IV Conference of the Italian Society of Statistical Physics - SIFS

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.167401

We uncover the connection between the Fitness-Complexity algorithm, developed in the economic complexity field, and the Sinkhorn-Knopp algorithm, widely used in diverse domains ranging from computer science and mathematics to economics. Despite minor formal differences between the two methods, both converge to the same fixed-point solution up to normalization. The discovered connection allows us to derive a rigorous interpretation of the Fitness and the Complexity metrics as the potentials of a suitable energy function. Under this interpretation, high-energy products are unfeasible for low-fitness countries, which explains why the algorithm is effective at displaying nested patterns in bipartite networks. We also show that the proposed interpretation reveals the scale invariance of the Fitness-Complexity algorithm, which has practical implications for the algorithm's implementation in different datasets. Further, analysis of empirical trade data under the new perspective reveals three categories of countries that might benefit from different development strategies.

Rankings simplify complex systems by ordering entities based on performance, aiding in resource allocation and recognition of top performers. However, they can also mislead, as top performance is often weakly correlated with actual skill, being influenced heavily by luck and the self-reinforcing "rich get richer" effect. An agent-based model was developed to investigate these dynamics in a synthetic society. The model examines how agents choose actions based on societal benefit and individual ability, factoring in the effects of imitation and randomness (serendipity). The model's simulations reveal that when imitation dominates, societal payoff is high but unevenly distributed, leading to inequality. Conversely, when randomness prevails, outcomes are more egalitarian but with lower overall payoff. A key transition point between these states is identified, characterized by a sharp change in the correlation between agents’ skills and their payoffs, indicating a shift towards a meritocratic society. The findings suggest that while imitation can concentrate success in a few, serendipitous outcomes foster a fairer distribution of success. This model highlights the complexity of achieving a meritocratic society and the significant role of chance in shaping equitable outcomes.

In recent years, there has been a notable resurgence of interest in the spectral properties of random graphs. In particular, the existence of eigenstates exhibiting properties intermediate between full localization and full ergodicity has acquired significance in various physical contexts, including Anderson localization and the Many-Body localization. In the many-body setting, multifractal eigenstates that do not cover the entire accessible Hilbert space may violate the eigenstate thermalization hypothesis, and thus they are often termed "non-ergodic". Random matrix models have been an invaluable tool to describe and help understanding complex physical systems, in particular those with quenched randomness. The physical mechanism at the origin of multiftactal eigenstates is one such problem, and various matrix ensembles (either sparse or dense) have been introduced as proxies to capture their peculiar spectral properties. In this talk, I will first address the generalized Rosenzweig-Porter model, which has recently been shown to host non-ergodic states [1]. Using replica methods, we have derived novel exact results about its spectral correlations [2], and here I will discuss their physical significance. Next, I will consider the Erdös-Rényi random graph with randomly distributed weights. Despite this model being well-known, we have recently revealed a previously unnoticed multifractal phase in a broad region of its parameter space, using a combination of analytical (cavity-based) and numerical approaches [3]. I will elucidate the physical mechanisms underlying the emergence of these states, rooted in the pronounced heterogeneity in the graph's topology. REFERENCES: [1] V. E. Kravtsov, I. M. Khaymovich, E. Cuevas, M. Amini, "A random matrix model with localization and ergodic transitions", New J. Phys. 17 122002 (2015). [2] D. Venturelli, L. F. Cugliandolo, G. Schehr, M. Tarzia, "Replica approach to the generalized Rosenzweig-Porter model", SciPost Phys. 14, 110 (2023). [3] L. F. Cugliandolo, G. Schehr, M. Tarzia, D. Venturelli, "Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs", arXiv:2404.06931 (2024).

Exploiting quantum dynamics pierced by repeated measurements we study first hitting time problems for quantum walks on a graph and for many-body spin systems. We discuss dark states and their relation to symmetry, the integer and fractional quantization of the recurrence time, large fluctuations and uncertainty principles.

Confining in space the equilibrium fluctuations of statistical systems with long-range correlations is known to result into effective forces on the boundaries. Here we demonstrate the occurrence of Casimir-like forces in the non-equilibrium context provided by flocking active matter. Free flocks, as described by the Toner-Tu theory, are characterized by a strongly fluctuating ordered phase displaying truly long-ranged order even in two spatial dimensions. Here we consider a system of aligning self-propelled particles in two spatial dimensions, confined in the direction transversal to that of flocking. We first discuss how bulk correlations are affected by such boundaries, then show that in the ordered flocking phase this confined active vectorial fluid is characterized by extensive boundary layers, as opposed to the finite ones usually observed in confined scalar active matter. Moreover we show that non-equilibrium fluctuations induce unusually strong Casimir-like forces, characterized by a remarkably slow algebraic decay. We explain our findings – which display a certain degree of universality – within a hydrodynamic description of the density and velocity fields.

Quasi-long ranged order is the hallmark of two-dimensional liquid crystals. At equilibrium, this property implies that the correlation function of the local orientational order parameter decays with distance as a power law: i.e. C(r) ∼ |r|^{–η}, with η a temperature-dependent exponent. While in general non-universal, η = 1/4 universally at the Kosterlitz-Thouless transition, where orientational order is lost due to disclination unbinding. Does this definition of liquid crystal order in two dimensions also apply to active liquid crystals? And if not, are these more or less ordered than their passive counterpart? Using a combination of analytical and computational techniques in this talk I will demonstrate that, in active liquid crystals the notion of quasi-long ranged order fundamentally differs from its equilibrium counterpart and is ultimately dictated by the interplay between translational and orientational dynamics. As a consequence, the exponent η is allowed to vary continuously in the range 0 < η ≤ 2, with the upper bound corresponding to the isotropic phase. I will support our theoretical predictions with a survey of recent experimental data, reflecting a wide variety of different realization of orientational order in two dimensions.

Active systems, due to the local breaking of equilibrium, allow for phenomena that their equilibrium counterparts cannot attain, such as meso/macroscopic structure formation. 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, a coil-to-globule transition occurs[1]. We discuss the properties of isolated polymers in bulk, with particular focus on an active Rouse theory for the coil-to-globule transition [2]. Further, we examine the system in cylindrical[3] as well as in corrugated[4] nano-channels and show that the dynamical properties of these systems can be rationalised with simple theoretical approaches. References [1] V. Bianco, E. Locatelli, and P. Malgaretti, Phys. Rev. Lett. 121, 217802 (2018). [2] P. Malgaretti, E. Locatelli, C. Valeriani, arXiv:2404.12470 (2024) [3] J.Martín-Roca, E. Locatelli, V. Bianco, P. Malgaretti, C. Valeriani, arXiv:2405.02192 (2024) [4] J.Martín-Roca, V. Bianco, E. Locatelli et.al., in preparation

We study, with analytical methods, the ordering kinetics of the long-range voter model. where agents on each vertex of a lattice take the opinion of another one at distance $r$ with probability $P(r) \propto r^{-\alpha}$. The model in $D$-dimensions exhibits different regimes, as $\alpha$ is varied. For $\alpha > D+2$, the behaviour is similar to that of the nearest-neighbor model. For $D <\alpha \leq D+2$, non-trivial stationary states appear even when $D<3$. Finally, for $\alpha \leq d$, the system behaves similarly as in the mean-field case.

Generative Autoregressive Neural Networks (ARNNs) excel in generative tasks across various domains, including images, language, and science. Particularly in physics, they have successfully applied to generate samples from statistical physics models. Despite their success, ARNN architectures often operate as black boxes without a clear connection to underlying physics or statistical models. This seminar explores the direct link between neural network architectures and physics models. I'll show how the neural network parameters align with Hamiltonian couplings and external fields, highlighting the emergence of residual connections and recurrent architectures from the derivation. By leveraging statistical physics techniques, we formulate ARNNs for specific systems, and I’ll discuss a new approach for sampling from sparse interacting systems, crucial for physics, optimization, and inference problems. Our findings validate a physically informed approach and suggest potential extensions to multivalued variables, paving the way for broader applications in scientific research.

In this talk I will review some recent results regarding continuous phase transition in active particles systems. In the first part of the talk I will focus on simulations of active particles interacting via a quorum-sensing (QS) mechanism by which particles change their swimming speed based on the number of perceived neighbors. I will show that if these particles slow down enough when interacting, the system undergoes a full motility-induced separation (MIPS) and that the coexistence curve terminates into a critical point belonging to the Ising universality class [1]. In contrast I will also show recent results demonstrating that, if these QS interactions have two competing scales, the MIPS is destabilized and the system forms an active micro-emulsion which is well described by a renormalized field-theory in a effective equilibrium framework. Finally I will discuss some recent experiments in which super-paramagnetic colloids activated by a bath of swimming E. coli undergo two-dimensional melting out of equilibrium [2]. I will show how the basic physics of the experimental active crystal is well reproduced by a schematic model of active particles and how the KTHNY-theory remains qualitatively valid in describing the melting scenario of this active solid. [1] N.Gnan and C. Maggi Soft Matter 18, 7654 (2022) [2] H. Massana-Cid, C. Maggi et al. arXiv:2401.09911 (2024)

Despite the widespread popularity of deep neural networks across various fields, exact results regarding their generalization properties remain elusive. Recently, a significant advancement has been made in the proportional limit, where both the hidden layer sizes and the number of training examples are taken to infinity while maintaining their ratio fixed. In this regime, the kernel that describes the architecture is identified as the (globally) renormalized Infinite Width kernel. This result, derived within a Bayesian framework, relies on a heuristic Gaussian equivalence. For this reason, it is crucial to compare the predictions of the effective theory against the outcome of training experiments. In this talk, I will present extensive numerical simulations of one-hidden-layer neural networks in the proportional regime using both real and synthetic datasets. Our findings indicate that the derived effective theory is predictive for finite-width networks. The good agreement between experiments and theory suggests that kernel renormalization is a critical mechanism for feature learning in Bayesian deep networks.

While the recent success of deep learning in applications is staggering, our understanding of why and how this paradigm works so well is lagging behind. This divide calls for a multi-disciplinary effort, to which physicists are contributing on both the theoretical and the empirical side. A key concept, somewhat underrepresented in other disciplines but central to physics, is that of universality. I will present the empirical discovery of a potentially universal feature of training dynamics in deep neural networks [1]. The observed universal behavior boils down to the presence, robustly across different training sets and architectures, of special data points that are exceptionally conserved and particularly influential for the generalization capacity of the trained model. [1] Ciceri et al., Nature Machine Intelligence 6, 40 (2024)

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.

We describe an experiment on an underdamped mechanical oscillator used as an information engine. The system is equivalent to an inertial Brownian particle confined in a harmonic potential whose center is controlled by a feedback protocol which measures the particle position at a specific sampling frequency 1/τ . Several feedback protocols are applied and the power generated by the engine is measured as a function of the oscillator parameters and the sampling frequency. The optimal parameters are then determined. The results are compared to the theoretical predictions and numerical simulations on overdamped systems. We highlight the specific effects of inertia, which can be used to increase the amount of power extracted by the engine. In the regime of large τ, we show that the produced work has a tight bound determined by information theories.

Phase-separating active systems display surprising phenomenology that is absent in passive fluid-fluid or liquid-vapor phase separation: activity can cause the Ostwald process to go into reverse, or capillary waves to become unstable. When this happens, active systems self-organize in novel types of phase-separated morphologies which are either impossible in passive systems or require fine-tuning to be obtained. The universal properties of these phase-separated states, such as the critical exponents associated with the roughening of the interface, also differ from those of passive fluids. I will discuss how such findings can be rationalized via field theoretical analysis, particle-based modeling, and their experimental relevance.

We discuss the problem of inferring the thermodynamic state of a system from partial observations. For a Gaussian process, we prove that it is impossible to distinguish an equilibrium system from an out-of-equilibrium one by observing a single variable unless a response experiment is performed. We show a possible way out when it is not possible to appropriately perturb the system to get the response but several observations recorded under different experimental conditions are available. We extend the discussion to Markov processes whose evolution is ruled by Langevin equations driven by a mixture of Gaussian and Poissonian white noises. These noises necessarily break the time-reversal symmetry, leading the system to non-equilibrium steady states for which the entropy production may be different from zero even for vanishing currents. We show that a direct measurement of entropy production is typically impractical but it is simpler and more robust to detect the time-reversal symmetry breaking by looking at higher order correlations and we provide analytical expressions in some cases. Finally we put it all together in order to analyze a real experiment on granular gases.

Vlasov equation appears in a variety of physical situations involving long-range interactions, the most well-known being plasma physics, where electrons and ions interact through electro-magnetic forces, and self-gravitating systems, where stars – for instance- interact through gravitation. My goal here is to study the qualitative dynamical behavior of Vlasov equation, with an emphasis on universal ones, that is those which do not depend on the underlying physical system. In particular, I will be interested in some bifurcations of the stationary states.

The understanding of the fundamental relation between electrophysiological activity and brain organization with respect to performing even simple tasks is a long-standing fascinating question. The ability of the brain to self-organize information processing in an efficient way is a crucial ingredient in biologically plausible models. Recent experiments have shown that the spontaneous brain activity is characterized by avalanches showing absence of characteristic size, result successfully interpreted in the context of criticality. The fundamental open question of the relation between spontaneous and evoked activity is addressed by means of the stochastic Wilson Cowan model. An approach inspired in non-equilibrium statistical physics allows to derive fluctuation-dissipation relations, suggesting that measurements of the spontaneous fluctuations in the global brain activity alone could provide a prediction for the system response to a stimulus. Theoretical predictions are in good agreement with MEG data for healthy patients performing visual tasks. The analysis is performed in a wide range of parameters, setting the system at and off criticality.

Several recent experiments in atomic, molecular and optical systems motivated an huge interest in the study of quantum long-range spin systems. The goal of the talk is to present a general description of their critical behavior and phases, devising a treatment valid in d dimensions with an exponent d+σ for the power-law decay of the couplings in the presence of an O(N) symmetry. I will first starting by reminding results on classical long-range systems. Then, by introducing a convenient ansatz for the effective action, one can determine the phase diagram for the N-component quantum rotor model with long-range interactions, with N=1 corresponding to the Ising model. The phase diagram in the σ− d plan shows a non trivial dependence on σ. As a consequence of the fact that the model is quantum, the correlation functions are genuinely strongly anisotropic in the spatial and time coordinates for σ smaller than a critical value and in this region the isotropy is not restored even at the criticality. Results for the correlation length exponent & the dynamical critical exponent and a comparison with numerical findings for them are presented.

A well known mathematical model of laser dynamics is revisited in the limit of a very fast relaxation of the atomic polarization (typical condition offered by fiber and semiconductor lasers). Direct simulations are unfeasible because of the multiple time scales, while a standard adiabatic elimination gives rise to unphysical divergences. I show that the theoretical failure is due to the closeness of the dynamics to a Hamiltonian model: a nonlinear wave equation of Klein-Gordon type accompanied by an exponential (Toda) potential. The additional presence of a perturbative forcing and dissipative terms is eventually responsible for the selection of the energy.

*Il fisico gentile (e resiliente)*

[Componimento semiserio di 7 stanze in ottava rima toscana.]
Cari adunati, qui per San Giovanni
tutti seguaci del fu Ludovico
per omaggiar chi è avanti negli anni
ma di lui, certo, il nom non ridico.
Ebbe i natali al borgo de' panni,
- spero non sia il mio dire lubrìco -
ma per lo studio si mosse a Florenza,
dove si diede alla fisica scienza.

Con Sergio e Roberto gli anni trascorre,
a macerarsi su quei fondamenti,
"sarà locale?" "ma certo che occorre!"
e lì a strizzar le quantiche menti.
Variabili occulte, lui le soccorre,
scrivendo il tutto ai Nuovi Cimenti.
Lontano lo porta l'Arno, a Pisa,
la QCD per un po' ei improvvisa.

Ma poi Angelo, Marco e compagni,
vanno a soccorrer lo sventurato,
torna a Firenze, "e di che ti lagni?",
della statistica fa noviziato,
d'hamiltoniane, di caos e di bagni,
ma la Lucania lo vuole associato!
Carco di automi e di transizioni,
a Santa Marta infin fa lezioni.

Ama disordin, catene, esponenti,
il disequilibrio, la biologia,
le interazion, quelle poco cadenti,
i campi medi, e l'enologia,
e quegl'insiemi dis-equivalenti,
vanno a comporre la sua antologia.
Visita il mondo, in largo, diciamo,
ma di Tergeste ode'l primo richiamo.

In Francia spesso lo fan professore,
tant'è che pare che fugga Florenza,
fa molti amici di grande spessore,
coi quali, gaudente, nutre la scienza,
ma del suo ritorno scoccan le ore,
e di Lión gli rimàn l'esperienza;
Delle merende ritrova i compagni,
ma anche i colleghi, quelli grifagni.

Trieste richiama e or lui risponde,
c'è da governar la barca d'Ulisse!
Dell'Adriatico or vede le sponde,
e della ciurma governa le risse
con la sua calma che intorno diffonde,
raggiunge le mete ch'eran prefisse.
Al quarantunnale, il Presidente,
riceve commosso, tra la sua gente.

Curioso e paziente fino all snervo,
con l'empatia di un fra' confessore,
sempre accogliente, giammai protèrvo,
ei d'ogni causa si fa intercessore.
E con StatPhys avrà saldo il nervo?
La storia son certo, gli farà onore!
Ed ora libiamo, bene auguranti,
agl'anni di Stefan, dietro e davanti!

24-25 maggio 2024

Recent experiments in active microrheology allow for the experimental investigation of the nonlinear viscosity of complex fluids, such as micellar fluids or polymer solutions. Depending on the probe's drag speed, multiple regimes may emerge, which still lack a microscopic understanding. Via Brownian molecular dynamics simulations, we are able to relate the different frictional regimes of the probe particle to changes in the microscopic structure of the polymer fluid, currently inaccessible to microrheological experiments. In particular, we identify hydrodynamic and non-hydrodynamic degrees of freedom of the polymers successively brought out of local equilibrium by the probe, and we suggest a more general phenomenology involving the onset of shear-thickening for long enough polymer chains. Our findings derive from studying a general mesoscopic model of complex fluids in which a spherical probe dragged by a moving harmonic trap interacts with many elastic chains of soft monomers. Our numerical study of the resulting Brownian dynamics reveals that such a model reproduces the phenomenology observed in the experiments and allows us to identify three different dynamical regimes in terms of the average motion and fluctuations of the probe particle. These three regimes and their typical time scales are then interpreted using simple theoretical considerations based on the dynamics of a few microscopic degrees of freedom of the polymers.

A liquid-liquid (LL) phase transition below water's freezing point, so-called supercooled regime, has emerged as a credible hypothesis for explaining its equilibrium state anomalies. The LLPT has nowadays been observed in several Molecular Dynamics (MD) simulations, with supporting evidence from experiments, albeit not directly observed. MD simulations provided evidence for a phase transition between a High Density Liquid (HDL) and a Low Density Liquid (LDL) [1]. Speculations on possible ferroelectric phase transition in water and, more generally, in polar liquids have persisted for some time. However, the two scenarios, namely LL and ferroelectric phase transitions, have never been correlated. Reanalyzing the water MD simulations in Ref. [1], a distinct correlation between density and total polarization emerges: while HDL retains paraelectric characteristics, the trend of LDL polarization suggests a ferroelectric character. In light of this result, we developed a classical density functional theory in a mean field approximation, with dipolar interaction treated perturbatively, that, starting from the microscopic potential interaction of a polar liquid, is able to describe the concomitant occurrence of ferroelectric and LL phase transitions. The peculiarity of our approach is the inclusion of the density-polarization coupling. which is inherent to dipolar interaction. Covering the critical point, the Widom and first-order LL phase transition lines, we compared the density and polarization phase diagrams of water obtained from MD simulations and theory, revealing significant alignment. As further confirmation of ferroelectric order existence in LDL, collective propagating modes, stemming from the spontaneous breaking of the continuous rotational symmetry group O(3), have been identified in MD results. Possible developments of the present theory involving the potential for improper ferroelectric transitions or glassy transition in dipolar degrees of freedom will be analyzed. [1] P. G. Debenedetti, F. Sciortino, and G. H. Zerze. Second critical point in two realistic models of water. Science 369, 289 (2020)

Despite the striking simplicity of the idea behind the Waddington Landscape, the identification of a quantity that approximates the differentiation potential is still an open area of research. Our goal is to identify a proxy for this differentiation potential avoiding biological assumptions, strong pre-processing and sophisticated approaches, focusing instead on the statistical and geometrical properties of single cell RNA-sequencing datasets. The mRNA count matrix contains the coordinates of N cells in the high-dimensional expression space, where the dimensions are the sequenced genes. Because of biological constraints, data points are not uniformly spread along each direction, but are rather embedded in a subspace of dimension lower than that of the original expression space. To prove it, we focus on the intrinsic dimension of this kind of data, which can be interpreted as the dimension of the manifold from which they are supposed to be drawn. Besides that, our main claim is that the intrinsic dimension reflects the level of potency of a cell population. We relied on different approaches to estimate intrinsic dimension, from projective (based on the decomposition of covariance matrix) to fractal ones: the main estimator we used is 2NN, a local quantity that leverages the statistics of distances between first and second nearest neighbors. We studied several datasets referring to different biological processes and animal models, and we observed that the intrinsic dimensionality actually decreases during specialization, justified by a progressive structuring of data due to gene regulation mechanisms.

I use a simple model to review basic results in the field of nonequilibrium thermodynamics based on Markov processes, and highlight some ideas that may lead to proper experimental validity and disourse around it.

The eigenstate thermalization hypothesis (ETH) was developed to explain the mechanism by which "chaotic" systems reach thermal equilibrium from a generic state. ETH is an ansatz for the matrix elements of physical operators in the basis of the Hamiltonian, and since its postulation, numerous studies have characterised these quantities in increasingly fine detail, providing a solid framework for understanding the (thermo)dynamics of quantum many-body systems. ETH can be viewed as a generalisation of random matrix theory and, in fact, within this ansatz matrix elements are modelled as random variables. In our work, we have generalised the ETH ansatz in order to take into account correlations between matrix elements which are essential to describe high-order correlation functions. By analogy with the theory of random matrices, one can assume a certain hierarchy between these correlations and show how this generalized ansatz underlies a relationship between ETH and free probability. This relationship allowed us to unveil a particular structure of the time-dependent correlation functions in thermal equilibrium in terms of free cumulants.

We explore the non-equilibrium dynamics of many-body quantum systems under the influence of measurement protocols. Recent studies have shown that measurements can induce different non-equilibrium regimes, leading to abrupt changes in the scaling laws of bipartite entanglement entropy. Specifically, we investigate measurement-induced phase transitions in a monitored Quantum Ising chain [1]. Employing continuous local projective measurements, we witness the transition investigating the out-of-equilibrium probability distribution functions of local observables. Additionally, we extend our investigation by introducing an analytical framework designed to assess the probability distributions of expectation values across possible quantum trajectories [2]. We demonstrate this method through the analysis of two scenarios: a single qubit subjected to magnetization measurements and a free particle undergoing position measurements. [1] Continuously monitored quantum systems beyond Lindblad dynamics, G. Lami, A. Santini, M. Collura, New J. Phys. 26 023041 (2024) [2] Full counting statistics as a probe of measurement-induced transitions in the quantum Ising chain, E. Tirrito, A. Santini, R. Fazio, M. Collura, SciPost Phys. 15, 096 (2023)

The Mpemba effect is the counterintuitive and controversial phenomenon that hot water cools faster than cold one, or in more formal words, the more a system is out of equilibrium, the faster it relaxes. We introduce an analogous effect in extended quantum systems, in which a symmetry explicitly broken by the initial state is dynamically restored by the time evolution after a quantum quench. Unexpectedly, we find that the more the symmetry is initially broken, the faster is restored. To study this phenomenon, we borrow methods from the theory of entanglement in many-body systems and we introduce a quantity, dubbed entanglement asymmetry, which measures how much a symmetry is broken in a subsystem. In contrast to the classical case, we can establish the criteria for its occurrence in arbitrary integrable quantum systems and provide direct experimental evidence using a trapped-ion quantum simulator.

We present a method, dubbed “cooperative quantum information erasure” (CQIE), which uses both cooperative and quantum effects to reset large registers of qubits. We discuss how to leverage cooperative effects to achieve better reset protocols and why it matters for quantum technologies. Indeed, at variance with the standard method based on the individual reset of each qubit in parallel, here the quantum register is treated as a whole, thus avoiding the well known ortogonality catstrophe weherby even an extremely high individual reset fidelity $f$ results in modest global fidelities $F=f^N$ for sufficiently large number $N$ of qubits. We will then discuss the implementation of CQIE on a commercial quantum annealer which achieved exceptionally high values of the measured global fidelity for a register of 5612 qubits.

A measurement process in quantum mechanics produces a distribution of possible outcomes. This distribution, or its Fourier transform known as the full counting statistics (FCS), contains much more information than say the mean value of the measured observable, and accessing it is sometimes the only way to obtain relevant information about the system. For integrable models, a particularly important set of observables are its conserved charges which, when restricted to a subsystem display nontrivial dynamics. In this talk I will discuss the FCS of such observables in integrable models quenched from integrable initial states. Using a method called space-time duality, I will show how it is possible to determine the early time behavior of the FCS and combine it with a quasiparticle picture to obtain the full-time dynamics. I will then use these results to determine a simple universal relation between the initial time and late time cumulants of the charges.

Active Particles are physical entities able to transform energy from the environment or internal reservoirs into directed self-propelled motion. From a theoretical standpoint, in recent years this class of systems gained a prominent role in statistical mechanics due to the display of intriguing properties as motility-induced phase separation [1], an inherent out of equilibrium character [2] and the occurrence of singularities in distributions of integrated observables associated to Dynamical Phase Transitions (DPTs) [3]. In this respect, Active Work, i.e. the work performed by the self-propulsion force, emerged as a key observable to monitor as at the same time it provides a measure of how efficiently energy is transformed into self propulsion [4], it is strictly related to the system entropy production [2] and its distribution has already signalled the occurrence of such singularities and DPTs [5]. In this proposed talk we would like to present our recent results on this subject from [6], in which we studied the Active Work fluctuations of a single Active Ornstein-Uhlenbeck Particle under the effect of a confining harmonic potential. The simple but not trivial framework of a single particle allowed us to tackle the problem analytically for both for stationary and generic uncorrelated initial states adopting the Large Deviations approach we developed in [7]. Our results showed that harmonic confinement can indeed induce singularities in the Active Work Rate Function, with linear tails at large positive and negative Active Work values appearing for sufficiently large self-propulsion force, harmonic confinement and/or initial values. In addition, by looking at the system trajectories we discovered these singularities to be associated to DPTs in turn originated from concentrated large values, or big jumps, in the displacement and the self-propulsion force at the initial or ending points of trajectories. Our results thus provided a connection between DPTs and a condensation-like physical mechanism and marked the relevance of boundary terms in the problem at hand. [1] Motility-Induced Phase Separation, M. E. Cates and J. Tailleur, Annual Review of Condensed Matter Physics (6) 2015 [2] Irreversibility and Biased Ensembles in Active Matter: Insights from Stochastic Thermodynamics, E. Fodor, R. L. Jack, and M. E. Cates, Annual Review of Condensed Matter Physics (13) 2022 [3] A first-order dynamical transition in the displacement distribution of a driven run-and-tumble particle, G. Gradenigo and S. N. Majumdar, Journal of Statistical Mechanics: Theory and Experiment (5) 2019 [4] Work fluctuations in the active Ornstein–Uhlenbeck particle model, M. Semeraro, A. Suma, I. Petrelli, F. Cagnetta, and G. Gonnella, Journal of Statistical Mechanics: Theory and Experiment (12) 2021 [5] Large fluctuations and dynamic phase transition in a system of self-propelled particles, F. Cagnetta, F. Corberi, G. Gonnella, and A. Suma, Physical review letters (119) 2017 [6] Work Fluctuations for a Harmonically Confined Active Ornstein-Uhlenbeck Particle, M. Semeraro, G. Gonnella, A. Suma, and M. Zamparo, Physical Review Letters (131) 2023 [7] Large deviations for quadratic functionals of stable Gauss–Markov chains and entropy production, M. Zamparo and M. Semeraro, Journal of Mathematical Physics (64) 2023

It has been recently discovered that SARS-CoV-2 alters chromatin 3D structure of the host genome [1] at multiple length scales, ranging from some kilobases to entire chromosomes. We used polymer-physics models to investigate the physical mechanisms underlying such re-structuring. In particular, we showed that a polymer model with altered chromatin phase-separation properties [3] accurately captures re-arrangements upon viral infection, as emerged from experimental data. Furthermore, Molecular Dynamics (MD) simulations of the model indicate that SARS-CoV-2 infection leads to a peculiar loss of structural specificity and impacts chromatin time dynamics, reducing the stability of the regulatory contact network of key genes involved in antiviral response. Overall, our study [3] provides the first polymer-physics based reconstruction of SARS-CoV-2 infected genome with mechanistic insights on the consequent gene mis-regulation. [1] R. Wang, et al., SARS-CoV-2 restructures host chromatin architecture. Nat. Microbiol. 2023 84 8, 679-694 (2023). 
[2] A. M. Chiariello, et al., Polymer physics of chromosome large-scale 3D organisation. Sci. Rep. 6, 29775 (2016). [3] A. M. Chiariello, A. Abraham, S. Bianco, A. Esposito, F. Vercellone, M. Conte, A. Fontana, M. Nicodemi, Multiscale modelling of chromatin 4D organization in SARS-CoV-2 infected cells. BioRxiv (2023). https://doi.org/10.1101/ 2023.07.27.550709

We discuss the properties of the energy Hessian spectrum of excitations of simple vector spin glasses at zero temperature. We consider two mean field models, the first defined on a fully-connected graph and the second on a sparse random graph. The models are shown to reproduce key features of the low energy modes of glassy systems: the vibrational density of states features a pseudo-gap at low frequency with quasi-localised excitations. We characterise the properties of soft modes with respect to the zero-temperature spin glass transition in an external magnetic field. We show that the zero-temperature transition is a delocalisation transition for soft modes, discussing the features of this phenomenon in the two different cases (dense and sparse).

Since its discovery, the Earth’s ionosphere has been treated in many different ways: initially, it was described rather roughly as a channel to communicate through electromagnetic waves with receivers beyond the horizon, due to its capacity of reflecting the signals. However, being a highly variable physical system, in the users’ mind the ionosphere has been viewed more often as a complication than as a tool: its variability was always seen as an annoying characteristic, and it is still regarded this way by a wide community of communication and positioning “users”. The highly variable ionosphere, however, is much more than an annoying detail disturbing the GPS technology, or the scarcely reliable channel for ground-to-ground communication: since some decades, physical aspects of the system gained importance in the scientific and users’ community. As physical models of the ionospheric dynamics grew more and more important, multi-disciplinary aspects of physics and mathematics became central: from plasma dynamics, to electromagnetics in random media; from photochemistry kinetic equations, to the kinetic theory of gases of many species; from turbulence theory, to forced criticality. In this short review, I will try to sketch some aspects under which the state-of-the-art of ionospheric physics and modelling, with its paramount role in Space Weather science, appears to be a scenario with serious opportunities of intervention for the Statistical Mechanics and Dynamical System community, with their unique expertise in non-equilibrium thermodynamics, stochastic theories, dissipative structures and the predictability assessment of chaotic systems.

In our project, we explored how the Wilson Cowan model operates as an associative memory by analyzing a network consisting of N distinct neuronal populations. Each population acts similarly to an Ising spin within the Hopfield model. Our investigation focused on the shift from a functional working memory to a chaotic model.

Our study investigates the synchronisation dynamics of a chain of coupled chaotic maps arranged in a parent-children configuration, with each parent node connected to two children nodes, one of which is also the parent of the next node. We analyse two distinct phenomena: parent-child synchronisation, characterised by the vanishing distance between consecutive nodes, and siblings synchronisation, for which the two children coalesce. Our investigation reveals strong differences in the synchronisation mechanisms between these two phenomena, which can be directly linked to the probability distribution of the parent. Theoretical analyses and simulations using the logistic map support our findings. Furthermore, we explore the propagation of perturbations in a synchronised chain by studying the rate of reabsorption of the perturbation.

In this work we investigate the possibilities and the shortcomings that arise when implementing nonreciprocal and reciprocal interaction on a lattice model, in particular on a classical XY model with a vision cone. Reference [1] showed that adding a vision cone in a nonreciprocal fashion, i.e. featuring a selfish energy (and not a total energy functional) with non-symmetric couplings, leads to a non-equilibrium state with a long-range order (LRO) phase at low temperatures. Here we consider two reciprocal variation of such a model: (i) the first one is characterized by a total energy functional obtained as the sum of the selfish energies, and whose equilibrium state still has a long-range order, thus showing that such feature is to be ascribed to the vision cone nature of the interactions and not to their nonreciprocity; (ii) the second one considers a particular energy functional with symmetric couplings, for which we introduce the concept of redundant bonds, that leads to a stable quasi-long-range order (QLRO) phase and to an order-by-disorder transition

We study the full probability distribution of the time-integrated velocity of a particle elevated to n-th power, with n greater than two, where the velocity follows the Ornstein-Uhlenbeck dynamics. Using the standard tools of renewal theory, we treat the problem as a decoupled continuous time random walk. The probability distribution of our initial observable is related to the problem of the area under the Ornstein-Uhlenbeck excursions, which we treat with the usual methods of first passage problems. By using a formalism of large deviations, we derive the full probability distribution of the first passage area under the excursions, and we find that it has two different phases, directly depending by the parameters of the initial process: a diffusive Brownian phase in the strong noise limit and an anomalous sub-exponential phase in the weak noise limit, with a dynamical phase transition at the deterministic limit. Once we get the waiting times and the areas statistics, we are able to reconstruct our desired probability distribution through the continuous time random walk mapping. After calculating its typical Gaussian fluctuations, the main focus of our work is on studying its rare events distribution using the single big jump principle. We discover in the study of the tail process that the single big jump formalism returns the same results of other works obtained by the optimal functional method, a path integral approach that identifies the source of the anomalous subexponential scaling with the presence of an instantonic solution in the weak noise regime. This formal analogy will be discussed and tested with extensive numerical simulations, showing that the single big jump principle is more general, and this opens the way to further extensions of our theory in the study of rare events of a broader class of Langevin processes;

Quantum computers require qubits to be initialized in a pure (i.e., cold) state for successful computation. Dynamic cooling offers a route to effectively lower qubit temperatures beyond what is possible with direct, physical cooling techniques. It works by cooling a subset of qubits, at the expense of heating others, by applying certain logic gates to the entire system. While it was initially dismissed as impractical for the high-temperature NMR-based quantum computers available at the time of its inception, we show how dynamic cooling is substantially more effective and efficient on the low-temperature quantum computers available today. In this talk, we will examine how optimal dynamic cooling scales with total system size, in terms of the minimal achievable final temperature, the work cost, and the complexity of the associated quantum circuits. We will observe the effect of hardware noise on cooling and share results of a successful demonstration of dynamic cooling with a 3-qubit system on a real quantum processor. Finally, we will propose a sub-optimal dynamic cooling scheme with fixed (low) complexity to improve the feasibility of implementation on noisy quantum hardware.

Turbulence is ubiquitous in space plasmas and arise from nonlinear dynamics as emergent collective behavior, from the largest scales of the energy injection to the smallest scales where dissipation occurs. The turbulent dynamics of velocity and magnetic field fluctuations in nearly collisionless plasmas, such as the solar wind, can be envisioned as a scale-to-scale Langevin process. This allows us to embed the statistics of magnetic field fluctuations in the framework of stochastic process theory, and then to resort to fundamental concepts of the recent theory of stochastic thermodynamics. Magnetic field increments as a function of the scale define the cascade trajectories (viz., the stochastic process) over which we have calculated the stochastic entropy variation. The total stochastic entropy produced along a trajectory can be expressed as the ratio between the path probability of the forward trajectory divided by the path probability of its reversal. Thus, the production of entropy expresses, on average, the imbalance of forward with respect to backward processes, which, in the case of turbulence, are proxies for direct and inverse cascades. By using the stochastic entropy we are able to identify two different regimes where fluctuations exhibit contrasting statistical properties. In the inertial range a net production of entropy is linked to an increase of the flatness, thus indicating the occurrence of intermittency in the sample of fluctuations. On the other hand, cascade trajectories associated with a decrease of entropy are assimilated to a global scale invariance. In the transition region between inertial and ion scales the scenario reverses: trajectories characterized by ΔS<0 exhibit a sudden increase of the flatness due to small-scale intermittency, whereas trajectories with ΔS>0 show a constant flatness. Results suggest how the broad framework of stochastic thermodynamics can provide new insights in the field of space plasma turbulence, allowing us to perform a precise classification of cascading trajectories with opposite behavior based on their stochastic entropy production/consumption only.

Optimal transport (OT) is a mathematical framework that deals with the efficient transportation of mass or resources from one configuration to another while minimizing an associated cost. We propose a null model for bipartite networks that can measure the distance of a real system from its optimal configuration. This distance is measured by a $\beta$ parameter, that controls the relative importance of the cost function. Notably, the $\beta\to 0$ limit of this model can be mapped into the Bipartite Weighted Configuration Model (BiWCM), the weighted version of the Bipartite Configuration Model (BiCM). These are Maximum Entropy null models, widely used in Network Theory for the reconstruction and validation of networks. On the other end, OT is reached at the limit for $\beta\to\infty$. We study this change as a phase transition, in which the order parameter is linked to the connectivity of the graph. The two known limits are the energy-driven state (OT solution) and the entropy-driven state (BIWCM) of the system. Finally, we propose a full study of the critical properties of this model, highlighting the link between the Optimal Transport problem and graph theory.

Principal Component Analysis is a powerful tool for dimension reduction and clustering of high-dimensional data. It has been widely studied in various theoretical settings to assess its performance in retrieving low rank structures inside high rank data matrices. One of the most relevant settings from an information theoretical perspective, is a teacher-student scenario, where a teacher plants a low rank structure, called spike, inside a noise matrix, and the student is tasked with reconstructing it at the best of their possibilities. It turns out that the student’s best possible performance is in direct correspondence with information theoretical quantities such as the mutual information (MI) between the data and the spike. Prior to our contribution [1], the MI was computed only in the hypothesis of i.i.d., and thus structureless, Gaussian noise. With a novel technique, inspired by the theory of spin glasses with rotational invariant couplings, we extended the type of noises allowed to a class of random matrix ensembles of trace-type, with low-degree polynomial matrix potential. The predicted student’s performance is shown to be in perfect agreement with an algorithm, that we named Bayes-optimal Approximate Message Passing, whose iterates are rigorously characterized step by step. Despite the seemingly strong assumption of rotation-invariant noise, our theory empirically predicts algorithmic performance on real data, pointing at strong universality properties. In recent times [2], we were able to extend our analysis to any kind of trace ensemble with an arbitrary matrix potential, and to identify an algorithm whose performance is predicted by theory. Tracking the iterates of the latter rigorously still remains open. [1] J. Barbier, F. Camilli, M. Mondelli, M. Sáenz, "Fundamental limits in structured principal component analysis and how to reach them”, Proceedings of the National Academy of Sciences 120 (30) e2302028120 (2023) [2] J. Barbier, F. Camilli, M. Mondelli, Y. Xu, in preparation.

G. Consolini (1) and P. De Michelis (2) 1) INAF-Istituto di Astrofisica e Planetologia Spaziali, Roma, Italy 2) Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy The dynamics of Earth's magnetosphere in response to changes in the solar wind and interplanetary conditions are very complex, often showing scale-invariant energy relaxation events during the occurrence of magnetospheric substorms. In this presentation, we examine auroral electrojet AL-index bursts during substorms and show how the enhancement of ionospheric electrojet currents shares similarities with crackling noise observed in front propagation models. Our findings make a significant contribution to understanding the small-scale dynamics of the magnetospheric plasma sheet and the mechanisms driving magnetospheric substorms.

The interest in quantum technologies has grown dramatically in recent years. In particular, the attempt to achieve the supremacy of quantum simulators over the classical counterpart, is one of the most challenging tasks nowadays. In this context, understanding properly the features of open quantum systems could be the key to the development of increasingly large and powerful quantum computers. Several approximate approaches were developed in recent years to simulate the dynamics of open quantum systems [1], however the results obtained so far are generally limited to small size systems. Our novel approach is based on the time-dependent Variational Monte Carlo method, used in [2], but it exploits the so-called unravelling of the master equations to obtain a set of quantum trajectories evolving with Stochastic Schrödinger Equations (SSE). By finding the solution for several independent trajectories, we will then be able to reconstruct time-dependent observables equivalent to those coming from the master equations. The application of this method to dissipative Ising models is then shown, employing various variational ansätze ranging from the basic Jastrow wavefunction to more sophisticated ones, such as the renowned Neural Network Quantum States. [1] H. Weimer, A. Kshetrimayum and R. Orús, Rev. Mod. Phys. 93 (2021) [2] M. J. Hartmann and G. Carleo, Phys. Rev. Lett. 122 (2019)

Results regarding spin glass models are, to this day, mainly confined to models of Ising spins. Models of continuous spins, which exhibit interesting new physics connected to the additional degrees of freedom, have primarily been studied on fully connected topologies. Only recently some advancements have been made in the study of continuous models on sparse graphs. We partially fill this void by introducing a method to solve numerically the Belief Propagation equations for systems of Heisenberg spins on sparse random graphs via a discretization of the sphere. We introduce techniques to study the finite-temperature, finite-connectivity case as well as novel algorithms to deal with the zero-temperature and large connectivity limits. As an application, we locate the de Almeida-Thouless line for the model and the critical field at zero temperature and show the full consistency of the methods presented. Aside from these results, the approaches presented can be applied in the much broader context of studying Heisenberg spin glasses. They can therefore be used as a stepping stone to study further the behavior of these systems, thus helping to gain a better understanding of continuous models of spin glasses.

We study the effect of time reversibility on the adiabatic preparation of populations in the few-level quantum system. The invariance of time-reversal symmetry implying reversibility in adiabatic processes is investigated by considering various sweep functions and system configurations. The Berry curvature and the transitions are pursued as a function of time. The results will be relevant for the optimization and acceleration of experimental protocols for efficient population transfer.

We investigate the dynamic properties of the two-dimensional Ising model with anisotropy or quenched defects. Perturbations in system homogeneity significantly impact the dynamical properties, generally favouring the dynamic disordered phase. We analyse separately the two models. For the anisotropic case, the dynamic critical temperature shares similar anisotropic behaviour to the static critical temperature (associated with the ferromagnetic-paramagnetic phase transition), and it goes to zero in the fully anisotropic case. For the model with quenched defects, the dynamic critical temperature decreases linearly with increasing defect fraction. We also find a good correlation between some suitably defined geometric metrics related to quenched defects and the dynamic properties of the system, such as dynamic susceptibility and critical temperature. These geometric metrics prove instrumental in understanding and forecasting the dynamic behaviour in these complex systems.

Neural processes occurring in the brain are a source of significant inspiration for the foundation of machine learning technologies. In particular, Deep Neural Networks are composed by a collection of simplified neurons, the nodes of the computing device, organized in successive layers and mutually linked via artificial synapsis. Despite these formal analogies, Deep Neural Networks work as static units, at variance with living brains that operate in a highly dynamical framework. To take one step forward in the direction of reconciling artificial computing networks and the actual brain modeling, we set to train biologically inspired continuous rate model for simple classification tasks. The dynamics is thus steered towards different attractors, depending on the category the supplied input belongs to and following a dedicated learning stage. Our algorithm demonstrates high-accuracy performance in the classification task of synthetically generated images. This conclusion was reached by testing the performance of the algorithm at varying noise levels, as superposed to the images to be classified, in both training and test phases, and furthermore, added as a trainable parameter in the dynamical system. This opens up the perspective to leverage on the inherent endogenous stochasticity – yet another biomimetic concept to be included in the formulation - to enhance the performance of the trained model under the scrutinized dynamical angle. Summing up, the objective of this study is to take a further step towards constructing a stronger conceptual bridge between the exploitation of computational neural networks and their biological foundations.

Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale invariant networks by leveraging the concept of a constant diffusion entropy production rate across scales in a renormalization-group coarse-graining setting. This framework enables us to differentiate between scale-free and scale-invariant networks, revealing distinct characteristics within each class. Furthermore, we offer a comprehensive inventory of genuinely scale-invariant networks, both natural and artificially constructed, demonstrating that the human connectome exhibits notable features of scale invariance. Our findings pave the way for novel avenues to investigate the scale-invariant structural properties crucial in biological and socio-technological systems.

Monitored quantum dynamics, i.e. the dynamics of an open quantum system subjected to external measurements, has been extensively studied in the recent years. In particular, the competition between unitary dynamics and monitoringit can give rise to measurement induced phase transitions (MIPTs), which can be understood in terms of the replica formalism in terms of a breaking of the permutational symmetry. The seminar will focus exact results obtained for the monitored Brownian Heisenberg (arXiv:2306.12166), showing how the presence of a transition can vanish as one takes the replica limit. Finally, some preliminary results on monitored random circuits will be presented.

Molecular Dynamics simulations play a crucial role in resolving the underlying conformational dynamics of complex biomolecules. However, their capability to reproduce and predict dynamics in agreement with experiments is limited also by the accuracy of the force-field model. This issue can be tackled by suitable integration with experimental data. To this aim, several approaches, some of them based on the maximum-entropy principle, were proposed in the literature. They can be distinguished in two main classes. The first class includes Ensemble Refinement methods, which act independently on each molecular system, lacking transferability to different systems. The second one encompass Force-Field Refinement approaches, based on a reasonable guess of the corrections to the potential energy, making them transferable to different molecules at the expense of a limited flexibility of the ensembles. These two classes of methods have been so far used in a disjoint fashion. In our work, we show how a suitable combination of them can result in a lower prediction error for a realistic case-study of RNA oligomers.

Several systems may display an equilibrium condensation transi- tion, where a finite fraction of a conserved quantity is spatially localized. The presence of two conservation laws may induce the emergence of such transition in an out-of-equilibrium setup, where boundaries are attached to two different and subcritical heat baths. We study this phenomenon in a class of stochastic lattice models, where the local energy is a general convex function of the local mass, mass and energy being both globally conserved in the isolated system. We obtain exact results for the nonequilibrium steady state (spatial profiles, mass and energy currents, Onsager coefficients) and we highlight important differences between equilibrium and out-of-equilibrium condensation.

Critical correlations in a bounded system with ordered boundary are argued to be function of a suitably chosen metric g. This locally isotropic metric rules the order parameter profile according to general scaling arguments. These statements are verified via extensive Monte Carlo simulations. A natural candidate for g is the solution of a differential geometry problem known as Yamabe problem i.e. find a local rescaling of a metric making curvature constant. The correct Yamabe problem to be considered entails a fractional (anomalous in physics) generalization of the Ricci scalar curvature.

Since the introduction of the electrocardiogram (ECG) by string galvanometer in 1901 by Prof. Einthoven, the interpretation of cardiac health has remained largely unchanged. Traditionally, experts analyze ECGs for diagnosis, but the increasing volume of data and advancements in computer-based methods necessitate new approaches for feature extraction. Network science is becoming a common language to describe complex systems. In network science, complex systems are represented as nodes connected with edges. Time series can be considered complex systems too and they can be translated into networks by using visibility graphs. It is possible to characterize these complex systems by calculating the graph properties and by using a cartography-based method. Cardiovascular signals, exhibiting strong pseudoperiodic behavior, present challenges in early detection of arrhythmias, a prevalent cardiovascular disorder. Early recognition as well a prediction of arrhythmias can potentially save many lives. We used the 2017 PhysioNet/CinC Challenge database, and we analysed 1,000 short ECG recordings (500 normal and 500 arrhythmic). One approach to ECG analysis via network science involves segmenting signals into chunks and transforming them into visibility graphs. The visibility condition states that it is possible to connect two time points if they are visible to each other, i.e. it is possible to connect the values of two time points without intersecting the values of the time points between them. Then, the multiple graphs from one ECG were overlapped, and the weights were normalised to obtain a weighted graph with weights between 0 and 1. We used an arbitrary threshold of 0.50 to cut the noisy edges. We obtained, in this way, a unique representative graph for the ECG of a subject. To extract the features that were used to classify an ECG, we performed community detection through Louvain algorithm, and we identified the roles of each node in the graph. The roles depend on the position of a node inside the community. We also calculated some properties of the graph spanning from the diameter to the density. The percentage of the number of nodes for each role, the total number of nodes, the average degree, the density, the diameter, and the average clustering were used as features for a random forest classifier. After optimising the hyperparameters of the machine learning classifier, we obtained an accuracy of 74% and an AUC of 0.81 on the test set (300 ECG recordings, 150 normal and 150 arrhythmic). This work can pave the path for revisiting the traditional ways of reading ECG based on the analysis of the typical ECG waves, such as the QRS complex, the P and the T waves. This work also presents an innovative way of using a cartography-based analysis of the network and of extracting new numerical features from an ECG signal. Finally, this work can help machines to better recognise the arrhythmic patterns absent in the normal signals.

I will present recent works on theoretical measurement protocols and experimental results on a probe of many-body quantum chaos namely; The spectral form factor (SFF). The SFF characterizes statistics of energy eigenvalues, making it a fundamental diagnostic of many-body quantum chaos. In addition, partial spectral form factors (PSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems. The PSFF have recently been measured using the randomized measurement protocol, which I will discuss through my poster.

We investigate temporal consequences of spatial thermalization in multimode nonlinear optical systems on the basis of waveguide arrays. The recent activities (see e.g. L.G. Wright, F.O. Wu, D.N. Christodoulides, F.W. Wise, Nature Physics, v. 18, 1018, 2022) indicate that spatial optical modes with a given frequency undergo thermalization with respect to propagation constant distribution and thus are characterized by “spatial” temperature and chemical potential. Our aim is to translate these thermal characteristics into the usual temporal domain placing hypothetically classical or quantum particle into the potential created by those spatial modes and study the dependence of temporal statistics of the particle on the “spatial” thermal characteristics of optical modes.

We consider second-order phase transitions in which the order parameter is a replicated overlap matrix. We focus on a tricritical point that occurs in a variety of mean-field models and that, more generically, describes higher order liquid-liquid or liquid-glass transitions. We show that the static replicated theory implies slowing down with a logarithmic decay in time. The dynamical equations turn out to be those predicted by schematic Mode Coupling Theory for supercooled viscous liquids at a A3 singularity, where the parameter exponent is λ=1. We obtain a quantitative expression for the parameter μ of the logarithmic decay in terms of cumulants of the overlap, which are physically observable in experiments or numerical simulations.

Contacts between genomic loci of the chromatin fibre are essential for the control of genetic expression, yet the mechanistic details of these interactions are not completely understood. Loop extrusion by motor proteins like cohesin mediates the attractive interactions in chromatin on the length scale of megabases, providing the polymer with a well-defined structure and at the same time determining its dynamics. Their duration can be observed in living cells by time–lapse fluorescence microscopy, although with limited spatial and temporal resolution. Combining simulations with simple analytical models, we show how to obtain important information about the mechanism of stabilisation of contacts by cohesin from the two–dimensional dynamics of the system on the focal plane. In particular, we find estimations of the relevant distance at which a cohesin-mediated contact occurs and of the cohesin velocity along the chain.

Can we quantify how abstract a representation is? We know that abstraction develops with depth along biological or artificial neural hierarchies. We know that abstraction has to do with data independence and invariances. These insights will be studied and tested quantitatively in deep belief networks. (either a talk or a poster will be fine)

Since its discovery, the Earth’s ionosphere has been treated in many different ways: initially, it was described rather roughly as a channel to communicate through electromagnetic waves with receivers beyond the horizon, due to its capacity of reflecting the signals. However, being a highly variable physical system, in the users’ mind the ionosphere has been viewed more often as a complication than as a tool: its variability was always seen as an annoying characteristic, and it is still regarded this way by a wide community of communication and positioning “users”. The highly variable ionosphere, however, is much more than an annoying detail disturbing the GPS technology, or the scarcely reliable channel for ground-to-ground communication: since some decades, physical aspects of the system gained importance in the scientific and users’ community. As physical models of the ionospheric dynamics grew more and more important, multi-disciplinary aspects of physics and mathematics became central: from plasma dynamics, to electromagnetics in random media; from photochemistry kinetic equations, to the kinetic theory of gases of many species; from turbulence theory, to forced criticality. In this short review, I will try to sketch some aspects under which the state-of-the-art of ionospheric physics and modelling, with its paramount role in Space Weather science, appears to be a scenario with serious opportunities of intervention for the Statistical Mechanics and Dynamical System community, with their unique expertise in non-equilibrium thermodynamics, stochastic theories, dissipative structures and the predictability assessment of chaotic systems.

(Silvia Scarpetta, Niccolò Morisi, Carlotta Mutti, Nicoletta Azzi, Irene Trippi, Rosario Ciliento, Ilenia Apicella, Vincenzo Palmieri, Giovanni Messuti, Marianna Angiolelli, Fabrizio Lombardi, Liborio Parrino, Anna Elisabetta Vaudano) The human brain consists of billions of neurons, interacting in highly nonlinear ways. Neuronal avalanches are bursts of neuronal activity that propagate through the brain network in a cascading manner. Historically, collective emergent behavior has been observed both in vivo and in vitro in cortical networks, at rest. Recently, it has been shown that neuronal avalanches during sleep exhibit power-law distributions in size and duration, signature of scale invariance. There has been speculation about correlations between sleep and its role in tuning the brain to criticality, as deviations from power-law behavior have been observed in subjects under sleep deprivation. In this study, we record EEG of 10 healthy subjects during sleep. We confirm the scale invariant behavior of the avalanches’ sizes and duration during sleep, demonstrating also its robustness to the threshold defining the occurrence of an avalanche. We find the critical exponents and the scaling relations connecting their critical exponents in agreement with the one predicted in Mean Field Direct Percolation universality class. The investigation on the sleep structure revealed important correlations of avalanches occurrences with the Cyclic Alternating Pattern (CAP), a specific pattern in EEGs typically observed during the deeper phases of NREM sleep. This finding suggests the presence of a functional link between avalanche occurrence and occurrence of CAP phase A during NREM sleep. The large fluctuations involved in the CAP activation phase are a fingerprint of vicinity to criticality. As a result, CAP cycles are a genuine hallmark of tuning to criticality during sleep.

Neural networks are the most used algorithm in modern machine learning and have achieved incredible performance on different tasks. However, their development relies not on a deep theoretical understanding but on trial and error. One of the main difficulties of understanding NNs lies in the problematic nature of their training dynamics, which seeks optima in a very high-dimensional rough landscape. At the same time, the models avoid becoming trapped in suboptimal minima and converge to points with good generalization, thus escaping the so-called curse of dimensionality. Intuitively, in regression tasks, the optimal representation of the data would be a low-dimensional manifold in which the points align, allowing for easy linear regression. We introduce a entropy-based measure to capture geometric compression and investigate this prediction. Our observations during training reveal a non-monotonic behavior, namely a first compression phase, followed by a subsequent decompression phase where our measure increases again. Such a result is remarkable and unobserved in regression NNs. We prove that this behavior is a property of feature learning, and is quite general for changes in hyperparameters and for different datasets. We hypothesize that the epoch of inversion is when the network has learned to predict the best linear regression possible, and the subsequent decompression phase may indicate a phase of generalization, in which the model becomes more flexible and needs representations decompressed to accommodate more complex functions. This behavior aligns with current literature suggesting that neural networks learn the data distribution's moments sequentially. We theorize that inversion happens when the network has learned the first two moments and starts learning from moments of higher order.

The theory of nucleus-on-nucleus scattering of Mileto’s model, suggest us that the e+e− signals, in relativistic heavy ion collisions, are the evidence of the fusion of electromagnetic and nuclear fields. At the beginning of the calculation, using the relativistic quantum field theory, we may analise the joining of the bosonization of coherent and real photons with the nuclear states coming from the Giant Dipole Resonance which is a nonlinear partial differential sixth-order problem in the calculation of the cross section. Other models fail to describe the whole spectrum of dielectrons, measured from the DLS collaboration at BEVALAC. These models calculate the dielectrons produced from different hadronic generators neglecting the coherent and bosonic effects of electromagnetic fields. Therefore, their calculations underestimate the experimentals results; instead, we present the solution of many body interaction with detailed calculations that are entirely in accordance with measured differential invariant mass spectra of dielectron cross section, for low and medium invariant masses, and with radiative corrections it can also explain high invariant masses. This model implements quantum entanglement. We conclude that, with this model, we may foresee the number of dielectrons produced rescaling the amplitudes and the wave functions with this number, like foreseen by Mileto-Baur-Bertulani-Preparata-Glauber quantum field theory; the calculated spectra are complementary with hadronic generators, and legalizing our model as the probable describer of the heavy ion pile-up scenery as confirmed in the 2019 CERN experiments, having found that γ − γ scattering is a fundamental property of nucleus-nucleus interactions and is a law confirmed with a confidence of 8 σ. This theory is able to explain not only the experimental data of nucleus-nucleus interactions, at relativistc eneergy, but also the data observed by Chandra and Gemini observers from the emission of matter and antimatter by the Pulsar J2030+4415 and other similar pulsars, whose states can be described by General Relativity. [1] Graziano Mileto, Teoria di campo quanto-relativistica - Una guida sia teorica che applicata e di ricerca scientifica, con esempi ed esercitazioni, pagine: 316, libro pubblicato dall’Aracne Editrice-Collana: Il nucleare, n. 14, ISBN 979-12-218-0465-2, 2023 [2] Graziano Mileto, Produzione di coppie di-elettroniche negli urti fra ioni in regime relativistico, pagine: 524, libro pubblicato dall’Aracne Editrice-Collana: Il nucleare, n. 16, ISBN 979-12-218-0688-5, 2023, 3] Graziano Mileto, Produzione di coppie dielettroniche nel regime relativistico, pagine: 212, libro pubblicato dall’Aracne Editrice, ISBN 978-88-548-8221-8, 2015 [4] Graziano Mileto, G. Preparata et al., “Coherent QED, giant resonances and e+e− in high energy nucleus-nucleus collisions”, Il Nuovo Cimento A (1971-1996) 112, 767– 781 (1999). https://doi.org/10.1007/BF03035885, republished: 09 January 2016 on https://link.springer.com/ [5] Graziano Mileto, “Dielectrons e+e− signals from fusion of QED coherent and nuclear states in relativistic heavy ion collisions”, Hadronic Journal. Volume 28, from pag. 409 to pag. 440; 2005, issue number 4 of September 2005. https://www.hadronicpress.com/ [6] Graziano Mileto, Bevalac’s energy ion collisions coherent isodileptons e+e− results fitted by using QED and Hadronic Mechanics, Hadronic Journal. Volume 29, from pag. 143 to pag. 168; issue number 2 of April 2006. [7] Graziano Mileto, M. Milea, Dielectrons e+e− signals from fusion of QED Coherence and Nuclear states (GDR) in Ca-Ca relativistic heavy ion collision (Il codice I.S.B.N. del CD ove `e incluso l’articolo `e: 9788896810040), per il Workshop ”Mathematica Italia 7◦ User Group Meeting, Università degli Studi di Napoli Federico II, 28-29 maggio 2015”, presso l’Accademia delle Scienze di Napoli, per cui `e stato creato un CD unico con tutti i contributi dei relatori. [8] Graziano Mileto, M. Milea, Dielectrons e+e− signals from fusion of QED Coherence and Nuclear states (GDR) in C-C relativistic heavy ion collision, (Il codice I.S.B.N. del CD ove `e incluso l’articolo `e: 9788896810040), per il Workshop ”Mathematica Italia 7◦ User Group Meeting, Universit`a degli Studi di Napoli Federico II, 28-29 maggio 2015”, presso l’Accademia delle Scienze di Napoli, per cui `e stato creato un CD unico con tutti i contributi dei relatori.

In recent years, much attention has been paid to the observation of non-Gaussian probability density functions for diffusing systems in a variety of experiments and theoretical models, as such property could entail new physical insight. Here, we solved analytically the Langevin equation of motion in the overdamped regime of a particle moving both in absence and in presence of a harmonic potential, assuming the diffusion coefficient to be a Telegraph Process, i.e. the diffusion coefficient changes stochastically between two states. We computed analytically the first four momenta of the distribution of the particle position observing a non-Gaussian behaviour for short times. We found that the duration of the non-Gaussian behaviour decreases with the strength of the confinement and increases with the increasing of the microscopic time scale of the subordinating process. The relations we determined can become a very useful tool in experiments to determine the value of the unknown microscopic time scale starting from the value of kurtosis.

In liquids, the vibrational density of states of glasses is replaced with the Instantaneous Normal Modes (INM) spectrum. While in glasses instantaneous system configurations correspond to minima of the potential energy landscape with the eigenvalues of the associated Hessian matrix all positive (stable modes), in liquids this is no longer the case, and negative eigenvalues (unstable modes) appear. The latter provide important information on liquid dynamics and transport properties, and have been characterized numerically in the past. A systematic deeper theoretical understanding of the matter is provided by the Heterogeneous Elasticity Theory (HET). Here, space-dependent fluctuating moduli are included in the elasticity equations, naturally reproducing many aspects of the low-frequency vibrational excitations in glasses. In this talk I will present our extension of the HET to the liquid state [1], where the instantaneous-normal-mode spectrum of the liquid is described as that of an elastic medium with local shear moduli exhibiting strong spatial fluctuations, including a large number of negative values. This view provides quantitative predictions which consistently reproduce the outcome of extensive Molecular Dynamics simulations of a model soft-spheres liquid. We have characterized in depth the spectrum of the Hessian matrix, which displays a sharp maximum close to zero energy and has a strongly temperature-dependent shape, symmetric at high temperatures and becoming rather asymmetric at low temperatures, close to the dynamical critical temperature. Most importantly, we have demonstrated that the theory naturally reproduces a surprising phenomenon, a zero-energy spectral singularity with a cusp-like character developing in the vibrational spectra upon cooling. This feature, although noticed in a few previous numerical studies, was generally overlooked due to a misleading representation of the data. I will provide a thorough analysis of these issues, based on both accurate predictions of the theory and simulation data for systems of large size. [1] S. Mossa, T. Bryk, G. Ruocco, W. Schirmacher, "Heterogeneous-elasticity theory of instantaneous normal modes in liquids", ​Sci. Rep. 13, 21442 (2023)​

It has been recently shown that, when an Hopfield Network stores examples generated as superposition of random features, new attractors appear in the model corresponding to such features. In this work we show that the network also develops attractors corresponding to previously unseen examples generated with the same set of features. We claim that this surprising behaviour is due to the formation of attractors in correspondence of mixtures of features, and we support this claim by calculating analytically the phase diagram. Finally, we discuss how this framework could be used to predict generalization capabilities of modern neural networks.

Active emulsions and liquid crystalline shells are intriguing and experimentally realizable types of topological matter. We numerically study the morphology and spatiotemporal dynamics emulsion, where one or two passive small droplets are embedded in a larger active droplet. We find that activity introduces a variety of rich and nontrivial nonequilibrium states in the system. First, a double emulsion with a single active droplet becomes self-motile, and there is a transition between translational and rotational motion: both of these regimes remain defect-free, hence topologically trivial. Second, a pair of particles nucleate one or more disclination loops, with conformational dynamics resembling a rotor or chaotic oscillator, accessed by tuning activity. In the first state, a single, topologically charged disclination loop powers the rotation. In the latter state, this disclination stretches and writhes in 3D, continuously undergoing recombination to yield an example of an active living polymer. These emulsions can be self-assembled in the lab and provide a pathway to form flow and topology patterns in active matter in a controllable way, as opposed to bulk systems that typically yield active turbulence.

I will present a comprehensive study of adiabatic quantum pumping through a resonant level model, consisting of a single-level quantum dot connected to two fermionic leads. A self-contained thermodynamic framework for this model is developed using adiabatic expansion techniques, incorporating variations in the energy level of the dot and the tunneling rates with the thermal baths. This approach enables a detailed analysis of various examples of pumping cycles, with key thermodynamic quantities such as entropy production and dissipated power being computed. Important insights are revealed into the relationship between these thermodynamic quantities and the system's transport properties, including the pumped charge and charge noise. Notably, the entropy production rate approaches zero in the charge quantization limit, while the dissipated power obeys a quantization rule. These findings enhance the understanding of quantum pumping mechanisms and contribute to the broader field of quantum thermodynamics by linking transport phenomena with fundamental thermodynamic principles.

In classification problems, the model has to predict class labels given the data features. However, in several datasets the classes are naturally organized in hierarchical structures. While classification task is defined at a given level of the class structure, labels with a finer granularity can be associated to the data points and used during training. For example, if we are interested in separating images of vehicles from images of animals, we can train the model directly using these two labels or, alternatively, on the multi-class problem defined by the finer labels associated to the specific type of vehicle or animal, such as car, ship, dog, cat etc. Empirical evidence suggests that the second strategy can be advantageous for performance. Our goal is to test the generality of this effect and understand its origin using real and synthetic datasets. We will show that training on fine-grained labels does not always boost the classification performance. The optimal training strategy significantly depends on the geometric structure of the data and its relation to the labels, rather than solely relying on the granularity of the labels. Factors such as the complexity of the task, dataset size, and model capacity also significantly influence the potential advantages of training with fine-grained labels.

Transfer Entropy (TE), the primary method for determining directed information flow within a network system, can exhibit bias—either in deficiency or excess—during both pairwise and conditioned calculations, owing to high-order dependencies among the dynamic processes under consideration and the remaining processes in the system used for conditioning. Here, we propose a novel approach. Instead of conditioning TE on all network processes except the driver and target, as in its fully conditioned version, or not conditioning at all, as in the pairwise approach, our method searches for both the multiplets of variables that maximize information flow and those that minimize it. This provides a decomposition of TE into unique, redundant, and synergistic atoms. Our approach enables the quantification of the relative importance of high-order effects compared to pure two-body effects in information transfer between two processes, while also highlighting the processes that contribute to building these high-order effects alongside the driver. We demonstrate the application of our approach in climatology by analyzing data from El Ni\~{n}o and the Southern Oscillation.

We investigate the formation and the stability of 2D structures in nonlinear quantum mechanics. In particular, we are comparing two mean-field models, motivated as models for either ultracold atoms with short-range interactions or for fuzzy cold dark matter with long-rang interactions. Future studies should extend our numerical simulations to include excitations beyond mean field using the truncated Wigner method of statistical physics.

Active matter can harness energy from its surroundings and propel itself away from equilibrium. Its constituents absorb energy from the environment and dissipate it, e.g. through motion or the exertion of mechanical forces. The investigation of these systems offers promising new perspectives on the field of non-equilibrium statistical physics, further paving the way for the design of innovative life-like materials and devices. In this work, we analyse the behaviour of a synthetic active matter system consisting of liquid Ethyl Silicate droplet surfers [1], whose self-propulsion decays over time, within a Sodium Dodecyl Sulfate (SDS) solution [2]. By relying on a synergetic combination of techniques, such as computer vision algorithms for accurate droplet detection [3] and analyses grounded on non-equilibrium statistical mechanics and graph theory, we quantitatively characterise all the stages of the dynamic evolution of the system, from its initial diffusive regime up to the generation of large clusters of droplets that appear as the activity wanes. The presented work showcases a comprehensive analysis of an actively evolving system, offering not only a general pipeline for the investigation of analogous problems, but also a deep perspective at the intersection between physics and synthetic biology. 1] C. Watanabe, S. Tanaka, R. J. Löffler, M. M. Hanczyc and J. Gorecki, Dynamic ordering caused by a source-sink relation between two droplets, Soft Matter, 2022, 18, 6465–6474. [2] Shinpei, Tanaka et al. “Dynamic Ordering in a Swarm of Floating Droplets Driven by Solutal Marangoni Effect.” Journal of the Physical Society of Japan 86 (2017): 101004. [3] Martin Weigert, Uwe Schmidt, Robert Haase, Ko Sugawara, and Gene Myers. Star- convex polyhedra for 3d object detection and segmentation in microscopy. In The IEEE Winter Conference on Applications of Computer Vision (WACV), March 2020.

Recent times have witnessed a burst of activity on the application of equilibrium  and non-equilibrium statistical mechanics to study the behaviour of large ecosystems, in particular their stability and the nature of their equilibria.  In particular, many results on the coexistence of many species have been obtained using the Generalized Lotka-Volterra model. The latter, under appropriate hypothesis  on the shape of the interaction matrix between species and the stochasticity concourring to  the dynamics (demographic noise), allows to recast the dynamical stability problem  in terms of equilibrium statistical mechanics. We present here for the first time results on  the equilibrium statistical mechanics of the Generalized Lotka-Volterra model with  an interaction network between species which is sparse (Bethe lattice). Our analysis, at variance with the standard approach which makes use of a dense interaction network, reveals novel and highly non-trivial heterogeneity effects in the populations distributions, as for instance strong deviations from Gaussianity when increasing the heterogeneity of intra-species interactions. These results are in accordance with data from real ecosystems and also with other different models for ecological communities, as in [J. Grilli, Nature communications 11(1), 4743 (2020)]. In this talk I will review how the effective Hamiltonian for species interactions derived in [A. Altieri, F. Roy, C. Cammarota, G. Biroli, Phys. Rev. Lett. 126, 258301 (2021)] can be used to generate local marginals for populations distribution abundance when interactions are sparse, and I will present the main results obtained varying both the temperature (strength of demographic noise) and the heterogeneity of species interactions.

We present two examples of complex systems modeled by stochastic differential equations: i) an ecosystem consisting of two interacting bacterial populations in a food product [1]; ii) a marine ecosystem described by the 0-dimensional stochastic version of the well known biogeochemical flux model (BFM) [2]. In the first system, two generalized Lotka-Volterra equations are used to describe the time behaviour of Listeria monocytogenes and lactic acid bacteria (LAB), during the fermentation period (168 h) of a typical Sicilian salami [1]. The two differential equations are set with the temperature (T ), pH, and water activity (aw ) being treated as stochastic variables. The dynamics of each of these variables indeed is governed by two ”drivers”: a linear decrease as a function of the time t; an additive noise term which mimics the effects of random fluctuations. Suitably setting both the values of the interaction coefficients between LAB and L. monocytogenes and the noise intensities, the model provides results in a better agreement with the experimental data in comparison with those obtained by the corresponding deterministic model. In the second system, starting from the experimental data of the solar irradiance, collected on the marine surface, which clearly show an intrinsic stochasticity, the ecosystem dynamics is studied by modeling the noisy fluctuations of the irradiance as a self-correlated Gaussian noise [2]. Nonmonotonic behaviours of the coefficient of variation (a proxy of the variance) of the biomasses are found as a function of both the intensity and the autocorrelation time of the noise source, which indicates a noise-induced transition of the ecosystem to an out-of-equilibrium steady state. Moreover, evidence of noise-induced effects on the organic carbon cycling processes, underlying the food web dynamics, are highlighted. We conclude noting that the stochastic modeling of biological systems can be fruitfully used to devise more realistic models for the dynamics of an ”agricoltural ecosystem”, a natural (open) system governed by nonlinear dynamics, including the effects of both deterministic environmental forcings and randomly varying perturbations. This idea agrees with the approach, used during the last two decades in predictive microbiology, which allowed to get better and more reliable predictions for bacterial growth in food products [1, 3]. [1] A. Giuffrida, DV, G. Ziino, B. Spagnolo, A. Panebianco, A stochastic interspecific competition model to predict the behaviour of Listeria monocytogenes in the fermentation process of a traditional Sicilian salami, Eur. Food Res. Technol. 228, 767 (2009). [2] R. Grimaudo, P. Lazzari, C. Solidoro, DV, Effects of solar irradiance noise on a complex marine trophic web, Sci. Rep. 12, 12163 (2022). [3] DV, G. Denaro, F. Giarratana, A. Giuffrida, S. Mazzola, G. Basilone, S. Aronica, A. Bonanno, B. Spagnolo, Modeling of sensory characteristics based on the growth of food spoilage bacteria, Math. Model. Nat. Phenom. 11, 119 (2016).

Generative Autoregressive Neural Networks (ARNNs) excel in generative tasks across various domains, including images, language, and science. Particularly in physics, they have successfully applied to generate samples from statistical physics models. Despite their success, ARNN architectures often operate as black boxes without a clear connection to underlying physics or statistical models. This seminar explores the direct link between neural network architectures and physics models. I'll show how the neural network parameters align with Hamiltonian couplings and external fields, highlighting the emergence of residual connections and recurrent architectures from the derivation. By leveraging statistical physics techniques, we formulate ARNNs for specific systems, and I’ll discuss a new approach for sampling from sparse interacting systems, crucial for physics, optimization, and inference problems. Our findings validate a physically informed approach and suggest potential extensions to multivalued variables, paving the way for broader applications in scientific research.

Recent research suggests that when a system has a "false time-reversal violation" the Onsager reciprocity relations hold despite the presence of a magnetic field. The purpose of this work is to clarify that the Onsager relations may well be violated in the presence of a "false time-reversal violation": that rather guarantees the validity of distinct relations, which we dub "false Onsager relations". We also point out that for quantum systems "false time-reversal violation" is omnipresent and comment that, per se, this has in general no consequence in regard to the validity of Onsager relations, or the more general non-equilibrium fluctuation relations, in the presence of a magnetic field. Our arguments are illustrated with the Heisenberg model of a magnet in an external magnetic field. M. Campisi, EPL 142 30002 (2023) https://doi.org/10.1209/0295-5075/acd023

We are interested in investigating the statistical properties of extreme values for strongly correlated variables. The starting motivation is to understand how the strong-correlation properties of power-law distributed processes affect the possibility of exploring the whole domain of a stochastic process (the real axis in most cases) when performing time-average numerical simulations and how this relates to the numerical evaluation of the autocorrelation function. We show that correlations decrease the heterogeneity of the maximum values. Specifically, through numerical simulations we observe that for strongly correlated variables whose probability distribution function decays like a power-law $1/x^\alpha$, the maximum distribution has a tail compatible with a $1/x^{\alpha+2}$ decay, while for i.i.d. variables we expect a $1/x^\alpha$ decay. As a consequence, we also show that the numerically estimated autocorrelation function converges to the theoretical prediction according to a factor that depends on the length of the simulated time-series $n$ according to a power-law: $1/n^{\alpha^\delta}$ with $\delta<1$, This accounts for a very slow convergence rate.

(Giovanni Messuti, Silvia Scarpetta, Ortensia Amoroso,Ferdinando Napolitano, Mariarosaria Falanga,Paolo Capuano) Deep Neural Networks (DNNs) demonstrated remarkable power in various domains, achieving state of the art performance in several tasks such as image recognition, natural language processing and so on. DNNs often face significant challenges with out-of-sample data, where the model encounters data points that differ substantially from the training set, producing unjustified overconfident predictions that lead to poor generalization. Ensemble learning is a technique where multiple models are trained to solve the same problem. Aggregating the predictions of several models, the ensemble can achieve better generalization and robustness than any individual model. Ensembles are also known to enhance uncertainty estimation, offering more reliable confidence intervals and mitigating the risks associated with out-of-sample data. In our study, we build an ensemble of Convolutional Neural Networks to classify seismic traces based on first motion polarity, aggregating the predictions of individual networks through Unweighted Model Averaging. Our ensemble model demonstrates a greater ability to manage out-of-sample data, mitigating the effect of overconfident predictions. As a result, noise-only waveforms and waveforms lacking polarity information are correctly distinguished from waveforms containing polarity information.