An alternative formula for the number of Euler trails for a class of digraphs. - Nicolas Macris; J. V. Pulé (Discret. Math., 1996)

Correlation inequalities: a useful tool in the theory of LDPC codes. - Nicolas Macris (ISIT, 2005)

Applications of correlation inequalities to low density graphical codes - Nicolas Macris (CoRR, 2005)

Exact solution of a p-spin model and its relationship to error correcting codes. - Satish Babu Korada; Nicolas Macris (ISIT, 2006)

Sharp Bounds for MAP Decoding of General Irregular LDPC Codes. - Shrinivas Kudekar; Nicolas Macris (ISIT, 2006)

On the relation between MAP and BP GEXIT functions of low density parity check codes. - Nicolas Macris (ITW, 2006)

Exact solution for the conditional entropy of Poissonian LDPC codes over the Binary Erasure Channel. - Satish Babu Korada; Shrinivas Kudekar; Nicolas Macris (ISIT, 2007)

On the concentration of the capacity for a code division multiple access system. - Satish Babu Korada; Nicolas Macris (ISIT, 2007)

Griffith-Kelly-Sherman Correlation Inequalities: A Useful Tool in the Theory of Error Correcting Codes. - Nicolas Macris (IEEE Trans. Inf. Theory, 2007)

Sharp Bounds on Generalized EXIT Functions. - Nicolas Macris (IEEE Trans. Inf. Theory, 2007)

Concentration of magnetization for linear block codes. - Satish Babu Korada; Shrinivas Kudekar; Nicolas Macris (ISIT, 2008)

Proof of replica formulas in the high noise regime for communication using LDGM codes. - Shrinivas Kudekar; Nicolas Macris (ITW, 2008)

Decay of correlations in low density parity check codes: Low noise regime. - Shrinivas Kudekar; Nicolas Macris (ISIT, 2009)

Sharp bounds for optimal decoding of low-density parity-check codes. - Shrinivas Kudekar; Nicolas Macris (IEEE Trans. Inf. Theory, 2009)

Coupled graphical models and their thresholds. - S. Hamed Hassani; Nicolas Macris; Rüdiger L. Urbanke (ITW, 2010)

Tight Bounds on the Capacity of Binary Input Random CDMA Systems. - Satish Babu Korada; Nicolas Macris (IEEE Trans. Inf. Theory, 2010)

Near concavity of the growth rate for coupled LDPC chains. - Seyed Hamed Hassani; Nicolas Macris; Ryuhei Mori (ISIT, 2011)

Chains of Mean Field Models - Seyed Hamed Hassani; Nicolas Macris; Rüdiger L. Urbanke (CoRR, 2011)

Threshold Saturation in Spatially Coupled Constraint Satisfaction Problems - Seyed Hamed Hassani; Nicolas Macris; Rüdiger L. Urbanke (CoRR, 2011)

Decay of Correlations for Sparse Graph Error Correcting Codes. - Shrinivas Kudekar; Nicolas Macris (SIAM J. Discret. Math., 2011)

A proof of threshold saturation for spatially-coupled LDPC codes on BMS channels. - Santhosh Kumar; Andrew J. Young; Nicolas Macris; Henry D. Pfister (Allerton Conference, 2012)

Lossy source coding via spatially coupled LDGM ensembles. - Vahid Aref; Nicolas Macris; Rüdiger L. Urbanke; Marc Vuffray (ISIT, 2012)

How to prove the Maxwell conjecture via spatial coupling - A proof of concept. - Andrei Giurgiu; Nicolas Macris; Rüdiger L. Urbanke (ISIT, 2012)

Beyond the Bethe free energy of LDPC codes via polymer expansions. - Nicolas Macris; Marc Vuffray (ISIT, 2012)

Polymer Expansions for Cycle LDPC Codes - Nicolas Macris; Marc Vuffray (CoRR, 2012)

Approaching the rate-distortion limit by spatial coupling with belief propagation and decimation. - Vahid Aref; Nicolas Macris; Marc Vuffray (ISIT, 2013)

And now to something completely different: Spatial coupling as a proof technique. - Andrei Giurgiu; Nicolas Macris; Rüdiger L. Urbanke (ISIT, 2013)

The space of solutions of coupled XORSAT formulae. - Seyed Hamed Hassani; Nicolas Macris; Rüdiger L. Urbanke (ISIT, 2013)

Displacement convexity - A useful framework for the study of spatially coupled codes. - Rafah El-Khatib; Nicolas Macris; Rüdiger L. Urbanke (ITW, 2013)

Spatial Coupling as a Proof Technique - Andrei Giurgiu; Nicolas Macris; Rüdiger L. Urbanke (CoRR, 2013)

Analysis of coupled scalar systems by displacement convexity. - Rafah El-Khatib; Nicolas Macris; Tom Richardson 001; Rüdiger L. Urbanke (ISIT, 2014)

Threshold Saturation for Spatially Coupled LDPC and LDGM Codes on BMS Channels. - Santhosh Kumar; Andrew J. Young; Nicolas Macris; Henry D. Pfister (IEEE Trans. Inf. Theory, 2014)

Approaching the Rate-Distortion Limit With Spatial Coupling, Belief Propagation, and Decimation. - Vahid Aref; Nicolas Macris; Marc Vuffray (IEEE Trans. Inf. Theory, 2015)

The mutual information in random linear estimation. - Jean Barbier; Mohamad Dia; Nicolas Macris; Florent Krzakala (Allerton, 2016)

Proof of threshold saturation for spatially coupled sparse superposition codes. - Jean Barbier; Mohamad Dia; Nicolas Macris (ISIT, 2016)

The velocity of the decoding wave for spatially coupled codes on BMS channels. - Rafah El-Khatib; Nicolas Macris (ISIT, 2016)

Threshold saturation of spatially coupled sparse superposition codes for all memoryless channels. - Jean Barbier; Mohamad Dia; Nicolas Macris (ITW, 2016)

The velocity of the propagating wave for general coupled scalar systems. - Rafah El-Khatib; Nicolas Macris (ITW, 2016)

Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula. - Jean Barbier; Mohamad Dia; Nicolas Macris; Florent Krzakala; Thibault Lesieur; Lenka Zdeborová (NIPS, 2016)

Bounds for Random Constraint Satisfaction Problems via Spatial Coupling. - Dimitris Achlioptas; Seyed Hamed Hassani; Nicolas Macris; Rüdiger L. Urbanke (SODA, 2016)

Spatial Coupling as a Proof Technique and Three Applications. - Andrei Giurgiu; Nicolas Macris; Rüdiger L. Urbanke (IEEE Trans. Inf. Theory, 2016)

The Bethe Free Energy Allows to Compute the Conditional Entropy of Graphical Code Instances: A Proof From the Polymer Expansion. - Nicolas Macris; Marc Vuffray (IEEE Trans. Inf. Theory, 2016)

The layered structure of tensor estimation and its mutual information. - Jean Barbier; Nicolas Macris; Léo Miolane (Allerton, 2017)

I-MMSE relations in random linear estimation and a sub-extensive interpolation method. - Jean Barbier; Nicolas Macris (ISIT, 2017)

Stability threshold and phase transition of generalized censored block models. - Chun Lam Chan; Nicolas Macris (ITW, 2017)

The stochastic interpolation method: A simple scheme to prove replica formulas in Bayesian inference. - Jean Barbier; Nicolas Macris (CoRR, 2017)

Phase Transitions, Optimal Errors and Optimality of Message-Passing in Generalized Linear Models. - Jean Barbier; Florent Krzakala; Nicolas Macris; Léo Miolane; Lenka Zdeborová (CoRR, 2017)

Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models. - Jean Barbier; Florent Krzakala; Nicolas Macris; Léo Miolane; Lenka Zdeborová (COLT, 2018)

Adaptive Path Interpolation for Sparse Systems: Application to a Simple Censored Block Model. - Jean Barbier; Chun Lam Chan; Nicolas Macris (ISIT, 2018)

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices. - Jean Barbier; Nicolas Macris; Antoine Maillard; Florent Krzakala (ISIT, 2018)

The committee machine: Computational to statistical gaps in learning a two-layers neural network. - Benjamin Aubin; Antoine Maillard; Jean Barbier; Florent Krzakala; Nicolas Macris; Lenka Zdeborová (NeurIPS, 2018)

Entropy and mutual information in models of deep neural networks. - Marylou Gabrié; Andre Manoel; Clément Luneau; Jean Barbier; Nicolas Macris; Florent Krzakala; Lenka Zdeborová (NeurIPS, 2018)

Rank-one matrix estimation: analysis of algorithmic and information theoretic limits by the spatial coupling method. - Jean Barbier; Mohamad Dia; Nicolas Macris; Florent Krzakala; Lenka Zdeborová (CoRR, 2018)

The Velocity of the Propagating Wave for Spatially Coupled Systems With Applications to LDPC Codes. - Rafah El-Khatib; Nicolas Macris (IEEE Trans. Inf. Theory, 2018)

Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method. - Jean Barbier; Chun Lam Chan; Nicolas Macris (ISIT, 2019)

Mutual Information for Low-Rank Even-Order Symmetric Tensor Factorization. - Jean Barbier; Clément Luneau; Nicolas Macris (ITW, 2019)

The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models. - Jean Barbier; Nicolas Macris (CoRR, 2019)

0-1 phase transitions in sparse spiked matrix estimation. - Jean Barbier; Nicolas Macris (CoRR, 2019)

Universal Sparse Superposition Codes With Spatial Coupling and GAMP Decoding. - Jean Barbier; Mohamad Dia; Nicolas Macris (IEEE Trans. Inf. Theory, 2019)

Displacement Convexity in Spatially Coupled Scalar Recursions. - Rafah El-Khatib; Nicolas Macris; Tom Richardson 001; Rüdiger L. Urbanke (IEEE Trans. Inf. Theory, 2019)

High-dimensional rank-one nonsymmetric matrix decomposition: the spherical case. - Clément Luneau; Nicolas Macris; Jean Barbier (ISIT, 2020)

All-or-nothing statistical and computational phase transitions in sparse spiked matrix estimation. - Jean Barbier; Nicolas Macris; Cynthia Rush (NeurIPS, 2020)

Information theoretic limits of learning a sparse rule. - Clément Luneau; Jean Barbier; Nicolas Macris (NeurIPS, 2020)

Tensor Estimation With Structured Priors. - Clément Luneau; Nicolas Macris (IEEE J. Sel. Areas Inf. Theory, 2020)

Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation. - Jean Barbier; Nicolas Macris; Mohamad Dia; Florent Krzakala (IEEE Trans. Inf. Theory, 2020)

Rank-one matrix estimation: analytic time evolution of gradient descent dynamics. - Antoine Bodin; Nicolas Macris (COLT, 2021)

Model, sample, and epoch-wise descents: exact solution of gradient flow in the random feature model. - Antoine Bodin; Nicolas Macris (NeurIPS, 2021)

Mismatched Estimation of rank-one symmetric matrices under Gaussian noise. - Farzad Pourkamali; Nicolas Macris (CoRR, 2021)

Statistical limits of dictionary learning: random matrix theory and the spectral replica method. - Jean Barbier; Nicolas Macris (CoRR, 2021)

Bell Diagonal and Werner State Generation: Entanglement, Non-Locality, Steering and Discord on the IBM Quantum Computer. - Elias Riedel Gårding; Nicolas Schwaller; Chun Lam Chan; Su Yeon Chang; Samuel Bosch; Frédéric Gessler; Willy Robert Laborde; Javier Naya Hernandez; Xinyu Si; Marc-André Dupertuis; Nicolas Macris (Entropy, 2021)

Adaptive Path Interpolation Method for Sparse Systems: Application to a Censored Block Model. - Jean Barbier; Chun Lam Chan; Nicolas Macris (IEEE Trans. Inf. Theory, 2021)

Mismatched Estimation of Non-Symmetric Rank-One Matrices Under Gaussian Noise. - Farzad Pourkamali; Nicolas Macris (ISIT, 2022)

Gradient flow in the gaussian covariate model: exact solution of learning curves and multiple descent structures. - Antoine Bodin; Nicolas Macris (CoRR, 2022)

Rectangular Rotational Invariant Estimator for General Additive Noise Matrices. - Farzad Pourkamali; Nicolas Macris (ISIT, 2023)

Gradient flow on extensive-rank positive semi-definite matrix denoising. - Antoine Bodin; Nicolas Macris (ITW, 2023)

Bayesian Extensive-Rank Matrix Factorization with Rotational Invariant Priors. - Farzad Pourkamali; Nicolas Macris (NeurIPS, 2023)

Solving Non-linear Kolmogorov Equations in Large Dimensions by Using Deep Learning: A Numerical Comparison of Discretization Schemes. - Raffaele Marino; Nicolas Macris (J. Sci. Comput., 2023)

Stochastic Gradient Flow Dynamics of Test Risk and its Exact Solution for Weak Features. - Rodrigo Veiga 001; Anastasia Remizova; Nicolas Macris (ICML, 2024)

Rectangular Rotational Invariant Estimator for High-Rank Matrix Estimation. - Farzad Pourkamali; Nicolas Macris (CoRR, 2024)

The PRODSAT phase of random quantum satisfiability. - Joon Lee; Nicolas Macris; Jean Bernoulli Ravelomanana; Perrine Vantalon (CoRR, 2024)

Matrix Inference in Growing Rank Regimes. - Farzad Pourkamali; Jean Barbier; Nicolas Macris (IEEE Trans. Inf. Theory, 2024)

Sampling in High-Dimensions using Stochastic Interpolants and Forward-Backward Stochastic Differential Equations. - Anand Jerry George; Nicolas Macris (AISTATS, 2025)

Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves. - Anand Jerry George; Rodrigo Veiga 001; Nicolas Macris (CoRR, 2025)

Analysis of Diffusion Models for Manifold Data. - Anand Jerry George; Rodrigo Veiga 001; Nicolas Macris (CoRR, 2025)