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Del Ferraro, G., Wang, C., Martì, D. & Mézard, M. (2016). Cavity Method: Message Passing from a Physics perspective. In: F. Krzakala et al. (Ed.), Statistical Physics, Optimization, Inference, and Message-Passing Algorithms: Lecture Notes of the Les Houches School of Physics - Special Issue October 2013. Oxford University Press
Open this publication in new window or tab >>Cavity Method: Message Passing from a Physics perspective
2016 (English)In: Statistical Physics, Optimization, Inference, and Message-Passing Algorithms: Lecture Notes of the Les Houches School of Physics - Special Issue October 2013 / [ed] F. Krzakala et al., Oxford University Press, 2016Chapter in book (Other academic)
Abstract [en]

In this three-sections lecture cavity method is introduced as heuristic framework from a Physics perspective to solve probabilistic graphical models and it is presented both at the replica symmetric (RS) and 1-step replica symmetry breaking (1RSB) level. This technique has been applied with success on a wide range of models and problems such as spin glasses, random constrain satisfaction problems (rCSP), error correcting codes etc. Firstly, the RS cavity solution for Sherrington-Kirkpatrick model---a fully connected spin glass model---is derived and its equivalence to the RS solution obtained using replicas is discussed. Then, the general cavity method for diluted graphs is illustrated both at RS and 1RSB level. The latter was a significant breakthrough in the last decade and has direct applications to rCSP. Finally, as example of an actual problem, K-SAT is investigated using belief and survey propagation.

Place, publisher, year, edition, pages
Oxford University Press, 2016
Keywords
cavity method, message passing, survey propagation, tree-like graphs
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-192102 (URN)
External cooperation:
Note

QC 20160905

Available from: 2016-09-05 Created: 2016-09-05 Last updated: 2016-09-05Bibliographically approved
Del Ferraro, G. (2016). Equilibrium and Dynamics on Complex Networkds. (Doctoral dissertation). Stockholm: KTH Royal Institute of Technology
Open this publication in new window or tab >>Equilibrium and Dynamics on Complex Networkds
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Complex networks are an important class of models used to describe the behaviour of a very broad category of systems which appear in different fields of science ranging from physics, biology and statistics to computer science and other disciplines. This set of models includes spin systems on a graph, neural networks, decision networks, spreading disease, financial trade, social networks and all systems which can be represented as interacting agents on some sort of graph architecture.

In this thesis, by using the theoretical framework of statistical mechanics, the equilibrium and the dynamical behaviour of such systems is studied.

For the equilibrium case, after presenting the region graph free energy approximation, the Survey Propagation method, previously used to investi- gate the low temperature phase of complex systems on tree-like topologies, is extended to the case of loopy graph architectures.

For time-dependent behaviour, both discrete-time and continuous-time dynamics are considered. It is shown how to extend the cavity method ap- proach from a tool used to study equilibrium properties of complex systems to the discrete-time dynamical scenario. A closure scheme of the dynamic message-passing equation based on a Markovian approximations is presented. This allows to estimate non-equilibrium marginals of spin models on a graph with reversible dynamics. As an alternative to this approach, an extension of region graph variational free energy approximations to the non-equilibrium case is also presented. Non-equilibrium functionals that, when minimized with constraints, lead to approximate equations for out-of-equilibrium marginals of general spin models are introduced and discussed.

For the continuous-time dynamics a novel approach that extends the cav- ity method also to this case is discussed. The main result of this part is a Cavity Master Equation which, together with an approximate version of the Master Equation, constitutes a closure scheme to estimate non-equilibrium marginals of continuous-time spin models. The investigation of dynamics of spin systems is concluded by applying a quasi-equilibrium approach to a sim- ple case. A way to test self-consistently the assumptions of the method as well as its limits is discussed.

In the final part of the thesis, analogies and differences between the graph- ical model approaches discussed in the manuscript and causal analysis in statistics are presented.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. p. 189
Series
TRITA-CSC-A, ISSN 1653-5723 ; 2016:17
Keywords
Statistical mechanics, complex networks, spin systems, non equilibrium dynamics, generalized belief propagation, message passing, cavity method, variational approaches
National Category
Other Physics Topics Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-191991 (URN)978-91-7729-058-2 (ISBN)
Public defence
2016-09-09, Kollegiesalen, Brinellvägen 8, plan 4, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20160904

Available from: 2016-09-04 Created: 2016-09-03 Last updated: 2016-09-05Bibliographically approved
Del Ferraro, G., Wang, C., Zhou, H.-J. & Aurell, E. (2016). On one-step replica symmetry breaking in the Edwards-Anderson spin glass model. Journal of statistical physics, Article ID 073305.
Open this publication in new window or tab >>On one-step replica symmetry breaking in the Edwards-Anderson spin glass model
2016 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, article id 073305Article in journal (Refereed) Published
Abstract [en]

We consider a one-step replica symmetry breaking description of the Edwards–Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on the extremal points of the Kikuchi approximation, which are also fixed points of a generalized belief propagation (GBP) scheme. We show that a generalized free energy can be constructed where these extremal points are exponentially weighted by their Kikuchi free energy and a Parisi parameter y, and that the Kikuchi approximation of this generalized free energy leads to second-level, one-step replica symmetry breaking (1RSB), GBP equations. We then proceed analogously to the Bethe approximation case for tree-like graphs, where it has been shown that 1RSB belief propagation equations admit a survey propagation solution. We discuss when and how the one-step-replica symmetry breaking GBP equations that we obtain also allow a simpler class of solutions which can be interpreted as a class of generalized survey propagation equations for the single instance graph case.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2016
Keywords
Region graph approximations, generalized belief propagation, survey propagation, generalized survey propagation, low temperature
National Category
Natural Sciences Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-192097 (URN)10.1088/1742-5468/2016/07/073305 (DOI)000381379800023 ()2-s2.0-85014438156 (Scopus ID)
Note

QC 20160905

Available from: 2016-09-05 Created: 2016-09-05 Last updated: 2019-10-02Bibliographically approved
Del Ferraro, G. & Aurell, E. (2015). Dynamic message-passing approach for kinetic spin models with reversible dynamics. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 92(1), Article ID 010102.
Open this publication in new window or tab >>Dynamic message-passing approach for kinetic spin models with reversible dynamics
2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 92, no 1, article id 010102Article in journal (Refereed) Published
Abstract [en]

A method to approximately close the dynamic cavity equations for synchronous reversible dynamics on a locally treelike topology is presented. The method builds on (a) a graph expansion to eliminate loops from the normalizations of each step in the dynamics and (b) an assumption that a set of auxilary probability distributions on histories of pairs of spins mainly have dependencies that are local in time. The closure is then effectuated by projecting these probability distributions on n-step Markov processes. The method is shown in detail on the level of ordinary Markov processes (n = 1) and outlined for higher-order approximations (n > 1). Numerical validations of the technique are provided for the reconstruction of the transient and equilibrium dynamics of the kinetic Ising model on a random graph with arbitrary connectivity symmetry.

Place, publisher, year, edition, pages
American physical society, 2015
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-172162 (URN)10.1103/PhysRevE.92.010102 (DOI)000358259400001 ()
External cooperation:
Note

QC 20150818

Available from: 2015-08-18 Created: 2015-08-14 Last updated: 2017-12-04Bibliographically approved
Barra, A., Del Ferraro, G. & Tantari, D. (2015). Erratum to: Mean field spin glasses treated with PDE techniques. European Physical Journal B: Condensed Matter Physics, 88(4), Article ID 100.
Open this publication in new window or tab >>Erratum to: Mean field spin glasses treated with PDE techniques
2015 (English)In: European Physical Journal B: Condensed Matter Physics, ISSN 1434-6028, E-ISSN 1434-6036, Vol. 88, no 4, article id 100Article in journal (Refereed) Published
Place, publisher, year, edition, pages
SPRINGER, 2015
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-242766 (URN)10.1140/epjb/e2015-60214-3 (DOI)000352725700001 ()2-s2.0-84928123260 (Scopus ID)
Note

QC 20190213

Available from: 2019-02-13 Created: 2019-02-13 Last updated: 2019-08-21Bibliographically approved
Del Ferraro, G. & Aurell, E. (2014). Perturbative large deviation analysis of non-equilibrium dynamics. Journal of the Physical Society of Japan, 83(8)
Open this publication in new window or tab >>Perturbative large deviation analysis of non-equilibrium dynamics
2014 (English)In: Journal of the Physical Society of Japan, ISSN 0031-9015, E-ISSN 1347-4073, Vol. 83, no 8Article in journal (Refereed) Published
Abstract [en]

Macroscopic fluctuation theory has shown that a wide class of non-equilibrium stochastic dynamical systems obey a large deviation principle, but except for a few one-dimensional examples these large deviation principles are in general not known in closed form. We consider the problem of constructing successive approximations to an (unknown) large deviation functional and show that the non-equilibrium probability distribution the takes a Gibbs-Boltzmann form with a set of auxiliary (non-physical) energy functions. The expectation values of these auxiliary energy functions and their conjugate quantities satisfy a closed system of equations which can imply a considerable reduction of dimensionality of the dynamics. We show that the accuracy of the approximations can be tested self-consistently without solving the full non- equilibrium equations. We test the general procedure on the simple model problem of a relaxing 1D Ising chain. 

Place, publisher, year, edition, pages
Physical society of Japan, 2014
Keywords
Macroscopic fluctuation theory, perturbative large deviation, dynamics Ising chain.
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-165789 (URN)10.7566/JPSJ.83.084001 (DOI)000339806400012 ()2-s2.0-84924898390 (Scopus ID)
Projects
NETADIS
Funder
EU, FP7, Seventh Framework Programme
Note

QC 20150505

Available from: 2015-04-29 Created: 2015-04-29 Last updated: 2017-12-04
Agliari, E., Barra, A., Del Ferraro, G., Guerra, F. & Tantari, D. (2013). Anergy in self-directed B lymphocytes: A statistical mechanics perspective. Journal of Theoretical Biology, 375, 21-31
Open this publication in new window or tab >>Anergy in self-directed B lymphocytes: A statistical mechanics perspective
Show others...
2013 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 375, p. 21-31Article in journal (Refereed) Published
Abstract [en]

Self-directed lymphocytes may evade clonal deletion at ontogenesis but still remain harmless due to a mechanism called clonal anergy. For B-lymphocytes, two major explanations for anergy developed over the last decades: according to Varela theory, anergy stems from a proper orchestration of the whole B-repertoire, such that self-reactive clones, due to intensive feed-back from other clones, display strong inertia when mounting a response. Conversely, according to the model of cognate response, self-reacting cells are not stimulated by helper lymphocytes and the absence of such signaling yields anergy. Through statistical mechanics we show that helpers do not prompt activation of a sub-group of B-cells: remarkably, the latter are just those broadly interacting in the idiotypic network. Hence Varela theory can finally be reabsorbed into the prevailing framework of the cognate response model. Further, we show how the B-repertoire architecture may emerge, where highly connected clones are self-directed as a natural consequence of ontogenetic learning. 

Place, publisher, year, edition, pages
Elsevier, 2013
Keywords
Immune networks, Lymphocyte homeostasis, Self-nonself-discrimination
National Category
Immunology
Identifiers
urn:nbn:se:kth:diva-165820 (URN)10.1016/j.jtbi.2014.05.006 (DOI)000354830700004 ()2-s2.0-84988807155 (Scopus ID)
Funder
EU, FP7, Seventh Framework Programme, 290038
Note

QC 20150430

Available from: 2015-04-29 Created: 2015-04-29 Last updated: 2017-12-04Bibliographically approved
Barra, A., Del Ferraro, G. & Tantari, D. (2013). Mean field spin glasses treated with PDE techniques. European Physical Journal B: Condensed Matter Physics, 86(7), Article ID 332.
Open this publication in new window or tab >>Mean field spin glasses treated with PDE techniques
2013 (English)In: European Physical Journal B: Condensed Matter Physics, ISSN 1434-6028, E-ISSN 1434-6036, Vol. 86, no 7, article id 332Article in journal (Refereed) Published
Abstract [en]

Following an original idea of F. Guerra, in this notes we analyze the Sherrington-Kirkpatrick model from different perspectives, all sharing the underlying approach which consists in linking the resolution of the sta- tistical mechanics of the model (e.g. solving for the free energy) to well-known partial differential equation (PDE) problems (in suitable spaces). The plan is then to solve the related PDE using techniques involved in their native field and lastly bringing back the solution in the proper statistical mechanics framework. Within this strand, after a streamlined test-case on the Curie-Weiss model to highlight the methods more than the physics behind, we solve the SK both at the replica symmetric and at the 1-RSB level, obtaining the correct expression for the free energy via an analogy to a Fourier equation and for the self-consistencies with an analogy to a Burger equation, whose shock wave develops exactly at critical noise level (triggering the phase transition).

Our approach, beyond acting as a new alternative method (with respect to the standard routes) for tackling the complexity of spin glasses, links symmetries in PDE theory with constraints in statistical mechanics and, as a novel result from the theoretical physics perspective, we obtain a new class of polynomial identities (namely of Aizenman-Contucci type, but merged within the Guerra’s broken replica measures), whose in- terest lies in understanding, via the recent Panchenko breakthroughs, how to force the overlap organization to the ultrametric tree predicted by Parisi. 

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2013
Keywords
spin glass, partial differential equations, sherrington kirkpatrick, replica symmetry breaking
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-165797 (URN)10.1140/epjb/e2013-40334-6 (DOI)000322175100036 ()
Projects
NETADIS
Note

QC 20150506.

Correction in: European Physical Journal B: Condensed Matter Physics, Volume: 88, Issue: 4, Article Number: 100

DOI: 10.1140/epjb/e2015-60214-3

WOS:000352725700001

Available from: 2015-04-29 Created: 2015-04-29 Last updated: 2017-12-04Bibliographically approved
Aurell, E. & Del Ferraro, G.A Cavity Master Equation for the continuous time dynamics of discrete spins models.
Open this publication in new window or tab >>A Cavity Master Equation for the continuous time dynamics of discrete spins models
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We present a new method to close the Master Equation representing the continuous time dynamics of Ising interacting spins. The method makes use of the the theory of Random Point Processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean field ferromagnet and the dynamics of the one dimensional Ising system. We then present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the Random Field Ising model, and the Viana-Bray spin-glass model.

Keywords
continuous time dynamics, master equation, cavity method, cavity master equation, dynamic message passing, disordered models
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-192100 (URN)
External cooperation:
Note

QC 20160905

Available from: 2016-09-05 Created: 2016-09-05 Last updated: 2016-09-05Bibliographically approved
Dominguez, E., Del Ferraro, G. & Ricci-Tersenghi, F. A simple approach to the dynamics of Ising spin systems.
Open this publication in new window or tab >>A simple approach to the dynamics of Ising spin systems
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We study a novel variational approach to solve the dynamics of Ising-like discrete spin systems. The equations are derived under mean-field approximations based on the cluster variational method. Comparison with the actual Glauber dynamics of models defined on Erdos-R\'enyi random graphs show that some of these approximations are extremely accurate, both at equilibrium and in the off-equilibrium regime, providing the same result of the Monte Carlo simulation in a much shorter time. The models studied are the ferromagnetic kinetic Ising model (both with symmetric and partially asymmetric interactions), the random field Ising model and the Viana-Bray model. Only for the latter model we find some small discrepancies in the very low temperature phase, probably due to the existence of a large number of metastable states.

Keywords
variational approximations, spin dynamics, Glauber dynamics, cluster variation method, path probability method
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-192098 (URN)
External cooperation:
Note

QC 20160905

Available from: 2016-09-05 Created: 2016-09-05 Last updated: 2016-09-05Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-1252-2899

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