We consider a $K$-layer hetero-associative neural-network and we carry out a statistical mechanical analysis. Our findings show that these networks exhibit spontaneous information processing capabilities that go far beyond those of auto-associative counterparts. In particular, they can perform frequency modulation and, when presented with a spurious state (e.g., a symmetric mixture made of $K$...
Recurrent neural networks (RNNs) based on model neurons that communicate via continuous signals have been widely used to study how neural circuits perform cognitive tasks. Training such networks to perform tasks that require information maintenance over a brief period (working memory tasks) remains a challenge. Inspired by the robust information maintenance observed in higher cortical areas...
Adaptive behavior relies on activity-dependent synaptic plasticity to sculpt internal models of the world. I introduce two complementary frameworks for how the brain encodes abstraction and probability. Regarding abstract representations, we first propose a three-factor plasticity rule for nonlinear dimensionality reduction in a three-layer network inspired by the Drosophila olfactory circuit....
Quantum integrable systems are characterised by an infinite number of conserved charges and stable quasi-particle excitations. When integrability is broken, interactions between quasi-particles are introduced, opening the way for a novel kinetic theory that incorporates both integrable and non-integrable processes. In this talk I will review recent advances in the development of such a kinetic...
In this talk, we use various tools of statistical physics to understand how some viruses (in particular, influenza A) actively navigate through a dense, extracellular environment. We will show that an asymmetric viral surface-protein distribution not only enhances directed, persistent motion, but enables a type of sensing of their local environment. This rebuts the view that viruses are...
During this lecture and workshop, we will introduce Fractal Space Curve Analysis (FSCA), a novel methodology for characterizing multidimensional data—particularly neuroimaging data—by examining their fractal properties. The core concept of FSCA is to transform multidimensional data (e.g., 2D, 3D, or 3+1D scans) into one-dimensional time series using space-filling curves (SFCs), primarily the...
The use of electronic circuits to model neural systems goes back to C. Mead and is present in models, from leaky-integrate-and-fire to Hodking-Huxley. Simulating neural networks with analog hardware is attractive: it allows to implement neurocomputations in real time without discretization approximations, it has perfect simulation-time scaling with system size, and it provides...
A two-states device such as the Brownian ratchet can be regarded as both a "heat engine" and an "information engine". From this dual perspective, long time series recorded in our centimeter-scale experimental setup [1] allow for a precise investigation of all the observables of interest. These are the heat flux supplied by the athermal hot bath at $kT_{\rm eff.}$, the work produced per time...
Celebrated fluctuation-dissipation theorem (FDT) linking the response function to time dependent correlations of observables measured in the reference unperturbed state is one of the central results in equilibrium statistical mechanics. In this letter we discuss an extension of the standard FDT to the case when multidimensional matrix representing transition probabilities is strictly...
In a study involving members of Marie Doumic's group at Ecole Polytechnique (Palaiseau, France) and Maria Teresa Teixeira's group at the Institut de Biologie Physico-Chimique (Paris, France), we present a stochastic model of growth of a cell population of cultured yeast cells with gradually decaying chromosome endings, called the telomeres. Telomeres play a major role in aging and...
The rapid succession of SARS-CoV-2 variants has underscored the importance of tracing the emergence of new subvariants with evolutionary advantages. Based on almost 15 million complete viral sequences from GISAID we investigated how the individual mutations that define Variants of Concern have emerged over time. We found that rather than accumulating mutations one at a time, key changes...
Understanding the biophysical mechanisms that govern gene expression pattern formation is crucial for reproducible and organized organ development. Although many genetic and mechanical factors involved in pattern formation are known, we still lack a comprehensive understanding of how cellular dynamics and biomechanical feedback are orchestrated to ensure precise and reproducible patterning. In...
Living systems are fundamentally thermodynamic structures operating far from equilibrium, characterized by continuous entropy production and driven by external energy fluxes. A key aspect of their long-term viability is their ability to adaptively regulate entropy dynamics in response to perturbations. In this contribution, we present a theoretical framework describing such entropy-driven...
We study a social network where agents correspond to people, and links are relationships between agents. Each agent possesses a set of attributes. Distinguishing the signs of relationships between agents can be performed for each attribute separately or considering all attributes together. In the former case, we assume a simple edge is positive/negative when the two agents hold the...
Despite wide recognition of the modular and hierarchical organization of neural circuits in the brain, our understanding of its influence on neural dynamics and information processing remains incomplete. To address this gap, we introduced a model of randomly connected neural populations (modules) and studied its dynamics by means of the mean-field theory and simulations. Our analysis uncovered...
Change is ubiquitous in living beings. In particular, the connectome and neural representations can change. Nevertheless, behaviors and memories often persist over long times. In a standard model, associative memories are represented by assemblies of strongly interconnected neurons. For faithful storage these assemblies are assumed to consist of the same neurons over time. We propose a...
It is a general experience that computation in a computer produces heat. A part of this heat appears because of the erasure of memory, which is an essential step for irreversible logic operations in regular computational processes. The laws of thermodynamics fix a limit for the heat evolution associated with this erasure step and eventually for the computation[1, 2]. In small systems with...
Whole genome sequencing is playing an increasingly central role in modern oncology, offering detailed insights that support the development of individualized treatment strategies, especially when combined with machine learning techniques. Traditional approaches that concentrate solely on identifying key driver mutations face limitations due to both the restricted sensitivity of current...
The fluctuations and the response of stochastic systems are related by fluctuation-dissipation theorems or, equivalently, fluctuation-response relations (FRRs). Originally introduced for systems in thermodynamic equilibrium, generalizations of such relations for non-equilibrium situations have been derived and studied since the 1970's and are particularly appealing for biological systems. In...
Extreme events, although rare, hold significant importance due to their huge impact in various areas of science (earthquakes, chemical reactions, population extinction, etc.). Typically, the kinetics of these events is described by Arrhenius laws, with exponentially distributed waiting times. However, this description may break down in the presence of long-term memory, i.e., for stochastic...
The g-subdiffusion equation is a subdiffusion equation containing the fractional Caputo time derivative with respect to another function g. The process described by this equation is interpreted as "ordinary" subdiffusion in which the time variable t has been replaced by an increasing function g(t). This function determines the frequency of jumps of the diffusing molecule. The g-subdiffusion...
Our workshop will begin with a presentation by Dr. Maria Ercsey-Ravasz on recently published methods for analyzing functional network (FN) dynamics in the brain (Varga et al., Cell Systems, 15, 1–17, 2024). This approach considers time lags when constructing functional brain networks and utilizes the statistical distribution of network properties rather than analyzing a single, averaged...
During this lecture and workshop, we will introduce Fractal Space Curve Analysis (FSCA), a novel methodology for characterizing multidimensional data—particularly neuroimaging data—by examining their fractal properties. The core concept of FSCA is to transform multidimensional data (e.g., 2D, 3D, or 3+1D scans) into one-dimensional time series using space-filling curves (SFCs), primarily the...
Understanding the neural basis of mental phenomena remains a great challenge. Statistical physics contributed to the development of attractor neural networks that are our best models linking mental states with the physical properties of the brain. Information (from senses and memory) is embedded in high-dimensional patterns of neural activity. It can be visualized by fMRI scans. Generative...
Memory effects are a ubiquitous feature of nanoscale systems, arising in particular from resistive junctions that give rise to memristive behavior. In this work, we investigate the learning capacity of memristive networks, with a focus on nanowire and nanoparticle architectures. We discuss two examples of learning, e.g., two-phase and contrastive learning with resistive and memristive...
The nucleation and growth theory, described by the Avrami equation (also called Johnson–Mehl–Avrami–Kolmogorov equation), and usually used to describe crystallization and nucleation processes in condensed matter physics, was applied to cancer physics as Avrami-Dobrzyński Model. This approach assumes the transforming system as a DNA chain including many oncogenic mutations. Finally, the...
Szegedy quantum walks represent a generalization of discrete random walks to the quantum domain, finding broad applications in quantum computing. Recent studies have demonstrated that classical resetting mechanisms can accelerate the arrival of a particle at its target, even in the context of quantum walks. This poster presents an approach to introducing purely quantum resetting into Szegedy...
Computer simulations were carried out to understand the processes that occur in organic light-emitting diode (OLED) devices at an atomic and macroscopic level. The main goal was to optimize the OLED structure by taking into account the transport of charge carriers, quantum efficiency and stability. The characteristics and morphology of subsequent layers and interlayer junctions were also...
Active matter is one of the hottest topics in physics nowadays. As a prototype of living systems operating in viscous environments it has usually been modeled in terms of the overdamped dynamics. Recently, active matter in the underdamped regime has gained a place in the spotlight. Here we unveil another remarkable face of active matter. In doing so we demonstrate and explain an...
The active Brownian particle model can exhibit directed motion when subjected to spatial gradients in activity, such as light‑induced motility in bacteria. In the absence of external forces, this rectification arises only in two or more dimensions. Here, we use computer simulations to study Vicsek‑like flocks of aligning active Brownian particles moving through two‑dimensional...
Thermodynamic uncertainty relations (TURs) provide fundamental constraints on the interplay between power fluctuations, entropy production, and efficiency in overdamped stationary autonomous heat engines. However, their validity in underdamped regimes remains limited and less explored. Here, we analytically and numerically study a physically realizable autonomous heat engine composed of two...
Modulated nematic phases, such as the twist-bend nematic (NTB) and splaybend nematic (NSB) phases, experimentally discovered within the last 15 years, are among the most intriguing liquid crystal phases due to their potential practical applications. A possible mechanism underlying the stabilization of these phases is flexopolarization-induced softening of the bend elastic constant. To...
A large amount of information about the singular type of virus caused by SARS-CoV-2 during the COVID-19 pandemic has provided unique insights into the stochastic processes connected to mutations at the DNA level and changes in system entropy. Predictions made by biophysical Single Hit Target Models associate DNA damage with an increase in system entropy. However, it turns out that not all...
Assessing the diffusion characteristics of tracer particles in complex environments, including soft matter and biological matter, yields valuable insights into material properties and biological processes. This is particularly evident in the transport of single molecules, viruses, and particles passing through natural and synthetic pores, which exhibit peculiar features that are the subject of...
Using measurements from the Alpha Magnetic Spectrometer AMS02 aboard the International Space Station, we have examined the long-term variations in galactic cosmic ray (GCR) proton fluxes in 2011–2018. The AMS02 data allow study of time profiles and the energy/rigidity dependence of the long-term GCR variations observed directly in space in a wide rigidity range, from ∼(1 - 100)GV. We have...
Most natural phenomena evolve through non-equilibrium pathways following non-linear dynamics involving the crossing of a potential energy barrier. During these processes the systems transit from one state to another. We intend to understand in detail the significance of these states, their positions, and associated intrinsic fluctuations. As these systems are inevitably subjected to...
The active vertex model is a widely used framework for studying mechanical properties, phase transitions, cell topology, and tissue organization in developmental biology. In this work, we extend the classical formulation by introducing a curvature energy term that captures bending at cell edges through interactions between neighboring vertices. By assigning different target curvature values to...
Biological neural networks can efficiently solve cognitive tasks with different levels of complexity. However, we still lack understanding of how structural and functional features of these networks are affected by increasing the complexity of the goal function. This raises the following fundamental questions: What structural/functional network motifs drive success? How do these motifs change...
Patterns such as stripes, spots, and digit arrangements in animals emerge from multicellular organization driven by gene regulatory networks and intercellular signaling. In developmental biology, these processes can be modeled as reaction–diffusion systems, where intracellular gene interactions act as reactions and protein-mediated communication between neighboring cells is captured by...
The first hitting times of a stochastic process, i.e. the first time a process reaches a particular level, are of significant interest across various scientific disciplines, including biology, chemistry, and economics. We modify the standard setup by allowing the target to spontaneously switch between two states, either active or inactive, and investigate the distribution of first hitting...
Signal detected by electroencephalography (EEG) exhibits a power spectrum with a predominant $1/f$ component. As such, the signal is nonstationary. When EEG is applied to the study of cortical response to stimuli, the event-related potential (ERP) technique is commonly used.
It led to innumerable insights into the mechanisms of cognition. However, it has significant limitations:
A) it relies...
In the age of data-driven decision-making, understanding how to assign a fair price to information has become a pressing and complex challenge. Information, in the form of intangible data that can be traded in exchange of money, does not follow the standard supply-demand rules that govern tangible assets. We address this problem by developing a game-theoretic and statistical physics framework...
Discontinuous phase transitions are a desirable phenomenon in models of opinion dynamics because they capture abrupt shifts in collective behavior, critical mass effects, and social hysteresis. These transitions help explain real-world phenomena such as political polarization, the persistence of vaccine hesitancy, and delayed responses to policy changes. Therefore, identifying the conditions...
Financial markets are data-rich systems where prices and their dynamics emerge from the continuous interaction of many agents. In this talk, I present a framework that combines deep learning with ideas from statistical physics to understand and predict short-term price movements in modern electronic markets. At the core of this framework is the Limit Order Book (LOB)—a high-frequency, tabular...
In the linear overdamped Langevin equation, the effect on a mesoscopic particle (e.g., a colloid) of its collisions with the molecules of the surrounding medium is described by instantaneous friction accompanied by a random force modeled by Gaussian white
noise, yielding a Markovian dynamics of the particle. Such a description hinges on the assumption of time-scale separation, i.e., that the...
In developing embryo cells determine their fate by reading diffusing chemical signals called morphogens. Yet, as the initially imposed morphogens wear out, the corresponding pattern of gene expression remains self-sustained in cells. In order to achieve this, the pattern-maintaining mechanism must be robust enough to overcome significant amounts of noise, inherent to the gene expression...
The fluctuation-dissipation theorem is the main tool for obtaining the response of a physical system. However, FDT fails in many situations (see [1] for review), such as phase transitions, spin glass, anomalous diffusion, and growth phenomena. We develop the hypothesis that the dynamics of a given system may lead to a fractal dimension $d_f$ different from the original spatial dimension $d$....
In my talk we consider the following topics:
1.Free and C-free probaility and completely positive maps.
2.Free independent projections as a model of Jozef Lukasiewicz
$n$-valued logic , $n>2$ and also model of continuous logic of Lukasiewicz-Tarski.
3.Main Theorem: : If $q$ is real number and $x,y$ are from interval $(0,1)$, then the Tsallis entropy is defined as
$$T_{q} (x,y) =...
In this talk, we present an integral equation formulation of run-and-tumble particles (RTPs) under two types of confinement: between parallel walls and within a harmonic potential. This reformulation allows us to obtain exact analytical results that are not accessible through the standard Fokker-Planck differential equation approach. A second objective is to draw analogies between the RTP...
Polymers are key materials in soft condensed matter with diverse applications. Recently, significant attention has been given to understanding the micromechanical behavior of single macromolecules under applied forces. Using molecular dynamics, we examined how constant and periodic forces affect polymer chain conformations in dilute solutions, modeled for good and poor solvents. We...
