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Lamberto Rondoni

Publications and source records attributed to Lamberto Rondoni.

At least 19 recordsLinked to original sources

Tackling Heterogeneity in Federated Learning via Variance-Reduced Boltzmann Sampling within Homogeneous Social Coalitions

Federated Learning (FL) enables privacy-preserving collaborative model training, but its effectiveness is often limited by client data heterogeneity. We introduce a client-selection algorithm that (i) dynamically forms nonoverlapping coalitions of clients based on asymptotic agreement and (ii) selects one representative from each coalition to minimize the variance of model updates. Our approach is inspired by social-network modeling, leveraging homophily-based proximity matrices for spectral clustering and techniques for identifying the most informative individuals to estimate a group's aggregate opinion. We provide theoretical convergence guarantees for the algorithm under mild, standard FL assumptions. Finally, we validate our approach by benchmarking it against three strong heterogeneity-aware baselines; the results show higher accuracy and faster convergence, indicating that the framework is both theoretically grounded and effective in practice.

cs.LG↗

Characterizing the Dynamics of Muscle Regeneration in the mdx Mouse Model

In this work, we explore a model of immune response in the skeletal muscle of the mdx mouse, the preferred animal model for studying Duchenne Muscular Dystrophy. The system studied is based on existing literature and describes the reaction of the tissue, and of the immune cells within it, to external damage, focusing specifically on the regeneration process. This work extends the analysis conducted by the authors of the original paper, highlighting interesting dynamical properties of the system, particularly in terms of longterm behavior and dependence on initial conditions. A modification is then introduced to the original equations, incorporating a diffusion term for immune cells. The dynamics of the system is numerically investigated in both the one-dimensional and two-dimensional cases. Specifically, we investigate the effect of diffusion under various boundary conditions, and the system's response to localized damage.

math.DS↗

Small-System Group: Thermodynamics as a Complete Self-Similarity Limit

We revisit the Rayleigh--Riabouchinsky paradox in dimensional analysis by making explicit the bridge between thermodynamics and the mechanical interpretation of temperature. Boltzmann's constant $k_B$ acts as a dimensional unifier, leading to an augmented $Π$-theorem with an additional dimensionless group that encodes system size. In the macroscopic thermodynamic limit this small-system group, $Π_B = k_B/(c\,\ell^3)$ -- the inverse heat capacity of a control volume of size $\ell^3$ in units of $k_B$ -- becomes irrelevant as the response becomes self-similar with respect to it, recovering Rayleigh's formulation. Under suitable conditions, macroscopic limits make the fluctuations of the observables of interest negligible compared to their expected values, hence the state of a system is characterized by a reduced set of parameters. We thus recast thermodynamics as the complete-similarity limit of statistical mechanics with respect to $Π_B$, which also controls thermodynamic fluctuations. We also discuss second-order phase transitions from the viewpoint of incomplete similarity.

physics.gen-ph↗

Computing Nonequilibrium Transport from Short-Time Transients: From Lorentz Gas to Heat Conduction in One Dimensional Chains

We test the Transient Time Correlation Function (TTCF) method to compute nonequilibrium transport coefficients, highlighting its conceptual and practical difference from the standard time-average approach. While time averages extract transport properties from long stationary trajectories and discard transient dynamics, TTCF adopts the complementary strategy: it exploits the information contained in short-time transients following the onset of an external perturbation, while discarding the long-time evolution once stationarity is reached. We revisit the theoretical framework of TTCF and assess its numerical performance through representative case studies, the Lorentz gas and a many-body system, namely a chain of oscillators with anharmonic pinning potential. By direct comparison with time averages, we show that for the Lorentz gas TTCF yields consistent transport coefficients in both linear and nonlinear regimes at a reduced computational cost. Moreover, the TTCF displays superior precision in the linear-response regime, and remains reliable in non-ergodic situations, revealing the presence of regions of phase space corresponding to different behaviors, as well as the possibility of phase transitions. For the anharmonic chain, we show that TTCF is a scalable and efficient alternative for the numerical study of nonequilibrium transport.

cond-mat.stat-mech↗

Dynamics of stochastic oscillator chains with harmonic and FPUT potentials

Inspired by recent studies on deterministic oscillator models, we introduce a stochastic one-dimensional model for a chain of interacting particles. The model consists of $N$ oscillators performing continuous-time random walks on the integer lattice $\mathbb{Z}$ with exponentially distributed waiting times. The oscillators are bound by confining forces to two particles that do not move, placed at positions $x_0$ and $x_{N+1}$, respectively, and they feel the presence of baths with given inverse temperatures: $β_L$ to the left, $β_B$ in the middle, and $β_R$ to the right. Each particle has an index and interacts with its nearest neighbors in index space through either a quadratic potential or a Fermi-Pasta-Ulam-Tsingou type coupling. This local interaction in index space can give rise to effective long-range interactions on the spatial lattice, depending on the instantaneous configuration. Particle hopping rates are governed either by the Metropolis rule or by a modified version that breaks detailed balance at the interfaces between regions with different baths.

cond-mat.stat-mech↗

Dynamics of the Kac Ring Model with switching scatterers

We introduce a generalized version of the Kac ring model in which particles are of two types, black and white. Black particles modify the environment through which all particles move, thereby inducing indirect and potentially long-range interactions among them. Unlike the inert scatterers of Kac's original model, the scatterers in our setting possess internal states that change upon interaction with black particles and can be interpreted as energy levels of the environment. This makes the model self-consistent, as it incorporates a form of particle interactions, mediated by the environment, that drives the system toward some kind of stationary state. Although indirect and long-range interactions do not necessarily promote thermodynamic states, interactions are necessary for energy to be shared among the elementary constituents of matter, enabling the establishment of equipartition, which is a prerequisite for defining temperature. Therefore, our model is one step forward in this direction, elucidating the role of interactions and energy exchange. We prove that any initial state of the system converges to a time periodic state (i.e. a phase space orbit) and describe basins of attraction for some of such asymptotic periodic states.

cond-mat.stat-mech↗

Dissipation functions and Brownian oscillators

We develop a general framework for response theory in diffusion processes governed by Fokker-Planck equations, based on the notion of the Dissipation Function. Using the analytically solvable Brownian oscillator model, we derive exact response formulae for both overdamped and underdamped dynamics of harmonically bound Brownian particles. We also demonstrate that for certain observables and under suitable time scaling, the operations of model reduction and response formula extraction commute.

cond-mat.stat-mech↗

Thermodynamics and Legendre Duality in Optimal Networks

Optimality principles in nonequilibrium transport networks are linked to a thermodynamic formalism based on generalized transport potentials endowed with Legendre duality and related contact structure. This allows quantifying the distance from non-equilibrium operating points, analogously to thermodynamic availability as well as to shed light on optimality principles in relation to different imposed constraints. Extremizations of generalized dissipation and entropy production appear as special cases that require power-law resistances and -- for entropy production -- also isothermal conditions. Changes in stability of multiple operating points are interpreted as phase transitions based on non-equilibrium equations of state, while cost-based optimization of transport properties reveals connections to the generalized dissipation in the case of power law costs and linear resistance law, but now with typically unstable operating points which give rise to branched optimal transport.

cond-mat.stat-mech↗

Microcanonical ensemble out of equilibrium

Introduced by Boltzmann under the name "monode," the microcanonical ensemble serves as the fundamental representation of equilibrium thermodynamics in statistical mechanics by counting all possible realizations of a system's states. Ensemble theory connects this idea with probability and information theory, leading to the notion of Shannon-Gibbs entropy and, ultimately, to the principle of maximum caliber describing trajectories of systems--in and out of equilibrium. While the latter phenomenological generalization reproduces many results of nonequilibrium thermodynamics, given a proper choice of observables, its physical justification remains an open area of research. What is the microscopic origin and physical interpretation of this variational approach? What guides the choice of relevant observables? We address these questions by extending Boltzmann's method to a microcanonical caliber principle and counting realizations of a system's trajectories--all assumed equally probable. Maximizing the microcanonical caliber under the imposed constraints, we systematically develop generalized detailed-balance relations, clarify the statistical origins of inhomogeneous transport, and provide an independent derivation of key equations from stochastic thermodynamics. This approach introduces a dynamical ensemble theory for nonequilibrium steady states in spatially extended and active systems. While verifying the equivalence of ensembles, e.g. those of Norton and Thevenin, our framework contests other common assumptions about nonequilibrium regimes, with supporting evidence provided by stochastic simulations. Our theory suggests further connections to the first principles of microscopic dynamics in classical statistical mechanics, which are essential for investigating systems where the necessary conditions for thermodynamic behavior are not satisfied.

cond-mat.stat-mech↗

Anomalous transport models for fluid classification: insights from an experimentally driven approach

In recent years, research and development in nanoscale science and technology have grown significantly, with electrical transport playing a key role. A natural challenge for its description is to shed light on anomalous behaviours observed in a variety of low-dimensional systems. We use a synergistic combination of experimental and mathematical modelling to explore the transport properties of the electrical discharge observed within a micro-gap based sensor immersed in fluids with different insulating properties. Data from laboratory experiments are collected and used to inform and calibrate four mathematical models that comprise partial differential equations describing different kinds of transport, including anomalous diffusion: the Gaussian Model with Time Dependent Diffusion Coefficient, the Porous Medium Equation, the Kardar-Parisi-Zhang Equation and the Telegrapher Equation. Performance analysis of the models through data fitting reveals that the Gaussian Model with a Time-Dependent Diffusion Coefficient most effectively describes the observed phenomena. This model proves particularly valuable in characterizing the transport properties of electrical discharges when the micro-electrodes are immersed in a wide range of insulating as well as conductive fluids. Indeed, it can suitably reproduce a range of behaviours spanning from clogging to bursts, allowing accurate and quite general fluid classification. Finally, we apply the data-driven mathematical modeling approach to ethanol-water mixtures. The results show the model's potential for accurate prediction, making it a promising method for analyzing and classifying fluids with unknown insulating properties.

q-bio.PE↗

Wavelet Scattering Transform for Gravitational Waves Analysis. An Application to Glitch Characterization

Gravitational waves, first predicted by Albert Einstein within the framework of general relativity, were confirmed in 2015 by the LIGO/Virgo collaboration, marking a pivotal breakthrough in astrophysics. Despite this achievement, a key challenge remains in distinguishing true gravitational wave signals from noise artifacts, or "glitches," which can distort data and affect the quality of observations. Current state-of-the-art methods, such as the Q-transform, are widely used for signal processing, but face limitations when addressing certain types of signals. In this study, we investigate the Wavelet Scattering Transform (WST), a recent signal analysis method, as a complementary approach. Theoretical motivation for WST arises from its stability under signal deformations and its equivariance properties, which make it particularly suited for the complex nature of gravitational wave data. Our experiments on the LIGO O1a dataset show that WST simplifies classification tasks and enables the use of more efficient architectures compared to traditional methods. Furthermore, we explore the potential benefits of integrating WST with the Q-transform, demonstrating that ensemble methods exploiting both techniques can capture complementary features of the signal and improve overall performance. This work contributes to advancing machine learning applications in gravitational wave analysis, introducing refined preprocessing techniques that improve signal detection and classification.

gr-qc↗

Universal hyper-scaling relations, power-law tails, and data analysis for strong anomalous diffusion

Strong anomalous diffusion is {often} characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes $ξ$ and $ζ$ for small and large moments, respectively, and by the critical moment $α$ of the crossover. The exponents $ξ$ and $ζ$ characterize the asymptotic scaling of the bulk and the tails of the probability distribution function of displacements, respectively. Here, we adopt asymptotic theory to match the behaviors at intermediate scales. The resulting constraint explains how distributions with algebraic tails imply strong anomalous diffusion, and it relates $α$ to the corresponding power law. Our theory provides novel relations between exponents characterizing strong anomalous diffusion, and it yields explicit expressions for the leading-order corrections to the asymptotic power-law behavior of the moments of displacement. They provide the time scale that must be surpassed to clearly discriminate the leading-order power law from its sub-leading corrections. This insight allows us to point out sources of systematic errors in their numerical estimates. Rather than separately fitting an exponent for each moment we devise a robust scheme to determine $ξ$, $ζ$ and $α$. The findings are supported by numerical and analytical results on five different models exhibiting strong anomalous diffusion.

math-ph↗

Thermodynamic Langevin Equations

The physical significance of the stochastic processes associated to the generalized Gibbs ensembles is scrutinized here with special attention to the thermodynamic fluctuations of small systems. The contact with the environment produces an interaction entropy, which controls the distribution of fluctuations and allows writing the generalized Gibbs ensembles for macrostates in potential form. This naturally yields exact nonlinear thermodynamic Langevin equations (TLEs) for such variables, with drift expressed in terms of entropic forces. The analysis of the canonical ensemble for an ideal monoatomic gas and the related TLEs show that introducing currents leads to nonequilibrium heat transfer conditions with interesting bounds on entropy production but with no obvious thermodynamic limit. For a colloidal particle under constant force, the TLEs for macroscopic variables are different from those for the microscopic position, typically used in the so-called stochastic thermodynamics; while TLEs are consistent with the fundamental equation obtained from the Hamiltonian, stochastic thermodynamics requires isothermal conditions and entropy proportional to position.

cond-mat.stat-mech↗

Particle transport in open polygonal billiards: a scattering map

Polygonal billiards exhibit a rich and complex dynamical behavior. In recent years polygonal billiards have attracted great attention due to their application in the understanding of anomalous transport, but also at the fundamental level, due to its connections with diverse fields in mathematics. We explore this complexity and its consequences on the properties of particle transport in infinitely long channels made of the repetitions of an elementary open polygonal cell. Borrowing ideas from the Zemlyakov-Katok construction, we construct an interval exchange transformation classified by the singular directions of the discontinuities of the billiard flow over the translation surface associated to the elementary cell. From this, we derive an exact expression of a scattering map of the cell connecting the outgoing flow of trajectories with the unconstrained incoming flow. The scattering map is defined over a partition of the coordinate space, characterized by different families of trajectories. Furthermore, we obtain an analytical expression for the average speed of propagation of ballistic modes, describing with high accuracy the speed of propagation of ballistic fronts appearing in the tails of the distribution of the particle displacement. The symbolic hierarchy of the trajectories forming these ballistic fronts is also discussed.

nlin.CD↗

Poissonian cellular Potts models reveal nonequilibrium kinetics of cell sorting

Cellular Potts models are broadly applied across developmental biology and cancer research. We overcome limitations of the traditional approach, which reinterprets a modified Metropolis sampling as ad hoc dynamics, by introducing a physical timescale through Poissonian kinetics and by applying principles of stochastic thermodynamics to separate thermal and relaxation effects from athermal noise and nonconservative forces. Our method accurately describes cell-sorting dynamics in mouse-embryo development and identifies the distinct contributions of nonequilibrium processes, e.g. cell growth and active fluctuations.

cond-mat.stat-mech↗

Detecting Phase Transitions through Nonequilibrium Work Fluctuations

We show how averages of exponential functions of path dependent quantities, such as those of Work Fluctuation Theorems, detect phase transitions in deterministic and stochastic systems. State space truncation -- the restriction of the observations to a subset of state space with prescribed probability -- is introduced to obtain that result. Two stochastic processes undergoing first-order phase transitions are analyzed both analytically and numerically: the Ehrenfest urn model and the 2D Ising model subject to a magnetic field. In presence of phase transitions, we prove that even minimal state space truncation makes averages of exponentials of path dependent variables sensibly deviate from full state space values. Specifically, in the case of discontinuous phase transitions, this approach is strikingly effective in locating the critical transition value of the control parameter. As this approach works even with variables different from those of fluctuation theorems, it provides a new recipe to identify order parameters in the study of nonequilibrium phase transitions, profiting from the often incomplete statistics that are available.

cond-mat.stat-mech↗

Destructive effect of fluctuations on the performance of a Brownian gyrator

The Brownian gyrator (BG) is often called a minimal model of a nano-engine performing a rotational motion, judging solely upon the fact that in non-equilibrium conditions its torque, angular momentum ${\cal L}$ and angular velocity $\cal W$ have non-zero mean values. For a time-discretized model, which is most adapted for the analysis of an essentially discrete-time data garnered in experiments or numerical simulations, we calculate the previously unknown probability density functions (PDFs) of ${\cal L}$ and $\cal W$. For finite time-step $δt$, the PDF of ${\cal L}$ has exponential tails and all moments are therefore well-defined, but the noise-to-signal ratio can attain big values for small $δt$. Conversely, the PDF of ${\cal W}$ exhibits heavy power-law tails and its mean ${\cal W}$ is the only existing moment. The BG is therefore not an engine in the common sense: it does not exhibit regular rotations on each run and its fluctuations are not only a minor nuisance -- on contrary, their effect is completely destructive for the performance. Our theoretical predictions are confirmed by numerical simulations and experimental data. We discuss some plausible improvements

cond-mat.stat-mech↗

Finite reservoirs and irreversibility corrections to Hamiltonian systems statistics

We consider several Hamiltonian systems perturbed by external agents, that preserve their Hamiltonian structure. We investigate the corrections to the canonical statistics resulting from coupling such systems with possibly large but finite reservoirs, and from the onset of processes breaking the time reversal symmetry. We analyze exactly solvable oscillators systems, and perform simulations of relatively more complex ones. This indicates that the standard statistical mechanical formalism needs to be adjusted, in the ever more investigated nano-scale science and technology. In particular, the hypothesis that heat reservoirs be considered infinite and be described by the classical ensembles is found to be critical when exponential quantities are considered, since the large size limit may not coincide with the infinite size canonical result. Furthermore, process-dependent emergent irreversibility affects ensemble averages, effectively frustrating, on a statistical level, the time reversal invariance of Hamiltonian dynamics, that is used to obtain numerous results.

cond-mat.stat-mech↗