III Conference of the Italian Society of Statistical Physics - SIFS

Within the cell nucleus of eukaryotic organisms, chromosomes are organized in a complex, non-random three-dimensional (3D) spatial structure, which is intimately linked to vital functional purposes. Indeed, a correct folding allows an efficient communication between genes and their distal regulatory elements while, if altered, can cause severe diseases. Here I will discuss how Polymer Physics, combined with Molecular Dynamics simulations and Machine Learning based inference, represent a powerful tool to quantitatively investigate the complexity of 3D organization of real genomes, as highlighted by recent microscopy and biochemical experiments. I will show that simple physical processes, widely studied in Statistical Mechanics, such as phase-separation of molecular aggregates and coil-globule polymer transitions, allow us to make sense of recent experimental observations including the tissue-specific DNA structure and the variability of chromatin at the single cell level. Finally, polymer models can be used to study the impact of disease-linked genetic mutations or the effect of viral infections as SARS-CoV-2, opening the way to new potential tools in Biomedicine.Refs.- Ringel A. R., Szabo Q., Chiariello A. M. et al. Repression and 3D restructuring resolves regulatory conflicts in evolutionarily rearranged genomes. Cell, 185, 3689-3704.e21, 2022;- Winick-Ng W. et al. (2021). Cell type specialization is encoded by specific chromatin topologies. Nature, 599, 684-691, 2021;

Proteins, the amazing molecular machines of life, are complex with myriad degrees of freedom. Linus Pauling [1] launched the field of molecular biology by developing the principles of quantum chemistry and applying them to predict the structures of protein modular building blocks, helices and strands assembled into sheets. Pauling and others, most notably Ramachandran [2] and Rose [3], adopted a backbone-based view, focusing on the importance of the backbone atoms, the avoidance of steric clashes, and hydrogen bonds. Over the last two decades there has been also a backbone-based concerted effort from the point of view of geometry and symmetry [4-7] within the context of a tube of non-zero thickness. An alternative sidechain centered view pointed out the additional vital importance of the role of the solvent, and the distinct hydrophobicity/hydrophilicity of amino acid chains, and the imperative to sequester the hydrophobic core from the solvent. This lead to an elegant picture of a folding funnel landscape [8,9]. I will present the results of ongoing work to reconcile these two approaches. The key step is to recognize that the protein building blocks are space filling structures. Using simple mathematical and physics ideas, we work out an interaction energy which promotes these structures, as well as a solvent mediated attraction that correctly assembles protein building blocks, while respecting their individual symmetries. Using analytic calculations and detailed Monte Carlo simulations, we explore the consequences of our theory. Our approach which deftly avoids the use of quantum chemistry, is in accord with experimental data, underscoring the consilience in the fit of chemistry and biology to the dictates of mathematics and physics. Our work has consequences for the energy landscape of proteins, the role of evolution in shaping sequences and functionalities, and supports the notion that discreteness, which underpins quantum mechanics, is also essential for life.References:[1] Pauling L, Corey RB, Branson HR, PNAS 1951; 37: 205 & Pauling L, Corey RB, PNAS 1951; 37: 729[2] Ramachandran GN, Sasisekharan V, Adv Prot Chem 1968; 23: 283[3] Rose GD, Fleming PJ, Banavar JR, Maritan A, PNAS 2006; 103: 16623[4] Maritan A, Micheletti C, Trovato A, Banavar JR, Nature 2000; 406: 287[5] Hoang TX, Trovato A, Seno F, Banavar JR, Maritan A, PNAS 2004; 101: 7960[6] Skrbic T, Hoang TX, Maritan A, Banavar JR, Giacometti A, Proteins 2019; 87: 176[7] Skrbic T, Maritan A, Giacometti A, Rose GD, Banavar JR, Phys Rev E 2021; 104: 014402[8] Bryngelson JD, Onuchic JN, Socci ND, Wolynes PG, Proteins 1995; 21: 167[9] Dill KA, Chan HS, Nat Struct Biol 1997; 4: 10

Cells in epithelial tissues can drastically deform their shapes and volume giving rise to collective behavior such as size oscillation and wave propagation. These phenomena have a strong impact in many biological contexts such as embryonic development, cardiac arrhythmias and uterine contraction.Following the recent formulation of active deformable particles, we introduce a lattice model of pulsating particles whose activity is given by the ability to change an internal degree of freedom at the single-particle level. The system then corresponds to a spatially-extended version of the periodically driven Potts model, exhibiting complex behavior already at fully-connected level; we show how the interplay between pulsation and synchronization gives rise to emergent behavior such as wave propagation. Fluctuating hydrodynamic equations are derived from microscopic dynamics and highlight the role of symmetry breaking. The latter proves to be a fundamental ingredient for wave propagation because of the competition between pulsating and arrested phases and its relation with reaction-diffusion systems.The model introduced thus stands as a suitable candidate to understand the targeted phenomenology and paves the way to the analysis of symmetry breaking in nonequilibrium field theories and many-body energetics, two of the main future directions in the growing field of pulsating active matter.

The celebrated Turing mechanism of morphogenesis is based on the counterintuitive notion that diffusion of activator and inhibitor molecular species can create non-homogeneous patterns. Recently, Turing's ideas have been extended to include demographic noise, the inevitable fluctuations in copy number of activator/inhibitor molecular species that result from processes such as gene expression. This extension significantly relaxes the restrictive conditions required for a classic Turing instability. Using combined experimental, analytical and computational theoretical approaches, we show that a classic two-component activator/inhibitor Turing model cannot account for the large variability of scales observed in two-dimensional, patterns of trichomes on wild-type Arabidopsis plant leaves, but that a noise-seeded, stochastic Turing mechanism can. These ideas should have widespread applicability in other natural pattern-forming systems.

Many complex systems in Nature, from metabolic networks to ecosystems, appear to be poised at the edge of stability, hence displaying enormous responses to external perturbations. This marginal stability condition is often the consequence of the complex underlying interaction network, which can induce large-scale collective dynamics, and therefore critical behaviors.In this talk, I will address some timely questions in theoretical ecology by presenting a disordered fully-connected version of the Generalized Lotka-Volterra model in the presence of demographic fluctuations and finite immigration.Leveraging on techniques rooted in spin-glass theory, I will unveil a very rich, eventually hierarchical, structure in the organization of the equilibria and relate the slowing down of the correlation functions to glass-like and aging properties.Finally, I will discuss some generalizations to non-logistic growth functions allowing us to capture positive feedback mechanisms, and therefore to pinpoint new phase transitions as a smoking-gun signature of criticality.

In theoretical Machine Learning, the teacher-student paradigm is often employed as an effective metaphor for real-life tuition. A student network is trained on data generated by a fixed teacher network until it matches the instructor’s ability to cope with the assigned task. The above scheme proves particularly relevant when the student network is overparameterized (namely, when larger layer sizes are employed) as compared to the underlying teacher network. Under these operating conditions, it is tempting to speculate that the student ability to handle the given task could be eventually stored in a sub-portion of the whole network. This latter should be to some extent reminiscent of the quenched teacher structure, according to suitable metrics, while being approximately invariant across different architectures of the student candidate network. Unfortunately, state-of-the-art conventional learning techniques could not help in identifying the existence of such an invariant subnetwork, due to the inherent degree of non-convexity that characterizes the examined problem. In this work, we take a decisive leap forward by proposing a radically different optimization scheme which builds on a spectral representation of the linear transfer of information between layers. The gradient is hence calculated with respect to both eigenvalues and eigenvectors with no increase in terms of computational and complexity load, as compared to standard training algorithms. Working in this framework, we could isolate a stable student substructure, that mirrors the true complexity of the teacher in terms of computing neurons, path distribution and topological attributes. When pruning unimportant nodes of the trained student, as follows a ranking that reflects the optimized eigenvalues, no degradation in the recorded performance is seen above a threshold that corresponds to the effective teacher size. The observed behavior can be pictured as a genuine second-order phase transition that bears universality traits.

Decades-long literature testifies to the success ofstatistical mechanics at clarifying fundamental aspects of deep learning.Yet the ultimate goal remains elusive: we lack a complete theoretical framework to predict practically relevant scores,such as the train and test accuracy, from knowledge of the training data.Huge simplifications arise in the infinite-width limit, where the number of units N_l in each hidden layer (l=1,.., L, L being the finite depth of the network) far exceeds the number P of training examples.This idealisation, however, blatantly departs from the reality of deep learning practice, where training sets are larger than the widths of the networks.Here, we show one way to overcome these limitations.The partition function for fully-connected architectures, which encodes information about the trained models,can be evaluated analytically with the toolset of statistical mechanics.The computation holds in the ``thermodynamic limit'' where both N_l and P are large and their ratio α_l = P/N_l,which vanishes in the infinite-width limit, is now finite and generic.This advance allows us to obtain(i) a closed formula for the generalisation error associated to a regression task in a one-hidden layer network with finite α_1;(ii) an approximate expression of the partition function for deep architectures (technically, via an "effective action'' that depends on a finite number of "order parameters'');(iii) a link between deep neural networks in the proportional asymptotic limit and Student's t processes;(iv) a simple criterion to predict whether finite-width networks (with ReLU activation)achieve better test accuracy than infinite-width ones.As exemplified by these results, our theory provides a starting point to tackle the problem of generalisation in realistic regimes of deep learning.

Exploiting invariances in the inputs is crucial for constructing efficient representations and accurate predictions in neural circuits. While the hallmark of convolutions, namely localised receptive fields that tile the input space, can be implemented with fully-connected neural networks, learning convolutions directly from inputs in a fully-connected network has so far proven elusive. In this talk, I will show how initially fully-connected neural networks solving a discrimination task can learn a convolutional structure directly from their inputs, resulting in localised, space-tiling receptive fields. I will provide an analytical and numerical characterisation of the pattern-formation mechanism responsible for this phenomenon in a simple model, which results in an unexpected link between receptive field formation and the tensor decomposition of higher-order input correlations. In more complex visual tasks, iterative magnitude pruning can yield local features by dynamically amplifying non-Gaussian statistics during learning. Non-Gaussianity of internal representations thus provides us with a framework to analyze feature learning in deep networks.

In this work we demonstrate that breathers, i.e., experimentally elusive oscillating fluxon-antifluxon bound states, can influence heat flow in a thermally biased long Josephson junction, leading to a measurable increase of local temperature. In fact, we report a breather-induced heating of nearly 40 mK in a specific realistic experimental setup. In this way, we provide a scheme for breather detection that does not require the destruction of the bound state. Furthermore, we show that the precise shape of the thermal profile in the presence of a breather depends on its frequency, which can be therefore measured experimentally. Finally, we exploit the simultaneous action of noise and ac drive to excite and stabilise a breathing mode, and we demonstrate the robustness of its thermal fingerprint to noisy fluctuations in a realistic scenario.

After a quantum quench the entanglement between a large, finite subsystem and the rest of the system generically displays a linear growth in time followed by saturation. While the subsystem is essentially at local equilibrium when the entanglement saturates, it is genuinely out-of-equilibrium in the growth phase. In particular, the slope of the growth carries vital information on the nature of the system's dynamics, and its characterisation is a key objective of current research. In the talk I will show that the slope of the entanglement growth can be determined by means of a space-time duality transformation. Namely, it coincides with the stationary density of entropy of the model obtained by exchanging the roles of space and time. Therefore, very surprisingly, the slope of the entanglement can be expressed as an equilibrium quantity. I will use this observation to find an explicit formula for the slope of R�nyi entropies in all integrable models treatable by thermodynamic Bethe ansatz and evolving from integrable initial states. I will then show that the duality approach can be generalised to the computation of full-counting statistics of conserved charges and symmetry resolved entanglement.

The present work is about a new method to sample the quantum fluctuations of relativistic fields by means of a pseudo-Hamiltonian dynamics in an enlarge space of variables. The proposed approach promotes the fictitious time of Parisi-Wu stochastic quantisation to a true physical parameter controlling a deterministic dynamics. The sampling of quantum fluctuations is guaranteed by the presence of new additionational conjugated momenta, which reprents the rate of variation of ordinary fields with respect to the newly added time variable. The main goal of this approach is to provide a numerical method to sample quantum fluctuations of fields directly in Minkowski space, whereas all existent methods allowed one so far to do this only in Euclidean space, therefore loosing important physics. From the pseudo-Hamiltonian dynanamics one is then able, assuming ergodicity, to retrieve the Feynman path integral as the Fourier transform of a pseudo-microcanonical partition function. The whole framework proposed is not only the source of a new numerical approach to study quantum fields but also and most importantly reveals important connections between quantum field theory, statistical mechanics and Hamiltonian dynamics.Here we will discuss the main ideas behind the formalism and the first succesful results of numerical tests, as well as the difficulties we encountered.

A main question for the nonequilibrium dynamics of extended quantum systems is whether time evolution eventually leads to some form of relaxation or can produce a different behavior. In the basic nonequilibrium setting, which corresponds to quantum quenches, we obtain for the first time analytical results for the time evolution of local observables in systems in d spatial dimensions. For homogeneous systems we show that oscillations undamped in time occur when the state produced by the quench includes single-quasiparticle modes and the observable couples to those modes. In particular, this occurs for a quench of the transverse field within the ferromagnetic phase of the Ising model in d > 1. For the more general inhomogeneous case in which the quench is performed only in a subregion of the whole d-dimensional space occupied by the system, the time evolution occurs inside a light cone spreading away from the boundary of the quenched region as time increases. In this case, the additional condition for undamped oscillations is that the volume of the quenched region is extensive in all dimensions.

One finds many examples of nonequilibrium steady states, from the climate scale to living cells and active matter. Entropy production and dissipation characterize these regimes. We introduce a variance sum rule (VSR) [1] for displacement and force variances, which allows us to measure the entropy production rate. This approach is based on the study of variances of positions and forces and is valid in arbitrary dimensions [2] for overdamped diffusive stochastic systems. We illustrate the VSR for an experiment with a Brownian particle driven by an optical trap and for analytically-solved two-dimensional models: a Brownian vortex and the well-known Brownian gyrator. The VSR is then extended to a reduced form that uses less information. With the reduced VSR applied to different experimental data, we measure an entropy production rate of active red-blood cells of millions of kT per second.References[1] Ivan Di Terlizzi et al, arXiv:2302.08565 (2023).[2] Ivan Di Terlizzi, Marco Baiesi, Felix Ritort, in preparation (2023).

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.

In this talk I will revisit various collaborations I've had with Riccardo in the last 30 years - from optimizing the dynamics of associative memory networks, to biologically plausible supervised plasticity rules with binary synapses, and finally understanding the role of dendritic non-linearities on neuronal computations.

In the last few years, the development of increasingly accurate high-throughput biochemical assays with massively parallel sequencing techniques has established large-scale genetic screening as a fundamental tool for the investigation of the relationship between evolution, fitness, and other important biological concepts that were behind the experimental research. In this presentation, I will describe the two main types of screening experiments - deep mutational scanning, and directed evolution - and the different inference frameworks we developed to analyze them.

Restricted Boltzmann Machines (RBM) can be interpreted as generalised Hopfield models, in which patterns are learned from the data and the energy of a configuration is a non-quadratic function of its projections along the patterns. In my talk I will focus on the problem of sampling transition paths in a RBM model. I will present both a Monte-Carlo algorithm to sample transition paths and a mean-field approach to compute optimal transition paths and other statistical physics properties, such as the probability to escape from a local minimum and the path entropy. I will then consider application to fitness landscapes inferred from in silico and real protein sequence data, more precisely, transition paths allowing for switching the binding specificity of a small protein binding domain.

Large Language Models (LLMs) have recently garnered global attention, but over the past few years the transformer architecture they are built upon has already demonstrated remarkable versatility across numerous and diverse domains. In this presentation, I will give an overview of the key aspects of transformer models in general and LLMs in particular - tokenization, embedding, attention mechanism, the transformer blocks, fine-tuning etc. with a particular focus in discussing the reasons that underlie the architectural choices made in the most successful models. I will conclude by briefly discussing limitations, some latest advances, future directions, and possible links with Statistical Physics.

Transformers are the type of neural networks that has revolutionised natural language processing and protein science. Their key building block is a mechanism called self-attention which is trained to predict missing words in sentences. Despite the practical success of transformers in applications it remains unclear what self-attention learns from data, and how. Here, we give a precise analytical and numerical characterisation of transformers trained on data drawn from a generalised Potts model with interactions between sites and Potts colours. While an off-the-shelf transformer requires several layers to learn this distribution, we show analytically that a single layer of self-attention with a small modification can learn the Potts model exactly in the limit of infinite sampling. We show that this modified self-attention, that we call ``factored'', has the same functional form as the conditional probability of a Potts spin given the other spins, compute its generalisation error using the replica method from statistical physics, and derive an exact mapping to pseudo-likelihood methods for solving the inverse Ising and Potts problem.

I will recall the genesis of the concept of multiple equilibria in natural sciences. I will then describe my contribution to the development of this concept in the framework of statistical mechanics. Finally, I will briefly mention the cornucopia of applications of these ideas both in physics and in other disciplines.

In this talk, I will summarize the many ideas that have been proposed in our community to connect algorithmic thresholds to the structure of the solutions space in random constraint satisfaction problems. In particular, I will present some recent results showing how the reweighting of the solution space can modify the phase diagrams, postponing algorithmic barriers, and can be used to infer to correct location of the algorithmic threshold in some models.

A general inference problem requires one to extract a hidden signal from a noisy dataset. In most inference problems, the signal can be detected by optimizing a proper high-dimensional function. Algorithms for optimization based on Monte Carlo methods are known to be robust and widely applicable. However, their performances in prototypical hard inference problems are not known in general. I will look at the limits and the performances of algorithms based on Monte Carlo (MC) methods for a prototypical problem: the planted coloring problem. I will show that MC algorithms are suboptimal in the recovery of the planted solution because they get attracted by glassy states that, instead, do not influence optimal message passing algorithms. I will propose an analytic estimation for the MC algorithmic threshold, confirmed by numerical simulations.I will then study an improved version of MC where several coupled replicas evolve together, showing analytical predictions and numerical evidence that the algorithmic threshold in this case coincides with the Bayes-optimal one. These findings support the idea that mismatching the parameters in the prior with respect to those of the generative model may produce an algorithm that is optimal and very robust.

Distributions of high-dimensional data can be learnt with unsupervised architectures, such as restricted Boltzmann machines (RBM). However, the resulting models are often uneasy to sample when the data distributions include multiple modes. I here consider deep tempering, a parallel tempering-like Monte Carlo sampling algorithm based on a chain of several restricted Boltzmann machines (RBM), where hidden configuration of a machine can be exchanged with the visible configurations of the next one along the chain. Replica exchanges between the different RBM is facilitated by the increasingly clustered representations learnt by deeper RBMs along the chain, allowing for fast transitions between the different modes of the data distribution. I will explain why deep tempering works on hierarchical data, and introduce a theoretical framework to understand how hyperparameters, such as the aspect ratios of the RBMs and the weight regularization should be chosen.

Adiabatic quantum annealing (AQA) is a quantum version of simulated annealing and is one of the potentially promising methods to obtain quantum speed up over classical methods for combinatoric optimization problems. AQA maintains a quantum system in the ground state of a Hamiltonian while slowly changing the Hamiltonian through a control parameter z. This procedure allows to change the system from a trivial initial ground state to a ground state that encodes the solution to the combinatoric optimization problem. The time complexity of the method is determined by the so-called minimal spectral gap, which occurs when the system goes through a phase transition at a critical value of the control parameter z*. The smaller the gap, the slower the annealing and the longer the time complexity. We study a class of AQA protocols for which we can analytically compute the minimal spectral gap as O(1/sqrt(N)) with N the total number of configurations of the problem. We also obtain an analytic expression for z* as a partition sum. For some problems, such as Grover search, z* can be efficiently computed and we can design an annealing schedule (how z changes with time) such that a quadratic speed up is obtained: the time complexity of AQA is O(sqrt(N), while a classical method would require O(N) time. However, in general z* is intractable to compute, making an efficient AQA design unfeasible for most practical combinatoric optimization problems. We conjecture that it is likely that this negative result also applies for any other instance independent transverse Hamiltonians.

Asymmetry in the synaptic interactions between neurons plays a crucial role in determining the memory storage and retrieval properties of recurrent neural networks. In this work, we analyze the problem of storing random memories in a network of neurons connected by a synaptic matrix with a definite degree of asymmetry. We study the corresponding satisfiability and clustering transi- tions in the space of solutions of the constraint satisfaction problem associated with finding synaptic matrices given the memories. We find, besides the usual SAT/UNSAT transition at a critical number of memories to store in the network, an additional transition for very asymmetric matrices, where the competing con- straints (definite asymmetry vs memories storage) induce enough frustration in the problem to make it impossible to solve. This finding is particularly striking in the case of a single memory to store, where no quenched disorder is present in the system.

The landscape properties of deep neural networks (DNNs) can completely affect performances both in optimization and prediction tasks. In turn, the overparameterized nature of the models themselves can smooth the highly non-convex landscapes, promoting algorithmic convergence whose learning dynamic doesn't seem to be characterised by barrier-crossing. Within this framework, I am going to present some recent works using methods from statistical physics to target solutions in the landscape that are highly attractive for the learning algorithms. I will refer to different NNs architectures in classification settings, showing that despite being non-rigorous, the method proves efficient in predicting the hardness algorithmic threshold of binary models. For these, the problem is algorithmically feasible at low constraint density thanks to the existence of a subdominant number of clustered solutions in the space of parameters, atypical with respect to the equilibrium measure. Hence, following their geometrical rearrangement when increasing the number of parameters can identify an atypical phase transition for the convergence of algorithms. It is induced by overparameterization and affects generalization performances. Since the transition coincides with the continuous breaking up of these dense clusters, to provide a comprehensive view, I will enforce the discussion in the end for an example of non-convex continuous model (i.e. the negative perceptron), showing that robustness of solutions correlates with geodesic connectivity. Consistently with the picture so far, as long as atypical solutions are connected by zero-energy paths, algorithms sampling robust solutions drift towards the clustered region.

Proliferating cells couple nutrient and environment sensing to growth. Recent work in bacteria has highlighted how for steady-growing cells this behavior leads to emergent macroscopic "growth laws" linking growth to cellular resource allocation. However we still know very little on this emergent behavior. For example, we lack an understanding on how cells couple nutrient sensing to resource allocation. Such mechanistic aspects of the regulation of cell growth are revealed by understanding the phase diagram of the limiting processes, by perturbations of the equilibrium “balanced growth” conditions, and by looking at the behavior of single-cells. This talk will cover our recent work in these directions, showing in particular that (i) nutrient sensing and transcriptional regulation of ribosome biogenesis naturally lead to oscillatory behavior, (ii) while ribosome autocatalysis sets the growth rate, total mRNA can affect growth by determining the amount of free ribosomes and (iii) single cell growth rates are not self-averaging. Such findings highlight the necessity of a statistical physics theory of cellular growth.

A goal of unsupervised machine learning is to build representations of complex high-dimensional data, with simple relations to their properties. Such disentangled representations make it easier to interpret the significant latent factors of variation in the data, as well as to generate new data with desirable features. The methods for disentangling representations often rely on an adversarial scheme, in which representations are tuned to avoid discriminators from being able to reconstruct information about the data properties (labels). Unfortunately, adversarial training is generally difficult to implement in practice. In this talk, I will describe a simple, effective way of disentangling representations without any need to train adversarial discriminators, and apply our approach to Restricted Boltzmann Machines, one of the simplest representation-based generative models. Our approach relies on the introduction of adequate constraints on the weights during training, which allows us to concentrate information about labels on a small subset of latent variables. The effectiveness of the approach is illustrated with four examples: the CelebA dataset of facial images, the two-dimensional Ising model, the MNIST dataset of handwritten digits, and the taxonomy of protein families. In addition, we show how our framework allows for analytically computing the cost, in terms of the log-likelihood of the data, associated with the disentanglement of their representations.

Gathering data from computer simulations is becoming increasingly easy as our available computational power keeps growing; the same goes for data collected from sources such as mobile phones, website traffic, internet of things and so on. While hoarding data is thus "easy", making sense of them is a fully different story. In this talk I will present methods developed in our group that aim at extracting information from data by leveraging reduced representations, that is, by looking at the system under examination in terms of a wisely chosen subset of its constituents. These methods, whose underpinnings take the moves from the theory of bottom-up coarse-grained modelling in soft matter, find easy and useful application in a range of cases spanning from computational biophysics to neural networks, passing through the stock market.

The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical states may indeed disappear,particles cannot, unless such degradation happens physically and should,thus, be accounted for explicitly. In this talk, I will describe a simple,yet general idea that allows one to derive the appropriate boundary conditions self-consistently from the (bio)chemical reaction scheme and the geometry of the physical reaction boundaries. This idea leads to physical insight that that could not be accessed through standard treatments and holds the potential to unveil new knowledge across a wide range range of systems, especially for what concerns the stochastic thermodynamics of cell sensing and intracellular signaling. ReferencesFrancesco Piazza, The physics of boundary conditions in reaction–diffusion problems, J. Chem. Phys. 157, 234110 (2022)

Recent advances in network science include the discovery that hyperbolic geometry captures the complex connectivity of real networks. Within this paradigm, we have been developing model-based methods for exploring their multiscale nature and their intrinsic dimensionality. More specifically, we produced a renormalization group technique  that progressively coarse-grains and rescales networks, revealing a hierarchy of layers at different resolutions. We found that the multiscale shells of real networks, such as connectomes of the human brain, exhibit self-similarity across multiple scales. This symmetry is also evident in the growth of some real networks, suggesting that evolution can be modeled by a reverse renormalization process. In addition, geometric renormalization has practical applications, allowing us to produce scaled down and scaled up replicas of real networks. Our results were obtained by embedding real networks in two-dimensional hyperbolic space, but we have also developed a method to infer their intrinsic dimensionality since there is not fundamental reason to believe that it must be two. Our analysis has revealed ultra low dimensionality and unexpected regularities across different domains, such as extremely low dimensionality in tissue-specific biomolecular networks, close-to-three-dimensional brain connectomes, and slightly higher dimensionality in social networks and the Internet.

The impact of symmetries and conservation laws on the dynamics of physical systems cannot be overstated, and spin systems are no exception. Not only conservation laws can change the low-temperature dispersion relations, but they can also radically change the dynamical criticalexponents.In dealing with systems where conservation laws are deeply relevant for the dynamics, the numerical integration of the reversible, Hamiltonian equations of motion is one of the most important methods. However, in order to make use of the theoretical framework of statistical mechanics, we always need to introduce fluctuations, and the usual way to employ a thermal bath in the equations of motion doesn't satisfy conservation laws existing for purely Hamiltonian dynamics.A new stochastic conservative thermostat is therefore introduced, which relaxes the energy of the system while still preserving the constant of motion.We tested the thermostat on the Heisenberg antiferromagnet in d = 3 and show that the method reproduces the correct values of the static and dynamic critical exponents, as well as the correct spin wave phenomenology at low temperatures.Finally, we show that the relaxational coefficient of the new thermostat is quantitatively connected to the microscopic parameters of an underlying model which produces fluctuations through lattice vibrations (phonons) coupled with the spin variables.

The weak ergodicity breaking hypothesis postulates that out-of-equilibrium glassy systems lose memory of their initial state despite being unable to reach an equilibrium stationary state. It is a milestone of glass physics, and has provided a lot of insight on the physical properties of glass aging. Despite its undoubted usefulness as a guiding principle, its general validity remains a subject of debate. I will present evidence that this hypothesis does not hold for a class of mean-field spin glass models.

The presence of knots has been observed in a small fraction of single-domain proteins and related to their thermodynamic and kinetic properties. Here, we will discuss how other entangled motifs, which generalize to open curves the notion of the concatenation of two closed curves, emerge in protein structures in a variety of contexts, being much more common than knots. Within this approach, entanglement is quantified by a generalization of the linking number to open discretized curves that we call Gaussian entanglement, a continuous index. For example, if all overlapping fragments of the same protein chain are considered, with one fragment looping between two contacting residues, their maximum Gaussian entanglement is a good predictor of the folding time, when experimental data sets of two-state and multi-state folders are analyzed. We will discuss how the 20% of domain-swapped dimers are concatenated, and how loops significantly intertwined with another chain fragment appear in 32% of protein domains and in 20% of trans-membrane protein domains. A specific signature of membrane proteins emerge when considering the chirality of entangled motifs. Finally we will investigate the role of entanglement in shaping folding kinetics, analyzing simulations of a coarse-grained, structure-based model. Despite its small size, a natively entangled antifreeze RD1 protein displays a rich refolding behavior, populating two distinct kinetic intermediates: a short-lived, entangled, near-unfolded state and a long-lived, non-entangled, near-native state. We will discuss how this fits the general idea that energetic frustration is introduced between the end residues of entangled loops to counter topological frustration, as verified also within toy lattice models.

Sea robins are fishes with sensory appendages (�legs�) that they use to walk and to dig live prey from within the substrate. Their predation strategy is so effective that they are often followed by other fish trying to steal their prey. I will discuss a set of behavioral experiments suggesting that these animals take advantage of sensory information from the water column as well as on sand. This �alternating� behavior, sampling sensory cues on substrates vs in the bulk of fluids, is well documented in rodents and dogs, suggesting that animals integrate both fluid-borne and substrate cues into a multi-modal navigation strategy. What dictates alternation between these two sensorimotor modalities in the context of olfactory navigation? I will switch from experiments to theory for olfactory navigation in turbulent flows. I will show optimal search strategies obtained through machine learning. Efficient searchers do indeed alternate between sampling the substrate and the bulk. Far from the target, the searcher is most likely to rely on bulk odors as the search is information limited. The exact moment when the searcher switches between substrate and bulk is dictated by a marginality condition that stems from an emergent cast-and-surge behavior that optimal searchers undertake. If time allows I will discuss ongoing work that uses temporal memory instead of spatial memory.

The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we propose and investigate a generalization of the standard setting that we name "Random-Features Hopfield Model". Here P binary patterns of length N are generated by applying to Gaussian vectors sampled in a latent space of dimension D a random projection followed by a non-linearity.Using the replica method from statistical physics, we derive the phase diagram of the model in the limit P,N,D to infinity with fixed ratios P/N and D/N. Besides the usual retrieval phase, where the patterns can be dynamically recovered from some initial corruption, we uncover a new phase where the features characterizing the projection can be recovered instead. We call this phenomena the "learning phase transition", as the features are not explicitly given to the model but rather are inferred from the patterns in an unsupervised fashion.

Using the path integral representation of the nonequilibrium dynamics, we compute the most probable path between arbitrary starting and final points that is followed by an active particle driven by persistent noise. We focus our attention on the case of active particles immersed in harmonic potentials, where the trajectory can be computed analytically. Once we consider the extended Markovian dynamics where the self-propulsive drive evolves according to an Ornstein-Uhlenbeck process, we can compute the trajectory analytically with arbitrary conditions on position and self-propulsion velocity. We test the analytical predictions against numerical simulations and we compare the analytical results with those obtained within approximated equilibrium-like dynamics.

In this work, we compute analytically the effect of training on the internalrepresentations of a Bayesian one-hidden layer neural network at finite-width,using the theoretical framework introduced in [1]. In particular, we investigatehow the kernel matrix related to these internal representations changes aftertraining. We observe that the kernel matrix elements differ from the infinitewidth ones by terms of order O(1/N) and we precisely compute this correction.We perform numerical experiments to validate our predictions using Gaussiandata, both with random labels and in a teacher-student setting and we presentpreliminary experiments with regression tasks from the CIFAR10datasets. [1] S Ariosto, R Pacelli, M Pastore, F Ginelli, M Gherardi, and P Rotondo.Statistical mechanics of deep learning beyond the infinite-width limit. arXivpreprint arXiv:2209.04882, 2022.

We study the stochastic version of the Wilson-Cowan model of neural dynamics, where the response function of neurons grows faster than linearly above the threshold, representing a cooperative effect of different synaptic inputs. The model shows a region of parameters where two attractive fixed points of the dynamics exist simultaneously, corresponding to lower and higher activity, and the dynamics switches between them as observed in up and down states of cortical neurons. Along with alternation of states, the model displays a bimodal distribution of the avalanches of activity, with a power law behavior corresponding to the state of low activity, and a bump of very large avalanches due to the high activity state. The bistability is due to the presence of a first order (discontinuous) transition in the phase diagram, and the observed critical behavior is connected with the line where the low activity state becomes unstable (spinodal line).

Decades-long literature testifies to the success of statistical mechanics at clarifying fundamental aspects of deep learning.Yet the ultimate goal remains elusive: we lack a complete theoretical framework to predict practically relevant scores, such as the train and test accuracy, from knowledge of the training data.Huge simplifications arise in the infinite-width limit, where the number of units N_l in each hidden layer (l=1,..., L, being L the finite depth of the network) far exceeds the number P of training examples.This idealisation, however, blatantly departs from the reality of deep learning practice, where training sets are larger than the widths of the networks. Here, we show one way to overcome these limitations.The partition function for fully-connected architectures, which encodes information about the trained models, can be evaluated analytically with the toolset of statistical mechanics.The computation holds in the ''thermodynamic limit'' where both N_l and P are large and their ratio alpha_l = P/N_l, which vanishes in the infinite-width limit, is now finite and generic.This advance allows us to obtain(i) a closed formula for the generalisation error associated to a regression task in a one-hidden layer network with finite alpha_1;(ii) an approximate expression of the partition function for deep architectures (technically, via an ''effective action'' that depends on a finite number of ''order parameters'');(iii) a link between deep neural networks in the proportional asymptotic limit and Student's t processes;(iv) a simple criterion to predict whether finite-width networks (with ReLU activation) achieve better test accuracy than infinite-width ones.As exemplified by these results, our theory provides a starting point to tackle the problem of generalisation in realistic regimes of deep learning.

Network science offers powerful tools to model real complex systems. Here we report a comprehensive analysis of the robustness of real-world complex weighted networks to errors and attacks toward nodes and links. We use measures of the network damage conceived for a binary and a weighted network structure. We find that removing a very small fraction of nodes and links with respectively higher strength and weight triggers an abrupt collapse of the weighted functioning measures while measures that evaluate the binary-topological connectedness are almost unaffected. Complex networks are the preferential framework to model spreading dynamics in several real-world complex systems. We numerically simulated, via a type-SIR model, epidemic outbreaks spreading on 50 real-world networks, and we then tested which NSIs, among 40, could a priori better predict the disease fate. We found that the i) "average normalized node closeness" and the "average node distance" are the best predictors of the initial spreading pace, and that ii) indexes of "topological complexity" of the network, are the best predictors of both the value of the epidemic peak and the final extent of the spreading. Furthermore, commonly used NSIs are unreliable predictors of the disease spreading extent in real-world networks.

In turbulence it has been widely shown that the energy transfer across different scales can be envisioned as a Langevin process. In the case of plasmas, the dynamical variables of such a Langevin process are represented by electromagnetic and velocity field fluctuations. For weakly-collisional plasmas, e.g., space plasmas, this scenario has been shown to be consistent with observations at both inertial and sub-ion scales. One of the striking features of the turbulent dynamics at scales below typical ion lengths is the “convergence” of the statistics towards a shape-invariant distribution of electromagnetic/velocity field fluctuations. In this work we show that in the non-diffusive limit of the Langevin equation it is then possible to derive a scaling law which presents a remarkable agreement with both satellite observations and numerical simulations of plasma turbulence. This allows us to establish a link between the Langevin-drift term and the scaling exponents of sub-ion scale fluctuations.

Generative Autoregressive Neural Networks (ARNN) have recently demonstrated exceptional results in image and language generation tasks, contributing to the growing popularity of generative models in both scientific and commercial applications. This work presents a physical interpretation of the ARNNs by reformulating the Boltzmann distribution of binary pairwise interacting systems into autoregressive form. The resulting ARNN architecture has weights and biases of its first layer corresponding to the Hamiltonian's couplings and external fields, featuring widely used structures like the residual connections and a recurrent architecture with clear physical meanings. Moreover, its architecture's explicit formulation allows using statistical physics techniques to derive new ARNNs for specific systems. As examples, new effective ARNN architectures are derived from two well-known mean-field systems, the Curie-Weiss and Sherrington-Kirkpatrick models, showing superior performances in approximating the Boltzmann distributions of the corresponding physics model compared to other commonly used architectures. The connection established between the physics of the system and the neural network architecture provides a way to derive new architectures for different interacting systems and interpret existing ones from a physical perspective.

Explainable and interpretable unsupervised machine learning helps understand the underlying structure of data. We introduce an ensemble analysis of machine learning models to consolidate their interpretation. Its application shows that restricted Boltzmann machines compress consistently into a few bits the information stored in a sequence of five amino acids at the start or end of alpha-helices or beta-sheets.The weights learned by the machines reveal unexpected properties of the amino acids and the secondary structure of proteins: (i) His and Thr have a negligible contribution to the amphiphilic pattern of alpha-helices; (ii) there is a class of alpha-helices particularly rich in Ala at their end; (iii) Pro occupies most often slots otherwise occupied by polar or charged amino acids, and its presence at the start of helices is relevant; (iv) Glu and especially Asp on one side, and Val, Leu, Iso, and Phe on the other, display the strongest tendency to mark amphiphilic patterns, i.e., extreme values of an effective hydrophobicity, though they are not the most powerful (non) hydrophobic amino acids.

Coupled oscillators have a wide range of applications in statistical mechanics. Often, systems under study might present several scales of description. In this case, each unit of the system might be as well composed by a finite number of oscillators. However, standard mean-field theories only deal with populations in the thermodynamic limit, which lead to deterministic solutions for the order parameters. In this talk, I will introduce a novel approach to tackle this problem, which applies to any population of oscillators subject to stochastic white noise. I will apply the theory to the stochastic Kuramoto model deriving formally the multiplicative noise emerging in the mesoscopic limit, as well as finding deterministic finite-size corrections. I will show how these results allow us to derive, for the first time, almost-exact closed solutions for the stochastic Kuramoto model, as well as new insights in the critical transition to synchrony.

A novel model to automated classification is introduced which exploits a fully trained discrete map steer items belonging to different categories toward distinct final state. These latter are incorporated into the model by taking advantage of the spectral decomposition of the operator that rules the linear evolution across the processing network. Non-linear terms are confined to a part of the network and allow to disentangle the data supplied as initial condition to the discrete dynamical system. The shape of the eigenvectors allows information to flow from the nonlinear part of the network to the linear part, where the output is read. The eigenvalues associated with the final states can be both real (RSN) and complex (C-RSN). In the second case the final state will turn out to be a not trivial function of time. The network can be equipped with several memory kernels which can be sequentially activated for serial datasets handling. Our novel approach to classification is successfully challenged against a standard dataset for image processing training.

The distinguishing feature of 3D turbulent flows is the onset of energy fluxes directed, on average, from the large forcing scale to the small dissipating one, i.e. from low to high wave numbers: a scenario called “direct energy cascade”. From a statistical mechanics point of view the cascade picture prevents the existence of detailed balance, thereby turbulent models, specifically simplified ones, are well suited to be tested and studied with the techniques of non-equilibrium statistical physics.In this talk we aim at characterizing the non-equilibrium properties of turbulent cascades in the SABRA shell model in two different ways . One is by observing how the irreversible character of the energy fluxes is revealed by a specific antisymmetric combination of time-correlation functions. The other by showing how significantly different the relaxation behavior of an energy perturbation is, when measured at scales smaller or larger than the perturbed one.

The heliosphere's space plasmas are in a turbulent state. Magnetic field fluctuations exhibit a power-law spectrum at large scales, or at frequencies lower than 0.1–1 Hz, with spectral exponents that are similar to those predicted by theories of fluid-like turbulence. The inertia of ions decouples from that of electrons at scales smaller than the ion-inertial length, or ion/sub-ion scales, and the spectrum of the magnetic field fluctuations exhibits a distinct dynamical regime that is yet not fully understood. By recasting the scale-to-scale coupling in this domain in terms of a stochastic Langevin-like dynamics, we provide recent results on the Markovian characteristics of the fluctuations at these scales. At sub-ion scales, a simple/global scale invariance indicates that the stochastic redistribution of energy plays a minor role.

Field Programmable Gate Arrays (FPGAs) are commonly used in physics experiments nowadays both in backend and in frontend detectors. Their endurance in radiation environment, their flexibility and their speed make them perfect candidates for experiments in high energy physics. We are exploiting a FPGA to perform image acquisition and we employ a neural network for continuous learning in a particle environment, specifically for image recognition. The purpose is to witness the physical damages and the corresponding ones inside the parameters of the network.It has been implemented using the FINN project (arXiv:1612.07119), a framework used for the implementation of neural networks on FPGAs handling optimal resource consumption. Particles interacting with cameras generate noise in the images acquired, inducing repercussions in the training and testing sessions of the network. We made a study concerning the effects of the noise with different implementations, fitting with real-life patterns, motivated by the work in arXiv:1803.08823 and we witness the corresponding consequences of such an effect in the training and testing parts.Due to the limited resources present on FPGAs, the network implemented using the FINN project incorporates a lightweight architecture. Thus, we optimize this architecture with respect to the inverse temperature criterion as presented in 10.1007/s00023-021-01027-2 and study the system changing the topology of the network but maintaining fixed the total number of neurons.

Spontaneous synchronization is a collective phenomenon that can be observed in many-body interacting systems across many different fields.With the recent advancements in the field of quantum technologies, synchronization can now be observed in the quantum regime. Understanding this collective phenomenon in the quantum realm has become increasingly important, and theoretical models are still lacking.In the classical case, a prototypical example of synchronization is given by the Kuramoto Model, a model describing a system of interacting rotors. Its phase diagram supports both a dynamically disordered phase and a synchronized one. In this poster, I will propose a generalization of this model to the quantum realm, the Quantum Kuramoto Model. I will present how to build the quantum model and how it behaves, focusing on the differences between the classical and quantum regimes.

In the ac-driven sine-Gordon model, thermal noise is shown to be crucial for localizing energy into breather states. We indeed observe the emergence of remarkably stable breathers locked to the external drive, if the temperature is high enough. The energy spatial correlations, which display a nonmonotonicity versus the thermal noise strength, provide an intuitive statistical measure of the phenomenon. In further confirmation of the key role of noise as a control parameter, the breather generation probability also behaves nonmonotonically against the noise intensity. Then, we discuss the reliability of the approach for different breathing frequencies, as well as the influence of both topology and noise on the full counting statistics of the number, position, and amplitude of the excited breathers. With applications ranging from seismology and biology to high-Tc superconductivity and quantum Josephson electronics, mastering the physics of sine-Gordon breathers is a critical research task. Here, we exploit our findings to face a long-unsolved challenge in nonlinear science, i.e., we propose a resistive switching experiment for detecting breathers in long Josephson junctions.Reference: D. De Santis, C. Guarcello, B. Spagnolo, A. Carollo, D. Valenti, Chaos, Solitons and Fractals 170 113382 (2023)

The interplay between a deterministic quantum evolution and a series of measurement processes can lead to a sudden change in the entanglement properties of a system, known as a measurement-induced phase transition (MIPT). Quantum Fisher information (QFI) measures the sensitivity of a quantum system to small changes in a parameter and is widely used to detect quantum phase transitions in different situations. It is natural to inquire whether QFI can also be employed to identify phase transitions driven by measurement processes. The distinctive characteristic of an MIPT is the abrupt alteration in the system's entanglement properties, typically assessed using entanglement entropy. However, with an appropriate metrological scheme, QFI not only detects entanglement but also provides more informative measurements than entanglement entropy. QFI detects multipartite entanglement and specifically highlights the presence of useful metrological entanglement. We show that QFI can distinguish among different phases in a MIPT for a non-Hermitian one-dimensional Ising chain and show the presence of a divergence of QFI at the critical point.

Diego Febbe (1), Riccardo Mannella (1), Riccardo Meucci (2), Angelo Di Garbo (3,1)(1) Dipartimento di Fisica dell’Università di Pisa, Pisa (Italia)(2) CNR – Istituto Nazionale di Ottica, Firenze (Italia)(3) CNR – Istituto di Biofisica, Pisa (Italia)This study presents a new mathematical model for a relaxation oscillator implemented using a unipolar junction transistor (UJT). The model is represented by a system of differential equations capable of reproducing the main features of experimental data. Then, the model was studied theoretically within the framework of nonlinear dynamical systems and the corresponding results were found to be in keeping with the numerical ones. In addition, the simulation show that when this dynamical system is subject to periodic modulation or to coupling, with an identical oscillators, chaotic dynamical regimes occur, in agreement with the experimental results.

Polymer translocation has long been a topic of interest in the field of biological physics given its relevance in both biological (protein and DNA/RNA translocation through nuclear and cell membranes) and technological processes (nanopore DNA sequencing, drug delivery).This contribution reports some recent results of the translocation of a semiflexible homopolymer through an extended pore driven by an end-pulling force applied to the polymer head. Similarly to pore-driven configurations, the end-pulled set-up presents regions of optimum in the mean translocation times as a function of the frequency of the driving –this latter applied either longitudinal to the pore or transversal to it– which are typical of the resonant activation effect. These minima are present for all the polymer rigidities studied, and reveal a linear relation between the optimum translocation time and the corresponding driving period independent of the parameter values.The end-pulling driving, that mimics the optical or magnetic force application, has the potential to evidence specific features of either a nucleic- or amino- acid chains that the translocating polymer model aims to depict, making it a feasible candidate for a valid sequencing method.BibliographyA. Fiasconaro, J.J. Mazo, and F. Falo, Phys. Rev. E 82, 031803 (2010)J.A. Cohen, A. Chaudhuri, and R. Golestanian, Phys. Rev. Lett. 107, 238102 (2011)A. Fiasconaro, J.J. Mazo, and F. Falo, J. Stat. Mech. Theory Exp. P11002 (2011)T. Ikonen, J. Shin, W. Sung, and T. Ala-Nissila, J. Chem. Phys. 136, 205104 (2012)A. Fiasconaro, J.J. Mazo, and F. Falo, New Journal of Physics 14, 023004 (2012)J.R. Moffitt, Y.R. Chemla, K. Aathavan, …, and C. Bustamante, Nature 457, 446 (2009)J.R. Moffitt, Y.R. Chemla and C. Bustamante, Proc. Natl. Acad. Sci. USA 107, 15739 (2010)A. Fiasconaro, J.J. Mazo, and F. Falo, Phys. Rev. E 91, 022113 (2015)A. Fiasconaro, J.J. Mazo, and F. Falo, Sci. Rep. 7, 4188 (2017)A. Fiasconaro, and F. Falo, Phys. Rev. E 98, 062501 (2018)A. Fiasconaro, G. Díez-Señorans, and F. Falo, Polymer 259, 125305 (2022)A. Sáinz-Agost, A. Fiasconaro, and F. Falo, Submitted (2023)

The study of water in solutions plays a key role in the research regarding water anomalies both because aqueous solutions are naturally found in large quantities and because the experimental conditions under which many thermodynamic quantities are measured are more complicated to achieve for bulk water. Here we show the calculations of the phase diagrams of sodium perchlorate solutions in supercooled water derived through molecular dynamics numerical simulations. These solutions are relevant due to the recent experimental evidences of liquid water in perchlorate solutions beneath the Martian soil. By modelling water using the TIP4P/2005 potential, we obtain an agreement with the hypothesis of existence of a second order liquid-liquid phase transition where the liquid-liquid critical point shifts to slightly higher temperatures and lower pressures. By investigating the structure of the systems, we find that even at the highest concentrations considered, water retained its anomalous behaviour.

Active systems, due to the local breaking of equilibrium, allow for phenomena that their equilibrium counterparts cannot attain. This correspondence between microscopic local equilibrium breaking and the meso/macroscopic structure formation is a general feature that have been observed in diverse systems including bacteria and synthetic swimmers. A similar behaviour can be observed also in the case of polar active polymers, i.e. polymers made of active monomers whose activity is directed as the local tangent to the polymer backbone. For example, a coil-to-globule-like transition takes place for isolated active chains in three dimension, highlighted by a marked change of the scaling exponent of the gyration radius[1]. Driven by the relevance of confinement and topology on the structural and dynamical properties of passive systems, we investigate the interplay between these latter and activity for tangentially active polymers. We explore the dynamics of active polymers in corrugated channels, highlighting the differences with respect to the passive case[2]. In the bulk, isolated rings display two different regimes at high enough activity: short rings tend to become ”stiffer” and to assume a disk-like conformation, whereas long rings collapse, forming tight structures that show the hallmarks of dynamical arrest[3]. Finally, when placed under confinement, suspensions of short active rings assemble in ordered phases [4].References[1] V. Bianco, E. Locatelli, and P. Malgaretti, Phys. Rev. Lett. 121, 217802 (2018).[2] J. Marti Roca, E. Locatelli, V. Bianco, P.Malgaretti and C. Valeriani, in preparation[3] E. Locatelli, V. Bianco, and P. Malgaretti, Phys. Rev. Lett. 126, 097801 (2021).[4] J.P. Miranda, E. Locatelli and C. Valeriani, in preparation

Unsupervised Machine learning with Boltzmann machines is the inverse problem of finding a suitable Gibbs measure to approximate an unknown probability distribution from a training set consisting of a large amount of samples. The minimum size of the training set necessary for a good estimation depends on both the properties of the data and of the machine. We investigate this problem in a controlled environment where a Teacher Restricted Boltzmann machine (T-RBM) is used to generate the dataset and another student machine (S-RBM) is trained with it. We consider different classes of unit priors and weight regularizers and we analyze both the informed and mismatched cases, viewed as the amount of information the student receives about the teacher model. We describe the results in terms of phase transitions in the posterior distribution, interpreted as a statistical mechanics system.In the analysis we give special attention to the Hopfield model case where it is possible to observe the differences between memorization and learning regimes. In particular, when data become large and confused the learning methodology overcomes memorization.References:Hopfield model with planted patterns: a teacher-student self-supervised learning model- Alemanno, F., Camanzi, L., Manzan, G., Tandari, D. (2023). arXiv:2304.13710.Phase diagram of restricted Boltzmann machines and generalized Hopfield networks with arbitrary priors- Barra, A., Genovese, G., Sollich, P., & Tantari, D. (2018). Physical Review E, 97(2), 022310.Phase transitions in restricted Boltzmann machines with generic prios- Barra, A., Genovese, G., Sollich, P., & Tantari, D. (2017). Physical Review E, 96(4), 042156.Restricted Boltzmann machine: Recent advances and mean-field theory- Decelle, A., & Furtlehner, C. (2021). Chinese Physics B, 30(4), 040202.On the equivalence of Hopfield networks and Boltzmann Machines- Barra, A., Bernacchia, A., Santucci, E., & Contucci, P. (2012). Neural Networks, 34, 1-9. Statistical Mechanics of Neural Networks-Huang, H. (2022). Springer. Theory of neural information processing systems -Coolen, A.C., Kühn, R. and Sollich, P. (2005). OUP OxfordStatistical physics of spin glasses and information processing: an introduction (No. 111)-Nishimori, H., 2001 Clarendon Press.

We study a lattice model in d dimensions for a system of multiple self- (and mutally-) avoiding chains. A bending rigidity and a non-consecutive nearest-neighbour monomer-monomer interaction are accounted for as well. First, we present an exact field-theoretical representation of the gran canonical partition function (based on the analogy between SAWs on a lattice and the O(n -> 0) model of a magnet) in the ensemble in which nor the total number of bonds nor the total number of chains is fixed. We then give a mean-field estimate of such partition function by means of a uniform saddle-point approximation, and hence derive expressions for physical observables. We find a discontinuity in the total monomer density as a function of the bond and chain fugacity, revealing the presence of a gas - liquid transition. All the results are compared with Monte Carlo computer simulations, showing a remarkable agreement. Lastly, we provide an expression for the free energy variation upon mixing, and discuss how our findings relate to the classical Flory-Huggins theory for polymer solutions.

We consider the four-vertex model, which is a special case of the six-vertex model in which two vertices are set to zero. Under specific choices of fixed boundary conditions, this model exhibits spatial phase separation, between frozen and disordered regions, sharply separated by a smooth curve, known as arctic curve. The most interesting aspect of the four-vertex model is that, even though it is interacting, it is still exactly solvable in a relatively simple way. Here we use the Tangent Method, which is an exact, although heuristic method, to compute the arctic curve.

An increasing amount of structural information about the protein capsid of viruses has been collected and is now available in the Protein Data Bank; yet, the intrinsically disordered nature of viral ssRNA structures poses a challenge for experimentalists, this being critical on account of the impact that the RNA structure has on its function. In this concern, molecular dynamics simulations might be powerful tools to achieve (putative) structural and dynamical insights on the behaviour of systems that are poorly characterized.In this poster, I will discuss the main results of our ongoing project on the development of new methodologies to characterize the unrestrained dynamics of a viral RNA fragment as well as under spatial constraints mimicking the protein capsid around it. I will then show the performance of simulating a trimer (the basic building block of the capsid) with an implicit solvent model with an in-house developed multi-resolution model. I will also describe a simple and general protocol to generate an initial configuration of the whole virion particle to perform all-atom MD simulations, starting from a PDB structure of the capsid and the sequence of the RNA fragment. This approach will provide detailed information about the structure and dynamics of the viral RNA, involving a description of the interactions between the nucleotides and the tails of the capsid, which is hardly explorable via experimental techniques. Finally, I will show some preliminary results obtained by simulating the virion and the capsid at atomistic resolution.

Quantum computing is attracting a lot of attention for its potential to greatly speed-up some computations and to perform efficient simulations of the dynamics of quantum systems. Among all the possible platforms, integrated linear optics allows for the realization of a compact device that operates at room temperature, exploiting boson statistics to perform quantum simulations and computations. EPIQUS (Electronic-Photonic Integrated QUantum Simulator) aims to build a reconfigurable, fully-integrated linear optical quantum hardware with single-photon sources and detectors. In this poster we describe the inner working of such a device, highlighting its capabilities as well as some of its shortcomings.

The steadily growing computing power has made vast amounts of high-throughput data available, opening new windows into complex systems such as cells, the brain, and human societies. However, while the staggering success of Artificial Intelligence and Machine Learning revealed the potential of neural networks, it also raised crucial theoretical questions about them, first and foremost: how does learning take place? In artificial neural networks, learning translates in tuning a large number of connection weights to minimise a loss function. The assumption of Gaussian i.i.d. inputs has been fundamental to the theoretical and computational study of high-dimensional learning; answering the question of whether and how far this hypothesis is restrictive has now become imperative. In our work we have taken advantage of enhanced sampling methods [1], developed in soft matter physics, to exhaustively explore the loss profile of networks with discrete weights, where the optimization landscape is severely rugged even for simple architectures. These tools have proven to be very powerful as they can be directly applied to real datasets, thus allowing us to explore the impact of dimensionality and structure of the data. In particular, we have investigated 4 widely used benchmark datasets: MNIST, FashionMNIST, CIFAR10 and MNIST1D. For each of them we analysed the role of the structure as well as the impact of the input-output correlation. Additionally, this approach enables us to prove whether or not the universality of linear classification with random labels [2] may be extended also in case of non-convex loss and for energetic states higher than the ground state. [1] Menichetti, R., Giulini, M., & Potestio, R. (2021). The European Physical Journal B, 94, 1-26.[2] Gerace, F., Krzakala, F., Loureiro, B., Stephan, L., & Zdeborová, L. (2022). arXiv preprint arXiv:2205.13303.

The relentless development of novel computer architectures and algorithms is steadily pushing forward the limits of the investigation of biological systems via "in silico" simulations. This process goes on par with an explosion in the amount of generated data, calling for the design of innovative and automated techniques able to rationalise the simulation outcomes and extract the biologically relevant insight out of them.In the analysis of such complex systems, the noise/signal discrimination quite often naturally passes through a coarse-grained filtering procedure in which, starting from the most detailed description available, a projection is performed that forces the system to be observed only in terms of a subset of its original degrees of freedom [1]---e.g., a fraction of atoms in a protein or of neurons in a neural network. While necessary for interpreting otherwise hardly-manageable high-dimensional datasets, this workflow results in a loss of statistical information on the system, loss that critically depends on the filter one selects to carry out the projection [2,3].In this work we discuss a recently introduced strategy aimed at identifying maximally informative simplified representations of a system that, despite a reduction in the observational level of detail, are capable of retaining the largest amount of information on the statistical properties of the high-resolution reference [3,4]. We apply this protocol to two very different classes of systems within the biological realm, namely proteins and memory-retrieving neural networks; in both cases, the resulting maximally informative representations are shown to single out biologically relevant regions of the system, either in the form of functional chemical fragments in the analysed protein, or in the form of strongly coupled neurons inside the synaptic matrix.Overall, these results demonstrate that this scheme can be successfully employed to extract crucial physicochemical information out of large simulation datasets in an unsupervised manner, further shedding light on the relation between coarse-graining and loss of statistical information.[1] M. Giulini, R.M. et al., Front. Mol. Biosci. 8 (2021).[2] J. F. Rudzinski and W. G. Noid, J. Chem. Phys. 135, 214101 (2011).[3] M. Giulini, R.M. et al., J. Chem. Theory Comput. 16, 6795 (2020).[4] R. Holtzman et al., Phys. Rev. E 106, 044101 (2022).

Double strand breaks (DSBs), i.e. the covalent cut of the DNA backbone over both strands, are a detrimental outcome of cell irradiation, bearing chromosomal aberrations and leading to cell apoptosis. In the early stages of the evolution of a DSB, the disruption of the residual interactions between the DNA moieties drives the fracture of the helical layout; in spite of its biological significance, the details of this process are still largely uncertain. Here, we address the mechanical rupture of DNA by DSBs via molecular dynamics simulations: the setup involves a 3855-bp DNA filament and diverse DSB motifs, i.e. within a range of distances between strand breaks (or DSB distance). By employing a coarse-grained model of DNA, we access the molecular details and characteristic timescales of the rupturing process. A sequence-nonspecific, linear correlation is observed between the DSB distance and the internal energy contribution to the disruption of the residual (Watson-Crick and stacking) contacts between DNA moieties, which is seemingly driven by an abrupt, cooperative process. Moreover, we infer an exponential dependence of the characteristic rupture times on the DSB distances, which we associate to an Arrhenius law of thermally-activated processes. This work lays the foundations of a detailed, mechanistic assessment of DSBs in silico, as a benchmark to both numerical simulations and data from single molecule experiments.

Financial markets are complex systems where many market participants act with different aims and needs. The overall behavior of the market depends by the interrelations of trading choices of market participants. We focus our attention on the category of households, confronting the trading choices of this wide category of market participants with other trading categories such as financial and non-financial companies. The data analyzed are obtained from the Euroclear clearing house that is the clearing house of the Nordic Stock Exchange. Data [1,2] cover the time span from January 1996 to December 2016 and cover the entire population of distinct Finnish legal entities. In our analysis, we compute semestral portfolios for each legal entity owning financial assets traded in the Nordic Stock Exchange. For the sake of simplicity, we chose to focus on the most liquid stocks, i.e., the ones included in the OMXH25 market index. We investigate heterogeneity of investors’ portfolios by quantifying the degree of concentration of each portfolio with the Herfindahl Index of it. The Herfindahl index is a measure of concentration, introduced in economics and widely used in many research areas.We compute the Herfindahl index [3] of portfolios of all Finnish households investing in the Nordic Stock Exchange on a semiannual basis for the entire time span of data. For the category of households, the mean value of the index decreases slowly but steadily over the years showing an increase of the diversification over the number of stocks selected in the portfolio over time. We compare the dynamics of the mean Herfindahl index with the dynamics of the overall portfolio owned by the category of households. Our analysis shows that the households’ market portfolio shows a different degree of heterogeneity than the one observed for the mean behavior of individual households. In fact, the aggregated portfolios for the households, which represent the largest category of investors, has a trend, over the years, that is similar to the aggregated portfolio of financial companies. This empirical observation suggests that households as an investors’ category distribute their resources in a way that is not too different form the distribution done by professionals. The different time profile of the Herfindahl index of portfolio of all the households and the mean Herfindahl index estimated portfolios of all of them, suggest that heterogeneity in wealth and asset selection is highly present in the households acting in this market.[1] Tumminello, M., Lillo, F., Piilo, J. and Mantegna, R.N., 2012. Identification of clusters of investors from their real trading activity in a financial market. New Journal of Physics, 14(1), p.013041.[2] Musciotto, F., Marotta, L., Piilo, J. and Mantegna, R.N., 2018. Long-term ecology of investors in a financial market. Palgrave Communications, 4(1), pp.1-1.[3] Hall, M.; Tideman, N.1967 Measures of concentration. J. Am. Stat. Assoc. 62, 162–168.Joint work with Federico Musciotto, Jyrki Piilo, Rosario N. Mantegna

I conjecture an identity among the determinant of the adjacency matrix of a graphene nanocone with Bloch b.c. and the characteristic polynomial p(z) of a Pascal matrix. The latter is analytically known only for z equal to some roots of unity, related to counting problems of partitions, or lozenge tilings of an hexagon, or dense loops on a cylinder.

Optical waves in active disordered media display the typical phenomenology of complex systems. Several spectral shots taken from the same piece of material in the lasing regime display strong fluctuations in the position of the intensity peaks, suggesting that there is no specific mode which is preferred in the amplification, but depending on the initial state, with the disorder kept fixed, the modes gaining the highest intensity change every time. In order to explain this behaviour, a spin-glass model has been developed, where the light modes are described as non-linearly interacting phasors on the so-called mode-locked diluted graph [1]. The specific mode-coupling selection rule, which naturally emerges in the study of lasing modes dynamics, impairs the analytical solution of the model out of the narrow bandwidth limit, where the interaction network is fully connected. In this talk we present recent results from numerical simulations of the mode-locked glassy random laser. A phenomenology compatible with a glass transition is revealed from the divergence of the specific heat and the non-trivial structure of the Parisi overlap distribution function. By means of a refined finite-size scaling analysis of the critical region, the transition is assessed to be compatible with a mean-field universality class [2]. A pseudo-localization transition to a phase where the intensity of light is neither properly localized on a single mode nor equiparted among all the modes is revealed from the measure of the inverse participation ratio and of the spectral entropy [3]. The two transitions occur at the same temperature as different manifestations of the same underlying phenomenon, the breaking of ergodicity.[1] F. Antenucci, C. Conti, A. Crisanti and L. Leuzzi, Phys. Rev. Lett. 114, 043901 (2015).[2] J. Niedda, G. Gradenigo, L. Leuzzi and G. Parisi, arXiv:2210.04362, (2022).[3] J. Niedda, L. Leuzzi and G. Gradenigo, arXiv:2212.05106 (2022).

A deterministic excitation (DE) paradigm is formulated [1], according to which the abrupt glacial-interglacial transitions that occurred after the Mid-Pleistocene Transition correspond to the excitation, by the orbital forcing, of nonlinear relaxation oscillations internal to the climate system in the absence of any stochastic parameterization. Specific threshold crossing rules parameterizing the activation of internal climate feedbacks leading to relaxation oscillation excitations, are derived according to the DE assumption. Such rules are then applied to the fluctuations of the glacial state simulated by an energy balance model subjected to realistic orbital forcing. The timing of the glacial terminations thus obtained in a reference simulation is found to be in good agreement with proxy records; besides, a sensitivity analysis insures the robustness of the timing. The role of noise in the glacial-interglacial transitions, and the problems arising in the implementation of theories in which noise is crucial (such as stochastic resonance) are finally discussed. In conclusion, the DE paradigm provides the simplest possible dynamical systems characterization of the link between orbital forcing and glacial terminations implied by the Milankovitch hypothesis.[1] Pierini, S., 2023: The deterministic excitation paradigm and the late Pleistocene glacial terminations. Chaos, 33, 033108, https://doi.org/10.1063/5.0127715.

In this work, I report on experimental time-resolved measurements of light transport through weakly scattering membranes based on a sub-ps optical gating imaging technique. We characterized simple scattering slabs comprising different volume densities of TiO2 nanoparticles, finding spatial intensity distributions which exhibit different profiles at different times, and which spread with an enhanced transverse propagation rate with respect to the nominal transport mean free path. We propose an analysis of the resulting spatio-temporal profiles based on the concept of “self-similarity”, that relies on the study of all spatial moments of displacements of the transient intensity profiles. Our results show the emergence of an anomalous transient regime which persists after several scattering events, and arises in spite of the homogeneous and isotropic structure of the investigated samples. Experimental data are in excellent agreement with numerical Monte Carlo simulations, showing that the concept of self-similarity is a particularly useful tool to study general transport phenomena and their deviations from standard diffusive propagation.

Confinement can have a considerable effect on the behavior of particle systems, and is therefore an effective way to discover new phenomena. A notable example is a system of identical bosons at low temperature under an external field mimicking an isotropic bubble trap, which constrains the particles to a portion of space close to a spherical surface. Using Path Integral Monte Carlo simulations, we examine the spatial structure and superfluid fraction in two emblematic cases. First, we look at soft-core bosons, finding the existence of supersolid cluster arrangements with polyhedral symmetry; we show how different numbers of clusters are stabilized depending on the trap radius and the particle mass, and we characterize the temperature behavior of the cluster phases. A detailed comparison with the behavior of classical soft-core particles is provided too. Then, we examine the case, of more immediate experimental interest, of a dipolar condensate on the sphere, demonstrating how a quasi-one-dimensional supersolid of clusters is formed on a great circle for realistic values of density and interaction parameters. We argue that the predicted phases can be revealed in magnetic traps with spherical-shell geometry. Our results pave the way for future simulation studies of correlated quantum systems in curved geometries.

The possibility of the protein backbone adopting lasso-like entangled motifs has attracted increasing attention. After discovering the surprising abundance of natively entangled single-domain proteins, it was shown that misfolded entangled subpopulations might become thermosensitive or escape the homeostasis network just after translation. To investigate the role of entanglement in shaping folding kinetics, we introduce a novel indicator and analyse simulations of a coarse-grained, structure-based model for a small single-domain protein. Despite its small size, a natively entangled antifreeze RD1 protein displays a rich refolding behavior, populating two distinct kinetic intermediates: a short-lived, entangled, near-unfolded state and a long-lived, non-entangled, near-native state. The entangled state promotes fast refolding, while the non-entangled state acts as a kinetic trap, consistently with known experimental evidence of two different characteristic times. Upon trapping, the natively entangled loop forms without being threaded by the N-terminal residues. After trapping, the native entangled structure emerges by either backtracking to the unfolded state or threading through the already formed but not yet entangled loop. Along the fast pathway, the earlier the native contacts form, the more their formation time may fluctuate. Trapping does not occur because the native contacts at the closure of the lasso-like loop form after those involved in the N-terminal thread, confirming previous predictions. Remarkably, a long-lived, near-native intermediate, with non-native entanglement properties, recalls what was observed in cotranslational folding.

In studying perceptual decision making, the common neuroscientific approach is to measurebehavior, its accuracy, and speed, and then analyze it with mathematical models to makeinferences on the underlying mechanism. In this work, we turn this approach around and froma model with the physical properties of a stimulus moving according to a non-equilibriumstationary stochastic process [1], we predict the decision time of human participants. In abehavioral experiment, we asked 21 young healthy participants to judge the motion directionof a visual stimulus moving with a given drift velocity and diffusion coefficient. The rate ofstochastic entropy production that emerged from the trajectory of the stimulus allowed us tomeasure the noise in the system. Results revealed an inverse proportionality relation betweenthe participants’ mean decision time and the rate of entropy production of the underlyingphysical process, establishing an analytical approach to predict the amount of time requiredto extract the signal under uncertainty. In addition to that, having a strong link between thedynamics of the stimulus trajectory and the decision outcomes led us to investigate the sourceof the variability in decision parameters and revealed a pattern of trial-by-trial evidenceintegration. Overall, our study shows that providing a detailed model of the physical propertiesof the stimuli to judge allows a better characterization of the variables influencing perceptualdecisions and refines our understanding of the temporal dynamics of efficient evidenceintegration.[1] E. Roldan, I. Neri, M. Dorpinghaus, H. Meyr, F. Julicher, Decision making in the arrow oftime. Physical review letters 115(25), 250, 602 (2015).

In the last 30 years, several hundred articles studied the interplay between the feedback loop between the evolution of an outbreak and the change in behavior of the involved individuals.Each model makes unique predictions about the distribution of self-protecting behavior and its clustering. For example, in imitation games, such as [FU2011], an individual will mimic the behavior of a neighbor with a higher payoff, leading to a higher level of homophily (clustering) within the network; conversely, with a game-theory approach, as in [XIA2013], a higher fraction of self-protecting neighbors decrease the perception of the risk and the self-protecting probability.This work studies the impact on several disease models and networks of behavior polarization and homophily.When the behavior of an agent represents the individual level of attention, and it rescales the infectivity $\beta$, we show that both homophily and polarization significantly impact an outbreak's evolution even if the average infectivity is fixed; This is an important insight for building compartmental models: knowing the average value of the infectivity of each agent is not enough to predict the evolution of an outbreak.[FU2011] Fu, Feng, et al. "Imitation dynamics of vaccination behaviour on social networks." Proceedings of the Royal Society B: Biological Sciences 278.1702 (2011): 42-49.[XIA2013] Xia, Shang, and Jiming Liu. "A computational approach to characterizing the impact of social influence on individuals' vaccination decision making." PloS one 8.4 (2013): e60373.

TBA

Engineering long-range interactions in experimental platforms has been achieved with great success in a large variety of quantum systems in recent years. Inspired by this progress, we propose a generalization of the classical Hamiltonian mean-field model to fermionic particles. We study the phase diagram and thermodynamic properties of the model in the canonical ensemble for ferromagnetic interactions as a function of temperature and hopping. At zero temperature, small charge fluctuations drive the many-body system through a first-order quantum phase transition from an ordered to a disordered phase. At higher temperatures, the fluctuation-induced phase transition remains first order initially and switches to second-order only at a tricritical point. Our results offer an intriguing example of tricriticality in a quantum system with long-range couplings, which bears direct experimental relevance. The analysis is performed by exact diagonalization and mean-field theory.

Within the realm of soft colloids a prominent role is played by the Gaussian Core Model (GCM) introduced by Stillinger in the 70’s [1]. The GCM describes point particles interacting by means of a Gaussian-shaped potential and is one of the simplest models for the description of systems such as polymer or dendrimer solutions [2, 3].Whereas at low temperatures and densities the GCM is believed to be described by an effective hard-sphere mapping, at high densities a mean-field description sets in, giving rise to re-entrant melting [4] and a glass state compatible with a geometric transition [5]. The broad intermediate glassy regime remains unexplored [6]. In this talk I will present results from molecular dynamics simulations exploring the slow dynamics of the GCM in this regime. In particular, I will discuss the transition from the low density hard-sphere-like glassy dynamics to the high density one, featuring novel interesting characteristics that we attribute to the interplay between temperature and soft decay tail of the GCM.[1] F. H. Stillinger, J. Chem. Phys. 65, 3968 (1976).[2] A. A. Louis et al., Phys. Rev. Lett. 85, 2522 (2000).[3] I. O. Goetze et al., J. Chem. Phys. 120, 7761 (2004).[4] A. Lang et al., J. Phys.: Condens. Matter 12, 5087 (2000).[5] D. Coslovich et al., Phys. Rev. E 93, 042602 (2016).[6] J-M. Bomont et al., Phys. Rev. E 105, 024607 (2022).

The field of multiscale modeling and simulation has enjoyed significant success in soft matter research within the past decade also thanks to the boost impressed by the necessity to overcome the expensive cost of a single, highly detailed resolution. Several methodologies have been developed in the past few years, where different system components are simultaneously modelled at different levels of resolution [1]. In the case of biomolecules, functionally relevant parts of the system can be modelled at a high a level of detail, while the remainder of the system can be represented using less expensive models. Here, we propose a novel multi-resolution scheme dubbed coarse-grained anisotropic network model for variable resolution simulations, or CANVAS, which allows one to employ and smoothly couple virtually any desired degree of coarse-graining within the same model [2]. The novelty of this method lies in the possibility of setting the level of resolution of the coarse-grained subdomains in a quasi-continuous range; furthermore, the interaction network within and between resolution domains is straightforwardly parametrized on the basis of the properties of the specific system under examination. The model is validated by comparing results from all-atom and multi-scale simulations of two biomolecules, namely the enzyme adenylate kinase and the IgG4 antibody pembrolizumab.[1] Giulini, M. et al., 2021. Frontiers in Molecular Biosciences, 8, p.676976.[2] Fiorentini, R. et al., 2023. Journal of Chemical Information and Modeling, 63(4), pp.1260-1275.

The analysis of experimental data of the solar irradiance, collected on the sea surface, highlights the intrinsic stochasticity of such an environmental variable. Given this result, the effects of randomly fluctuating irradiance on the population dynamics of a marine ecosystem are studied on the basis of the stochastic 0-dimensional biogeochemical flux model (BFM). The noisy fluctuations of the irradiance are formally described by a multiplicative Ornstein-Uhlenbeck process, i.e., a self-correlated Gaussian noise. Nonmonotonic behaviours of the variance of the marine populations’ biomass are found with respect to the intensity and the autocorrelation time of the noise source, manifesting a noise-induced transition of the ecosystem to an out-of-equilibrium steady state. Moreover, noise-induced effects in the organic carbon cycling processes, underlying the food web dynamics, are observed. These findings clearly show the profound impact the stochastic behaviour of environmental variables can have on both biological and chemical components of a marine trophic network.

Rapid innovations in Molecular Biology have shed light on the 3D arrangement of DNA within the cell nucleus, revealing its complex, non-random character, and its connection to gene regulation. In any case, the mechanisms that regulate DNA-DNA contacts are still poorly understood to date. Polymer physics and Machine learning approaches are proving to be excellent tools for investigating these phenomena. In this work, we infer from only Hi-C data the cell-type-specific arrangement of DNA binding sites able to recapitulate, through polymer physics, contact patterns genome wide. The binding site types fall in classes that show an overlapping, combinatorial organization along chromosomes necessary to accurately explain contact specificity. The chromatin signatures of the binding site types return a code linking chromatin states to 3D conformation. The code is validated by de novo predictions of Hi-C maps in independent chromosomes. Furthermore, we investigate the range of applicability of this code among cell types by making predictions on Hi-C data from another cell line, different from the one used to obtain the code itself. Overall, our results shed light on how 3D information is encrypted in 1D chromatin via the specific combinatorial arrangement of binding sites.Ref:-Esposito A. et al. Polymer physics reveals a combinatorial code linking 3D chromatin architecture to 1D chromatin states. Cell Reports, 2022.-Conte M. et al. Unveiling the Machinery behind Chromosome Folding by Polymer Physics Modeling. International Journal of Molecular Sciences, 2023.

The assumption of rational traders has been the subject of a harsh debate in theoretical economics for the past 40 years. Recent experimental evidence gathered by cognitive neuroscientists suggests that the way we learn in simple tasks is in stark contrast with the rationality assumption: the way we learn is biased. Confirmation bias, for example, is the tendency to incorporate the information in line with our priors and disregard the information in contrast with them.These findings beg for an explanation. In particular, if evolution selected such biases, they should be beneficial in some circumstances: for example, in tasks with two asymmetric bandits, there are 'optimal biases' which allow individuals to increase the average earned reward. The reason for these additional gains is that biased beliefs are magnifying, allowing one to distinguish more clearly between two similar options.Interestingly, in these contexts, the optimal bias corresponds to a learning dynamics that breaks detailed balance, leading, therefore, to irreversible dynamics, even in the stationary state. We argue, by means of analytical calculations and numerical simulations, that the optimal bias corresponds to dynamics that maximise the entropy production in the stationary state. In particular, in this context, the stationary state with maximum entropy production allows agents to safely explore the environment without being stuck in a sub-optimal belief.