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  • 1.
    Agliari, Elena
    et al.
    Dipartimento di Fisica, Universita` degli Studi di Parma, viale G. Usberti 7, 43100 Parma, Italy.
    Barra, Adriano
    Del Ferraro, Gino
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Guerra, Francesco
    Tantari, Daniele
    Anergy in self-directed B lymphocytes: A statistical mechanics perspective2013In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 375, p. 21-31Article in journal (Refereed)
    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. 

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  • 2.
    Aurell, Erik
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Del Ferraro, Gino
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    A Cavity Master Equation for the continuous time dynamics of discrete spins modelsManuscript (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.

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  • 3.
    Aurell, Erik
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). Depts of Information and Computer Science and Applied Physics, Aalto University, Finland.
    Del Ferraro, Gino
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Causal analysis, Correlation-Response, and Dynamic cavity2016In: International Meeting on High-Dimensional Data-Driven Science (HD3-2015), Institute of Physics (IOP), 2016, article id 012002Conference paper (Refereed)
    Abstract [en]

    The purpose of this note is to point out analogies between causal analysis in statistics and the correlation-response theory in statistical physics. It is further shown that for some systems the dynamic cavity offers a way to compute the stationary state of a non-equilibrium process effectively, which could then be taken an alternative starting point of causal analysis.

  • 4.
    Aurell, Erik
    et al.
    KTH, School of Biotechnology (BIO), Centres, Albanova VinnExcellence Center for Protein Technology, ProNova. KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Del Ferraro, Gino
    Department of Computational Biology, AlbaNova University Center, SE-106, 91 Stockholm, Sweden.
    Dominguez, E.
    Univ Havana, Phys Fac, Dept Theoret Phys, Grp Complex Syst & Stat Phys, Havana, Cuba..
    Mulet, R.
    Univ Havana, Phys Fac, Dept Theoret Phys, Grp Complex Syst & Stat Phys, Havana, Cuba..
    Cavity master equation for the continuous time dynamics of discrete-spin models2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 95, no 5, article id 052119Article in journal (Refereed)
    Abstract [en]

    We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of 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 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.

  • 5.
    Barra, Adriano
    et al.
    Univ Roma La Sapienza, Dipartimento Fis, I-00185 Rome, Italy..
    Del Ferraro, Gino
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Tantari, Daniele
    Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy..
    Erratum to: Mean field spin glasses treated with PDE techniques2015In: European Physical Journal B: Condensed Matter Physics, ISSN 1434-6028, E-ISSN 1434-6036, Vol. 88, no 4, article id 100Article in journal (Refereed)
  • 6.
    Barra, Adriano
    et al.
    Dipartimento di Fisica, Sapienza Università di Roma, P.le Aldo Moro 5, Rome, Italy.
    Del Ferraro, Gino
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Tantari, Daniele
    Dipartimento di Matematica, Sapienza Università di Roma, P.le Aldo Moro 5, Rome, Italy.
    Mean field spin glasses treated with PDE techniques2013In: European Physical Journal B: Condensed Matter Physics, ISSN 1434-6028, E-ISSN 1434-6036, Vol. 86, no 7, article id 332Article in journal (Refereed)
    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. 

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  • 7.
    Del Ferraro, Gino
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Equilibrium and Dynamics on Complex Networkds2016Doctoral 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.

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  • 8.
    Del Ferraro, Gino
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Aurell, Erik
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Aalto University, Finland.
    Dynamic message-passing approach for kinetic spin models with reversible dynamics2015In: 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)
    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.

  • 9.
    Del Ferraro, Gino
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Aurell, Erik
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Perturbative large deviation analysis of non-equilibrium dynamics2014In: Journal of the Physical Society of Japan, ISSN 0031-9015, E-ISSN 1347-4073, Vol. 83, no 8Article in journal (Refereed)
    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. 

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  • 10.
    Del Ferraro, Gino
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    Wang, Chuang
    Martì, Dani
    Mézard, Marc
    Cavity Method: Message Passing from a Physics perspective2016In: 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.

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  • 11.
    Del Ferraro, Gino
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Wang, Chuang
    Zhou, Hai-Jun
    Aurell, Erik
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Aalto University, Finland.
    On one-step replica symmetry breaking in the Edwards-Anderson spin glass model2016In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, article id 073305Article in journal (Refereed)
    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.

  • 12. Dominguez, Eduardo
    et al.
    Del Ferraro, Gino
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Ricci-Tersenghi, Federico
    A simple approach to the dynamics of Ising spin systemsManuscript (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.

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  • 13.
    Dominguez Vazquez, Eduardo
    et al.
    Univ Havana, Henri Poincare Grp Complex Syst, Havana 10400, Cuba.;Univ Havana, Dept Theoret Phys, Fac Phys, Havana 10400, Cuba..
    Del Ferraro, Gino
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB. KTH, School of Biotechnology (BIO), Centres, Albanova VinnExcellence Center for Protein Technology, ProNova.
    Ricci-Tersenghi, Federico
    Univ Roma La Sapienza, Ist Nazl Fis Nucl, Sez Roma 1, Dipartimento Fis, Piazzale Aldo Moro 5, I-00185 Rome, Italy.;Univ Roma La Sapienza, CNR Nanotec, Piazzale Aldo Moro 5, I-00185 Rome, Italy..
    A simple analytical description of the non-stationary dynamics in Ising spin systems2017In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 033303Article in journal (Refereed)
    Abstract [en]

    The analytical description of the dynamics in models with discrete variables (e.g. Ising spins) is a notoriously di. cult problem, which can only be tackled under some approximation. Recently a novel variational approach to solve the stationary dynamical regime has been introduced by Pelizzola ( 2013 Eur. Phys. J. B 86 120), where simple closed equations are derived under meanfield approximations based on the cluster variational method. Here we propose to use the same approximation based on the cluster variational method also for the non- stationary regime, which has not been considered up to now within this framework. We check the validity of this approximation in describing the nonstationary dynamical regime of several Ising models defined on Erdos-Renyi random graphs: we study ferromagnetic models with symmetric and partially asymmetric couplings, models with random fields and also spin glass models. A comparison with the actual Glauber dynamics, solved numerically, shows that pone of the two studied approximations (the so-called `diamond' approximation) provides very accurate results in all the systems studied. Only for the spin glass models do we find some small discrepancies in the very low temperature phase, probably due to the existence of a large number of metastable states. Given the simplicity of the equations to be solved, we believe the diamond approximation should be considered as the `minimal standard' in the description of the nonstationary regime of Ising-like models: any new method pretending to provide a better approximate description to the dynamics of Ising-like models should perform at least as good as the diamond approximation.

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