# Nicolas Macris

#### Senior Scientist

nicolas.macris@epfl.ch 41 21 693 81 14 http://ipg.epfl.ch

**EPFL IC IINFCOM LTHC **

INR 134 (Bâtiment INR)

Station 14

CH-1015 Lausanne

Web site: Web site: https://lthcwww.epfl.ch/

41 21 693 81 14

Office: INR 134

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### Biography

publications.pdf

cv.pdf

### Current and Past PhD students

Farzad Poukamali

Clement Luneau

Eric Chun Lam Chan

Mohamad Dia

Rafah El-Khatib Analysis of Spatially Coupled Systems using the Potential Functional wth Applications to Coding Theory (2016)

Andrei Giurgiu Sparse Probabilistic Models: Phase Transitions and Solutions via Spatial Coupling (2015)

Hamed Hassani Polarization and Spatial Coupling: two techniques to boost performance (2013) - Information Theory Society 2014 Thomas Cover dissertation Award.

Marc Vuffray The cavity Method in Coding Theory (2013)

Shrinivas Kudekar Statistical Physics Methods for Sparse Graph Codes (2009).

Satish Korada Polar Codes for Channel and Source Coding (2009) - ABB 2010 Thesis Award.

Christian Ferrari Aspects of Two Dimensional Schrödinger operators: Quantum Hall Systems and Magnetic Stark Resonances (2003)

Claude Alain Piguet Long-range orders in models of itinerant electrons interacting with classical or quantum fields (1999)

## Publications

### Selected publications

Jean Barbier, Chun Lam Chan and Nicolas MacrisLong version with detailed proofs of ISIT 2018 submission "Adpative Path Interpolation for Sparse Systems: Application to a Simple Censored Block Model" |
Adaptive Path Interpolation Method for Sparse Systems: Application to a censored Block Model |

Dimitris Achlioptas, S. Hamed Hassani, Nicolas Macris and Ruediger Urbankepreprint pp. 1-63 |
New bounds for random constraint satisfaction problems via spatial coupling |

A. Giurgiu, N. Macris, R. UrbankeTransactions on Information Theory |
Spatial coupling as a proof technique |

S. Kumar, A. Young, N. Macris, H. Pfister
preprint, arXiv 1301.6111v2, submitted IEEE Transactions on Information Theory |
A proof of treshold saturation for spatially coupled LDPC codes on BMS channels |

Rafah El-Khatib, Nicolas Macris, Ruediger Urbankeextended version of ITW Sevilla 2013, arXiv 1304.6026v2 pp. 1-12 |
Displacement Convexity - A useful framework for the study of spatially coupled codes |

Vahid Aref, Nicoals Macris, Marc Vuffraypreprint arXiv 1307.5210v2 |
Approaching the Rate Distortion Limit with Spatial Coupling Belief Propagation and Decimation |

S. Hamed Hassani, Nicolas Macris and Ruediger UrbankeIEEE Information Theory Workshop - ITW Dublin pp 1-5 (2010) |
Coupled Graphical Models and Their Thresholds |

S. B. Korada, N. MacrisIEEE Transactions on Information Theory, vol 56, no 11, November 2010 |
Tight bounds on the capacity of binary input random CDMA systems |

Macris, NIEEE Transactions in Information Theory, vol 53, no 7, pp 2365-2375 (2007) |
Sharp bounds on generalised exit functions |

Macris, NIEEE Transactions in Information Theory, vol. 53, num. 2 (2007), p. 664-683. |
Griffiths Kelly Sherman correlation inequalities: a useful tool in the theory of error correcting codes |

Dionys Baeriswyl, Nicolas MacrisCours de Troisieme Cycle de la Physique en Suisse Romande (donne en 2002, 2005 et 2008) |
N-Body Methods in Condensed Matter |

Nicolas Macrisunpublished preprint 2003 |
On the equality of edge and bulk conductance in the integer Hall effect: microscopic analysis |

Macris, NJournal of Physics A: Mathematical and General, vol. 36, num. 1565-1581 (2003), p. 1565 |
Spectral flow and level spacing of edge states for quantum Hall hamiltonians |

Macris, N; Martin, Ph A; PuleJournal of Physics A: Mathematical and General, vol. 32 (1999), p. 1985-1996 |
On edge states in semi-infinite quantum Hall systems |

Dorlas, T C; Macris, N; Pule, J VCommunications in Mathematical Physics, vol. 204, num. 2 (1999), p. 367-396 |
Characterisation of the spectrum of the Landau Hamiltonian with delta impurities |

Joel. L. Lebowitz and Nicolas MacrisJournal Mathematical Physics, vol 38 pp. 2084-2103 (1997) (special issue on condensed matter physics) |
Ground states and low temperature phases of itinerant electrons interacting with classical fields |

N. Macris, B. NachtergaeleJournal of Statistical Physics, vol 85 pp. 745-761 (1996) |
On the flux phase conjecture at half filling: an improved proof |

Antoine Maillard, Jean Barbier, Florent Krzakala, Nicolas Macris |
The Mutual Information in Random Linear Estimation Beyond i.i.d Matrices |

### Other publications

#### Publication list

### Research

#### Brief description

I am also interested in quantum information theory and notably in quantum constraint satisfaction problems.

I have also worked in the field of mathematical physics on quantum Coulomb systems, quantum fermion models related to condensed matter physics, random magnetic Schroedinger operators, and aspects of the integral quantum Hall effect.

A few recent (and older) selected projects are briefly described below. This research is supported by grants of the Swiss National Foundation for Science.

#### Spatial coupling in coding and constraint satisfac

We have investigated the underpinnings of this excellent behavior in various directions beyond coding theory and found that it is quite universal. In particular dynamical phase transition thresholds (or spinodal lines) are pushed towards static phase transition thresholds and the metastable states disappear. Condensation and sat-unsat thresholds (of glassy models) are not affected by coupling.

Coupled graphical models and their thresholds, IEEE Information Theory Workshop - ITW Dublin pp 1-5 (2010), S. Hamed Hassani, Nicolas Macris and Ruediger Urbanke

The following paper contains a conceptually simple proof of threshold saturation for general LDPC ensemble on general binary memoryless channels. The proof uses a "generic" variational formulation for this class of problems.

A proof of treshold saturation for spatially coupled LDPC preprint 2013 (S. Kumar, A. Young, N. Macris, H. Pfister)

We have also investigated spatial coupling, not so much from the point of view of an engineering construction, but as a new proof technique.

In particular we find that simple mathematically analysable algorithms behave much better on the coupled instances, a fact that allows to derive new rigorous lower bounds on the SAT-UNSAT thresholds of various constraint satisfaction problems. Remarkably these bounds can be proven to be valid for the original un-coupled system.

New bounds for random constraint satisfaction problems via spatial coupling prerpint 2014 (D. Achlioptas, H. Hassani, N. Macris, R. Urbanke)

It has been conjectured for some time that for LDPC codes on general binary memoryless channels the replica symmetric formula for the conditional Shannon entropy (average free energy of the associated spin glass) is exact. We prove this conjecture (theorem 6). The proof analyzes the spatially coupled ensemble and projects back onto the original un-coupled LDPC ensemble.

Spatial coupling as a proof technique preprint 2013 (A. Giurgiu, N. Macris, R. Urbanke)

#### Displacement convexity: new applications in coding

Analysis of Coupled Scalar Systems by Displacment Convexity preprint 2013 and ITW 2013 (R. El-Khatib, N. Macris, R. Urbanke)

Analysis of coupled scalar recursions by displacement convexity ISIT 2014 (R. El-Khatib, N. Macris, T. Richardson and R. Urbanke)

#### Rigorous methods of stat mech in coding, communica

The Bethe free energy allows to compute the conditional entropy of graphical code instances. A proof from the polymer expansion preprint 2013 (N. Macris, M. Vuffray).

Decay of corelations for sparse graph error correcting codes SIAM J. Discrete Math. vol 25, no 2, pp. 956-988 (2011) (special section on constraint satisfaction problems and message passing algorithms), (S. Kudekar, N. Macris).

Tight bounds on the capacity of binary input random CDMA systems

IEEE Transactions on Information Theory, vol 56, no 11, November 2010 (S. B. Korada, N. Macris)

Sharp bounds on generalised exit functions IEEE Transactions in Information Theory, vol 53, no 7, pp 2365-2375 (2007) (N. Macris)

Griffith Kelly Sherman correlation inequalities: a useful tool in the theory of error correcting codes IEEE Transactions in Information Theory, vol. 53, num. 2 (2007), p. 664-683 (N. Macris)

#### Localization in magnetic fields and Hall effect

On the equality of edge and bulk conductance in the integer Hall effect: microscopic analysis unpublished 2003, N. Macris

Spectral flow and level spacing of edge states for quantum Hall hamiltonians Journal of Physics A: Mathematical and General, vol. 36, num. 1565-1581 (2003), p. 1565, N. Macris

On edge states in semi-infinite quantum Hall systems Journal of Physics A: Mathematical and General, vol. 32 (1999), p. 1985-1996, N. Macris, P. A. Martin and J. V. Pule

Characterisation of the spectrum of the Landau Hamiltonian with delta impurities

Communications in Mathematical Physics, vol. 204, num. 2 (1999), p. 367-396, T. C. Dorlas, N. Macris and J. V. Pule

The nature of the spectrum for a Landau hamiltonian with delta impurities, Journal of Statistical Physics, vol 87 pp. 847-875 (1997), T. C. Dorlas, N. Macris and J. V. Pule

Localization in a single band approximation to random Schroedinger operators in a magnetic field, Helvetica Physica Acta, vol 68 pp 329-364 (1995), T. C. Dorlas, N. Macris and J. V. Pule

#### Quantum statistical mechanics

The Falicov-Kimball model: a review of exact results and extensions, Helvetica Physica Acta, vol 69 pp. 850-907 (1996), (special issue in honor of K. Hepp and W. Hunziker) authors: C. Gruber, N. Macris

Ground states and low temperature phases of itinerant electrons interacting with classical fields, Journal Mathematical Physics, vol 38 pp. 2084-2103 (1997) (special issue on condensed matter physics), Joel. L. Lebowitz and Nicolas Macris

On kink states of ferromagnetic chains, Physica A, vol 279 pp. 386-397 (2000), (special issue in honor of Joel Lebowitz) authors: Ky-Thuan Bach and Nicolas Macris

Higher period ordered phases on the Bethe lattice, Physical Review B, vol 63 pp. 165111:1-11 (2001), C. Gruber, N. Macris, Ph. Royer and J.K. Freericks

Diamagnetic Currents, Communications in Mathematical Physics, 117, 215-241 (1988), N. Macris, P. A. Martin and J. V. Pule

Large volume asymptotics of Brownian integrals and orbital magnetism, Large volume asymptotics of Brownian integrals and orbital magnetism, Annales Institut Henri Poincare, section A, tome 66, no 2 pp.147-183 (1997)

Ionization equilibrium in the electron-proton gas, Journal of Staistical Physics, vol 60, no5/6 (1990), N. Macris, P. A. Martin

Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: a model study, Journal of Staistical Physics, vol 67, no5/6 (1992), J. L. Lebowitz, N. Macris, P. A. Martin (1992)

Long range order in the Falicov-Kimball model near the symmetry point: extension of Kennedy-Lieb theorem, Reviews in Mathematical physics, vol 06, pp.927-946, (1994) (also reprinted in the State of Matter a volume dedicated to E.H.Lieb) authors: J. L. Lebowitz, N. Macris

### Teaching & PhD

#### Teaching

Communication Systems

Computer Science