Posters
Ada Altieri
We analyze the non-convex perceptron model by performing a small-coupling Plefka-like expansion of the free energy. The perceptron model, a simple instance of continuous constraint satisfaction problem, has been proven to fall in the same universality class as hard spheres near jamming and hence allows us to obtain exact results in high dimensions for more complex settings. Our method enables to define an effective potential (or Thouless-Anderson-Palmer free energy), namely a coarse-grained functional, which depends on the generalized forces and the effective gaps between particles. We then generalize the computation to the analysis of third-order corrections to the effective potential that - albeit irrelevant in a mean-field framework in the thermodynamic limit - might instead play a fundamental role in considering finite-size effects. Our analysis reveals that the third order contributions vanish in the jamming limit in the so-called SAT phase, both for the potential and the generalized forces, in agreement with the argument proposed by Wyart and coworkers invoking isostaticity. Finally, we analyze the relevant scalings emerging close to the jamming line. Such relations are also beneficial in defining a crossover regime, which connects the control parameters of the model to an effective temperature.
Ada Altieri
The critical behavior and a consequent diagrammatic analysis of spin glasses in zero (and non-zero) field have been the object of the intense study. We then present an analytical investigation of a class of observables that are often measured in numerical simulations. In particular, we aim to provide a complete characterization of the fluctuations and correlations of the squared overlap in the Edwards-Anderson spin-glass model in zero external field. In analogy with what already done for the linear operator $Q_{ab}$, we analyze the problem for quadratic operators $Q_{ab} Q_{cd}$ in the replica symmetric (RS) phase and compute their anomalous dimensions. The analysis reveals that the energy-energy correlation function (and thus the specific heat) has a different critical behavior than the fluctuations of the link overlap, even though the average energy and the average link overlap are characterized by the same critical properties. More precisely, the link-overlap fluctuations are larger than the specific heat according to a computation at first order in the (6-ε) expansion. An unexpected outcome is that the link-overlap fluctuations have a subdominant power-law contribution characterized by an anomalous logarithmic prefactor, which is absent in the specific heat. In order to compute the ε expansion, we consider the problem of the renormalization of quadratic composite operators both in a scalar and in a generic multicomponent cubic field theory. Note that the results obtained thus far have a range of applicability beyond spin-glass theory (such as for SAW and percolation problems once they are mapped into a Potts model).
Daniele Ancora
One of the biggest challenges in the field of biomedical imaging is the comprehension and the exploitation of the photon scattering through disordered media. Many studies have pursued the solution of this riddle achieving light-focusing control or for reconstructing images in complex media. In the present work, we investigate how statistical inference could help the calculation of the transmission matrix in a multimode fiber, thus making possible to use it like a normal optical element. We convert a linear input-output transmission problem into a statistical formulation based on pseudolikelihood minimization, enabling the inference of the coupling matrix via a random sampling of different intensity realizations. Our desired goal is to uncover insights from the scattering problem, encouraging the development of novel imaging techniques for better medical investigations.
Maria Chiara Angelini
We propose a new perturbative expansion for a generic model in finite dimensions, around the mean-field solution of the same model on the Bethe lattice. This new expansion can be applied to all the models that admit a solution on the Bethe lattice, such as statistical mechanics models (with or without quenched disorder) at finite temperature but also systems where there is no Hamiltonian at all like percolation or zero temperature systems. The advantage to expand around the Bethe lattice with respect to the standard field theoretical expansion around the fully connected (FC) model is that some phase transitions display essential differences when studied on the Bethe lattice rather than on the FC lattice - some examples are the spin-glass in field, the random field Ising model, the Anderson localization, the percolation - and finite dimensional models are usually more similar to the Bethe lattice model because they share the finite connectivity property. When the transition is the same on the Bethe lattice and on the FC model, the results of the new expansion are the same of the standard expansion around the FC model, as we show explicitly for the spin glass in a field in the infinite connectivity limit.
Alessia Annibale
Cell differentiation is one of the most fascinating areas of developmental biology. This was long thought to be an irreversible process, however it has been shown recently that it is possible to reprogramme fully differentiated cells into a state of induced pluripotency, which strongly resembles embryonic stem cells, via the introduction of a few transcription factors. This opens up exciting perspectives in the field of regenerative medicine, however, no universally accepted theory exists that explains the phenomena. The purpose of this work is to drive forward our understanding of cell reprogramming by introducing an analytical model for transitions between cell types. Inspired by neural networks theory, we model cell types as hierarchically organized dynamical attractors corresponding to cell cycles. Stages of the cell cycle are fully characterised by the configuration of gene expression levels, and reprogramming corresponds to triggering transitions between such configurations. Two mechanisms were found for reprogramming: cycle-state specific perturbations and a noise-induced switching. The former corresponds to a directed perturbation that induces a transition into a cycle-state of a different cell type in the potency hierarchy (e.g. a stem cell) whilst the latter is a priori undirected and could be induced, e.g. by a (stochastic) change in the cellular environment. In addition, the mechanism for the effective interactions arising between genes, is studied by means of a bipartite graph model, that integrates the genome and transcriptome into a single regulatory network. With this perspective, we are able to deduce important features of the regulatory network that exists in every cell type.
Claudia Artiaco e Paolo Baldan
The Potential Energy Landscape plays a fundamental role in the understanding of the properties of glass-forming systems: mechanical and thermodynamical properties of a glass can be understood in terms of those of the landscape, that are supposed to play an important role at a dynamical level too. However, in spite of their importance, glassy landscapes are still not well understood. We present here the study of the Landscape of a glassy system on the edge of the Jamming Transition following two different but complementary approaches.
In the first we model the system as a hard-spheres glass and bring it to the jamming point starting both from an equilibrium and an out-of-equilibrium point: the number of different jammed configurations found in the two cases is compared; distances between different jammed configurations are computed and used to investigate the ultrametric structure of the landscape. In the second the system is modelled as a harmonic-spheres glass and brought to the over-compressed region: energy minima distribution is computed and a cross-over temperature between ground and transition states is identified. Distances between energy minima are used to compute the equilibrium distribution of distances in phase space and connected to the properties of small-oscillation matrix around energy minima. By the comparison of the two approaches we will have a better understanding of the jamming transition and also a proof of the consistency of the results.
Fernanda Benetti
We propose a class of mean-field models for the isostatic transition of systems of soft spheres, in which the contact network is modeled as a random graph and each contact is associated to d degrees of freedom. We study such models in the hypostatic, isostatic, and hyperstatic regimes. The density of states is evaluated by both the cavity method and exact diagonalization of the dynamical matrix. We show that the model correctly reproduces the main features of the density of states of real packings and, moreover, it predicts the presence of localized modes near the lower band edge. Finally, the behavior of the density of states D(ω) ∼ α for ω → 0 in the hyperstatic regime is studied. We find that the model predicts a nontrivial dependence of α on the details of the coordination distribution.
Gioia Boschi
In order to understand the collective behaviour of the society and its response to external unexpected events, we propose a model in which there are a number of agents interacting on a network, and the opinion of each individual is influenced by the opinion of the others, as well as their own ideas and some external influences. We can find examples of similar models in the literature. Interestingly in our model we insert time-changing interactions couplings between agents, influenced by their agreement or disagreement in the past. This introduces as a new element in the dynamics the memory of previous opinions of the agents and develops interesting collective phenomena. For instance, we can show through simulations that with this system we can “store” a number of opinion patterns and retrieve them with a suitable polarizing signal. A similar storing mechanism is observed in the Hopfield model, except that in our case the patterns are learned by the system as a result of an external stimuli that can change with time, while in the Hopfield model the patterns are fixed and imposed by the model.
Angelo Giorgio Cavaliere
I study the critical behavior of an Ising spin model on a cubic lattice with nearest-neighbor random couplings Jij . The couplings Jij are drawn from a probability distribution P(J) that is identified with the canonical distribution of the Z2 gauge model at temperature TG. By varying TG one can tune the amount of frustration: frustration is maximal for infinite T G (we expect the usual spin-glass behavior) anddecreases as the temperature is lowered. For TG = 0 the system is unfrustrated and therefore we recover (using the temporal gauge) the usual ferromagnetic Ising system. I am studying the model for TG = Tc , where Tc is the critical temperature of the gauge system.
Francesco Concetti
Quenched complexity in mean-field spin-glass models with continuous replica symmetry breaking
The quenched complexity of the spherical 2+4-spin glass is computed in the regime where the equilibrium phase is continuous (full) replica symmetry breaking (f-RSB). The complexity dependence on the free energy is obtained by calculating the averaged partition function of m × n replicas of the system, with the symmetry among these explicitly broken according to a generalization of the ‘two-group’ ansatz, that involves the presence of two additional n × n matrices A and B, besides the Parisi overlap matrix Q. The quenched average is computed by imposing the Parisi ansatz for all the three matrices. The stable solution has non-vanishing additional order parameters A and B; this corresponds to a supersymmetry breaking in the direct computation of the of the Thouless-Anderson-Palmer (TAP) solutions. The complexity is null at the critical temperature Tc , where the system undergoes a continuous transition from the replica-symmetric (RS) to the f-RSB phase, and grows up continuously with the lowering of temperature. At T < Tc , the complexity is maximal at m = 0 and vanishes at the value m c ∼ O(T−Tc ), corresponding to the equilibrium free energy f eq . The maximal complexity scales as (Tc−T)^6 near the critical temperature. As in the Sherrington-Kirkpatrick model, the annealed approximation of the complexity is exact at low values of m. At higher m, we have a continuous transition toward a Two-group-f-RSB solution with three order parameters q(x), a(x) and b(x). The orders parameters start form 0 at x = 0 and reach a plateau at some point x = xc , that vanishes at f = f c and increases to x = 1 at f = feq . The solution is obtained using high order perturbative expansions over T−Tc , x and q(xc), for all the low-temperature and low-free-energy regime. Supersymmetry is restored at the equilibrium free energy: the diagonal and continuous Parisi order parameters go to the equilibrium value and the additional order parameters vanish.
Rafael Diaz
Making predictions about the dynamics of glassy systems has proven to be a challenging problem despite the large amount of research carried out using a wide range of techniques. In this work, we propose to investigate how the local structure of a particle determines its dynamics, at least for short times. Starting from 3d jammed configurations of hard spheres, we shrank the particles’ radius by a small amount and then performed extensive molecular dynamics simulations where we analysed the squared displacement of individual particles, thus obtaining an estimation of the single particle diffusivity. Our results show that the particles’ diffusivities have well defined distributions for the different values of packing fraction considered here, and that this is a persistent feature during the temporal evolution. These results provide evidence that the local structure of a particle strongly determines its mobility.
Francesco De Santis
Bethe Lattice Spin Glasses are models with finite connectivity which undergo a Replica Symmetry Breaking (RSB) phase transition in field, at zero temperature. We compute numerically the RSB order parameter of the model near the transition, in the case of minimum connectivity (z = 3) and bimodal distribution of the couplings (J = 1). The method is based on a universal formula which relates the order parameter to the joint probability distribution of the energy difference and overlap of excitations induced by a convenient perturbation to the Hamiltonian.
Giampaolo Folena
Given a classical statistical model at equilibrium, its thermodynamic properties strictly depend on the macroscopic environment parameters (T, P...). On the contrary, many amorphous materials never reach equilibrium and their properties can strongly be influenced by their history. Here I present a fully connected spin-glass model that can bear this dependence. Analysing the zero temperature off-equilibrium dynamics of a (3 + 4)-spin spherical model, we find evidence that asymptotic states depend on the temperature from which the system has been pushed out of equilibrium, even starting inside the paramagnetic ergodic phase, i.e. from a temperature higher than the dynamical one. The system do not forget its initial conditions!
Giorgio Gosti
We analyze the evolution of neural rosettes which are a well know 2D model of neural tube development. In neural tube development, ectoderm cells differentiate into neural ectoderm cells, and in this process self-organize in a highly symmetric cylindrical structure. Errors in the neural tube development are the cause of spina bifida and anencephaly. While this phenomenon is a remarkable example of self-organization and symmetry breaking, we only partially understand it from complementary perspectives: as either a cell differentiation process or a cell sorting process. Unfortunately, an explanation based exclusively on cell differentiation does not describe the emergence of spatial organization, and an explanation based exclusively on cell sorting does not explain cell fate determination. An interdisciplinary approach is required to understand how cell fate determination and collective behavior together determine this process. Thus, we have designed a setup composed of an epifluorescent microscope and a stage-top incubator with temperature and CO2 control capable of acquiring 1-2 weeks time-lapse sequences. This setup allows us to capture the emergence of neural rosettes from the very beginning of hiPSC differentiation. We have differentiated hiPSCs in which the nuclear protein FUS/TLS is expressed in fusion with a red fluorescent protein, tagRFP, resulting in permanent labeling of cell nuclei. We use image analysis to identify the thermodynamic phase transition of the cell population. Preliminary results indicate that rosettes are symmetry-breaking emergent cells structures, which emerge from local density fluctuations.
Tomer Goldfriend
Quasi-integrable systems, i.e., whose Hamiltonian slightly differs from an integrable one, appear in various areas such as planetary motion, weak turbulence, and linear quantum chains. We study the dynamics of such systems, focusing on the Fermi-Pasta-Ulam-Tsingou chain. We show how slow evolution in time is dictated by weakly non-conserved quantities, which in turn allows us to describe the system with a generalized Gibbs ensemble. This description can be employed to devise a fast numerical integration, and underlies a fluctuation theorem for quasi-integrable systems.
Giacomo Gradenigo
The mode-locked p-spin: evidence of a Random-First Order transition in model for random lasers
It has been recently proposed that the fluctuations in the emission spectra of random lasers can be understood in terms of a thermodynamic phase transition to a glassy phase: this is a regime where the amplitudes and phases of light normal modes are frozen in the same disordered configuration for the whole duration of the pulse. So far the only analytical predictions on the thermodynamics of this phase have been obtained in the so-called narrow band approximation, that is by assuming a light-modes interaction network that is fully connected and in whose constitution the mode frequencies play no role at all. We present the first numerical results, obtained from highly optimized GPU-codes, showing that a glass transition Random First Order is present in the system also when the light modes are put on the less dense and correlated network, termed mode-locking graph, best reproducing the true interaction network. We also sketch how the thermodynamics of the model can be solved exactly even for this non fully-connected model by introducing replicas along the lines of [E. Marinari, G. Parisi, F. Ritort, J. Phys. A: Math. Gen. 27, 7615-7645 (1994)], where this technique was successfully used to study a non-disordered model.
Velimir Ilic
Generic Architectures for Memory Efficient Decoding of LDPC codes
Efficient decoding is one of the most challenging tasks in the theory of LDPC codes. Commonly used belief propagation (BP) decoder has good bit error rate performances, but high memory storage requirements. In this work we present shuffled scheduled uniformly reweighted APP decoder (URAPP), which is a suboptimal variant of BP decoder that can be implemented in a memory efficient way. We provide a framework for URAPP complexity analysis and discuss the simulation results on finite geometry codes.
Velimir Ilic
Generalized entropies for random graph models - thermostatistics and extensivity
In this work we consider generalized thermostatistics based on generalized entropies and provide conditions for their extensivity. An application to random graph models is presented.
Yoshiyuki Kabashima
Semi-analytic resampling in Lasso
An approximate method for conducting resampling in Lasso, the l1 penalized linear regression, in a semi-analytic manner is developed, whereby the average over the resampled datasets is directly computed without repeated numerical sampling, thus enabling an inference free of the statistical fluctuations due to sampling finiteness, as well as a significant reduction of computational time. The proposed method is employed to implement bootstrapped Lasso (Bolasso) and stability selection, both of which are variable selection methods using resampling in conjunction with Lasso, and it resolves their disadvantage regarding computational cost. To examine approximation accuracy and efficiency, numerical experiments were carried out using simulated datasets. Moreover, an application to a real-world dataset, the wine quality dataset, is presented. To process such real-world datasets, an objective criterion for determining the relevance of selected variables is also introduced by the addition of noise variables and resampling. This is a joint work with Tomoyuki Obuchi.
Thibault Lesieur
Low-rank matrix factorisation: optimal inference and the zoology of phase diagrams
The Low rank matrix factorization is the problem of recovering some matrices U ∈ R^{N×r} , V ∈ R^{M ×M} from the noisy observation of the multiplication of two matrices Y ∈ R^{N ×M} where we assume that Y = U V^T + noise. Even though this problem is easy too formulate a surprisingly number of practical problems can be translated in this framework (sparse PCA, community detection, clustering of points). By making some assumption on the process that generated U, V and the matrix Y one can use Bayesian inference and tools coming from statistical physics to study this problem and answer some interesting question like “when is it possible to recover the matrix U and V?”. Depending on the precise form that U and V have the system can have radically different properties that are encoded in its phase diagram. In this work we classify and analyze these phase diagrams and establish a zoology of such phase diagram that one can expect from these systems in the setting where the rank r = 1.
Matteo Lulli
Structural Glasses display a wide range of non-linear behaviors in response to a change in temperature. Upon temperature jumps, one can observe several non-linearities in the volume relaxation of the system. In order to show the memory properties of a fragile structural glass, Kovacs (in the classic [A.J. Kovacs, Fortschr. Hochpolym.-Forsch. 3, 394-507 (1964)]) performed several discontinuous changes in temperature interleaved by annealing periods, showing what is known as "Kovacs memory effect" and "tau effective expansion gap paradox". In this poster, we will show how a recently proposed Distinguishable Particles Lattice Model (DPLM) can qualitatively capture all of the effects studied in [A.J. Kovacs, Fortschr. Hochpolym.-Forsch. 3, 394-507 (1964)]. DPLM is a simplified dynamic model of structural glass. Hopping distinguishable particles interact through random couplings which, rather than being quenched on the lattice edges, are both edge and particle dependent, and are thus quenched in the space of all possible particle configurations. Then, the realized disorder changes as the particles configuration does. The non-trivial dynamics show many well-known properties of structural glasses, including out-of-equilibrium relaxation properties comprising Kovacs' results.
Cosimo Lupo
The ability of the immune system to recognize and kill a huge range of external pathogens is ensured by a high diversity in the binding sites of membrane Receptors in B-Cell lymphocytes (BCR). The resulting repertoire of BCRs is updated and increased via a 2-step stochastic process for the creation (recombination) and the evolution (affinity maturation) of each nucleotide sequence encoding the receptors. The common picture of the recombination process involves a random choice of the genes from the germline DNA, plus some nucleotide deletions and insertions (briefly, indels) at the junctions of such genes. Instead, the affinity maturation of the sequence involves some context-dependent point mutations, namely the exchange of some nucleotide bases. Our analysis focuses on the possibility of experiencing indels not just at the junctions between the germline genes in the recombination process, but directly in the bulk of the most variable (V) gene in the chain during the affinity maturation stage, further enhancing the variability of the repertoire. These indels appear prominently in the BCR of both healthy people and HIV-responding broadly neutralising antibodies. We evaluate the probability of such indels, with the aim of developing a likelihood-based approach for their inference from real data and for the generation of more reliable synthetic sequences.
Enrico Malatesta
The traveling salesman problem (TSP) is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We characterize the optimal cycle for every convex and increasing cost function when the points are thrown independently and with an identical probability distribution in a compact interval. This result is valid both on bipartite and on complete graph cases. We also establish general connections with other random combinatorial optimization problems, such as the matching and the 2-factor problem. On bipartite graph, for example, we prove that the cost of the optimal cycle is not smaller than twice the cost of the optimal assignment of the same set of points. We show that this bound is saturated in the thermodynamic limit. We study the problem in higher dimensions showing that, on bipartite graph, the same result found in one dimension holds also in two dimensions.
Ilaria Paga
At the glassy temperature T G a 3D spin glass presents a continuous second order phase transition, which is characterized by an infinite correlation length. A thin glassy film, as soon as the correlation length is equal to the thickness L, performs a dimensional crossover and it acts as a bidimensional system. In this way, the system acts as a paramagnetic system always above its glassy temperature and it achieves the equilibrium easily. In this work, we investigated in detail this dimensional crossover and its equilibrium properties.
Valerio Parisi
As well know, the explicit solution of the classic gravitational N-body problem, does not exist, therefore it is necessary to resort to numerical approximations. The problem is chaotic, anyway if dealing with few bodies and restricting to a time ”small” compared to the Lyapunov time, it is almost ”deterministic”, and, therefore, the right solution can be approached ad libitum by mean of standard integration algorithms for system of ordinary differential equations, both symplectic and not. When aiming to the study of many-body motion over a ”long” time compared to that of Lyapunov, what is actually looked for is not an approximation of the ”exact” solution, but rather the best possible estimates of the statistical properties of the possible solutions. In such cases and which such aims, the defect of classic algorithms is that of being unnecessarily ”precise”, expensive, delicate and complex. So, we are proposing a completely different type of algorithm, which in spite of a loss of (unnecessary) precision results to be cheaper, simple and robust in giving reliable evaluation of relevant statistical indicators. The key idea of this type of algorithm is that of replacing the gravitational potential between two bodies, smoothly varying with the inverse of their distance, with a potential, which is kept constant along a certain number of tracts. In such scheme, the gravitational attraction as function of mutual distance assumes a more bizarre behaviour: for almost all distances it is absent except for some distances for which it is infinite. This new problem admits solutions that resemble the ”right” solution to arbitrary precision provided an improvement of the approximation of potential, by an increasing refinement of the stepping.
Francesca Pelusi
Flow of soft-glassy materials in confined microchannels: does roughness shape matter?
We perform numerical simulations of confined microfluidic channels, where highly confined and packed oil-in-water emulsions with "crystal-like regularity" are driven with a constant volume force (pressure gradient). We quantitatively assess the impact of surface roughness on the mass flow-rate through the channel at changing different roughness shapes. Our results point to the fact that the roughness parameter, commonly defined as the ratio between real surface area and projected area, is insufficient to parametrize the reduction in mass flow-rate with respect to a flat channel. Some preliminary ideas on the different mechanisms at play are presented. We also present preliminary results on the impact of the roughness on the ``crystal regularity'' by identifying, for a given pressure gradient, a critical roughness at which a segregation of coalescence is triggered close to the rough wall.
Francesca Pietracaprina
Detecting many body localization in a compressed configuration basis
The investigation of the many-body localized phase using exact numerical methods is strongly limited to small systems due to the exponential increase of the rank of the Hamiltonian matrix with the system size. In this poster presentation we show that it is possible to recover almost all information about a many-body localized state from the exact diagonalization of a substantially reduced matrix, which is obtained from the Hamiltonian matrix by a suitable cut in the configurational basis followed by a strong-disorder renormalization of some of its elements. This allows to access big system sizes in 1D and 2D at high disorder.
Andrea Puglisi
Within a single experimental setup in different conditions of vibro-fluidization, density and applied external forcing, the dynamics of a massive intruder displays several interesting phenomena: liquid-like cage effects, superdiffusion at high density and low temperature, violations of the Einstein relation, non-linear rheology.
Valentina Ros
The spiked tensor model has recently attracted a lot of attention in inference and high-dimensional statistics; it generalizations correspond to a spherical p-spin Hamiltonian with a ferromagnetic multi-body interaction term, and are simple modesl capturing the competition between a deterministic signal and stochastic noise. We describe the phase transitions that occur in the structure of the energy landscape when changing the signal-to-noise ratio, and highlight the implications for the associated inference task of recovery of the signal from a set of noisy observations.
Gabriele Sicuro
Matching problems are combinatorial optimization problems traditionally considered in the realm of computer science and combinatorics. However, when, instead of a given instance of an optimization problem, a whole ensemble of realizations is considered, methods, ideas, and tools that physicists have developed in the context of statistical mechanics of systems with frustration and disorder can be applied and have been shown to be very effective. Here some old and recent results are given on both mean-field problems and Euclidean problems in presence of randomness.