measure with support on S. As the number of constraints per variable increases, this measure first decomposes into an exponential number of pure states ("clusters") and subsequently condensates over the largest such states. Above the condensation point, the mass carried by the n largest states follows a Poisson-Dirichlet process. For typical large instances, the two transitions are sharp. We determine their precise location. Further, we provide a formal definition of each phase transition in terms of different notions of correlation between distinct variables in the problem. The degree of correlation naturally affects the performances of many search/sampling algorithms. Empirical evidence suggests that local Monte Carlo Markov chain strategies are effective up to the clustering phase transition and belief propagation up to the condensation point. Finally, refined message passing techniques (such as survey propagation) may also beat this threshold.

View details for DOI 10.1073/pnas.0703685104

View details for Web of Science ID 000247500000006

View details for PubMedID 17567754

• A generalization of the finite-length scaling approach beyond the BEC 2007 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-7 Ezri, J., Montanari, A., Urbanke, R. 2007: 1011-1015
• Asymptotic rate versus design rate 2007 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-7 Measson, C., Montanari, A., Urbanke, R. 2007: 1541-1545
• Reconstruction for models on random graphs 48TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS Gerschenfeld, A., Montanari, A. 2007: 194-204
• How to Find Good Finite-Length Codes: From Art Towards Science European Transactions on Telecommunications Amraoui, A., Montanari, A., Urbanke, R. 2006
• From Large Scale Rearrangements to Mode Coupling Phenomenology Physical Review Letters Montanari, A., Semerjian, G. 2005
• How to Compute Loop Corrections to Bethe Approximation Journal of Statistical Mechanics Montanari, A., Rizzo, T. 2005
• Tight bounds for LDPC and LDGM codes under MAP decoding IEEE Transactions on Information Theory Montanari, A. 2005
• Instability of one-step replica-symmetry-broken phase in satisfiability problems Journal of Physics A Montanari, A., Parisi, G., Ricci-Tersenghi, F. 2004
• On the stochastic dynamics of disordered spin models Journal of Statistical Physics Semerjian, G., Cugliandolo, L., F., Montanari, A. 2004
• The Phase Diagram of Random Heteropolymers Physical Review Letters Montanari, A., Mueller, M., Mezard, M. 2004
• Glassy phases in Random Heteropolymers with correlated sequences Journal of Chemical Physics Mueller, M., Montanari, A., Mezard, M. 2004
• On the cooling-schedule dependence of the dynamics of mean-field glasses Physical Review B Montanari, A., Ricci-Tersenghi, F. 2004
• A microscopic description of the aging dynamics: fluctuation-dissipation relations, effective temperature and heterogeneities Physical Review Letters Montanari, A., Ricci-Tersenghi, F. 2003
• Alternative translation techniques for propositional and first-order modal logics JOURNAL OF AUTOMATED REASONING Montanari, A., POLICRITI, A., Slanina, M. 2002; 28 (4): 397-415
• The dynamic phase transition for decoding algorithms Physical Review E Franz, S., Leone, M., Montanari, A., Ricci-Tersenghi, F. 2002; 66
• Optimizing searches via rare events Physical Review Letters Montanari, A., Zecchina, R. 2002
• The glassy phase of Gallager codes The European Physical Journal B Montanari, A. 2001
• Asymptotically free models and discrete non-Abelian groups Physics Letters B Caracciolo, S., Montanari, A., Pelissetto, A. 2001
• Hairpin formation and elongation of biomolecules Physical Review Letters Montanari, A., Mezard, M. 2001
• A guided tour through some extensions of the event calculus COMPUTATIONAL INTELLIGENCE Cervesato, I., Franceschet, M., Montanari, A. 2000; 16 (2): 307-347
• Turbo codes: the phase transition The European Physical Journal B Montanari, A. 2000
• The statistical mechanics of turbo codes The European Physical Journal B Montanari, A., Sourlas, N. 2000
• Operator product expansion on the lattice: a numerical test in the two-dimensional non-linear sigma-model Journal of High Energy Physics Caracciolo, S., Montanari, A., Pelissetto, A. 2000
• A general modal framework for the Event Calculus and its skeptical and credulous variants JOURNAL OF LOGIC PROGRAMMING Cervesato, I., Montanari, A. 1999; 38 (2): 111-164
• Testing the efficiency of different improvement programs Nuclear Physics B Caracciolo, S., Montanari, A., Pelissetto, A. 1999
• Event Calculus with explicit quantifiers FIFTH INTERNATIONAL WORKSHOP ON TEMPORAL REPRESENTATION AND REASONING - PROCEEDINGS Cervesato, I., Franceschet, M., Montanari, A. 1998: 81-88
• COEVAL AR-40/AR-39 AGES OF 65.0 MILLION YEARS AGO FROM CHICXULUB CRATER MELT ROCK AND CRETACEOUS-TERTIARY BOUNDARY TEKTITES SCIENCE Swisher, C. C., GrajalesNishimura, J. M., Montanari, A., MARGOLIS, S. V., Claeys, P., Alvarez, W., Renne, P., CedilloPardo, E., Maurrasse, F. J., Curtis, G. H., Smit, J., McWilliams, M. O. 1992; 257 (5072): 954-958

#### Abstract

(40)Ar/(39)Ar dating of drill core samples of a glassy melt rock recovered from beneath a massive impact breccia contained within the 180-kilometer subsurface Chicxulub crater in Yucatán, Mexico, has yielded well-behaved incremental heating spectra with a mean plateau age of 64.98 +/- 0.05 million years ago (Ma). The glassy melt rock of andesitic composition was obtained from core 9 (1390 to 1393 meters) in the Chicxulub 1 well. The age of the melt rock is virtually indistinguishable from (40)Ar/(39)Ar ages obtained on tektite glass from Beloc, Haiti, and Arroyo el Mimbral, northeastern Mexico, of 65.01 +/- 0.08 Ma (mean plateau age for Beloc) and 65.07 +/- 0.10 Ma (mean total fusion age for both sites). The (40)Ar/(39)Ar ages, in conjunction with geochemical and petrological similarities, strengthen the recent suggestion that the Chicxulub structure is the source for the Haitian and Mexican tektites and is a viable candidate for the Cretaceous-Tertiary boundary impact site.

View details for Web of Science ID A1992JH82700032

View details for PubMedID 17789640

### Books and Book Chapters

• Graphical Models Concepts in Compressed Sensing in Compressed Sensing Montanari, A. Cambridge university PRess. 2012: 1
• Gibbs Measures and Phase Transitions on Sparse Random Graphs Brazilian Journal of Probability and Statistics Dembo, A., Montanari, A. 2008 Brazilian School of Probability. 2010: 1
• Information, Physics, and Computation Mezard, M., Montanari, A. Oxford University Press. 2009
• Modern Coding Theory: The Statistical Mechanics and Computer Science Point of View Les Houches Summer School on Mathematical Statistical Physics Montanari, A., Urbanke, R. Elsevier. 2007: 1
• Two Lectures on Iterative Coding and Statistical Mechanics Les Houches Summer School on Mathematical Statistical Physics Montanari, A. Elsevier. 2006: 1
• Approximate analysis of search algorithms with “physical” methods Phase Transitions and Algorithmic Complexity Cocco, S., Monasson, R., Montanari, A., Semerjian, G. Oxford. 2006: 1

### Conference Proceedings

• The Dynamics of Message Passing on Dense Graphs, with Applications to Compressed Sensing Bayati, M., Montanari, A. IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. 2011: 764-785
• Compressed Sensing over l(p)-balls: Minimax Mean Square Error Donoho, D., Johnstone, I., Maleki, A., Montanari, A. IEEE. 2011: 129-133
• Gossip PCA Korada, S., Montanari, A., Oh, S. 2011
• Distributed Storage for Intermittent Energy Sources: Control Design and Performance Limits Kanoria, Y., Montanari, A., Tse, D., Zhang, B. 2011
• Learning Networks of Stochastic Differential Equations Bento, J., Ibrahimi, M., Montanari, A. 2010
• Tight Thresholds for Cuckoo Hashing via XORSAT Dietzfelbinger, M., Goerdt, A., Mitzenmacher, M., Montanari, A., Pagh, R., Rink, M. 2010
• The LASSO risk: asymptotic results and real world examples Bayati, M., Bento, J., Montanari, A. 2010
• Fast Convergence of Natural Bargaining Dynamics in Exchange Networks Kanoria, Y., Bayati, M., Borgs, C., Chayes, J., Montanari, A. 2010
• The Spread of Innovations in Social Networks Montanari, A., Saberi, A. 2010
• Generating Random Graphs with Large Girth Bayati, M., Montanari, A., Saberi, A. 2009
• Matrix Completion from a Few Entries Keshavan, R., Montanari, A., Oh, S. 2009
• Matrix Completion from Noisy Entries Keshavan, R., Montanari, A., Oh, S. 2009
• Which graphical models are difficult to learn? Bento, J., Montanari, A. 2009
• An Implementable Scheme for Universal Lossy Compression of Discrete Markov Sources Jalali, S., Montanari, A., Weissman, T. 2009
• How to find good finite-length codes: from art towards science Amraoui, A., Montanari, A., Urbanke, R. WILEY-BLACKWELL. 2007: 491-508

View details for DOI 10.1002/ett.1182

View details for Web of Science ID 000248443400007

• Detailed Network Measurements Using Sparse Graph Counters: The Theory Lu, Y., Montanari, A., Prabhakar, B. 2007
• TP Decoding Lu, Y., Montanari, A., Measson, C. 2007
• Counting Good Truth Assignmants for Random Satisfiability Formulae Montanari, A., Shah, D. 2007
• Solving Constraint Satisfaction Problems through Belief Propagation-guided Decimation Montanari, A., Ricci-Tersenghi, F., Semerjian, G. 2007
• Finite-Length Scaling for Gallager A Ezri, J., Montanari, A., Urbanke, R. 2006
• The Asymptotic Error Floor of LDPC Ensembles Under BP Decoding Montanari, A. 2006
• Analysis of Belief propagation for Non-Linear Problems: The Example of CDMA (or: How to Prove Tanaka's Formula) Montanari, A., Tse, D. 2006
• Why We Can Not Surpass Capacity: The Matching Condition Measson, C., Montanari, A., Urbanke, R. 2005
• Belief Propagation Based Multi–User Detection Montanari, A., Prabhakar, B., Tse, D. 2005
• Life Above Threshold: From List Decoding to Area Theorem and MSE Measson, C., Montanari, A., Richardson, T., Urbanke, R. 2004
• Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes Amraoui, A., Montanari, A., Richardson, T., Urbanke, R. 2004
• Tight bounds for LDPC codes under MAP decoding Montanari, A. 2004
• Finite-length scaling for iteratively decoded LDPC ensembles Amraoui, A., Montanari, A., Richardson, T., Urbanke, R. 2003
• Discrete non-Abelian groups and asymptotically free models Caracciolo, S., Montanari, A., Pelissetto, A. 2001
• Statistical mechanics and turbo codes Montanari, A., Sourlas, N. 2001
• Finite-size scaling and metastable states of good codes Montanari, A. 2001
• Spin models on Platonic solids and asymptotic freedom Caracciolo, S., Montanari, A., Pelissetto, A. 2001
• Composite operators from operator product expansion: what can go wrong? Caracciolo, S., Montanari, A., Pelissetto, A. 1999
• Operator product expansion and non-perturbative renormalization Caracciolo, S., Montanari, A., Pelissetto, A. 1998
• Improved actions for the two-dimensional sigma-model Caracciolo, S., Montanari, A., Pelissetto, A. 1997