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.

Academic Appointments


Professional Education


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

Stanford Advisees


  • Doctoral Dissertation Reader (AC)
    Sohom Bhattacharya, Shi Dong, Michael Feldman, Yanjun Han, Jonathan Lacotte, Youngtak Sohn, Lisa Yamada, Qian Zhao
  • Postdoctoral Faculty Sponsor
    Joe Zhong
  • Doctoral Dissertation Advisor (AC)
    Michael Celentano, Kabir Chandrasekher, Theodor Misiakiewicz, Yuchen Wu
  • Master's Program Advisor
    Chandra Rajyam
  • Doctoral (Program)
    Kabir Chandrasekher, Qijia Jiang, Daria Reshetova, Khaled Saab, Basil Saeed

All Publications


  • The Landscape of the Spiked Tensor Model COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS Ben Arous, G., Mei, S., Montanari, A., Nica, M. 2019; 72 (11): 2282–2330

    View details for DOI 10.1002/cpa.21861

    View details for Web of Science ID 000486251500002

  • Fundamental Limits of Weak Recovery with Applications to Phase Retrieval FOUNDATIONS OF COMPUTATIONAL MATHEMATICS Mondelli, M., Montanari, A. 2019; 19 (3): 703–73
  • The spectral norm of random inner-product kernel matrices PROBABILITY THEORY AND RELATED FIELDS Fan, Z., Montanari, A. 2019; 173 (1-2): 27–85
  • Optimization of the Sherrington-Kirkpatrick Hamiltonian Montanari, A., IEEE IEEE COMPUTER SOC. 2019: 1417–33
  • A Statistical Model for Motifs Detection IEEE TRANSACTIONS ON INFORMATION THEORY Javadi, H., Montanari, A. 2018; 64 (12): 7594–7612
  • THE LANDSCAPE OF EMPIRICAL RISK FOR NONCONVEX LOSSES ANNALS OF STATISTICS Mei, S., Bai, Y., Montanari, A. 2018; 46 (6): 2747–74

    View details for DOI 10.1214/17-AOS1637

    View details for Web of Science ID 000443987700008

  • Spectral Algorithms for Tensor Completion COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS Montanari, A., Sun, N. 2018; 71 (11): 2381–2425

    View details for DOI 10.1002/cpa.21748

    View details for Web of Science ID 000444411800006

  • Generating Random Networks Without Short Cycles OPERATIONS RESEARCH Bayati, M., Montanari, A., Saberi, A. 2018; 66 (5): 1227–46
  • A mean field view of the landscape of two-layer neural networks PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Mei, S., Montanari, A., Phan-Minh Nguyen 2018; 115 (33): E7665–E7671
  • A mean field view of the landscape of two-layer neural networks. Proceedings of the National Academy of Sciences of the United States of America Mei, S., Montanari, A., Nguyen, P. 2018

    Abstract

    Multilayer neural networks are among the most powerful models in machine learning, yet the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires optimizing a nonconvex high-dimensional objective (risk function), a problem that is usually attacked using stochastic gradient descent (SGD). Does SGD converge to a global optimum of the risk or only to a local optimum? In the former case, does this happen because local minima are absent or because SGD somehow avoids them? In the latter, why do local minima reached by SGD have good generalization properties? In this paper, we consider a simple case, namely two-layer neural networks, and prove that-in a suitable scaling limit-SGD dynamics is captured by a certain nonlinear partial differential equation (PDE) that we call distributional dynamics (DD). We then consider several specific examples and show how DD can be used to prove convergence of SGD to networks with nearly ideal generalization error. This description allows for "averaging out" some of the complexities of the landscape of neural networks and can be used to prove a general convergence result for noisy SGD.

    View details for PubMedID 30054315

  • ONLINE RULES FOR CONTROL OF FALSE DISCOVERY RATE AND FALSE DISCOVERY EXCEEDANCE ANNALS OF STATISTICS Javanmard, A., Montanari, A. 2018; 46 (2): 526–54

    View details for DOI 10.1214/17-AOS1559

    View details for Web of Science ID 000431125400004

  • Contextual Stochastic Block Models Deshpande, Y., Montanari, A., Mossel, E., Sen, S., Bengio, S., Wallach, H., Larochelle, H., Grauman, K., CesaBianchi, N., Garnett, R. NEURAL INFORMATION PROCESSING SYSTEMS (NIPS). 2018
  • On the Limitation of Spectral Methods: From the Gaussian Hidden Clique Problem to Rank One Perturbations of Gaussian Tensors IEEE TRANSACTIONS ON INFORMATION THEORY Montanari, A., Reichman, D., Zeitouni, O. 2017; 63 (3): 1572-1579
  • EXTREMAL CUTS OF SPARSE RANDOM GRAPHS ANNALS OF PROBABILITY Dembo, A., Montanari, A., Sen, S. 2017; 45 (2): 1190-1217

    View details for DOI 10.1214/15-AOP1084

    View details for Web of Science ID 000398966500013

  • Universality of the Elastic Net Error Montanari, A., Phan-Minh Nguyen, IEEE IEEE. 2017: 2338–42
  • Inference in Graphical Models via Semidefinite Programming Hierarchies Erdogdu, M. A., Deshpande, Y., Montanari, A., Guyon, Luxburg, U. V., Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., Garnett, R. NEURAL INFORMATION PROCESSING SYSTEMS (NIPS). 2017
  • How Well Do Local Algorithms Solve Semidefinite Programs? Fan, Z., Montanari, A., Hatami, H., McKenzie, P., King ASSOC COMPUTING MACHINERY. 2017: 604–14
  • High dimensional robust M-estimation: asymptotic variance via approximate message passing PROBABILITY THEORY AND RELATED FIELDS Donoho, D., Montanari, A. 2016; 166 (3-4): 935-969
  • Phase transitions in semidefinite relaxations PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Javanmard, A., Montanari, A., Ricci-Tersenghi, F. 2016; 113 (16): E2218-E2223

    Abstract

    Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is large, as is often the case for modern datasets. A popular idea is to construct convex relaxations of these combinatorial problems, which can be solved efficiently for large-scale datasets. Semidefinite programming (SDP) relaxations are among the most powerful methods in this family and are surprisingly well suited for a broad range of problems where data take the form of matrices or graphs. It has been observed several times that when the statistical noise is small enough, SDP relaxations correctly detect the underlying combinatorial structures. In this paper we develop asymptotic predictions for several detection thresholds, as well as for the estimation error above these thresholds. We study some classical SDP relaxations for statistical problems motivated by graph synchronization and community detection in networks. We map these optimization problems to statistical mechanics models with vector spins and use nonrigorous techniques from statistical mechanics to characterize the corresponding phase transitions. Our results clarify the effectiveness of SDP relaxations in solving high-dimensional statistical problems.

    View details for DOI 10.1073/pnas.1523097113

    View details for Web of Science ID 000374393800005

    View details for PubMedID 27001856

    View details for PubMedCentralID PMC4843421

  • Non-Negative Principal Component Analysis: Message Passing Algorithms and Sharp Asymptotics IEEE TRANSACTIONS ON INFORMATION THEORY Montanari, A., Richard, E. 2016; 62 (3): 1458-1484
  • Statistical analysis of a low cost method for multiple disease prediction. Statistical methods in medical research Bayati, M., Bhaskar, S., Montanari, A. 2016: 962280216680242-?

    Abstract

    Early identification of individuals at risk for chronic diseases is of significant clinical value. Early detection provides the opportunity to slow the pace of a condition, and thus help individuals to improve or maintain their quality of life. Additionally, it can lessen the financial burden on health insurers and self-insured employers. As a solution to mitigate the rise in chronic conditions and related costs, an increasing number of employers have recently begun using wellness programs, which typically involve an annual health risk assessment. Unfortunately, these risk assessments have low detection capability, as they should be low-cost and hence rely on collecting relatively few basic biomarkers. Thus one may ask, how can we select a low-cost set of biomarkers that would be the most predictive of multiple chronic diseases? In this paper, we propose a statistical data-driven method to address this challenge by minimizing the number of biomarkers in the screening procedure while maximizing the predictive power over a broad spectrum of diseases. Our solution uses multi-task learning and group dimensionality reduction from machine learning and statistics. We provide empirical validation of the proposed solution using data from two different electronic medical records systems, with comparisons over a statistical benchmark.

    View details for DOI 10.1177/0962280216680242

    View details for PubMedID 27932665

  • Sparse PCA via Covariance Thresholding JOURNAL OF MACHINE LEARNING RESEARCH Deshpande, Y., Montanari, A. 2016; 17
  • Finding One Community in a Sparse Graph JOURNAL OF STATISTICAL PHYSICS Montanari, A. 2015; 161 (2): 273-299
  • THE SET OF SOLUTIONS OF RANDOM XORSAT FORMULAE ANNALS OF APPLIED PROBABILITY Ibrahimi, M., Kanoria, Y., Kraning, M., Montanari, A. 2015; 25 (5): 2743-2808

    View details for DOI 10.1214/14-AAP1060

    View details for Web of Science ID 000360868800010

  • Finding Hidden Cliques of Size root N/e in Nearly Linear Time FOUNDATIONS OF COMPUTATIONAL MATHEMATICS Deshpande, Y., Montanari, A. 2015; 15 (4): 1069-1128
  • UNIVERSALITY IN POLYTOPE PHASE TRANSITIONS AND MESSAGE PASSING ALGORITHMS ANNALS OF APPLIED PROBABILITY Bayati, M., Lelarge, M., Montanari, A. 2015; 25 (2): 753-822

    View details for DOI 10.1214/14-AAP1010

    View details for Web of Science ID 000350708000012

  • Bargaining dynamics in exchange networks JOURNAL OF ECONOMIC THEORY Bayati, M., Borgs, C., Chayes, J., Kanoria, Y., Montanari, A. 2015; 156: 417-454
  • A Low-Cost Method for Multiple Disease Prediction. AMIA ... Annual Symposium proceedings / AMIA Symposium. AMIA Symposium Bayati, M., Bhaskar, S., Montanari, A. 2015; 2015: 329-338

    Abstract

    Recently, in response to the rising costs of healthcare services, employers that are financially responsible for the healthcare costs of their workforce have been investing in health improvement programs for their employees. A main objective of these so called "wellness programs" is to reduce the incidence of chronic illnesses such as cardiovascular disease, cancer, diabetes, and obesity, with the goal of reducing future medical costs. The majority of these wellness programs include an annual screening to detect individuals with the highest risk of developing chronic disease. Once these individuals are identified, the company can invest in interventions to reduce the risk of those individuals. However, capturing many biomarkers per employee creates a costly screening procedure. We propose a statistical data-driven method to address this challenge by minimizing the number of biomarkers in the screening procedure while maximizing the predictive power over a broad spectrum of diseases. Our solution uses multi-task learning and group dimensionality reduction from machine learning and statistics. We provide empirical validation of the proposed solution using data from two different electronic medical records systems, with comparisons to a statistical benchmark.

    View details for PubMedID 26958164

  • Computational implications of reducing data to sufficient statistics ELECTRONIC JOURNAL OF STATISTICS Montanari, A. 2015; 9 (2): 2370-2390

    View details for DOI 10.1214/15-EJS1059

    View details for Web of Science ID 000366270900030

  • On the Concentration of the Number of Solutions of Random Satisfiability Formulas RANDOM STRUCTURES & ALGORITHMS Abbe, E., Montanari, A. 2014; 45 (3): 362-382

    View details for DOI 10.1002/rsa.20501

    View details for Web of Science ID 000341194800002

  • Hypothesis Testing in High-Dimensional Regression Under the Gaussian Random Design Model: Asymptotic Theory IEEE TRANSACTIONS ON INFORMATION THEORY Javanmard, A., Montanari, A. 2014; 60 (10): 6522-6554
  • Confidence Intervals and Hypothesis Testing for High-Dimensional Regression JOURNAL OF MACHINE LEARNING RESEARCH Javanmard, A., Montanari, A. 2014; 15: 2869-2909
  • Accelerated Time-of-Flight Mass Spectrometry IEEE TRANSACTIONS ON SIGNAL PROCESSING Ibrahimi, M., Montanari, A., Moore, G. S. 2014; 62 (15): 3784-3798
  • The Replica Symmetric Solution for Potts Models on d-Regular Graphs COMMUNICATIONS IN MATHEMATICAL PHYSICS Dembo, A., Montanari, A., Sly, A., Sun, N. 2014; 327 (2): 551-575
  • Information-Theoretically Optimal Compressed Sensing via Spatial Coupling and Approximate Message Passing IEEE TRANSACTIONS ON INFORMATION THEORY Donoho, D. L., Javanmard, A., Montanari, A. 2013; 59 (11): 7434-7464
  • Optimal Coding for the Binary Deletion Channel With Small Deletion Probability IEEE TRANSACTIONS ON INFORMATION THEORY Kanoria, Y., Montanari, A. 2013; 59 (10): 6192-6219
  • Localization from Incomplete Noisy Distance Measurements FOUNDATIONS OF COMPUTATIONAL MATHEMATICS Javanmard, A., Montanari, A. 2013; 13 (3): 297-345
  • Accurate Prediction of Phase Transitions in Compressed Sensing via a Connection to Minimax Denoising IEEE TRANSACTIONS ON INFORMATION THEORY Donoho, D. L., Johnstone, I., Montanari, A. 2013; 59 (6): 3396-3433
  • 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 δ(n,M,N) = n/(MN), rank fraction ρ=rank(X0)/min {M,N}, and aspect ratio β=M/N. Specifically when the measurement matrices Ai have independent standard Gaussian random entries, a curve δ*(ρ) = δ*(ρ;β) exists such that, if δ > δ*(ρ), NNM typically succeeds for large M,N, whereas if δ < δ*(ρ), 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+λ||X||*. When optimally tuned, this scheme achieves the asymptotic minimax mean-squared error M(ρ;β) = lim(M,N → ∞)inf(λ)sup(rank(X) ≤ ρ · M)MSE(X,X(λ)), where M/N → . We report extensive experiments showing that the phase transition δ*(ρ) in the first problem, matrix recovery from Gaussian measurements, coincides with the minimax risk curve M(ρ)=M(ρ;β) in the second problem, matrix denoising in Gaussian noise: δ*(ρ)=M(ρ), for any rank fraction 0 < ρ < 1 (at each common aspect ratio β). 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

    View details for PubMedCentralID PMC3666686

  • 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
  • The mutual information of a class of graphical channels 51st Annual Allerton Conference on Communication, Control, and Computing Abbe, E., Montanari, A. IEEE. 2013: 20–25
  • Linear Bandits in High Dimension and Recommendation Systems 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton) Deshpande, Y., Montanari, A. IEEE. 2013: 1750–1754
  • Nearly Optimal Sample Size in Hypothesis Testing for High-Dimensional Regression 51st Annual Allerton Conference on Communication, Control, and Computing Javanmard, A., Montanari, A. IEEE. 2013: 1427–1434
  • 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 IEEE International Symposium on Information Theory Bayati, M., Lelarge, M., Montanari, A. IEEE. 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
  • Graphical Models Concepts in Compressed Sensing in Compressed Sensing Montanari, A. Cambridge university PRess. 2012: 1
  • Information-Theoretically Optimal Compressed Sensing via Spatial Coupling and Approximate Message Passing IEEE International Symposium on Information Theory Donoho, D. L., Javanmard, A., Montanari, A. IEEE. 2012
  • ACCELERATED TIME-OF-FLIGHT MASS SPECTROMETRY IEEE Statistical Signal Processing Workshop (SSP) Ibrahimi, M., Montanari, A., Moore, G. S. IEEE. 2012: 432–435
  • Subsampling at Information Theoretically Optimal Rates IEEE International Symposium on Information Theory Javanmard, A., Montanari, A. IEEE. 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
  • The Dynamics of Message Passing on Dense Graphs, with Applications to Compressed Sensing IEEE International Symposium on Information Theory Bayati, M., Montanari, A. IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. 2011: 764–85
  • 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

  • Gossip PCA Korada, S., Montanari, A., Oh, S. 2011
  • 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
  • Distributed Storage for Intermittent Energy Sources: Control Design and Performance Limits Kanoria, Y., Montanari, A., Tse, D., Zhang, B. 2011
  • Fast Convergence of Natural Bargaining Dynamics in Exchange Networks 22nd Annual ACM/SIAM Symposium on Discrete Algorithms Kanoria, Y., Bayati, M., Borgs, C., Chayes, J., Montanari, A. SIAM. 2011: 1518–1537
  • Localization from Incomplete Noisy Distance Measurements IEEE International Symposium on Information Theory (ISIT) Javanmard, A., Montanari, A. IEEE. 2011: 1584–1588
  • Compressed Sensing over l(p)-balls: Minimax Mean Square Error IEEE International Symposium on Information Theory (ISIT) Donoho, D., Johnstone, I., Maleki, A., Montanari, A. IEEE. 2011: 129–133
  • Information Theoretic Limits on Learning Stochastic Differential Equations IEEE International Symposium on Information Theory (ISIT) Bento, J., Ibrahimi, M., Montanari, A. IEEE. 2011: 855–859
  • Subexponential convergence for information aggregation on regular trees 50th IEEE Conference of Decision and Control (CDC)/European Control Conference (ECC) Kanoria, Y., Montanari, A. IEEE. 2011: 5317–5322
  • 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

    View details for PubMedCentralID PMC2996710

  • 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. IEEE. 2010: 1503–1507
  • 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
  • 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
  • Ising models on locally tree-like graphs Annals of Applied Probability Dembo, A., Montanari, A. 2010
  • Fast Convergence of Natural Bargaining Dynamics in Exchange Networks Kanoria, Y., Bayati, M., Borgs, C., Chayes, J., Montanari, A. 2010
  • The LASSO risk: asymptotic results and real world examples Bayati, M., Bento, J., Montanari, A. 2010
  • Majority dynamics on trees and the dynamic cavity method Annals of Applied Probability Kanoria, Y., Montanari, A. 2010
  • The Spread of Innovations in Social Networks Montanari, A., Saberi, A. 2010
  • Graphical Models Concepts in Compressed Sensing Montanari, A. 2010
  • The dynamics of message passing on dense graphs, with applications to compressed sensing 2010 IEEE International Symposium on Information Theory Bayati, M., Montanari, A. IEEE. 2010: 1528–1532
  • Tight Thresholds for Cuckoo Hashing via XORSAT 37th International Colloquium on Automata, Languages and Programming Dietzfelbinger, M., Goerdt, A., Mitzenmacher, M., Montanari, A., Pagh, R., Rink, M. SPRINGER-VERLAG BERLIN. 2010: 213–225
  • On the deletion channel with small deletion probability 2010 IEEE International Symposium on Information Theory Kanoria, Y., Montanari, A. IEEE. 2010: 1002–1006
  • An Empirical Scaling Law for Polar Codes 2010 IEEE International Symposium on Information Theory Korada, S. B., Montanari, A., Telatar, E., Urbanke, R. IEEE. 2010: 884–888
  • 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

    View details for PubMedCentralID PMC2767368

  • 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 47th Annual Allerton Conference on Communication, Control, and Computing Keshavan, R. H., Montanari, A., Oh, S. IEEE. 2009: 1216–1222
  • 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
  • Information, Physics, and Computation Mezard, M., Montanari, A. Oxford University Press. 2009
  • An Implementable Scheme for Universal Lossy Compression of Discrete Markov Sources Jalali, S., Montanari, A., Weissman, T. 2009
  • Matrix Completion from a Few Entries IEEE International Symposium on Information Theory (ISIT 2009) Keshavan, R. H., Oh, S., Montanari, A. IEEE. 2009: 324–328
  • Convergence to Equilibrium in Local Interaction Games 50th Annual IEEE Symposium on Foundations of Computer Science Montanari, A., Saberi, A. IEEE COMPUTER SOC. 2009: 303–312
  • An Iterative Scheme for Near Optimal and Universal Lossy Compression IEEE Information Theory Workshop on Networking and Information Theory Jalali, S., Montanari, A., Weissman, T. IEEE. 2009: 231–235
  • Generating random Tanner-graphs with large girth IEEE Information Theory Workshop (ITW) Bayati, M., Keshavan, R., Montanari, A., Oh, S., Saberi, A. IEEE. 2009: 154–157
  • Generating Random Graphs with Large Girth 20th Annual ACM-SIAM Symposium on Discrete Algorithms Bayati, M., Montanari, A., Saberi, A. SIAM. 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 IEEE Information Theory Workshop Lu, Y., Montanari, A., Prabhakar, B. IEEE. 2008: 220–221
  • Finite Size Scaling for the Core of Large Random Hypergraphs Annals of Applied Probability Dembo, A., Montanari, A. 2008
  • Counter Braids: A Novel Counter Architecture for Per-Flow Measurement International Conference on Measurement and Modeling of Computer Systems Lu, Y., Montanari, A., Prabhakar, B., Dharmapurikar, S., Kabbani, A. ASSOC COMPUTING MACHINERY. 2008: 121–32
  • Counter Braids: Asymptotic Optimality of the Message Passing Decoding Algorithm 46th Annual Allerton Conference on Communication, Control and Computing Lu, Y., Montanari, A., Prabhakar, B. IEEE. 2008: 209–216
  • Learning Low Rank Matrices from O(n) Entries 46th Annual Allerton Conference on Communication, Control and Computing Keshavan, R. H., Montanari, A., Oh, S. IEEE. 2008: 1365–1372
  • Computing the threshold shift for general channels IEEE International Symposium on Information Theory Ezri, J., Urbanke, R., Montanari, A., Oh, S. IEEE. 2008: 1448–1452
  • An Implementable Scheme for Universal Lossy Compression of Discrete Markov Sources 19th Data Compression Conference Jalali, S., Montanari, A., Weissman, T. IEEE COMPUTER SOC. 2008: 292–301
  • The Slope Scaling Parameter for General Channels, Decoders, and Ensembles IEEE International Symposium on Information Theory Ezri, J., Montanari, A., Oh, S., Urbanke, R. IEEE. 2008: 1443–1447
  • Smooth compression, Gallager bound and Nonlinear sparse-graph codes IEEE International Symposium on Information Theory Montanari, A., Mossel, E. IEEE. 2008: 2474–2478
  • How to find good finite-length codes: from art towards science 4th International Symposium on Turbo Codes and Related Topics 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

  • 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

  • Asymptotic rate versus design rate IEEE International Symposium on Information Theory Measson, C., Montanari, A., Urbanke, R. IEEE. 2007: 1541–1545
  • 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
  • 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
  • A generalization of the finite-length scaling approach beyond the BEC IEEE International Symposium on Information Theory Ezri, J., Montanari, A., Urbanke, R. IEEE. 2007: 1011–1015
  • Reconstruction for models on random graphs 48th Annual IEEE Symposium on Foundations of Computer Science Gerschenfeld, A., Montanari, A. IEEE COMPUTER SOC. 2007: 194–204
  • Rigorous inequalities between length and time scales in glassy systems JOURNAL OF STATISTICAL PHYSICS Montanari, A., Semerjian, G. 2006; 125 (1): 22-54
  • On the dynamics of the glass transition on Bethe lattices JOURNAL OF STATISTICAL PHYSICS Montanari, A., Semerjian, G. 2006; 124 (1): 103-189
  • Precision electroweak measurements on the Z resonance PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS Schael, S., Barate, R., Bruneliere, R., Buskulic, D., De Bonis, I., Decamp, D., Ghez, P., Goy, C., Jezequel, S., Lees, J. P., Lucotte, A., Martin, F., Merle, E., Minard, M. N., Nief, J. Y., Odier, P., Pietrzyk, B., Trocme, B., Bravo, S., Casado, M. P., Chmeissani, M., Comas, P., Crespo, J. M., Fernandez, E., Fernandez-Bosman, M., Garrido, L., Grauges, E., Juste, A., Martinez, M., Merino, G., Miquel, R., Mir, L. M., Orteu, S., Pacheco, A., Park, I. C., Perlas, J., Riu, I., Ruiz, H., Sanchez, F., Colaleo, A., Creanza, D., De Filippis, N., de Palma, M., Iaselli, G., Maggi, G., Maggi, M., Nuzzo, S., Ranieri, A., Raso, G., Ruggieri, F., Selvaggi, G., Silvestris, L., Tempesta, P., Tricomi, A., Zito, G., Huang, X., Lin, J., Ouyang, Q., Wang, T., Xie, Y., Xu, R., Xue, S., Zhang, J., Zhang, L., Zhao, W., Abbaneo, D., Bazarko, A., Becker, U., Boix, G., Bird, F., Blucher, E., Bonvicini, B., Bright-Thomas, P., Barklow, T., Buchmuller, O., Cattaneo, M., Cerutti, F., Ciulli, V., Clerbaux, B., Drevermann, H., Forty, R. W., Frank, M., Greening, T. C., Hagelberg, R., Halley, A. W., Gianotti, F., Girone, M., Hansen, J. B., Harvey, J., Jacobsen, R., Hutchcroft, D. E., Janot, R., JOST, B., Knobloch, J., Kado, M., Lehraus, I., Lazeyras, P., Maley, R., Mato, P., May, J., Moutussi, A., Pepe-Altarelli, M., Ranjard, F., Rolandi, L., Schlatter, D., Schmitt, B., Schneider, O., Tejessy, W., Teubert, F., Tomalin, I. 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I., van der Aa, O., Delaere, C., Leibenguth, G., Lemaitre, V., Bauerdick, L. A., Blumenschein, U., van Gemmeren, P., Giehl, I., Holldorfer, F., Jakobs, K., Kasemann, M., Kayser, F., Kleinknecht, K., Muller, A. S., Quast, G., Renk, B., Rohne, E., Sander, H. G., Schmeling, S., Wachsmuth, H., Wanke, R., Zeitnitz, C., Ziegler, T., Aubert, J. J., Benchouk, C., Bonissent, A., Carr, J., Coyle, P., Curtil, C., Ealet, A., Etienne, F., Fouchez, D., Motsch, F., Payre, P., Rousseau, D., Tilquin, A., Talby, M., Thulasides, M., Aleppo, M., Antonelli, M., Ragusa, F., Buscher, V., David, A., Dietl, H., Ganis, G., Huttmann, K., Lutjens, G., Mannert, C., Manner, W., Moser, H. G., Settles, R., Seywerd, H., Stenzel, H., Villegas, M., Wiedenmann, W., Wolf, G., Azzurri, P., Boucrot, J., Callot, O., Chen, S., Cordier, A., Davier, M., Duflot, L., Grivaz, J. F., Heusse, P., Jacholkowska, A., Le Diberder, F., Lefrancois, J., Mutz, A. M., Schune, M. H., Serin, L., Veillet, J. J., Videau, I., Zerwas, D., Azzurri, P., Bagliesi, G., Bettarini, S., Boccali, T., Bozzi, C., Calderini, G., Dell'Orso, R., Fantechi, R., Ferrante, I., Fidecaro, F., Foa, L., Giammanco, A., Giassi, A., Gregorio, A., Ligabue, F., Lusiani, A., Marrocchesi, P. S., Messineo, A., Palla, F., Rizzo, G., Sanguinetti, G., Sciaba, A., Sguazzoni, G., Spagnolo, P., Steinberger, J., Tenchini, R., Venturi, A., Vannini, C., Venturi, A., Verdini, P. G., Awunor, O., Blair, G. A., Cowan, G., Garcia-Bellido, A., Green, M. G., Medcalf, T., Misiejuk, A., Strong, J. A., Teixeira-Dias, P., Botterill, D. R., Clifft, R. W., Edgecock, T. R., Edwards, M., Haywood, S. J., Norton, P. R., Tomalin, I. R., Ward, J. J., Bloch-Devaux, B., Boumediene, D., Colas, P., Emery, S., Fabbro, B., Kozanecki, W., Lancon, E., Lemaire, M. C., Locci, E., Perez, P., Rander, J., Renardy, J. F., Roussarie, A., Schuller, J. P., Schwindling, J., Tuchming, B., Vallage, B., Black, S. N., Dann, J. H., Kim, H. Y., Konstantinidis, N., Litke, A. M., McNeil, M. A., Taylor, G., Booth, C. N., Cartwright, S., Combley, F., Hodgson, P. N., LEHTO, M., Thompson, L. F., Affholderbach, K., Barberio, E., Bohrer, A., Brandt, S., Burkhardt, H., Feigl, E., Grupen, C., Hess, J., Lutters, G., Meinhard, H., Minguet-Rodriguez, J., Mirabito, L., Misiejuk, A., Neugebauer, E., Ngac, A., Prange, G., Rivera, F., Saraiva, P., Schafer, U., Sieler, U., Smolik, L., Stephan, F., Trier, H., Apollonio, M., Borean, C., Bosisio, L., Della Marina, R., Giannini, G., Gobbo, B., Musolino, G., Pitis, L., He, H., Kim, H., Putz, J., Rothberg, J., Armstrong, S. R., Bellantoni, L., Berkelman, K., Cinabro, D., Conway, J. S., Cranmer, K., Elmer, P., Feng, Z., Ferguson, D. P., Gao, Y., Gonzalez, S., Grahl, J., Harton, J. L., Hayes, O. J., Hu, H., Jin, S., Johnson, R. P., Kile, J., McNamara, P. A., Nielsen, J., Orejudos, W., Pan, Y., Saadi, Y., Scott, I. J., Sharma, V., Walsh, A. M., Walsh, J., Wear, J., von Wimmersperg-Toeller, J. H., Wiedenmann, W., Wu, J., Wu, S. L., Wu, X., Yamartino, J. M., Zobernig, G., Dissertori, G., Abdallah, J., Abreu, P., Adam, W., Adye, T., Adzic, P., Ajinenko, I., Albrecht, T., Alderweireld, T., Alekseev, G. D., Alemany-Fernandez, R., Allmendinger, T., Allport, P. P., Almehed, S., Amaldi, U., Amapane, N., Amato, S., Anashkin, E., Anassontzis, E. G., Andersson, P., Andreazza, A., Andringa, S., Anjos, N., Antilous, P., Apel, W. D., Arnoud, Y., Ask, S., Asman, B., Augustin, J. E., Augustinus, A., Baillon, P., Ballestrero, A., Bambade, P., Barao, F., Barbiellini, G., Barbier, R., Bardin, D., Barker, G., Baroncelli, A., Battaglia, M., Baubillier, M., Becks, K. H., Begalli, M., Behrmann, A., Beilliere, P., Belokopytov, Y., Belous, K., Ben-Haim, E., Benekos, N., Benvenuti, A., Berat, C., Berggren, M., Berntzon, L., Bertini, D., Bertrand, D., Besancon, M., Besson, N., Bianchi, F., Bigi, M., Bilenky, M. S., Bizouard, M. A., Bloch, D., Blom, M., Bluj, M., Bonesini, M., Bonivento, W., Boonekamp, M., Booth, P. S., Borgland, A. W., Borisov, G., Bosio, C., Botner, O., Boudinov, E., Bouquet, B., Bourdarios, C., Bowcock, T. J., Boyko, I., Bozovic, I., Bozzo, M., Bracko, M., Branchini, P., Brenke, T., Brenner, R., Brodet, E., Bruckman, P., Brunet, J. M., Bugge, L., Buran, T., Burgsmueller, T., Buschbeck, B., Buschmann, P., Cabrera, S., Caccia, M., Calvi, M., Rozas, A. J., Camporesi, T., Canale, V., Canepa, M., Carena, F., Carroll, L., Caso, C., Gimenez, M. V., Castro, N., Cattai, A., Cavallo, F., Cerruti, C., Chabaud, V., Chapkin, M., Charpentier, P., Chaussard, L., Checchia, P., Chelkov, G. A., Chen, M., Chierici, R., Chliapnikov, R., Chochula, P., Chorowicz, V., Chudoba, J., Chung, S. U., Cieslik, K., Collins, P., Colomer, M., Contri, R., Cortina, E., Cosme, G., Cossuti, F., Costa, M. J., Cowell, J. H., Crawley, H. B., Crennell, D., Crepe, S., Crosetti, G., Cuevas, J., Czellar, S., D'Hondt, J., Dalmagne, B., Dalmau, J., Damgaard, G., Davenport, M., da Silva, T., Da Silva, W., Deghorain, A., Della Ricca, G., Delpierre, P., Demaria, N., De Angelis, A., De Boer, W., de Brabandere, S., De Clercq, C., De Lotto, B., De Maria, N., De Min, A., de Paula, L., Dijkstra, H., Di Ciaccio, L., Di Diodato, A., Di Simone, A., Djannati, A., Dolbeau, J., Doroba, K., Dracos, M., Drees, J., Drees, K. A., Dris, M., Duperrin, A., Durand, J. D., Ehret, R., Eigen, G., Ekelof, T., Ekspong, G., Ellert, M., Elsing, M., Engel, J. P., Erzen, B., Santo, M. C., Falk, E., Fanourakis, G., Fassouliotis, D., Fayot, J., Feindt, M., Fenyuk, A., Fernandez, J., Ferrari, P., Ferrer, A., Ferrer-Ribas, E., Ferro, F., Fichet, S., Firestone, A., Fischer, P. A., Flagmeyer, U., Foeth, H., Fokitis, E., Fontanelli, F., Franek, B., Frodesen, A. 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N., Jacobsson, R., Jalocha, P., Janik, R., Jarlskog, C., Jarlskog, G., Jarry, P., Jean-Marie, B., Jeans, D., Johansson, E. K., Johansson, P. D., Jonsson, P., Joram, C., Juillot, P., Jungermann, L., Kapusta, F., Karafasoulis, K., Katsanevas, S., Katsoufis, E., Keranen, R., Kernel, G., Kersevan, B. P., Kerzel, U., Khomenko, B. A., Khovanski, N. N., Kiiskinen, A., King, B. T., Kinvig, A., Kjaer, N. J., Klapp, O., Klein, H., Kluit, P., Knoblauch, D., Kokkinias, P., Konopliannikov, A., Koratzinos, M., Kostioukhine, V., Kourkoumelis, C., Kouznetsov, O., Krammer, M., Kreuter, C., Kriznic, E., Krstic, J., Krumstein, Z., Kubinec, P., Kucewicz, W., Kucharczyk, M., Kurowska, J., Kurvinen, K., Lamsa, J., Lanceri, L., Lane, D. W., Langefeld, P., Lapin, V., Laugier, J. 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L., Woods, M., Word, G. B., Wright, T. R., Wyss, J., Yamamoto, R. K., Yamartino, J. M., Yang, X. Q., Yashima, J., Yellin, S. J., Young, C. C., Yuta, H., Zapalac, G., Zdarko, R. W., Zeitlin, C., Zhou, J. 2006; 427 (5-6): 257-454
  • How to Find Good Finite-Length Codes: From Art Towards Science European Transactions on Telecommunications Amraoui, A., Montanari, A., Urbanke, R. 2006
  • Finite-Length Scaling for Gallager A Ezri, J., Montanari, A., Urbanke, R. 2006
  • Two Lectures on Iterative Coding and Statistical Mechanics Les Houches Summer School on Mathematical Statistical Physics Montanari, A. Elsevier. 2006: 1
  • 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
  • Approximate analysis of search algorithms with “physical” methods Phase Transitions and Algorithmic Complexity Cocco, S., Monasson, R., Montanari, A., Semerjian, G. Oxford. 2006: 1
  • From large scale rearrangements to mode coupling phenomenology in model glasses PHYSICAL REVIEW LETTERS Montanari, A., Semerjian, G. 2005; 94 (24)
  • Why We Can Not Surpass Capacity: The Matching Condition Measson, C., Montanari, A., Urbanke, R. 2005
  • 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
  • Belief Propagation Based Multi–User Detection Montanari, A., Prabhakar, B., Tse, D. 2005
  • Weight distributions of LDPC code ensembles: Combinatorics meets statistical physics IEEE International Symposium on Information Theory Di, C. Y., Montanari, A., Urbanke, R. IEEE. 2004: 102–102
  • Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes Amraoui, A., Montanari, A., Richardson, T., Urbanke, R. 2004
  • Instability of one-step replica-symmetry-broken phase in satisfiability problems Journal of Physics A Montanari, A., Parisi, G., Ricci-Tersenghi, F. 2004
  • Tight bounds for LDPC codes under MAP decoding Montanari, A. 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
  • Life Above Threshold: From List Decoding to Area Theorem and MSE Measson, C., Montanari, A., Richardson, T., Urbanke, R. 2004
  • Maxwell's construction: The hidden bridge between maximum-likelihood and iterative decoding IEEE International Symposium on Information Theory Measson, C., Montanari, A., Urbanke, M. IEEE. 2004: 225–225
  • Further results on finite-length scaling for iteratively decoded LDPC ensembles IEEE International Symposium on Information Theory Amraoui, A., Urbanke, R., Montanari, A., Richardson, T. IEEE. 2004: 103–103
  • On the nature of the low-temperature phase in discontinuous mean-field spin glasses EUROPEAN PHYSICAL JOURNAL B Montanari, A., Ricci-Tersenghi, F. 2003; 33 (3): 339-346
  • Finite-length scaling for iteratively decoded LDPC ensembles Amraoui, A., Montanari, A., Richardson, T., Urbanke, R. 2003
  • 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
  • Discrete non-Abelian groups and asymptotically free models Caracciolo, S., Montanari, A., Pelissetto, A. 2001
  • The glassy phase of Gallager codes The European Physical Journal B Montanari, A. 2001
  • Statistical mechanics and turbo codes Montanari, A., Sourlas, N. 2001
  • Finite-size scaling and metastable states of good codes 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
  • Spin models on Platonic solids and asymptotic freedom Caracciolo, S., Montanari, A., Pelissetto, A. 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
  • Composite operators from operator product expansion: what can go wrong? Caracciolo, S., Montanari, A., Pelissetto, A. 1999
  • Event Calculus with explicit quantifiers 5th International Workshop on Temporal Representation and Reasoning Cervesato, I., Franceschet, M., Montanari, A. I E E E, COMPUTER SOC PRESS. 1998: 81–88
  • 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
  • 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