arXiv subjects

Duccio Fanelli

Publications and source records attributed to Duccio Fanelli.

At least 19 recordsLinked to original sources

arXiv2026

Reverse engineering of mechano-kinetic parameters from stochastic force profiles in heterogeneous ensembles of molecular motors and tracks

Heterogeneity in contractile systems of molecular motors interacting with their tracks plays a key role in numerous cellular physiological and pathological processes. However, its effects cannot be captured by theoretical models assuming identical mechano-kinetic properties for all motors. We developed a stochastic framework to describe heterogeneous ensembles of myosin motors comprising two populations with distinct mechano-kinetic properties. Assuming that motors interact with the actin filament (their track) as independent force generators, we derived the probability distribution of the isometric force and characterised the statistics of finite-size force fluctuations. The proposed framework includes an estimation procedure that simultaneously infers the mechano-kinetic parameters and the size of the motor ensemble, eliminating the need to prescribe it a priori. Validation against synthetic and experimental data shows the model accurately captures force fluctuations and provides realistic estimates of the ensemble size. Furthermore, the framework enables a quantitative assessment of ensemble heterogeneity and the inference of an unknown motor species properties. This approach provides a quantitative tool for characterising heterogeneous actin-myosin systems, such as those arising from the co-presence of different protein isoforms in cardiac and skeletal muscle, or from the partial replacement of native proteins with mutation-derived or engineered variants.

cond-mat.stat-mech↗

arXiv2026

Optimal Navigation on Simplicial Complexes

The navigation time and optimal search strategies deriving from random dynamical processes on binary graphs have been extensively explored and analyzed, being of prominent interest in the network science field. In this work, we study an extension of these topological measures for simplicial complexes: a specific type of geometric and algebraic structures that encapsulates higher-order interactions. Here, the explorability analysis of simplicial complexes has been conducted in terms of the mean first passage times between nodes, i.e. the 0th-order simplices, with the inclusion of a long-range stochastic teleportation term modulated with respect to the local random walk hopping across the various dimensions. We also provide a perturbative approximation scheme recovering the modulation parameter between pure random walk and teleportation mode (for higher-order setting) acting as the expansion parameter.

cond-mat.stat-mech↗

arXiv2026

Spectral Higher-Order Neural Networks Have Sharp Expressivity Bounds

Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning. Yet, their deployment has proven demanding: the number of weighted hyperedges required leads to an intractable parameter explosion. However, a novel parametrization that leverages spectral attributes for neural hypergraphs has been recently proposed, that enables to recycle parameters via a weight sharing scheme and consequently yields a significant reduction of the associated computational cost. Preliminary tests carried out on spectral higher-order architectures pointed to meaningful improvements in both performance and interpretability. Building on these results, we advance the benchmarking efforts by evaluating the spectral higher order framework on N-bit parity tasks, a well-established testbed known to be particularly challenging. As we will convincingly argue, Spectral Higher-Order Neural Networks (SHONNs) possess a versatile and highly tunable hypothesis space.

cs.LG↗

arXiv2026

Approximating velocity fields with planted attractors via Neural-ODEs for classification purposes

In this work, Neural ODEs equipped with a curated collection of equilibrium points have been successfully employed for classification tasks. The planted attractors serve as indicators for the target classes, while the velocity field leveraging the universal approximation capabilities of the architecture shapes the dynamical landscape. This process defines the basins of attraction of the trained model, effectively directing each input (provided as an initial condition) toward its corresponding destination target.

cond-mat.dis-nn↗

arXiv2026

Noise seeded oscillators: on the role of demographic fluctuations in a multi-populations model

Stochastic oscillations can emerge from a two-population model as triggered by endogenous finite size fluctuations. Here, an extended dynamical scenario is considered in which a third fluctuating species is added to a proto-typical scheme of neuronal interaction. As we shall prove both analytically and numerically, the third added species can enhance or even suppress the emergence of quasi-cycles, namely the coherent oscillations of the two original populations, as instigated by the demographic noise component. In general, investigating the coupled dynamics of noisy oscillators of the type considered could yield an extended framework for synchronization studies, beyond the pioneering setting introduced by Kuramoto.

nlin.AO↗

arXiv2026

Model of Simplicial Complexes with dimension-wise preferential attachment

Network science is a powerful framework allowing to model complex systems, it is capable to describe and take into account the intricate web of connections existing among the constituting basic element of the system. Recently scholars have brought to the fore the relevance of higher-order networks, namely structures allowing to encode for many-body interaction, differently from the pairwise case handled by networks. This novel research field opens new avenues of research with applications ranging from neurosciences to social sciences; there is thus a need for generative models of higher-order network capable to reproduce features present in empirical data. In this work we present a model for growing simplicial complex rooted on a preferential attachment process acting dimension-wise, i.e., returning a power law distribution for the generalized degree of simplexes of different dimension.

cond-mat.stat-mech↗

arXiv2026

Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality

We introduce a technique that enables Neural-ODEs to approximate arbitrary velocity fields with a priori planted fixed-points. Specifically, a recipe is given to explicitly accommodate for a finite collection of points in the reference multi-dimensional space of the Neural-ODE where the velocity field is exactly equal to zero. In this way, the gradient-based training is rigorously constrained inside the prescribed hypothesis class while leaving the expressive power of the Neural-ODE unaltered. We rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points. Our method is then tested on two paradigmatic physical models.

cond-mat.dis-nn↗

arXiv2026

Spectral Higher-Order Neural Networks

Neural networks are fundamental tools of modern machine learning. The standard paradigm assumes binary interactions (across feedforward linear passes) between inter-tangled units, organized in sequential layers. Generalized architectures have been also designed that move beyond pairwise interactions, so as to account for higher-order couplings among computing neurons. Higher-order networks are however usually deployed as augmented graph neural networks (GNNs), and, as such, prove solely advantageous in contexts where the input exhibits an explicit hypergraph structure. Here, we present Spectral Higher-Order Neural Networks (SHONNs), a new algorithmic strategy to incorporate higher-order interactions in general-purpose, feedforward, network structures. SHONNs leverages a reformulation of the model in terms of spectral attributes. This allows to mitigate the common stability and parameter scaling problems that come along weighted, higher-order, forward propagations.

cs.LG↗

arXiv2026

Smart Walkers in Discrete Space

We study the statistical properties of trainable agents moving in discrete space. After introducing the mathematical framework, we first analyze the dynamics of two completely random walkers, mutually competing in a chaser-target interaction scheme. The statistics of the encounters is analytically obtained and the predictions tested versus numerical simulations. We then move forward to extend the baseline case to agents capable of learning and adapting to an external reward signal, using reinforcement learning. Smart walkers morph the statistics of the encounter, to maximize their cumulated reward, as confirmed by combined numerical and analytical insights. More interestingly, configuration entropy proves a reliable proxy to gauge the acquired ability of the agents to cope with the assigned task when no other information about them (i.e. reward signal, policy, etc) is present. We further test the proposed measure of learned skills by operating the Stockfish chess engine against a quasi-random untrained opponent. The obtained conclusions corroborate our claim. Summing up, our primary contribution is to propose and test a quantitative measure of agents' awareness that naturally correlates with the inherent complexity of the task being performed.

cond-mat.stat-mech↗

arXiv2026

Random Walks Across Dimensions: Exploring Simplicial Complexes

We introduce a novel operator to describe a random walk process on a simplicial complex. Walkers are allowed to wonder across simplices of various dimensions, bridging nodes to edges, and edges to triangles, via a nested organization that hierarchically extends to higher structures of arbitrary large, but finite, dimension. The asymptotic distribution of the walkers provides a natural ranking to gauge the relative importance of higher order simplices. Optimal search strategies in presence of stochastic teleportation are addressed and the peculiar interplay of noise with higher order structures unraveled.

cond-mat.stat-mech↗

arXiv2025

Generalized Wilson-Cowan model with short term synaptic plasticity

A generalized version of the Wilson-Cowan (WC) model is proposed which accounts for the evolution of the synaptic resources. Adiabatic elimination of the fast variables is performed to yield a simplified framework for the coupled interaction between active excitatory and inhibitory neurons. The latter model is shown to smoothly converge to the benchmark WC model, when the appropriate limit is performed. Different dynamical regimes are identified for the reduced model and commented upon with reference to the original formulation of the generalized dynamics. This includes identifying limit cycle oscillations for population of available resources.

cond-mat.dis-nn↗

arXiv2025

Train Stochastic Non Linear Coupled ODEs to Classify and Generate

A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the dynamical system amounts to shaping the architecture of inter-nodes connection to steer the evolution towards the assigned equilibrium, as a function of the class to which the item - supplied as an initial condition - belongs to. Under the stochastic perspective, point attractors are turned into probability distributions, made analytically accessible via the linear noise approximation. The addition of noise proves beneficial to oppose adversarial attacks, a property that gets engraved into the trained adjacency matrix and therefore also inherited by the deterministic counterpart of the optimized stochastic model. By providing samples from the target distribution as an input to a feedforward neural network (or even to a dynamical model of the same typology of the adopted for classification purposes), yields a fully generative scheme. Conditional generation is also possible by merging classification and generation modalities. Automatic disentanglement of isolated key features is finally proven.

cond-mat.dis-nn↗

arXiv2025

Spectral Architecture Search for Neural Network Models

Architecture design and optimization are challenging problems in the field of artificial neural networks. Working in this context, we here present SPARCS (SPectral ARchiteCture Search), a novel architecture search protocol which exploits the spectral attributes of the inter-layer transfer matrices. SPARCS allows one to explore the space of possible architectures by spanning continuous and differentiable manifolds, thus enabling for gradient-based optimization algorithms to be eventually employed. With reference to simple benchmark models, we show that the newly proposed method yields a self-emerging architecture with a minimal degree of expressivity to handle the task under investigation and with a reduced parameter count as compared to other viable alternatives.

cs.LG↗

arXiv2024

Stochastic quasi-cycles as a simple explanation for the time evolution of the Cape Rodney-Okakari Point Marine ecological reserve

The dataset collected at the Cape Rodney-Okakari Point Marine (CR-OPM) reserve on the North Island of New Zealand is rather unique. It describes the cyclic time evolution of a rocky intertidal community, with the relative abundances of the various coastal species that have been meticulously monitored for more than 20 years. Past theoretical studies, anchored on a deterministic description, required invoking ad hoc mechanisms to reproduce the observed dynamical paths. Following a maximum likelihood approach to interpolate individual stochastic trajectories, we here propose quasi-cycles as an alternative and simpler mechanism to explain the oscillations observed in the population numbers of the ecosystem. From a general standpoint, we also show that it is possible to return conclusive evidence on the existence of stochastic quasi-cycles, without resorting to global fitting strategies which necessitate handling a large collection of independent replicas of the dynamics, a possibility that is often precluded in real life applications.

q-bio.PE↗

arXiv2024

Deterministic versus stochastic dynamical classifiers: opposing random adversarial attacks with noise

The Continuous-Variable Firing Rate (CVFR) model, widely used in neuroscience to describe the intertangled dynamics of excitatory biological neurons, is here trained and tested as a veritable dynamically assisted classifier. To this end the model is supplied with a set of planted attractors which are self-consistently embedded in the inter-nodes coupling matrix, via its spectral decomposition. Learning to classify amounts to sculp the basin of attraction of the imposed equilibria, directing different items towards the corresponding destination target, which reflects the class of respective pertinence. A stochastic variant of the CVFR model is also studied and found to be robust to aversarial random attacks, which corrupt the items to be classified. This remarkable finding is one of the very many surprising effects which arise when noise and dynamical attributes are made to mutually resonate.

cs.LG↗

arXiv2024

A short introduction to Neural Networks and their application to Earth and Materials Science Science

Neural networks are gaining widespread relevance for their versatility, holding the promise to yield a significant methodological shift in different domain of applied research. Here, we provide a simple pedagogical account of the basic functioning of a feedforward neural network. Then we move forward to reviewing two recent applications of machine learning to Earth and Materials Science. We will in particular begin by discussing a neural network based geothermobarometer, which returns reliable predictions of the pressure/temperature conditions of magma storage. Further, we will turn to illustrate how machine learning tools, tested on the list of minerals from the International Mineralogical Association, can help in the search for novel superconducting materials.

physics.data-an↗

arXiv2024

Resolving the kinetics of an ensemble of muscle myosin motors via a temperature-dependent fitting procedure

A data fitting procedure is devised and thoroughly tested to provide self-consistent estimates of the relevant mechanokinetic parameters involved in a plausible scheme underpinning the output of an ensemble of myosin II molecular motors mimicking the muscle contraction. The method builds on a stochastic model accounting for the force exerted by the motor ensemble operated both in the low and high force-generating regimes corresponding to different temperature ranges. The proposed interpretative framework is successfully challenged against simulated data, meant to mimic the experimental output of a unidimensional synthetic nanomachine powered by pure muscle myosin isoforms.

cond-mat.stat-mech↗

arXiv2024

Force and kinetics of fast and slow muscle myosin determined with a synthetic sarcomere-like nanomachine

Myosin II is the muscle molecular motor that works in two bipolar arrays in each thick filament of the striated (skeletal and cardiac) muscle, converting the chemical energy into steady force and shortening by cyclic ATP--driven interactions with the nearby actin filaments. Different isoforms of the myosin motor in the skeletal muscles account for the different functional requirements of the slow muscles (primarily responsible for the posture) and fast muscles (responsible for voluntary movements). To clarify the molecular basis of the differences, here the isoform--dependent mechanokinetic parameters underpinning the force of slow and fast muscles are defined with a unidimensional synthetic nanomachine powered by pure myosin isoforms from either slow or fast rabbit skeletal muscle. Data fitting with a stochastic model provides a self--consistent estimate of all the mechanokinetic properties of the motor ensemble including the motor force, the fraction of actin--attached motors and the rate of transition through the attachment--detachment cycle. The achievements in this paper set the stage for any future study on the emergent mechanokinetic properties of an ensemble of myosin molecules either engineered or purified from mutant animal models or human biopsies.

cond-mat.stat-mech↗