II Conference of the Italian Society of Statistical Physics - SIFS

We present a model of filling of a knowledge corpus by random contributions. Contributions form a cluster if there is a minimum overlap among pairs of them. The dynamics of the model shows first scattered, isolated contributions, followed by accretion and finally fusion of clusters, forming a giant component. The process can be seen as a kind of growing k-core percolation. By studying the cluster structure for a fixed number of contributions we see that the maximum cluster span (i.e., the maximum "collective knowledge" of clusters) shows a maximum for a well-defined number of cluster members (for a corpus size), reminiscent of what emerges in observations on the optimal group size for solving complex problems.

Understanding the interplay between structure and dynamics is still one of the major challenges in network science. A central question concerns the robustness of a system against perturbations, since it can advance the development of powerful analytical techniques to explain and unravel rich phenomenology, as well as it can provide a solid ground for informed interventions. A main assumption behind the analysis of robustness is that for a system to be functional, it needs to be connected. Hence, concepts and techniques from percolation theory become useful and are frequently employed. This is a completely static approach, where a fraction of nodes (or links), either selected uniformly at random or based on topological or non-topological descriptors, is removed from the network. From a dynamical point of view, small failures placed in the network may evolve --according to some rules that depend on the phenomenon one is trying to model-- causing system-wide catastrophic cascades. For the sake of mathematical tractability, cascades are assumed to spread via direct contacts. However, be it because the physical mechanisms behind the failure propagation permit far-off malfunctions, be it because the knowledge on the observed network topology is incomplete and the failure propagates through hidden or unobserved edges, real-world cascades display nonlocal features. From a modeling standpoint, some mechanisms like flow redistribution can lead to nonlocal spreading of failures but the mathematical treatment has been hitherto under-researched due to its sophistication and there is no direct way to control the underlying properties of the nonlocal events, seriously undermining our understanding of the phenomenon. To better reconcile theory and observations, we propose a dynamical model of nonlocal failure spreading that combines local and nonlocal effects. We assume that the cascade unfolds in a timescale much faster than the recovery of nodes, and that a disrupted unit cannot be visited more than once by the failure. This fact causes the failure to be no longer Markovian and, for modeling purposes, a natural choice is to consider a Self-Avoiding Random Walk-like (SARW) dynamics on the network. To cope with the nonlocality, we introduce a teleporting probability: at each step t the failure proceeds as in a SARW --uniformly choosing an operational neighbor and transitioning there-- with probability 1 - α ∈ [0,1], otherwise with probability α it teleports to any operative node according to a teleporting rule T_t(k),time- and degree-dependent. We name this the self-avoiding teleporting random walk (SATRW), which interpolates between percolation (purely nonlocal process, α = 1) and the growing SARW (purely local process, α = 0). We have characterized the rich critical behavior of our model by providing analytical expressions for several quantities employed to assess the systems robustness, such as the time-dependent degree distribution p_t(k), the size of the giant component in the residual network as the process evolves s_t , the cascade first-stop time distribution, and the mean value of S^(STOP) , the giant component at the cascade stop. These robustness descriptors display an excellent agreement with simulations in synthetic systems characterized by different types of complexity in terms of the heterogeneity of their structural connectivity. We find remarkable differences between homogeneous and heterogeneous systems, e.g., their dependence, or lack thereof, on the particular network parameters. However, we also report some hidden similarities between them, such as a dynamical version of the popular robust-yet-fragile feature to static attacks. It is worth noticing that, despite our framework is expected to work for locally tree-like networks lacking topological correlations, such as degree-degree ones, it still works in empirical settings as we have shown for the case of a biomolecular system, namely the interactome of the nematode C. elegans, and an infrastructural system, namely a national air traffic network. Our findings provide a solid ground for the analytical study of network robustness, in particular, and for nonlocal non-Markovian processes, in general. The article has been published recently in Phys. Rev. E 105, 044126 (2022).

Temporal networks are essential for modeling and understanding systems whose behavior varies in time, from social interactions to biological systems. Often, however, real-world data are prohibitively expensive to collect or unshareable due to privacy concerns. A promising solution is `surrogate networks', synthetic graphs with the properties of real-world networks. Until now, the generation of realistic surrogate temporal networks has remained an open problem, due to the difficulty of capturing both the temporal and topological properties of the input network, as well as their correlations, in a scalable model. Here, we propose a novel and simple method for generating surrogate temporal networks. By decomposing graphs into temporal neighborhoods surrounding each node, we can generate new networks using neighborhoods as building blocks. Our model vastly outperforms current methods across multiple examples of temporal networks in terms of both topological and dynamical similarity. We further show that beyond generating realistic interaction patterns, our method is able to capture intrinsic temporal periodicity of temporal networks, all with an execution time lower than competing methods by multiple orders of magnitude.

We developed a stochastic model to interpret the experimental output of a synthetic nanomachine constituted by an ensemble of muscle myosin II molecular motors in interaction with an actin filament. The mechanical output of the nanomachine is measured with dual laser optical tweezers which act as a force transducer. The ensemble is capable of performing isometric contraction under the implementation of a length-clamp control, reproducing the collective mechanism of muscle myosin II in situ. A stochastic model that assumes one detached and two different force-generating attached states allows to predict the force distribution resulting from the cumulative action of the motors. The computed distribution can be superposed to the homologous experimental profile via a non-linear fitting procedure which seeks to simultaneously adjust the kinetic parameters and the value of the isometric force developed by a single molecular motor. The fitting scheme is first validated against synthetically generated data and then applied to experimental distributions. Analysing the performance of the small ensemble of motors with a reverse engineering procedure made it possible to shed light onto the functional differences between slow and fast myosin isoforms from rabbit skeletal muscles and to recover single motor properties, to be compared with in vivo studies. This approach enables one to infer the behaviour of a single molecular motor from the analysis of the dynamics of a small ensemble, and could pave the way for the study of unknown myosin isoforms.

One of the most important tasks performed by the brain is Associative Memory, namely the ability to recognize similarities between slightly distorted versions of a given stimulus, tracing them back to one single archetype. Hopfield-like neural networks are a form of Artificial Intelligence designed to mimic this ability. They consist of a collection of binary spins endowed with a stochastic dynamics, which must be such as to create finite basins of attraction around a predetermined set of configurations (memories). When initialized to a configuration similar to one of the memories, the network will be driven towards the corresponding attractor, resulting in error correcting performance. Among the possible strategies to build such a dynamics, the linear perceptron algorithm and Hebbian unlearning are two of the most influential. The first is a supervised learning algorithm, meaning that it needs to be fed explicitly the information about the patterns to be learned. The second is unsupervised, and exploits the information contained in the attractor landscape generated by Hebb's biologically inspired learning rule. In this talk, I will introduce both paradigms, illustrate some unexpected similarities in the performance of these apparently very different algorithms, and speculate on a possible explanation for them.

The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including an intermediate phase, between quiescence and saturation, that exhibits the key features of "asynchronous states" in cortical networks. Remarkably, in the inhibition-dominated case, it also captures a wealth of non-trivial features of spontaneous brain activity, such as collective excitability, hysteresis, tilted avalanche shapes, and partial synchronization, allowing us to rationalize striking empirical findings within a common parsimonious framework.

In recent years there has been evidence that simple demographic mechanisms at individual level are usually sufficient to explain patterns at macroscales in a wide range of ecological systems. Therefore, the fine details of the biological processes that drive ecosystems are not necessary as long as we focus on coarse scales. Starting from this basic observation, I will first discuss a stochastic and spatially-explicit model, which can be treated analytically and is able to make several predictions in agreement with empirical datasets. Even though this model can connect patterns across scales, it does not tell us much about the origin of coexistence in large communities, and why they look stable on several generation scales. I will then move on to a different model, which explicitly addresses the problem of coexisting species and provides an explanation on general grounds. From this latter model one can derive realistic features of the distribution of species populations.

Braids composed by two intertwined filaments naturally arise in biological systems, such as during DNA replication [1] and in amyloid fibrils [2]. Interestingly, braids subject to a pulling force display a phase transition [3]: when the linking number between the two strands exceeds a critical number, the braid, initially straight, writhes in 3D forming structures known as plectonemes. Nowadays, single-molecule experiments can easily investigate the physics behind such a transition and plectonemes diffusion along the braided structure [4]. In the last few years, we developed a polymer model which, combined with a stochastic field theory, allows to visualise plectonemes as structures interacting through phenomena typical of liquid-gas systems [5]. Moreover, a further application of the polymer model has allowed to investigate site-selection mechanisms of retroviruses into DNA braids revealing spatio-temporal correlations between consecutive integration events [6]. In this talk I will summarise our main results providing insights about polymer braids, their applications and possible future research areas. [1] A. Mariezcurrena and F. Uhlmann. Genes & Development 31, 2151 (2017). [2] C. Ionescu-Zanetti, R. Khurana, J. R. Gillespie, J. S. Petrick, L. C. Trabachino, L. J. Minert, S. A. Carter, and A. L. Fink. Proceedings of the National Academy of Sciences 96, 13175 (1999). [3] G. Charvin, A. Vologodskii, D. Bensimon, and V. Croquette. Biophysical Journal 88, 4124 (2005). [4] M. T. J. van Loenhout, M. V. de Grunt, and C. Dekker. Science 338, 94 (2012). [5] G. Forte, M. Caraglio, D. Marenduzzo, and E. Orlandini. Physical Review E 99, 052503 (2019). [6] G. Forte, D. Michieletto, D. Marenduzzo, and E. Orlandini. Journal of the Royal Society Interface 18, 20210229 (2021).

Large scale data on single-cell gene expression have the potential to unravel the specific transcriptional programs of different cell types. The structure of these expression datasets suggests a similarity with several other complex systems that can be analogously described through the statistics of their basic building blocks. Transcriptomes of single cells are collections of messenger RNA abundances transcribed from a common set of genes just as books are different collections of words from a shared vocabulary, genomes of different species are specific compositions of genes belonging to evolutionary families, and ecological niches can be described by their species abundances. Following this analogy, we identify several emergent statistical laws in single-cell transcriptomic data closely similar to regularities found in linguistics, ecology or genomics. A simple mathematical framework can be used to analyze the relations between different laws and the possible mechanisms behind their ubiquity. Importantly, treatable statistical models can be useful tools in transcriptomics to disentangle the actual biological variability from general statistical effects present in most component systems and from the consequences of the sampling process inherent to the experimental technique.

Polymer translocation, the process of forcing polymers through narrow pores, has long been studied for its complex nonequilibrium properties, as well as for its practical relevance for e.g. DNA sequencing. The important case where the structure of the polymer chain is itself altered by translocation is, however, still largely unexplored. A prototypic illustration is offered by DNA nanopore unzipping, where one of the two strands of DNA is driven through a narrow pore, while the other one remains outside it. Here we address DNA unzipping by integrating theory and simulations and establish two main results. First, we discover multiple dynamical regimes and a rich phenomenology that has no analogue in conventional polymer translocation. Second, using the theory of stochastic processes we demonstrate that the nonequilibrium unzipping trajectories can be harnessed to derive the detailed thermodynamic landscape of process. The theoretical framework used to establishthis result is general and opens new exciting perspectives regarding analysis and interpretation of nonequilibrium experiments.

Molecular sorting is a fundamental process that allows eukaryotic cells to distill and concentrate specific chemical factors in appropriate cell membrane subregions, thus endowing them with different chemical identities and functional properties. A phenomenological theory of this molecular distillation process has recently been proposed [10.1103/PhysRevLett.126.088101], based on the idea that molecular sorting emerges from the combination of: a) phase-separation-driven formation of sorting domains, and b) domain-induced membrane bending, leading to the production of submicrometric lipid vesicles enriched in the sorted molecules. In this framework, a natural parameter controlling the efficiency of molecular distillation is the critical size of phase-separated domains. In the experiments, sorting domains appear to fall into two classes: unproductive domains, characterized by short lifetimes and low probability of extraction, and productive domains, that evolve into vesicles that ultimately detach from the membrane system. It is tempting to link these two classes to the different fates predicted by classical phase separation theory for subcritical and supercritical phase-separated domains. Here, we discuss the implication of this picture in the framework of the previously introduced phenomenological theory of molecular sorting. Several predictions of the theory are verified by numerical simulations of a lattice-gas model. Sorting is observed to be most efficient when the number of sorting domains is close to a minimum. To help in the analysis of experimental data, an operational definition of the critical size of sorting domains is proposed. Comparison with experimental results shows that the statistical properties of productive/unproductive domains inferred from experimental data are in agreement with those predicted from numerical simulations of the model, compatibly with the hypothesis that molecular sorting is driven by a phase separation process.

Human chromosomes have a complex 3D structure in the nucleus of the cells. Such an organization is crucial in the regulation of genomic functions, as, for instance, genes and their distal regulators have to form specific physical contacts to regulate transcription. However, how the system self-organizes to shape the folding of our genome and its functions is only poorly understood. Here, I discuss our theories from polymer physics showing that chromosome architecture is controlled by thermodynamic mechanisms of phase transition [1]. Those theories, validated by recent microscopy and biochemical experiments [1,2,3], are shown to be quantitative powerful tools to predict in-silico the effects of disease-associated mutations on genome 3D structure [4,5]. [1] Conte et al. Nature Communications, 11, 3289 (2020) [2] Fiorillo, Musella, Conte et al. Nature Methods, 18, 482-490 (2021) [3] Huang et al. Nature Genetics, 53, 1064-1074 (2021) [4] Bianco et al. Nature Genetics, 50, 662-667 (2018) [5] Kubo et al. Nature Structural & Molecular Biology, 28, 152-161 (2021)

Recent technologies, such as Hi-C, have revealed that the mammalian genome has a complex, far from random three-dimensional (3D) organization, intimately linked to vital biological processes. To rationalize the complexity of experimental data, polymer models from Statistical Physics and a variety of computational methods have been developed. However, they usually cannot explain data at the scale of the full genome. In this talk, I will present the first genome-wide extension of PRISMR, our approach that combines Machine Learning and Polymer Physics to infer the different types of DNA binding sites determining genome 3D structure. The genome-wide study allowed us to develop a code linking chromosome 3D structure to chromatin states through our inferred binding domains. Interestingly, they have an overlapping, combinatorial organization along chromosomes necessary to accurately explain contact specificity. The binding domains and the associated architectural code were tested by making predictions on the changes of the 3D structure caused by a set of genomic mutations at the Sox9 locus linked to human diseases and our predictions were confirmed by independent data from cells carrying such mutations. Finally, in a reverse approach based on the discovered code, we predicted de novo the 3D structure of an independent set of chromosomes from only their 1D chromatin marks, thus validating the inferred epigenetic-architecture code. Overall, our results shed light on how 3D information is encrypted in 1D chromatin via the specific combinatorial arrangement of binding sites. References: Esposito et al., "Polymer physics reveals a combinatorial code linking 3D chromatin architecture to 1D chromatin states", Cell Reports (2022)

Complex networks usually exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales reflecting structural insights that are not manifest from analyses of the network topology. Moreover, small-world effects correlate the different network hierarchies complicating the identification of coexisting mesoscopic structures and functional cores. We present a communicability analysis of effective information pathways throughout complex networks based on information diffusion to shed further light on these issues. This will lead us to a formulation of a new and general renormalization group scheme for heterogeneous networks. The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is particularly challenging due to correlations between intertwined scales. To date, the explorations are based on hidden geometries hypotheses. Here, we propose a Laplacian RG diffusion-based picture for complex networks, defining both the Kadanoff supernodes concept, the momentum space procedure and applying this RG scheme to real networks in a natural and parsimonious way.

Zipf's law describes the empirical size distribution of the components of many natural and artificial complex systems. Diversity, on the other hand, is a central concept in ecology, economics, information theory, and other natural and social sciences and can be quantified by diversity indices which characterize the system under study from dif- ferent angles. I will discuss the co-occurrence of Zipf's law with the maximization of the diversity of the component sizes, understanding here the number of different sizes represented. I will present the law ruling the increase of such diversity with the total dimension of the system and its relation with Heaps' law. As an example, I will compare analytical results with datasets from linguistics and urbanistics. Mazzarisi, Onofrio, Amanda de Azevedo-Lopes, Jeferson J. Arenzon, and Federico Corberi. "Maximal Diversity and Zipf's Law." Physical Review Letters 127, no. 12 (2021): 128301.

We calculate the diffusion coefficient of an active tracer in a crowded environment, represented as a lattice gas of passive particles with hardcore interactions. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system.

Contact tracing is a crucial measure to control epidemic spreading without disrupting societal activities, especially in the presence of asymptomatic and presymptomatic transmission. Large gatherings can be a source of superspreading events, however the effects of tracing in large groups have not been fully assessed so far. Within the framework of simplicial adaptive temporal networks, we model contact tracing on large groups. We show that alongside forward tracing, which reconstructs to whom disease spreads, and backward tracing, which searches from whom disease spreads, a third type of tracing is active in groups, the sideward tracing. This is an indirect tracing, which exploits the simplicial nature of social interactions, acting on asymptomatic individuals, even if they have neither been infected by nor they have transmitted the infection to the index case. We analyze this effect on an epidemic model for SARS-CoV-2 and we estimate the contribution of the three tracing mechanisms to the suppression of the epidemic, showing the relevance of sideward tracing and suggesting optimal tracing strategies. We also test our results on an empirical dataset of gatherings in the University of Parma, collected through the WiFi connections during COVID-19 restrictions.

High-order, beyond-pairwise interdependencies are at the core of biological, economic, and social complex systems, and their adequate analysis is paramount to understand, engineer, and control such systems. We present a framework to measure high-order interdependence that disentangles their effect on each individual pattern exhibited by a multivariate system.

I will review some recent progress on exact analytic treatment of simple models of interacting quantum and deterministic classical dynamics. There have been three particularly fruitful threads. Firstly, exact solutions for the steady state density matrix of boundary driven Lindblad equation for integrable quantum spin chains gave birth to new, quasi-local conservation laws which provide rigorous bounds on ballistic transport at high temperature. Secondly, certain interacting reversible cellular automata admit exact matrix product solutions for the dynamics of local observables, which facilitates an explicit computation of dynamical structure factors and a rigorous control of coexistence of conductive and convective transport. Finally, discovery of exactly solvable but non-integrable quantum circuits, such as self-dual kicked Ising model and the more general dual unitary circuits, gave rigorous proof of random matrix spectral statistics and explained `unreasonable effectiveness of random matrix theory' for description of quantum lattice models with local interactions.

Distinguishing genuine quantum correlation (entanglement) from spurious statistical one in out-of-equilibrium open quantum many-body systems is in general a challenging task. In this talk I will review some recent efforts to describe the entanglement dynamics in the presence of Markovian dissipation. In particular, I will focus on free-fermion and free-bosons subjected to global linear dissipation as well as to localized one. I will show that, at least for free systems, it is possible to incorporate the effects of dissipation in a hydrodynamic description for the entanglement spreading (quasiparticle picture).

Various methods are proposed to coherently control noisy quantum systems. We show how periodic driving may be used to steer systems coherently into specific target states. The stability of the protocols is studied to readjust and optimize the driving protocol. Static parameter errors can be compensated by appropriately controlling the interactions between systems and vice versa. All these ideas allow for a comprehensive control of small building blocks of larger quantum networks.

Discrete Floquet time crystals (DFTC) are characterized by the spontaneous breaking of the discrete time-translational invariance characteristic of Floquet driven systems. Higher-order time-crystalline phases, i.e. oscillations whose period is a multiple p > 2 of the Floquet driving period, where recently discovers. In our work we introduced a new order parameter which is able to unambiguously detect crystalline phases regardless of the value of p and, at the same time, is a useful tool for chaos diagnostic. This new paradigm allowed us to investigate the phase diagram of the long-range (LR) kicked Ising model to an unprecedented depth, unveiling a rich landscape characterized by self-similar fractal boundaries. Our theoretical picture is also able to capture the emergent Z_p symmetry in the Floquet-Bloch waves.

In this talk I will illustrate the properties of a Sherrington-Kirkpatrick model with an additional Mattis interaction favoring a ground state, a "pattern", drawn from a certain distribution. The free energy of the model is rigorously expressed in terms of an infinite dimensional variational principle over two order parameters: the Parisi overlap distribution and the Mattis magnetization. I will then establish a correspondence with the rank-one matrix estimation problem in a mismatched setting, a popular problem in the Statistical Inference community. In this problem, a Statistician has to estimate a rank-one matrix from a noisy observation of it, under the hypothesis of Gaussian additive noise. However, there is a mismatch between the prior they use in the Bayes posterior and the true distribution used to generate the aforementioned pattern, namely the leading eigenvector of the blurred rank-one matrix. The phase diagram of the specific mismatch between Bernoulli and Gaussian priors is analyzed in detail and shown to contain a glassy region.

The highly structured character of data used in training deep networks is a crucial ingredient of their performance. Yet theoretical work has largely overlooked this structure. Modelling structured data, analyzing the learning and the generalization of deep networks trained on this data, are major challenges. This talk will describe several recent developments in this direction.

During this session the Assembly of the Members of the Italian Society of Statistical Physics - SIFS will take place and only SIFS members can attend.

Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of parameters to train, but in practice they do not. Here we employ results from replica mean field theory to compute the generalisation gap of machine learning models with quenched features, in the teacher-student scenario and for regression problems with quadratic loss function. Notably, this framework includes the case of DNNs where the last layer is optimised given a specific realisation of the remaining weights. We show how these results -- combined with ideas from statistical learning theory -- provide a stringent asymptotic upper bound on the generalisation gap of fully trained DNN as a function of the size of the dataset P. In particular, in the limit of large P and Nout (where Nout is the size of the last layer) and Nout<

A novel strategy to automated classification, termed Recurrent Spectral Network (RSN), is introduced which exploits a fully trained dynamical system to steer items belonging to different categories toward distinct asymptotic attractors. These latter are incorporated into the model by taking advantage of the spectral decomposition of the operator that rules the linear evolution across the processing network. Non-linear terms act for a transient and allow to disentangle the data supplied as initial condition to the discrete dynamical system, shaping the boundaries of different attractors. The network can be equipped with several memory kernels which can be sequentially activated for serial datasets handling.

After reviewing the Baik, Ben Arous, Pechet transition in the context of random matrix theory and its early applications in various fields, I will discuss its use in revealing relevant aspects of algorithmic transitions in inference problems, some surprising features of high dimensional cost rough landscapes associated with them, and how a new type of BBP transition emerges in specific cases.

M. Becchi [SISSA Trieste], A. Stopar [SISSA Trieste], A. Suma [University of Bari], V. Carnevale [Temple University] and C. Micheletti [SISSA Trieste] Olympic gels, made by polymer ring concatenated to each other, are of great interest both for they biological relevance in DNA kinetoplasts, and for their possible use as metamaterials with exotic mechanical properties. Despite much ongoing research and advancements, the goal of programming the realization of olympic gels with designed properties remains elusive. Here we report on a combined theoretical and computational study where an efficient realization of olympic gels is achieved via self-assembly of realistic supramolecular constructs. We show that the local network properties of the gels can be finely tuned via the concentration of the self-assembling monomers, leading to starkly different global properties, from metric footprint to spectral dimensionality. The emergent mechanical properties of the tunable olympic gels are finally studied by applying anisotropic pressures.

The goal of the talk is to present a review of recent results concerning time reversibility in presence of a magnetic field and its implication for statistical properties of a physical system. In particular, for classical and quantum non-relativistic and spin systems results like the Onsager reciprocal relations and the so-called fluctuation theorems, are consequently obtained, without recourse to the Casimir modification. Interestingly, the spin-field interaction does not break the time reversal invariance (TRI) of the dynamics, and that it does not require additional conditions for such a symmetry to hold, compared to the spinless cases. These outcomes are relevant for experiments such as diffusion in solutions, thermoelectricity and spin charge transport. Indeed, no violation of the Onsager relations has been found in presence of a magnetic field, contrary to general expectations.

Size fluctuations close to polymers critical point originate the non-Gaussian diffusion of their center of mass. Static universal exponents γ and ν-depending on the polymer topology, on the dimension of the embedding space, and on equilibrium phase—concur to determine the potential divergency of a dynamic response, epitomized by the center-of-mass kurtosis. Prospects in experiments and stochastic modeling brought about by this result are briefly outlined.

"Correlation is not causation" is the common-wisdom statement that correctly summarizes the idea that correlation measures only "coexistence" and not "dependence". However, we discuss how the Fluctuation-Response theory suggests a proper employ of time-correlations that yet allows causal relationships to be extracted between variables of a multidimensional Markov process. Indeed, Fluctuation-Response formalism can be used not only, to find the direct causal links between the variables of a system, but also to define a cumulative-in-time causation indicator with a straightforward physical interpretation. Interestingly, the simple relationship between correlations and response, rigorously valid for linear systems, can be extended to systems with weak nonlinear interactions. As a practical application, we show that our approach, properly complemented by the Transfer-Entropy analysis, is potentially able to establish causal links between temperature, CO2 concentration, and astronomical forcing during the glacial cycles of the last 800 kyr based on Antarctic ice core records.

The dynamics of sine-Gordon (SG) breathers is studied in the presence of lossy and stochastic perturbations. In the noise-free scenario, a breather decays into radiation within a time interval of the order of the inverse damping coefficient. Starting from a stationary breather with a random phase value, the performed simulations indicate that a spatially-homogeneous noisy source enables this solitonic state to last far beyond its deterministic lifetime. Interestingly, a nonmonotonic behavior of an average characteristic time for the breather emerges as a function of the noise intensity, which is a signature of the noise-enhanced stability effect. Both the frequency domain and the energy localization illustrate the efficacy of the phenomenon, which also appears robust against an additional thermal background. This framework is useful for tackling the long-standing problem of the breather's detection in long Josephson junctions and its applications, e.g., in information transmission and quantum computation. Also, given the degree of universality of the SG model, studies focusing on its fundamental excitations possess an inherently interdisciplinary relevance, e.g., in cuprate superconductors, geology, and DNA systems.

We study a scalar harmonic network with pair interactions and a binary collision rule, exchanging the momenta of a randomly-chosen couple of sites. We consider the case of the isolated network where the total energy is conserved. In the first part, we recast the dynamics as a stochastic map in normal modes (or action-angle) coordinates and provide a geometric interpretation of it. We formulate the problem for generic networks but, for completeness, also reconsider the translation-invariant lattices. In the second part, we examine the kinetic limit and its range of validity. A general form of the linear collision operator in terms of eigenstates of the network is given. This defines an \textit{action network}, whose connectivity gives information on the out-of-equilibrium dynamics. We present a few examples (ordered and disordered chains and elastic networks) where the topology of connections in action spaces can be determined in a neat way. As an application, we consider the classic problem of relaxation to equipartition from the point of view of the dynamics of linear actions. We compare the results based on the spectrum of the collision operator with numerical simulation, performed with a novel scheme based on direct solution of the equation of motion in normal modes coordinates.

We study the problem of the energetic cost of information erasure by looking at it through the lens of the Jarzynski equality. We observe that the Landauer bound, ≥ kT ln 2, on average dissipated work associated to an erasure process, literally emerges from the underlying second law bound as formulated by Kelvin, ≥ 0, as consequence of a spontaneous breaking of the Crooks-Tasaki fluctuation-symmetry, that accompanies logical irreversibility. We illustrate and corroborate this insight with numerical simulations of the process of information erasure performed on a 2D Ising ferromagnet L. Buffoni and M. Campisi, Journal of Statistical Physics 186, 31 (2022) https://doi.org/10.1007/s10955-022-02877-8

Microscopic systems operating far from equilibrium appear to be fundamentally constrained by thermodynamics. In particular, the precision and the duration of nonequilibrium processes is limited by their dissipation. I will review these bounds [1,2], add further results that point to a general dissipation-speed-reliability trade-off [3], but also enquire about their actual domain of applicability in complex mesoscopic systems. [1] Unifying thermodynamic uncertainty relations G Falasco, M Esposito, JC Delvenne New Journal of Physics 22 (5), 053046 [2] Dissipation-time uncertainty relation G Falasco, M Esposito Physical Review Letters 125 (12), 120604 [3] Beyond thermodynamic uncertainty relations: nonlinear response, error-dissipation trade-offs, and speed limits G Falasco, M Esposito, JC Delvenne Journal of Physics A: Mathematical and Theoretical 55 (12), 124002

Active matter may sometimes behave almost indistinguishably from equilibrium matter. This is particularly evident for some particle-based models [1] and active field-theories close to a critical point which falls in the Ising universality class [2]. In this talk I will show however that, even when critical, active particles strongly violate the equilibrium fluctuation-dissipation in the high-wave-vector and high-frequency regime [3]. Conversely, at larger spatiotemporal scales the theorem is progressively restored and the critical dynamics is in effective equilibrium. I will show that a faithful field-theoretical description of this phenomenology can be developed by employing a space-time correlated noise field. A dynamic renormalization group analysis shows that such a "colored" noise does not change the equilibrium critical exponents, in agreement with our numerical results [1]. I will discuss how the overall scenario, stemming from theory and simulations, shows that a correlated noise field is an important ingredient to describe critical active matter at the coarse-grained level. [1] C. Maggi et al. Soft Matter 17, 3807 (2021) [2] F. Caballero et al. Phys. Rev. Lett. 124, 240604 (2020) [3] C. Maggi et al. Communications Physics 5, 55 (2022)

The unprecedented COVID-19 pandemic we witnessed showed us the critical role played by human interactions in the advance of a new disease. Severe social-distancing measures -such as strict lockdown restrictions and travel bans- had proven to be highly effective in diminishing the impact of the pandemic as second-wave scenarios emerged when restrictions were lifted. Thus, characterizing how human mobility flows had changed during this period is crucial for developing mitigation strategies and preparing for upcoming outbreaks. At the same time, as scientists, this scenario provides a natural experiment that allows us to test the robustness of individual mobility patterns. Our goal in this research is to understand and quantify how human mobility patterns changed with the appearance of the COVID-19 pandemic and the consequent government restrictions. We analyzed a large dataset of GPS trajectories -obtained by smartphone apps- from January to September 2020. We included over 180,000 trajectories of people living in Massachusetts and considered movements across the U.S.A. For our results, we consider three different scenarios regarding the COVID-19 lockdown restrictions: before (from January to mid-March), during (from mid-March to May), and After (from June to September). We have calculated how the shape of the distribution of single trajectory's observables such as displacement length and radius of gyration. Our results provide quantitative measures for the evolution individual human trajectories during the pandemic that would allow for improved modeling of the impact of mobility to disease spreading. Understanding human social patterns in the context of a global pandemic is challenging but crucial from a public health perspective to the development of appropriate interventions for upcoming outbreaks.

Intracellular protein clusters such as Cajal bodies or transcription factories are generically seen in eukaryotic nuclei, and their biological function is beginning to be characterised. Much less is known, however, on their dynamics: a lot of studies assume these clusters are liquid-like, but experimental observations point to a more nuanced behaviour, with clusters formed by different proteins possessing different properties. Here, we study the dynamics and structural features of chromatin-bound protein droplets arising through the ``bridging-induced attraction'', which has been suggested to underlie nuclear body biogenesis, and has recently been demonstrated in vitro. We show that the emergent clusters display a liquid-to-solid transition, triggered for instance by increasing the magnitude of the protein-chromatin affinity. If specific protein-chromatin interactions are presents alongside non-specific ones, the solid state is glassy and structurally disordered. We predict the liquid-to-solid and liquid-to-glass transitions should leave signatures detectable by fluorescence recovery after photobleaching experiments, and that the solid or glassy state should be accompanied by dynamical heterogeneity, with two populations of fast and slow particles coexisting within the clusters.

Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of parameters to train, but in practice they do not. Here we employ results from replica mean field theory to compute the generalisation gap of machine learning models with quenched features, in the teacher-student scenario and for regression problems with quadratic loss function. Notably, this framework includes the case of DNNs where the last layer is optimised given a specific realisation of the remaining weights. We show how these results -- combined with ideas from statistical learning theory -- provide a stringent asymptotic upper bound on the generalisation gap of fully trained DNN as a function of the size of the dataset P. In particular, in the limit of large P and Nout (where Nout is the size of the last layer) and Nout<

The on-lattice φ^4 model is a paradigmatic example of continuous real variables model undergoing a continuous symmetry braking phase transition (SBPT). In this poster we present the study of the equipotential hypersurfaces of the Z2-symmetric mean-field version without the quadratic term of the local potential. Obviously, this simplification is directly extensible to the other symmetry groups for which the model undergoes a SBPT. We show that the Z2-SBPT is not affected by the quadratic term, and that the potential energy landscape turns out greatly simplified. In particular, there exist only three critical points, to confront with an amount growing as e^N (N is the number of degrees of freedom) of the model with non-vanishing quadratic term. In our opinion, this is a crucial feature for deepening the understanding of the link between SBPTs and the truly essential geometric-topological properties of the energy potential landscape for Z2-symmetric systems. References https://doi.org/10.48550/arXiv.1911.00233 https://doi.org/10.1103/PhysRevE.100.012124 https://doi.org/10.1103/PhysRevE.102.012119 https://doi.org/10.1140/epjb/e2020-100374-5

The Covid-19 pandemic affected the behavior of people all over the world in an unprecedented way. Governmental containment measurements altered the mobility of citizens on a large scale and changed the way cities, as complex systems, process information. Quantifying how urban flows of individuals had changed during this omnipresent crisis can be crucial to analyzing and improving possible measurements in upcoming pandemics. Furthermore, it can help to improve cities' general organization, for instance, by adapting the public transport system. In this work, we took a mobility network approach using a rich dataset provided by Cuebiq and focused on the functional changes of the network structure in cities in the U.S., with Boston as a first approach. Then, we characterized the network with two quantities: integration and segregation. On the one hand, as a proxy for integration, we used the normalized Global Communication Efficiency - the average shortest path length of the network, taking into account the weights of the edges-. On the other hand, segregation is measured with the modularity of the network -how much the network can be divided into clusters using the Louvain method for community detection-. Contrary to expectations, namely that cities' efficiency would decrease during the pandemic due to lockdown restrictions and travel bans, our preliminary result found the opposite for inner-city movements. In Boston, between February and April of 2020, integration increased in the months of solid restrictions and decreased in the summer months when Covid-cases dropped again. A possible explanation for this finding might be that the network during the pandemic strongly organise around hubs that more efficiently bridge between different areas of the city. In the following steps, we aim to extend our analysis to other cities -such as New York, Washington DC, Austin, and Seattle- to have a broader perspective and compare results. Then, inter-city flows will be analyzed to systematically understand how networks of urban flows changed on larger scales. A. Baumgartner, L.G. Alvarez-Zuzek, S. Centellegher, L. Lucchini, F. Privitera, B. Lepri, M. De Domenico, R. Gallotti

One of the fundamental open problems in knot theory is their classification, which aims to discriminate whether two given closed curves are topologically equivalent or not. The problem might be tackled with knot invariants, such as the Alexander polynomial, quantities that are the same for equivalent knots. Nevertheless, algorithms implementing knot recognition through invariants might take extremely large time or even fail. In this work, we study the problem of knot classification in polymers by using deep learning. In particular, we resorted to convolutional neural networks (CNN) and long-short term memory (LSTM). We simulated polymers, including different chain lengths and knots types. After the simulation, we computed different sets of features along the polymer chains and we used them to train the CNN and the LSTM. Our preliminary results are encouraging and seem to lead to a flexible and quick method for detecting knots in polymers.

Collective motion - or flocking - is an emergent phenomenon that underlies many biological processes of relevance, from cellular migrations to animal groups movement. In this work, we derive scaling relations for the fluctuations of the mean direction of motion and for the static density structure factor (which encodes static density fluctuations) in the presence of a homogeneous, small external field. This allows us to formulate two different and complementary criteria capable of detecting instances of directed motion exclusively from easily measurable dynamical and static signatures of the collective dynamics, without the need to detect correlations with environmental cues. The static one is informative in large enough systems, while the dynamical one requires large observation times to be effective. We believe these criteria may prove useful to detect or confirm the directed nature of collective motion in in vivo experimental observations, which are typically conducted in complex and not fully controlled environments.

The third law of thermodynamics, also known as the Nernst unattainability principle, puts a fundamental bound on how close a system, whether classical or quantum, can be cooled to a temperature near absolute zero. On the other side, a fundamental assumption of quantum computing is to start any computation from a register of qubits initialized in a pure state at zero temperature. This problem at the interface between quantum computing and thermodynamics is often overlooked or, at best, addressed only at a single-qubit level. Here, we will argue how the existence of a small, but finite, effective temperature, which makes the initial state a mixed state, poses a real challenge for the scaling of quantum computers. The theory, carried out for a generic quantum circuit with N-qubits input states, is validated by experiments performed on an IBM quantum computer.

Active (or self-propelled) particles constantly consume internal energy to move in the environment, breaking time-reversal symmetry at the local level and leaving the system out of equilibrium. This allows for a variety of fascinating phenomena to appear, such as the phase separation into a dense and a dilute phase in the complete absence of attractive interactions, known as motility-induced phase separation (MIPS) [1]. Although MIPS retains many aspects of a phase separation at equilibrium, its inherent non-equilibrium origin leads to a new physical phenomenology. Here we illustrate some of the peculiar features of the MIPS dynamics of active disks in two spatial dimensions emerging from numerical simulations [2]. We show the presence of another ordering mechanism beyond the equilibrium-like phase separation, namely the micro-phase separation of hexatic domains and vapor bubbles within dense clusters of particles [3]. We studied the steady-state size of these structures and found that it can be directly controlled by tuning the self-propulsion strength of the individual particles. We then provide a detailed analysis of the dynamics of individual clusters during the phase separation process. We show that active clusters have diffusive behavior that is enhanced by the self-propulsion strength and that the diffusion coefficient depends in a non-trivial way on the total mass of the cluster. We explain this anomalous behavior by the appearance of correlations between active forces in the clusters, which is a pure non-equilibrium effect induced by self-propulsion. [1] Cates M., Tailleur J. Annu. Rev. Condens. Matter Phys. (2015) [2] Digregorio P., Levis D., Suma A., Cugliandolo L.F., Gonnella G., Pagonabarraga I. Phys. Rev. Lett. (2018). [3] Caporusso C.B., Digregorio P., Levis D., Cugliandolo L.F., Gonnella G. Phys. Rev. Lett. (2020)

Epithelial tissues are essential in a number of biological processes, such as morphogenesis and cancer development. A fundamental understanding of their dynamics, however, is limited by the current lack of knowledge of the symmetries underlying cells' collective motion. An important progress in this respect, was recently achieved by Saw et. al. [1], who suggested that epithelial tissues could in fact behave as active nematic liquid crystals. In this work, we use a combination of in vitro experiments, numerical simulations and analytical work to identify the emergent order of epithelial tissues. Upon generalizing the standard shape tensor to arbitrary ranks, we find that both nematic and hexatic order is in fact present in epithelial layers, with the former being relevant at the large scales and the latter at the short scales. This separation of length scales affects both the topological and dynamical properties of the system. Importantly, neglecting hexatic order leads to a misidentification of topological defects and the appearance of unphysical disclination lines. Finally, we discuss how such an emergent hexanematic order crucially affects the hydrodynamic feedback at different lengthscales. [1] Saw et al. Nature volume 544, 212–216 (2017)

Multibath models were proposed in late '90, providing a rather simple class of systems naturally out of equilibrium. Moreover, it has been shown that annealed and quenched averages of disordered systems amount to particular temperatures of a multibath system. However, multibath models have still to be examined in great details. We have studied a 1 dimensional Ising spin-glass, where the spins are in contact with a first thermal bath and the coupling constants with a second one, with a temperature much higher than the one of the spins. To characterize the dynamics, we considered Glauber transition rates. Contrarily to the standard Ising model, we have found that the system stationarizes and that the correlators among the so-called "gauge" variables play a central role to describe the dynamics. We can give also some insights into the two-time-correlation functions and the fluctuation-dissipation relation in this system.

Very recent embedded systems has been launched by Xilinx company, called Versal ACAP. These are the next generation of FPGAs and could be used in modern physics experiments, such as colliders detectors or space missions, in order to speed up response times and efficiency. The main issue of such electronic devices in these kind of experiments lies in their interaction with particles, including neutrons, protons, ions and photons. Before being used in physics experiments, for image recognition for example, the behaviour of this Versal ACAP must be studied when struck by these types of particles. In order to do so, we implement neural networks and study its behaviour while the board is irradiated by condensed beams of particles. In this way, we can have a global idea of the board response after being used for several years in physics experiments.

We present a numerical study of emulsions in homogeneous and isotropic turbulence (HIT) at Reλ=137. The problem is addressed via direct numerical simulations, where the volume of fluid is used to represent the complex features of the liquid-liquid interface. We consider a mixture of two iso-density fluids, where fluid properties are varied with the goal of understanding their role in turbulence modulation. We observe the -10/3 and -3/2 scaling on droplet size distributions, suggesting that the dimensional arguments that led to their derivation are verified in HIT conditions. Furthermore, we report significant modulation of the canonical single-phase turbulence, showing that the interface is indeed responsible for energy transport across scales.

Michele Delvecchio^{1,2}, Francesco Petiziol^{3}, Ennio Arimondo^{4,5}, Sandro Wimberger^{1,2} 1 Department of Mathematical, Physical and Computer Sciences, University of Parma, Parco Area delle Scienze 7/A, 43124, Parma, Italy 2 National Institute for Nuclear Physics (INFN), Milano Bicocca Section, Parma Group, Parco Area delle Scienze 7/A, 43124, Parma, Italy 3 Institut für Theoretische Physik, Fakultatat II Mathematik und Naturwissenschaften, Technische Universitat Berlin, Eugene-P.-Wigner-Gebaude, Hardenbergstr. 36, 10623 Berlin-Charlottenburg, Germany 4 Dipartimento di Fisica E. Fermi, Università di Pisa - Largo B. Pontecorvo 3, 56127 Pisa, Italy 5 INO-CNR, via G. Moruzzi 1, 56124 Pisa, Italy Quantum computers are currently affected by many sources of decoherence. These prevent us from performing high-fidelity quantum operations, but various techniques can be adopted to increase the performance of a quantum system. In particular, in our study, we faced the problem with two approaches: in the first one, we analyzed different counter-diabatic state-transfer protocols affected by various decoherence channels. The study was performed on a single-qubit system and two-qubit entangling gate. The results show that, according to the decoherence channel affecting the system, one can mitigate the degradation of the fidelity by properly optimize the driving [1]; in the second, instead, we exploit the interatomic interactions for compensating static errors in the control parameters. We show that the interaction can be tuned in order to recover essentially the error-free dynamics of the atoms. Our calculations show that there exists a specific condition for which the compensation is indeed optimal [2]. A natural experimental realization are ultracold Rydberg atoms with imperfect excitation pulses. Their nonlocal interaction allows for many possible scenarios for the realization of qubit gates and excitation transport. [1] M. Delvecchio, F. Petiziol, and S. Wimberger, The Renewed role of Sweep Functions in Noisy Shortcuts to Adiabaticity, Entropy, 23(7), 897 (2021) [2] M. Delvecchio, F. Petiziol, E. Arimondo, and S. Wimberger, Atomic interactions for qubit-error compensations, Phys. Rev. A 105, 042431 (2022)

Giordano De Marzo, Andrea Gabrielli, Andrea Zaccaria and Luciano Pietronero. Black Swans have been introduced by Nassim Taleb to describe events that are unexpected, unpredictable, and characterized by extreme consequences. Examples of such events often found in the literature are World War I or the 9/11 terrorist attacks. Since the work of Taleb, this concept has been widely used and also during the Covid19 pandemic many public institutions and journals improperly referred to the virus as a Black Swan. In our work we address the challenging task of developing a scientifically grounded and quantitative approach to Black Swans, that up to now have been analyzed only qualitatively. We identify the mathematical ingredients needed for producing Black Swans as the presence of an inherent power law distribution and a jump dynamics of its upper cutoff. After an appropriate analysis we can define a parameter, the Blackness, capable of quantifying the degree of unexpectedness of an event. In this way it is possible to decide if the event is a real Black Swan, a Grey Swan or just a White Swan. Using the Blackness we analyze a number of social and natural events. For instance we confirm on a quantitative basis that World War I and 9/11 attacks are Black Swan and we find new examples of Black Swans, such as Lionel Messi. On the other hand we determine that World War II and 1987 Black Monday are not Black Swans. Finally, we apply these techniques to possible future events, being able to determine how large they should be in order to be classified as really ''unexpected'' and so to fall in the category of Black Swans. For example, a pandemic should kill almost 6 billion people in order to be a Black Swan, while no fluctuation of the Dow Jones index, no matter how large, could be totally unexpected.

It is known that many-body systems near a quantum phase transition (QPT) exhibit several properties which makes them appealing for metrological purposes. Indeed, it is now well established and widely used that the divergences of the quantum Fisher information observed near a QPT can be used to increase the precision in the estimation of a parameter. Meanwhile, when it comes to the simultaneous estimation of multiple parameters, the benefits of criticality are much harder to analyze due to possible incompatibilities arising from the Heisenberg uncertainty. This involves the use of quite convoluted quantities, as the Holevo-Cramer-Rao bound, which are far from straightforward to evaluate in systems of interest. Here we study the quantumness (R), a scalar index, which provides an asymptotic bound on the compatibility of a metrological scheme. The advantage of this approach is that R can be easily evaluated once the Quantum Fisher information and the mean Uhmlann curvature are known. Moreover, a scaling analysis of R reveals that many-body criticalities generally improve the compatibility in a multi-parameter framework. In fact, we show that the quantum critical point is a good place to look for compatibility. We corroborate these general statements with numerical simulations performed on some representative systems, such as Ising chain and XY chain, in which we find this positive criticality effects.

The description of quantum molecular dynamics as influenced by a polarizable and dynamically evolving environment is critical to understand the nature of various physical processes, from solvation phenomena to photobiological processes in protein environments, and transport of charge carriers and excitons in nanostructures. Indeed, experimental molecular systems, S, are not closed systems due to the interaction with the surrounding environment, generically denoted the bath, B. Large effects on S dynamics can be expected depending on the nature of the environment as well as on the SB interaction strength. The typically used dielectric continuum picture for B [1,2] is likely to fail when dealing with nonequilibrium solvation effects. On the other hand, fully atomistic first principles quantum calculations are hardly feasible due to the large number of environmental degrees of freedom. Against this background, we present the effect of a dynamic environment on a time-evolving molecular system, using the Quantum-Classical Reduced Hydrodynamic (QCRH) approach [3]. In particular, the hydrodynamic formalism naturally describes density, current and heat transport phenomena. Accordingly, the QCRH theory can describe molecular relaxation in condensed dynamic phases, complementing typically used dielectric continuum models for the environment.[1,2] At present, we have extended the QCRH approach in order to deal with orientational solvation processes in charge-transfer phenomena, using a Maxwellian closure for the hydrodynamic hierarchy. References [1] J. Tomasi, B. Mennucci, R. Cammi Chem. Rev. 105, 2999-3094 (2005) [2] A. Klamt, G. Schüürmann, J. Chem. Soc., Perkin Trans. 2 799-805 (1993) [3] I. Burghardt, B. Bagchi, Chem. Phys. 329, 343-356 (2006)

We identify and investigate the occurrence and the control of phase errors in realistic realizations of elementary quantum gates. Our final goal is to propose robust experimental protocols for quantum-error correction, insensitive to static and dynamical phase fluctuations also during the pulses actually applied in the protocol. First results hint on the possibility of error compensation by inter-qubit interactions, additional phase correction pulses, or simply adapting the pulse parameters.

Flocking - the collective motion exhibited by certain active matter (AM) systems capable of spontaneously breaking their rotational symmetry - is a ubiquitous phenomenon, observed in a wide array of different living systems and on an even wider range of scales. Examples range from fish schools and flocks of birds to bacteria colonies and cellular migrations, down to the co-operative behaviour of molecular motors and biopolymers at the subcellular level. The bulk flocking state, as described by the celebrated Toner & Tu (TT) theory, is characterized by a strongly fluctuating ordered phase endowed by long-ranged massless correlations. While our knowledge of the bulk behaviour of free collective motion is now fairly complete, at least when the surrounding fluid may be safely neglected (the so-called "dry approximation"), much less is known regarding the collective behaviour of confined flocking AM. This is a problem of great relevance for many experimental realizations with active colloids, where confinement by hard boundaries is practically unavoidable. While it has been argued that the hydrodynamic bulk fluctuations should be left unchanged by the local interaction with hard boundaries confining the TT fluid in the direction(s) transversal to collective motion, little is known about the behaviour of fluctuations near such boundaries. In the work I will work I describe for the first time genuinely long-ranged forces that arise confining flocking AM between flat reflecting boundaries - either elastic or inelastic - in the directions transversal to collective motion. Direct numerical simulations and analytical results show that non-equilibrium fluctuations induce an unusually strong Casimir-like force, characterized by a rather slow algebraic decay. I also argue that this behaviour, while directly controlled by an inhomogeneous density profile in the transversal direction, is ultimately related to the scaling of transversal velocity fluctuations with the confinement size L.

Here, we present a novel supervised deep learning method to perform automatic detection and classification of multiplets in one-dimensional proton NMR spectra. The method consists of a probabilistic deep learning approach based on an ensemble of deep convolutional neural networks. The training set is composed of a large number of synthetic spectra containing classes of basic non- overlapping multiplets only. All networks in the ensemble produce the same prediction for basic multiplets, while resonances not represented in the training set cause arbitrary errors that differ across the networks. Therefore, high output variance in the ensemble is an indicator of the presence of overlapping multiplets. Being able to distinguish between basic and overlapping multiplets is a decisive stage. Together with classification within different resonance categories, it helps to perform automated peak picking and coupling constants extraction. We show that our model can discriminate signal regions effectively and minimize classification errors between different categories of resonances. Most importantly, we demonstrate that the network generalizes remarkably well on real experimental proton NMR spectra.

A geometrical conjecture based on the fractional Yamabe equation is applied to three-dimensional percolation with objects placed continuously in space. By comparing the prediction of the order parameter profile with the result of simulations, we extract its critical exponent \eta with higher precision than previous methods.

Deep Feedforward Neural Networks (NNs) play a central role in the Machine Learning field. They are usually trained in the space of nodes, by adjusting the weights of existing links via suitable optimization protocols. Recently a radically new approach has been proposed [Giambagli et al. Nature Communications 2021]. By anchoring the learning process to reciprocal space, the new targets of the optimization process are eigenvectors and eigenvalues of the transfer operators between layers. Shifting the focus on such fundamental mathematical structures we have been able to understand the pivotal role they have in training and analyzing NNs. Indeed, while seeking for a small subset of trainable variables capable of carrying out the training procedure, eigenvalues are what to look for [Chicchi et al. PRE 2022]. Indeed, their number scales linearly with the nodes inside the network, at variance with the quadratic scale of the connections. Choosing them as trainable parameters allows the optimizer to exploit the parallel adjustment of several randomly initialized weights, the ones underlined by the corresponding eigenvector, and therefore made their after-training interpretation possible. Eigenvalues magnitude at the end of the training procedure, has been empirically and heuristically proven being a proxy of information handling across the network during the optimization process. Thanks to the establishment of a precise correspondence between nodes and eigenvalues a novel pruning procedure has been introduced. Remarkably, the nodes related with low magnitude eigenvalues can be removed without impacting significantly on the network performance; letting us implementing a novel spectral network compression algorithm [arXiv preprint: https://arxiv.org/abs/2108.00940].

In the last years the dark-matter detection has become a promising and fruitful research field. Josephson junctions (JJs) have been supposed to interact with axions, the hypothetical elementary particles proposed as a possible component of cold dark matter. Unexplained experimental effects on Josephson systems can be well justified on the basis of the axion-JJ theory. This hypothesis, thus, has paved the way for the possibility of thinking of JJs as possible axion detectors. Here, we propose an axion-detection mechanism based on the measurable voltage drop induced in the JJ when the combined action of bias current and thermal fluctuations causes the JJ to switch from the superconducting to the resistive state. The analysis of the mean switching times (MSTs) reveals the occurrence of an axion-induced resonant activation phenomenon. The latter is characterized by a nonmonotonic behavior of the MST, with a minimum, versus the ratio of the axion energy to the Josephson plasma one. We demonstrate how this effect could be experimentally measured and exploited to probe the presence of the axion field through Josephson-based experiments.

The experimental measure of the complete equilibrium distribution of the overlap in a replica symmetry breaking thermodynamic phase is a challenging objective since the introduction of the Parisi solution to the Sherrington-Kirkpatrick model. We tackle the problem on random laser statistical physics models. We first introduce a theory of multimode light amplification in random media. The leading model, derived from fundamental light-matter interaction, is a phasor spin-glass model with multi-mode mode-locking couplings, undergoing an overall intensity constraint induced by gain saturation, i. e., a spherical complex multi-p-spin model. Through analytic theoretical approaches, numerical simulations and experimental measurements we investigate random laser models, displaying properties such as a lasing phase transition, ergodicity breaking, glassiness at high power pumping, energy condensation, and nonlinear mode-locking. Replica Symmetry Breaking theory allows to identify a laser critical point and a glassy regime in the high pumping regime. An intensity fluctuation overlap (IFO) parameter is introduced, measuring the correlation between intensity fluctuations of light waves. In mean-field fully connected spherical models the IFO can be proved to be in a one-to-one correspondence with the Parisi overlap, and it allows to identify the laser transition and the high pumping glassy phase purely in terms of emission spectra data, the only data so far accessible in random laser experimental measurements. Though phasors configurations are not accessible, intensity configurations can, thus, be observed by means of emission spectra. Investigating pulse-to-pulse fluctuations in organic solid random lasers, indeed, the distribution of intensity fluctuation overlaps can be constructed and yields evidence of a transition to a glassy light phase compatible with a replica symmetry breaking. To bridge exact analytic results and coarse-grained experimental results numerical simulation of  models of random lasers are presented. Going beyond the fully connected approximation, a realistic random lasers undergoes mode-locking, similarly to the ordered multimode ultrafast lasers, though self-induced rather than built with ad hoc nonlinear devices. The mode-locking causes a dilution in the interaction network, with a consequent breakdown of energy equipartition among light modes that we observe both numerically and experimentally right at the random laser transition point. Essential biblio: F. Antenucci, C. Conti, A. Crisanti, and L. Leuzzi, 2015. General Phase Diagram of Multimodal Ordered and Disordered Lasers in Closed and Open Cavities. Phys. Rev. Lett. 114, 043901. Antenucci, F., Crisanti, A. & Leuzzi, L. 2015. The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra. Sci. Rep. 5, 16792. Ghofraniha N, Viola I, Di Maria F, Barbarella G, Gigli G, Leuzzi L, Conti C. 2015. Experimental evidence of replica symmetry breaking in random lasers. Nat. Commun. 6, 6058. Gradenigo, G., Antenucci, F. and Leuzzi, L. 2020. Glassiness and lack of equipartition in random lasers: The common roots of ergodicity breaking in disordered and nonlinear systems. Phys. Rev. Research 2, 023399. Antenucci, Lerario, Silva Fernandéz, De Marco, De Giorgi, Ballarini, Sanvitto, and Leuzzi, 2021. Demonstration of Self-Starting Nonlinear Mode Locking in Random Lasers. Phys. Rev. Lett. 126, 173901.

Active systems, due to the local breaking of equilibrium, allow for phenomena that their equilibrium counterparts cannot attain. This correspondence between microscopic local equilibrium breaking and the meso/macroscopic structure formation is a general feature that have been observed in diverse systems including bacteria and synthetic swimmers. A similar behaviour can be observed also in the case of polar active polymers, i.e. polymers made of active monomers whose activity is directed as the local tangent to the polymer backbone. For example, a coil-to-globule-like transition takes place for isolated active chains in three dimension, highlighted by a marked change of the scaling exponent of the gyration radius[1]. Driven by the relevance of confinement and topology on the structural and dynamical properties of passive systems, we investigate the interplay between these latter and activity for tangentially active polymers. We show that, in the bulk, isolated rings display two different regimes at high enough activity: short rings tend to become "stiffer" and to assume a disk-like conformation, whereas long rings collapse, forming tight structures that show the hallmarks of dynamical arrest[2]. Finally, when placed under confinement, suspensions of short active rings assemble in ordered phases [3]. References: [1] V. Bianco, E. Locatelli, and P. Malgaretti, Phys. Rev. Lett. 121, 217802 (2018). [2] E. Locatelli, V. Bianco, and P. Malgaretti, under revision in Phys Rev. Lett. [3] J.P. Miranda, E. Locatelli and C. Valeriani, in preparation

Authors: Lorenzo Gaetano Amato, Alberto Vergani, Michael Lassi, Riccardo Mannella, Alberto Mazzoni. Alzheimer's disease (AD) is a neurological pathology constituting 60% of all cases of dementia. It affects both mesoscopic dynamics and macroscopic brain structures. Due to the degenerative nature of AD, finding the signatures of the risk of developing this pathology before its onset is a crucial step. Clinicians are interested in characterizing the AD prodromal phase (pAD), in which brain alterations are present without evident symptoms. Nowadays, there is no agreement on how pAD condition could be estimated from non-invasive recordings such as EEG. Herein, we propose a cortical mean field model able to characterize pAD stages in both dynamic and functional connectivity (FC) features, allowing a causal characterization of disease staging. We then validated EEG simulations against experimental recordings. The cortical model used to simulate EEG signals is based on the The Virtual Brain platform (TVB). It comprises 76 Regions of Interest (ROIs), each described by a modified Jansen and Rit neural mass model. ROIs were connected with a standard TVB connectome modified with pAD pathophysiological constraints. EEG recordings are relative to four pAD subjects (two Subjective Cognitive Decline (SCD) and two Mild Cognitive Impairment (MCI)) and two healthy age-matched controls. Signals were analyzed determining FC and Power Spectra Distribution (PSD). We then simulated EEG from the model and computed PSD and FC. The model was able to capture the relevant features displayed by real data, i.e., I) increase of theta and beta band power in the SCD and MCI cases, II) reduction of alpha/delta power ratio in the MCI case, III) increase of alpha/delta power ratio in the SCD case. Moreover, the model successfully depicted the FC across pAD phases, with an overall FC increasing in both pathological stages, more evident in SCD. Interestingly, we found the Randic Index, describing network’s connectivity, to anti-correlate with network resilience to structural damage. This index links the FC state to the underlying structural pAD alterations, highlighting how functional connectivity behaves non-monotonously during the disease course, with an initial increase being reversed by the progression of structural damage. This trend is confirmed by FCs derived from experimental data. As expected, the lower the index, the higher the FC, which is the proof that neuroplasticity can increase resilience and therefore FC in pAD. This study paves the way for a subject-dependent, EEG based pAD model, that could determine the evolution of the disease when combined with non-invasive exams.

Stochastic resonance is a well established phenomenon which proves relevant for a wide range of applications and disciplinary contexts. The basic mechanism can be understood by considering a one dimensional bistable stochastic system, subject to a deterministic double well potential, and perturbed by an additive noise. In presence of a periodic forcing, by tuning properly the noise intensity, the dynamics of the system can be synchronized with the frequency of the forcing. In some physical contexts, as e.g. population dynamics at low copy number, bistability is induced by the nonlinear nature of the multiplicative noise. Is it possible to realize stochastic resonance in a system that displays bistability due to multiplicative noise? In this work we provide an affirmative answer to this question. To this end we set to study systems that are bistable only due to multiplicative noise, as revealed by their associated stationary probability distribution. A candidate model which enables for analytical progress to be made is in particular proposed. Working with reference to this case study, we elaborated on the conditions for the onset of the stochastic resonance mechanism. Moreover, a novel periodic regime is identified and thoroughly characterized. This latter stems for the subtle interplay between nonlinearities, as associated to both deterministic and stochastic terms. At odds with the traditional scenario, no lower bound exists for the frequencies which can be detected, at a given noise intensity.

We study a totally-asymmetric simple-exclusion process with local resetting at the injection node and open boundary conditions. We investigate the stationary state of the model, using both mean-field approximation and kinetic Monte Carlo simulations, and identify three regimes, depending on the way the resetting rate scales with the lattice size. The most interesting regime is the intermediate-resetting one, where we find pure phases and phase-separation phenomena, including a low-density/high-density phase separation. We discuss the density profiles, characterizing bulk regions and boundary layers, and nearest-neighbour covariances, finding a remarkable agreement between mean-field and simulation results. The steady-state phase diagram is mapped out analytically at the mean-field level, but we conjecture that it may be exact in the thermodynamic limit.

We numerically study the effective dynamics of a dense suspension of elongated pusher-like microswimmers, described as a polar active fluid by the two-dimensional Toner-Tu-Swift-Hohenberg equation, in a confined circular domain. We observe the transition from the isotropic mesoscale turbulent regime to a different one, characterized by large scale structures, if bacteria activity and aligning interactions are strong enough. We describe the features of these structures and how they are the resultant between the tendency to flocking and the instability responsible of active turbulence. We investigate the Eulerian properties of this regime, showing that the characteristics of these large vortices depend on intensity of aligning interactions, but also on confinement size, and demonstrating that this flow is qualitatively different from the ones already investigated. We also show that, because of the interaction with the wall, eventually the flocking tendency manages to prevail, giving rise to a new ordered phase, with some peculiar features reminiscing of the previous regime.

Recently, a simple topological descriptor for polymers inspired by the linking number, called "Gaussian Entanglement" [1], was introduce to quantify the amount of backbone self-entanglement in protein native states. Remarkably, up to 32% of protein domains have a topologically entangled motif identified by this descriptor. Using Molecular Dynamics within a coarse-grained, structure-based model we probe the folding kinetics of a small, two-state protein (Type III Antifreeze Protein RD1) having an entangled motif in its native state. We observed that contacts related to the entanglement tend to form in the late stages of the folding, in agreement with the hypothesis [2] that entangled proteins evolved to postpone the formation of these contacts to keep under control the folding. Moreover, at low temperatures the entangled RD1 protein may populate a non-trivial kinetic compact intermediate characterized by the absence of the native entanglement, whereas a reference small and two-state protein (SH3 domain) maintains its two-state folding behavior. This kinetic intermediate highlights the profound influence an entangled native topology may have on the folding process. [1] Baiesi, M. et al. Sci Rep 6, 33872 (2016) [2] Baiesi, M., et al. Sci Rep 9, 8426 (2019)

In recent years great interest arose in providing a thermodynamic description of Active Matter Systems, a class of non-equilibrium systems in which the single components transform energy into self-propelled motion. A measure of how efficiently energy is transformed into self propulsion is represented by the Active Work performed by active particles, whose possible distribution singularities are the indication of Dynamical Phase Transitions (DPTs) [1]. Using the large deviation theory recently developed in [2] for quadratic functionals of stable Gauss-Markov chains, the analytic expression of the scaled cumulant generating function (SCGF) of the Active Work for a single harmonically trapped Active Ornstein-Uhlenbeck Particle can be obtained. In this talk I will then show the main steps of the calculation, describe the results and their limits into less complex systems and finally discuss the main physical implications. In particular, I will demonstrate that the SCGF is not steep in many physical situations. Through Legendre-Fenchel transform, this leads to rate functions with affine stretches associated to specific class of trajectories and signal of DPTs in our system. [1] F. Cagnetta, F. Corberi, G. Gonnella and A. Suma, https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.158002 [1] M. Zamparo and M. Semeraro, arXiv:2204.08059

Directed evolution experiments represent a tool to mimic the natural evolution process on a much shorter time scale. Starting from a unique sequence named wild type, some rounds of mutation and selection are performed, so to explore the fitness landscape around the ancestor sequence. In order to derive information about proteins structure and functionality, a subset of the rounds is sequenced, providing a set of multiple sequence alignments (MSA). Standard inference approach such as Direct Coupling Analysis can be applied to infer an energy function, serving as a proxy of the related fitness. However, one could leverage the inherently dynamical nature of the underlying process to extract more accurate information. We proposed an inference method named AMaLa (Annealed Mutational approximated Landscape) which models the MSA related to different rounds as instances of a dynamical process. We tested the performances of the method on actual experimental data, both for fitness reconstruction and contact prediction. Moreover, with the aid of extensive simulations, the potentialities and limitations of the method are analyzed.

Lennard-Jones mixtures represent one of the popular systems for the study of glass-forming liquids. Spatio/temporal heterogeneity and rare (activated) events are at the heart of the slow dynamics typical of these systems. Such slow dynamics is characterised by the development of a plateau in the mean-squared displacement (MSD) at intermediate times, accompanied by a non-Gaussianity in the displacement distribution identified by exponential tails. As pointed out by some recent works, the non-Gaussianity persists at times beyond the MSD plateau, leading to a Brownian yet non-Gaussian regime and thus highlighting once again the relevance of rare events in such systems. Single-particle motion of glass-forming liquids is usually interpreted as an alternation of rattling within the local cage and cage-escape motion and therefore can be described as a sequence of waiting times and jumps. In this talk, I will present a simple yet robust algorithm to extract jumps and waiting times from single-particle trajectories obtained via Molecular Dynamics simulations. Moreover, I will discuss the presence of temporal negative correlations among waiting times, which becomes more and more pronounced when lowering the temperature.

We consider the non-equilibrium dynamics of the 2d quantum Ising model in the regime of strong ferromagnetic coupling. We study the dynamics of domain walls separating regions of reversed spin orientation. For many initial configurations we are able to map the problem to a fermionic chain, and show that at leading order there is an emergent integrability. The particular case of a large corner is investigated in details and we then discuss how integrability is broken when the ferromagnetic coupling is large but finite. We demonstrate that a symmetry-breaking longitudinal field gives rise to a robust ergodicity breaking in two dimensions, a phenomenon underpinned by Stark many-body localization of the emergent fermionic excitations of the interface. We give also some preliminary results for the case of a random longitudinal field, showing that the system always remains ergodic, but with slow dynamics.

Being able to predict the failure of materials based on structural information is a fundamental issue with enormous practical and industrial relevance for the monitoring of devices and components. Thanks to recent advances in deep learning, accurate failure predictions are becoming possible even for strongly disordered solids, but the sheer number of parameters used in the process renders a physical interpretation of the results impossible. Here we address this issue and use machine learning methods to predict the failure of simulated two dimensional silica glasses from their initial undeformed structure. We then exploit Gradient-weighted Class Activation Mapping (Grad-CAM) to build attention maps associated with the predictions, and we demonstrate that these maps are amenable to physical interpretation in terms of topological defects and local potential energies. We show that our predictions can be transferred to samples with different shape or size than those used in training, as well as to experimental images. Our strategy illustrates how artificial neural networks trained with numerical simulation results can provide interpretable predictions of the behavior of experimentally measured structures. Font-Clos, F., Zanchi, M., Hiemer, S. et al. Predicting the failure of two-dimensional silica glasses. Nat Commun 13, 2820 (2022). https://doi.org/10.1038/s41467-022-30530-1