Posters

Elisabeth Agoritsas*, Vivien Lecomte

Scalings, saddle points and Gaussian variational method revisited for the 1D interface in random media

We discuss as a case study the scaling properties of a one-dimensional interface at equilibrium, at finite temperature and in a disordered environment with a finite disorder correlation length. We focus our approach on the scalings of its geometrical fluctuations, specifically of the variance of its relative displacements at a given length scale. This ‘roughness’ follows at large length scales a power law whose exponent characterises a superdiffusive behaviour, which in 1+1 dimension is known to be the characteristic 2/3 exponent of the Kardar-Parisi-Zhang (KPZ) universality class. On the other hand, the Flory exponent of this model, obtained by a power counting argument on the interface Hamiltonian, is equal to 3/5 and thus does not yield the correct KPZ roughness exponent. However, a standard Gaussian-Variational-Method (GVM) computation of the roughness is supposedly bound to predict the Flory exponent instead of the physical KPZ one. In this work, we first review some of the available power-counting options, and examine the distinct exponent values that they predict. Their (in)validity is shown to depend on the existence (or not) of well-defined optimal trajectories in a large-size or low-temperature asymptotics. We identify the crucial role of the ‘cut-off’ lengths of the model — the disorder correlation length and the system size — which one has to carefully follow throughout the scaling analysis. In particular, we report new results obtained within a GVM computation scheme which includes explicitly a finite system size, allowing us to avoid the usual Flory pitfall regarding the asymptotic roughness exponent.

Reference: Elisabeth Agoritsas and Vivien Lecomte, J. Phys. A 50 104001 (2017).

Fabian Aguirre Lopez*, Anthonius C.C. Coolen

Imaginary replica analysis of loopy regular random graphs

We present an analytical approach for describing spectrally constrained maximum entropy ensembles of finitely connected regular loopy graphs, valid in the regime of weak loop-loop interactions. We derive an expression for the leading two orders of the expected eigenvalue spectrum, through the use of infinitely many replica indices taking imaginary values. We apply the method to models in which the spectral constraint reduces to a soft constraint on the number of triangles, which exhibit `shattering' transitions to phases with extensively many disconnected cliques, to models with controlled numbers of triangles and squares, and to models where the spectral constraint reduces to a count of the number of adjacency matrix eigenvalues in a given interval. Our predictions are supported by MCMC simulations based on edge swaps with nontrivial acceptance probabilities. The generalisation to arbitrary degree distributions will also be discussed.

Ada Altieri*, Giulio Biroli

Replica symmetry breaking scenario towards glassy behaviors in critical ecosystems

Very different models (Cascade predation, Plant-Pollinator, Consumer-Resource interactions) can be reasonably well described by a much simpler reference framework, a random Lotka-Volterra (LV) model. All relevant properties of the community can be encapsulated in a few control parameters defining the fitness spread and the specific type of interaction. Despite its minimal structure, the LV model turns out to be very beneficial for studying collective properties of high-dimensional critical ecosystems and capturing emergent phase transitions, in particular between a single equilibrium (RS) regime and a multiple equilibria (RSB) phase, once the randomness in the couplings is progressively increased.

We especially focus on the multiple attractor phase, obtaining a complete phase diagram in temperature and characterising - via a replica symmetry breaking computation - its energy landscape properties, thus corroborating the existence of a Gardner phase. We also perform a stability analysis in the presence of a non-linear, cubic interaction potential in order to model a multiplicative Allee effect and then explain invasions and depensation in biological populations.

Shunta Arai*

Statistical mechanical analysis of reverse annealing for code-division multiple-access multiuser demodulator

Code-division multiple-access multiuser demodulator (CDMA) system has been used in wireless communication systems [1]. The problem setting is that users transmit their information to the base station thorough channels. In CDMA, we estimate the original information from noisy outputs and spread code sequences which are prepared for each user beforehand. When the length of the spread code sequences are not enough, two solutions for successful and failed demodulation coexist. This phenomena shows us the existence of the first-order phase transition in this problem. The first-order phase transition degrades the performance of demodulation. In this poster, we utilize quantum fluctuations to demodulate signals [2]. To mitigate or avoid the difficulty of demodulation, for example the existence of the first-order phase transition, we apply reverse annealing [3] to CDMA. Reverse annealing is the method which iteratively updates the initial solutions and performs quantum annealing. We analyze the average performance of demodulation with reverse annealing by using replica method. We also investigate whether replica symmetry is recovered or not by introducing quantum fluctuations [4].

[1] T.Tanaka, EPL54,540 (2001) [2] Y.Otsubo et al, Rev.E 90,012126 (2014) [3] M.Ohkuwa et al, Rev.A.98,022314 (2018) [4] S.Arai et al, in preparation

Francesco Arceri*, Eric Corwin

Vibrational spectrum of nearly jammed amorphous solids

Thermal properties of amorphous solids are directly related to the density of vibrational states. In this work we present a novel protocol based on the use of the effective logarithmic potential between hard spheres, able to produce configurations typical of a colloidal glass. We performed a spectrum analysis and present how the density of vibrational modes evolves when the system gets closer to jamming. The features of the low-frequency modes we found agree with former numerical studies in the soft side of the jamming transition, we than conclude that near jamming there is a smooth crossover between hard and soft spheres, and that this protocol is able to track the structural features that rule the vibrational density of low temperature glasses.

Claudia Artiaco*

The quantum perceptron

Claudia Artiaco, Paolo Baldan*, Giorgio Parisi

An exploratory study of glassy landscapes near jamming

The discovery of a Gardner transition in several mean-field glass formers provides a new theoretical framework to understand the process giving rise to vitrification. One of the most important predictions of the theory is the ultrametric organization of thermodynamic states, consequence of the fullRSB structure of the transition.

Carlo Baldassi, Enrico M. Malatesta*, Riccardo Zecchina

Properties of the geometry of solutions and capacity of multi-layer neural networks with Rectified Linear Units activations

Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for the so called vanishing gradient problem which can undercut stochastic gradient descent (SGD) learning in networks composed of multiple layers. Here we provide analytical results on the effects of ReLUs on the capacity and on the geometrical landscape of the solution space in two-layer neural networks with either binary or real-valued weights. We study the problem of storing an extensive number of random patterns and find that, quite unexpectedly, the capacity of the network remains finite as the number of neurons in the hidden layer increases, at odds with the case of threshold units in which the capacity diverges. Possibly more important, a large deviation approach allows us to find that the geometrical landscape of the solution space has a peculiar structure: While the majority of solutions are close in distance but still isolated, there exist rare regions of solutions which are much more dense than the similar ones in the case of threshold units. These solutions are robust to perturbations of the weights and can tolerate large perturbations of the inputs. The analytical results are corroborated by numerical findings.

Stefan Boettcher*, Dominic M. Robe, Paolo Sibani

Relaxation and aging in rapidly quenched glasses

We provide a unified description of "aging", the increasingly sluggish dynamics widely observed in the relaxation dynamics of disordered materials that are rapidly quenched into a jammed state. Relaxation requires ever larger, record-sized rearrangements in an uncorrelated sequence of intermittent events (avalanches or quakes) that irreversibly release energy. In such a statistic of records, these rearrangements occur at a rate ~ 1/t. Hence, in the ensuing log-Poisson process, the number of events between a waiting time t_w and any later time t integrates to ~ ln(t/t_w), such that any two-time observable inherits the (t/t_w)-dependence that is the hallmark of pure aging. Based on this "record dynamics" description, we can explain the relaxation observed numerically and experimentally in a broad range of materials, such as low-temperature spin glasses and high-density colloids and granular piles [1,2,3]. We have proposed a phenomenological model of record dynamics that reproduces salient aspects, for example, the van-Hove distribution of displacements, intermittency and dynamic heterogeneity [3,4]. Our studies also rule out some other explanations of aging based on trap models and continuous-time walks [5].

[l] (https://arxiv.org/abs/1802.08845) P. Sibani and SB, Phys. Rev. B 98, 054202 (2018); [2] (https://arxiv.org/abs/1802.05350) D. M. Robe, et. al., EPL 116, 38003 (2016); [3] (https://arxiv.org/abs/1802.05350) D. M. Robe and SB, Soft Matter 14, 9451-9456 (2018) [4] (https://arxiv.org/abs/1401.6521) N. Becker, et. al., J. Phys.: Condens. Mat. 26, 505102 (2014); [5] (https://arxiv.org/abs/1803.06580) SB et al, Phys. Rev. E 98, 020602 (2018).

Stefan Boettcher*, Stefan Falkner

Extrapolating finite-size scaling exponents for Edwards-Anderson ground state energies to the mean-field limit

Extensive computations of ground-state energies of the Edwards-Anderson spin glass on bond-diluted, hypercubic lattices are conducted in dimensions d=3, ..., 7 [1]. Results are presented for bond densities deep within the glassy regime, where finding ground states is among the hardest combinatorial optimization problems. Finite-size corrections of the form N^{-ω} are shown to be consistent throughout with the prediction ω=1 - y/d, where y refers to the "stiffness" exponent that controls the formation of domain wall excitations at low temperatures [2]. In the glassy phase, ω does not approach its anticipated mean-field value of 2/3, obtained from simulations of the Sherrington-Kirkpatrick spin glass on an N-clique graph. Instead, the value of ω reached at the upper critical dimension, d_u=6, matches another type of mean-field spin glass models, namely those on sparse random networks of regular degree called Bethe lattices.

[1] Boettcher & Falkner, EPL98(2012)47005 (arXiv:1110.6242); [2] Boettcher, PRL95(2005)197205 (arXiv:cond-mat/0508061).

Alfredo Braunstein, Giovanni Catania*, Luca Dall'Asta

Density consistency on discrete graphical models

Computing marginal distributions of discrete graphical models is a fundamental problem with a vast number of applications in many fields of science. However, the problem is typically intractable as it scales exponentially with the system size and therefore approximation schemes are needed to estimate marginal distributions. We present a new family of approximation schemes called Density Consistency. The scheme computes exact marginals on acyclic graphs as Belief Propagation: in addition, it includes some loop corrections, i.e. it takes into account correlations coming from long cycles in the factor graph. The method is also similar to Adaptive TAP but with a different consistency condition. Results on random connectivity and finite dimensional Ising and Edward-Anderson models show a significant improvement with respect to the Bethe (tree) approximation in all cases, and significant improvement with respect to Cluster Variational Methods and other loop correction schemes in many cases. We also estimate the phase diagram of homogeneous Ising Models on hypercubic lattices. In particular, for the critical inverse temperature the 1/d expansion of 1/(dβc ) of the proposed scheme turns out to be exact up to 4th order.

Louise Budzynski*, Guilhem Semerjian, Federico Ricci-Tersenghi

Biased landscapes in random Constraint Satisfaction Problems

The typical complexity of Constraint Satisfaction Problems can be studied using random ensemble of instances. One observes several threshold phenomena when the density of constraints increases. We will be interested in the clustering threshold above which typical solutions shatter into disconnected components. We concentrate on the bicoloring of random hypergraphs. By introducing a bias that breaks the uniformity among solutions, we can delay the clustering threshol to higher density of constraints, and that has a positive impact on the performances of Simulated Annealing.

Angelo Giorgio Cavaliere*, Thibault Lesieur, Federico Ricci-Tersenghi

Biased thermodynamics can explain the behaviour of smart algorithms looking for jammed configurations

We consider a continuous version of the coloring problem on sparse random graphs (it is also equivalent to a Mari Kurchan Krzakala model in d=1). For some choice of the parameters, it clearly displays a random first order transition when changing the connectivity or the temperature in the system, thus making it an interesting mean-field model to study dynamical and jamming transitions (both analytically and numerically).

Rafael Diaz Hernandez Rojas*, Giorgio Parisi, Federico Ricci-Tersenghi

Inferring the particle-wise dynamics of nearly jammed configurations of hard spheres

In this work we address the question of what is the relation between the statics and the dynamics in disordered solids. In particular, we studied the trajectories of individual particles in a 3d configuration near to its jamming point. By considering the network of contacts at jamming, we were able to find two relevant variables that show a significant correlation with the statistics of the particles motion, such as the first and second moments of their displacement. We tested our methodology by using two different protocols for exploring the dynamics of the system, namely Monte Carlo and Molecular Dynamics simulations.

Davide Facoetti*, Giulio Biroli, Jorge Kurchan, David Reichmann

Classical Glasses, Black Holes, and Strange Quantum Liquids

From the dynamics of a broad class of classical mean-field glass models one may obtain a quantum model with finite zero-temperature entropy, a quantum transition at zero temperature, and a time-reparametrization (quasi-)invariance in the dynamical equations for correlations. The low eigenvalue spectrum of the resulting quantum model is directly related to the structure and exploration of metastable states in the landscape of the original classical glass model. This mapping reveals deep connections between classical glasses and the properties of SYK-like models.

Luis A. Fernandez, Enzo Marinari, Victor Martín-Mayor, Ilaria Paga* and Juan J. Ruiz-Lorenzo

The dimensional crossover in spin-glasses: from bulk systems to thin films

In the last five years, a new experimental protocol, introduced by the Austin group has challenged theorists. Indeed, by studying the time growth of spin-glass correlation length on multilayer samples of thin film, the lower critical dimension has been measured experimentally [S. Guchhait and R. L. Orbach Phys. Rev. Lett. 112, (2014) 126401] and precision measurements of the aging rate has been obtained [Q. Zhai et al. Phys. Rev. B 95 (2017) 054304, S. Guchhait and R. L. Orbach Phys. Rev. Lett. 118,(2017) 157203].

Giampaolo Folena*

Memories from the Ergodic Phase

Silvio Franz, Thibaud Maimbourg*, Giorgio Parisi, Antonello Scardicchio

Low-temperature anomalies in structural glasses: impact of jamming criticality

We present a novel mechanism for the anomalous behaviour of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the spherical perceptron, suggests that there exists a crossover temperature above which the specific heat scales linearly with temperature while below it a cubic scaling is displayed. This relies on two crucial features of the phase diagram: (i) The marginal stability of the free-energy landscape, which induces a gapless phase responsible for the emergence of a power-law scaling (ii) The vicinity of the classical jamming critical point, as the crossover temperature gets lowered when approaching it. This scenario arises from a direct study of the thermodynamics of the system in the quantum regime, where we show that, contrary to crystals,the Debye approximation does not hold.

Silvio Franz, Antonio Sclocchi*, Pierfrancesco Urbani

Critical behavior in the UNSAT phase of the linear perceptron

We consider the perceptron beyond the limit of capacity and we study the landscape of local minima for the linear cost function. We show that in the glassy (replica symmetry broken) region of the phase diagram, local minima are critical even far away from the jamming transition line. This result brings new insights about the jamming universality class.

Benjamin Guiselin*, Ludovic Berthier, Gilles Tarjus

Random-Field Ising Model criticality in a model glass-former

To account for the dramatic slowing down of supercooled liquids approaching the glass transition, the Random First Order Transition (RFOT) theory predicts that a genuine phase transition between the liquid phase and an ideal glass phase takes place at a temperature below the experimental glass transition. Besides, when two replicas of the same supercooled liquid are coupled attractively, a first-order phase transition line and a critical point in the universality class of the Random Field Ising Model emerge, depending on the attraction strength and the temperature. We present extensive computer simulations of a model supercooled liquid in 3 dimensions coupled with advanced numerical techniques to establish the existence of this first-order transition line and the associated random critical point. Overall, we show that mean-field results and growing thermodynamic fluctuations are still relevant in physical dimensions.

Giancarlo Jug*

The cellular model of glasses: structure, physical properties and state transformation

Some of the most compelling questions about the physics of glasses will be addressed from the point of view of lower temperatures investigations, both theoretical and experimental. From such viewpoint, the ideal glass model appears to be unstable and to give way to a cellular model -- glasses presenting themselves rather as 'failed poly-crystalline solids' than as 'arrested liquids'. Evidence will be presented that most questions can be resolved by modeling amorphous solids at the nano-scale rather than at the microscopic atomic level.

Joyjit Kundu, Ludovic Berthier, Patrick Charbonneau*

Echo of the dynamical criticality in supercooled liquids

Measuring the critical properties of a spinodal point is notoriously difficult, because activated processes compete with the accompanying critical dynamical slowing down, and thus limit how close that point can be approached. Here, we investigate the spinodal criticality associated with the (avoided) dynamical transition of liquid glass formers, which was first predicted by the mode- coupling theory of glasses. Using the SWAP algorithm to equilibrate configurations well above that transition and a robust numerical scheme to screen out the contribution of activated processes, we observe the finite-dimensional echo of the mean-field square-root singularity of the typical cage size. This approach provides estimates of the correction to the square-root singularity and its vanishing at the upper critical dimension.

Vivien Lecomte*, Elisabeth Agoritsas

A numerical method to assess the Gaussian Variational Method in disordered elastic systems — case study of the 1D interface

While several analytical arguments support power-law scaling behaviours in disordered elastic systems, those are often restricted to special dimensionalities and/or classes of disorder. The Gaussian Variational Method offers a simplification that consists in finding the “best” quadratic Hamiltonian representing the initial problem (after introducing replicæ and integrating over disorder). It provides an approximation allowing one to determine correlation functions and their scalings, at the price of solving a variational equation. The GVM can present two sorts of issues: (i) a technical one: solving the variational equation can be difficult and (ii) a physical one: the scaling exponents can be wrong. As a benchmark study, we consider here the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length and at finite temperature (whose scaling exponents belong to the KPZ universality class and are known exactly). We unveil the crucial role played by two ‘cut-off’: the disorder correlation length and the system size. We focus in this poster on a numerical approach to solve the variational equation, based on a fixed-point approach. Results supports the idea that correctly taking into account the finiteness of cut-offs allows one to capture correct scaling exponents through GVM.

Ref: Elisabeth Agoritsas and Vivien Lecomte, J. Phys. A 50 104001 (2017)

Andrey Lokhov*

Efficient learning of Gibbs distributions and probing of RSB predictions

We study the statistical learning problem of reconstruction of a model from independent configurations sampled from a rough landscape corresponding to a certain Gibbs distribution. In our recent work (arXiv:1902.00600), we have introduced the first universal method that provably reconstructs any Hamiltonian in a tractable fashion with a number of observations that are near-independent of the system dimension. This method, coined the Generalized Interaction Screening, avoids the pitfall of computing partition functions and allows for very efficient implementations which makes it particularly well-suited to uncovering Hamiltonians of very large systems. A rigorous theoretical analysis of our estimator for discrete graphical models, such as disordered Ising spin glass/p-spin/Potts models, shows that it is currently state-of-the-art in unsupervised learning for all of these problems, strictly achieving the information-theoretic bounds for several models and thus being sample-optimal. Discovery of sample-optimal algorithms also turned out to be conceptually intriguing due to established paradoxical relations between the complexities of sampling, inference and learning tasks for different model subclasses. Our approach opens ways for testing the predictions of the RSB picture, by reconstructing effective Hamiltonians produced by Glauber or Langevin dynamics stuck in some regions of the phase space. In our current work, we empirically study dynamics in p-spin models and test different hypothesis of the spin glass theory, including temperatures of local effective Hamiltonians and pure-state clustering organization of the free energy landscape.

Based on references: AY Lokhov, M Vuffray, S Misra, M Chertkov, Optimal structure and parameter learning of Ising models, Science Advances, 4, e1700791 (2018); M Vuffray, S Misra, AY Lokhov, Efficient learning of discrete graphical models, arXiv:1902.00600 (2019); F Sheldon, M Vuffray, AY Lokhov, in preparation (2019)

Cosimo Lupo*, Giorgio Parisi, Federico Ricci-Tersenghi

The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism

The ferromagnetic XY model on sparse random graphs in a randomly oriented field is analyzed via the belief propagation algorithm. At variance with the fully connected case and with the random field Ising model on the same topology, we find strong evidence of a tiny region with replica symmetry breaking (RSB) in the limit of very low temperatures. This RSB phase is robust against different choices of the external field direction, while it rapidly vanishes when increasing the graph mean degree, the temperature or the directionl bias in the external field. The crucial ingredients to have such a RSB phase seem to be the continuous nature of vector spins, mostly preserved by the O(2)-invariant random field, and the strong spatial heterogeneity, due to graph sparsity. We also uncover that the ferromagnetic phase can be marginally stable despite the presence of the random fied. Finally, we study the proper correlation functions approaching the critical points to identify the ones that become more critical.

[1] C. Lupo, G. Parisi, F. Ricci-Tersenghi - J. Phys. A: Math. Theor. 52, 284001 (2019)

Alessandro Manacorda*, Grégory Schehr, Francesco Zamponi

Solving the infinite-dimensional dynamics of particle systems

Silvia Pappalardi*, Anatoli Polkolnikov and Alessandro Silva

Quantum echo dynamics in the Sherrington-Kirkpatrick model with transverse field

Questions about irreversibility and exponential sensitivity to small perturbations in quantum systems have been debated for a long time. The topic was recently revived with the name of scrambling, due to the proposal to probe chaotic dynamics using out-of-time-order correlators. In this work, we study echo dynamics of the Sherrington-Kirkpatrick (SK) model with transverse field under effective time reversal and we investigate numerically its quantum and semiclassical dynamics, using the truncated Wigner approximation. We explore how chaotic many-body quantum physics leads to exponential divergence of the echo observables and we show that it is a result of three requirements, namely the nature of the initial state, the observable and the existence of a well-defined semi-classical limit. Under these conditions, the time-reversal procedure leads to an exponential growth of the echo, which is characterized by the same exponent of the semi-classical limit. We also discuss a short-range version of the SK model and show how how the absence of a semi-classical limit results in a slow-down of the echo dynamics, at most polynomial in time. Our findings provide new additional insights to the understanding of scrambling and echo dynamics systems and may have relevance to access these concepts experimentally.

Giorgio Parisi, Gianmarco Perrupato*, Gabriele Sicuro

Random-link matching problems on random regular graphs

We study the random-link matching problem on random regular graphs, alongside with two relaxed versions of the problem, namely the fractional matching and the so-called“loopy” fractional matching. We estimated the asymptotic average optimal cost using the cavity method. Moreover, we also study the finite-size corrections due to rare topological structures appearing in the graph at large sizes. We estimate these contributions using the cavity approach, and we compare our results with the output of numerical simulations.The analysis also clarifies the meaning of the finite-size contributions appearing in the fully-connected version of the problem, that has been already analyzed in the literature.

Anshul D. S. Parmar*, Misaki Ozawa, Andrea Ninarello, Ludovic Berthier

Preparing ultrastable metallic glasses using swap Monte Carlo

We devise new models for multi-component metallic glasses for which swap Monte-Carlo works well and can produce, for well-adjusted parameters, ultrastable configurations. This achievement paves the way to deeper understanding of thermodynamic, mechanical and dynamical properties of metallic glasses over a broad range of glass stabilities, including ultrastable systems. We illustrate this by exploring yielding and configurational entropy and Adam Gibbs relation for a range of models studied in the computer down to Tg .

Francesca Pietracaprina

Logarithmic growth of local entropy and total correlations in many-body localized dynamics

Andrea Plati*, Andrea Gnoli, Andrea Baldassarri, Giacomo Gradenigo, Andrea Puglisi

Dynamical collective memory in fluidized granular material

Recent experiments with rotational diffusion of a probe in a vibrated granular media revealed a rich scenario, ranging from the dilute gas to the dense liquid with cage effects and an unexpected superdiffusive behavior at large times. Here we setup a simulation that reproduces quantitatively the experimental observations and allows us to investigate the properties of the host granular medium, a task not feasible in the experiment. We discover a persistent collective rotational mode which emerges at high density and low granular temperature: a macroscopic fraction of the medium slowly rotates, randomly switching direction after very long times. Such a rotational mode of the host medium is the origin of probe’s superdiffusion. Collective motion is accompanied by a kind of dynamical heterogeneity at intermediate times (in the cage stage) followed by a strong reduction of fluctuations at late times, when superdiffusion sets in.

Paolo Rissone*, Cristiano V. Bizarro, Felix Ritort

Base pair free energies derivation in RNA by single-molecule experiments

Single-molecules (SM) experiments are a powerful to investigate the fundamental features (energy, elastic properties, kinetics) of nucleic acids. By mechanically pulling apart the two free strands of an hairpin, it is possible to measure a force-extension curve (FDC) exhibiting a sequence dependent pattern that completely characterizes that molecule. The development of this technique in the last decades made possible the direct measure of the 10 nearest-neighbor base-pair (NNBP) free energy values (then reduced to 8 by introducing the circular symmetry) that predict the DNA duplex formation. Despite the accuracy that this method provides, similar experiments to measure the NNBP free energies of RNA molecules have never been carried out beacause both of the complexity in the sinthesis of long RNA hairpins and the multiplicity of intermediate states enclosed between the folded and the unfolded configurations, i.e. strong hysteresis effects.

Masato Suzuki*, Yoshiyuki Kabashima

Statistical mechanics of the minimum vertex cover problem in stochastic block models

The minimum vertex cover (Min-VC) problem is one of the well-known NP-hard problems. Earlier studies showed that the problem defined over the Erdös-Rényi random graph with mean degree c typically exhibits the computational difficulty in searching the Min-VC set above a critical point c=e=2.7182…. We address a question of how the difficulty is influenced by the mesoscopic structures of graphs. For this, we evaluate the critical condition of the difficulty for the stochastic block model of two equal size communities, which are characterized by in- and out- degrees c_in and c_out. Our analysis based on the cavity method indicates that the solution search becomes difficult once for c_in + c_out > e, but gets easy again in the region where c_out is relatively larger than c_in. Experiments based on the simulated annealing support the theoretical prediction.

Takashi Takahashi*, Yoshiyuki Kabashima

Replicated vector approximate message passing for resampling problem

Resampling techniques are widely used in statistical inference and ensemble learning, in which estimators' statistical properties are essential. However, existing methods are computationally demanding, because repetitions of estimation/learning via numerical optimization/integral for each resampled data are required. In this study, we introduce a computationally efficient method to resolve such problem: replicated vector approximate message passing. This is based on a combination of the replica method of statistical physics and an accurate approximate inference algorithm, namely the vector approximate message passing of information theory. The method provides tractable densities without repeating estimation/learning, and the densities approximately offer an arbitrary degree of the estimators' moment in practical time. In the experiment, we apply the proposed method to the stability selection method, which is commonly used in variable selection problems. The numerical results show its fast convergence and high approximation accuracy for problems involving both synthetic and real-world datasets.

Yu Terada*, Tomoyuki Obuchi, Takuya Isomura, Yoshiyuki Kabashima

Efficient and accurate inference for couplings in neuronal networks

Inferring directional couplings from the spike data of networks is desired in various scientific fields such as neuroscience. Here, we apply a recently proposed objective procedure to the spike data obtained from the Hodgkin–Huxley type models and in vitro neuronal networks cultured in a circular structure. As a result, we succeed in reconstructing synaptic connections accurately from the evoked activity as well as the spontaneous one. To obtain the results, we invent an analytic formula approximately implementing a method of screening relevant couplings. This significantly reduces the computational cost of the screening method employed in the proposed objective procedure, making it possible to treat large-size systems as in this study.

Masahiko Ueda, Shin-ichi Sasa

Replica symmetry breaking in trajectory space for the trap model

We study the localization in the one-dimensional trap model in terms of statistical mechanics of trajectories. By numerically investigating overlap between trajectories of two particles on a common disordered potential, we find that there is a phase transition in the path ensemble. We characterize the low temperature phase as a replica symmetry breaking phase in trajectory space.