arXiv subjects

Francesco Caravelli

Publications and source records attributed to Francesco Caravelli.

At least 37 records · Page 2Linked to original sources

arXiv2025

A unifying approach to self-organizing systems interacting via conservation laws

We present a unified framework for embedding and analyzing dynamical systems using generalized projection operators rooted in local conservation laws. By representing physical, biological, and engineered systems as graphs with incidence and cycle matrices, we derive dual projection operators that decompose network fluxes and potentials. This formalism aligns with principles of non-equilibrium thermodynamics and captures a broad class of systems governed by flux-forcing relationships and local constraints. We extend this approach to collective dynamics through the PRojective Embedding of Dynamical Systems (PrEDS), which lifts low-dimensional dynamics into a high-dimensional space, enabling both replication and recovery of the original dynamics. When systems fall within the PrEDS class, their collective behavior can be effectively approximated through projection onto a mean-field space. We demonstrate the versatility of PrEDS across diverse domains, including resistive and memristive circuits, adaptive flow networks (e.g., slime molds), elastic string networks, and particle swarms. Notably, we establish a direct correspondence between PrEDS and swarm dynamics, revealing new insights into optimization and self-organization. Our results offer a general theoretical foundation for analyzing complex networked systems and for designing systems that self-organize through local interactions.

cond-mat.soft↗

arXiv2025

Voltage-Controlled Oscillator and Memristor-Based Analog Computing for Solving Systems of Linear Equations

Matrix computations have become increasingly significant in many data-driven applications. However, Moores law for digital computers has been gradually approaching its limit in recent years. Moreover, digital computers encounter substantial complexity when performing matrix computations and need a long time to finish the computations, and existing analog matrix computation schemes require a large chip area and power consumption. This paper proposes a linear algebra system of equations based on integrators, which features low power consumption, compact area, and fast computation time. Due to the simple structure of the ring oscillator, the ring oscillator-based integrator exhibits a compact area and low power consumption. Therefore, ring oscillator-based integrators are introduced into the linear algebra system of equations, and this system can be used to compute the linear algebra equations of the matrix with either positive or negative values. This paper provides a detailed analysis and verification of the proposed circuit structure. Compared to similar circuits, this work has significant advantages in terms of area, power consumption, and computation speed.

eess.SY↗

arXiv2025

Classical Criticality via Quantum Annealing

Quantum annealing provides a powerful platform for simulating magnetic materials and realizing statistical physics models, presenting a compelling alternative to classical Monte Carlo methods. We demonstrate that quantum annealers can accurately reproduce phase diagrams and simulate critical phenomena without suffering from the critical slowing down that often affects classical algorithms. To illustrate this, we study the piled-up dominoes model, which interpolates between the ferromagnetic 2D Ising model and Villain's fully frustrated ``odd model''. We map out its phase diagram and for the first time, employ finite-size scaling and Binder cumulants on a quantum annealer to study critical exponents for thermal phase transitions. Our method achieves systematic temperature control by tuning the energy scale of the Hamiltonian, eliminating the need to adjust the physical temperature of the quantum hardware. This work demonstrates how, through fine-tuning and calibration, a quantum annealer can be employed to apply sophisticated finite-size scaling techniques from statistical mechanics. Our results establish quantum annealers as robust statistical physics simulators, offering a novel pathway for studying phase transitions and critical behavior.

cond-mat.stat-mech↗

arXiv2025

DebtStreamness: An Ecological Approach to Credit Flows in Inter-Firm Networks

Understanding how credit flows through inter-firm networks is critical for assessing financial stability and systemic risk. In this study, we introduce DebtStreamness, a novel metric inspired by trophic levels in ecological food webs, to quantify the position of firms within credit chains. By viewing credit as the ``primary energy source'' of the economy, we measure how far credit travels through inter-firm relationships before reaching its final borrowers. Applying this framework to Uruguay's inter-firm credit network, using survey data from the Central Bank, we find that credit chains are generally short, with a tiered structure in which some firms act as intermediaries, lending to others further along the chain. We also find that local network motifs such as loops can substantially increase a firm's DebtStreamness, even when its direct borrowing from banks remains the same. Comparing our results with standard economic classifications based on input-output linkages, we find that DebtStreamness captures distinct financial structures not visible through production data. We further validate our approach using two maximum-entropy network reconstruction methods, demonstrating the robustness of DebtStreamness in capturing systemic credit structures. These results suggest that DebtStreamness offers a complementary ecological perspective on systemic credit risk and highlights the role of hidden financial intermediation in firm networks.

econ.GN↗

arXiv2025

Correlation between upstreamness and downstreamness in random global value chains

This paper is concerned with upstreamness and downstreamness of industries and countries. Upstreamness and downstreamness measure respectively the average distance of an industrial sector from final consumption and from primary inputs. Recently, Antràs and Chor reported a puzzling and counter-intuitive finding in data from the period 1995-2011, namely that (at country level) upstreamness appears to be positively correlated with downstreamness, with a correlation slope close to $+1$. We first analyze a simple model of random Input/Output tables, and we show that, under minimal and realistic structural assumptions, there is a natural positive correlation emerging between upstreamness and downstreamness of the same industrial sector/country, with correlation slope equal to $+1$. This effect is robust against changes in the randomness of the entries of the I/O table and different aggregation protocols. Secondly, we perform experiments by randomly reshuffling the entries of the empirical I/O table where these puzzling correlations are detected, in such a way that the global structural constraints are preserved. Again, we find that the upstreamness and downstreamness of the same industrial sector/country are positively correlated with slope close to $+1$. Our results strongly suggest that (i) extra care is needed when interpreting these measures as simple representations of each sector's positioning along the value chain, as the ``curse of the input-output identities'' and labor effects effectively force the value chain to acquire additional links from primary factors of production, and (ii) the empirically observed puzzling correlation may rather be a necessary consequence of the few structural constraints (positive entries, and sub-stochasticity) that Input/Output tables and their surrogates must meet.

stat.AP↗

arXiv2025

The dipolar Aleppo lattice: Ground state ordering and ergodic dynamics in the absence of vertex frustration

We introduce the Aleppo spin ice geometry, another variation of decimated square ice patterns, which in contrast to similar systems previously studied, does not exhibit vertex frustration. Using synchrotron-based photoemission electron microscopy, we directly visualize low-energy states achieved after thermal annealing, in addition to temperature-dependent moment fluctuations. The results reveal the observation of ground state patterns and the absence of ergodicity-breaking dynamics. Our observations further confirm vertex frustration to be an important criterion for the emergence of ergodicity transitions.

cond-mat.mes-hall↗

arXiv2024

R-Ising: Effective resistance in random magnetic nanowires networks

Random assemblies of magnetic nanowires represent a unique class of materials with promising applications in spintronics and information storage. These assemblies exhibit complex behavior due to the combination of magnetic dipolar interactions between the nanowires and electronic transport properties governed by tunneling barriers at magnetic tunnel junctions (MTJs). The intricate interplay of these phenomena makes the study of magnetic nanowire networks a rich area of research. In this study, we develop a theoretical framework to analyze the resistive behavior of random magnetic nanowire networks. By employing a combination of graph theoretical approaches and mean-field theory, we derive an effective resistance model that encapsulates the contributions of magnetic interactions between the nanowires. Our findings show the importance of considering both the magnetic and electrical properties of nanowire networks in the design and optimization of amorphous resistive devices.

cond-mat.stat-mech↗

arXiv2024

Universally-Charging Protocols for Quantum Batteries: A No-Go Theorem

The effectiveness of a quantum battery relies on a robust charging process, yet these are often sensitive to initial state of the battery. We introduce the concept of a universally-charging (UC) protocol, defined as one that either increases or maintains the average battery energy for all initial states, without ever decreasing it. We show that UC protocols are impossible for closed quantum batteries, thus necessitating interactions with auxilliary quantum systems. To that end, we prove a no-go theorem which prohibits UC protocols for closed quantum batteries with finite-dimensional Hilbert spaces. Leveraging a no-go theorem for topological quantum walks, we argue that even for infinite-dimensional Hilbert spaces, while unitary UC operators exist, they cannot be generated by physically reasonable Hamiltonian protocols. However, regardless of the dimension, non-unitary UC protocols can be achieved in open quantum batteries. To illustrate this, we present a general model with a control qubit, whose state interpolates between universal-charging and universal-discharging protocols.

quant-ph↗

arXiv2024

Neuromorphic Overparameterisation and Few-Shot Learning in Multilayer Physical Neural Networks

Physical neuromorphic computing, exploiting the complex dynamics of physical systems, has seen rapid advancements in sophistication and performance. Physical reservoir computing, a subset of neuromorphic computing, faces limitations due to its reliance on single systems. This constrains output dimensionality and dynamic range, limiting performance to a narrow range of tasks. Here, we engineer a suite of nanomagnetic array physical reservoirs and interconnect them in parallel and series to create a multilayer neural network architecture. The output of one reservoir is recorded, scaled and virtually fed as input to the next reservoir. This networked approach increases output dimensionality, internal dynamics and computational performance. We demonstrate that a physical neuromorphic system can achieve an overparameterised state, facilitating meta-learning on small training sets and yielding strong performance across a wide range of tasks. Our approach's efficacy is further demonstrated through few-shot learning, where the system rapidly adapts to new tasks.

cond-mat.mes-hall↗

arXiv2024

Uncontrolled learning: co-design of neuromorphic hardware topology for neuromorphic algorithms

Hardware-based neuromorphic computing remains an elusive goal with the potential to profoundly impact future technologies and deepen our understanding of emergent intelligence. The learning-from-mistakes algorithm is one of the few training algorithms inspired by the brain's simple learning rules, utilizing inhibition and pruning to demonstrate self-organized learning. Here we implement this algorithm in purely neuromorphic memristive hardware through a co-design process. This implementation requires evaluating hardware trade-offs and constraints. It has been shown that learning-from-mistakes successfully trains small networks to function as binary classifiers and perceptrons. However, without tailoring the hardware to the algorithm, performance decreases exponentially as the network size increases. When implementing neuromorphic algorithms on neuromorphic hardware, we investigate the trade-offs between depth, controllability, and capacity, the latter being the number of learnable patterns. We emphasize the significance of topology and the use of governing equations, demonstrating theoretical tools to aid in the co-design of neuromorphic hardware and algorithms. We provide quantitative techniques to evaluate the computational capacity of a neuromorphic device based on the measurements performed and the underlying circuit structure. This approach shows that breaking the symmetry of a neural network can increase both the controllability and average network capacity. By pruning the circuit, neuromorphic algorithms in all-memristive device circuits leverage stochastic resources to drive local contrast in network weights. Our combined experimental and simulation efforts explore the parameters that make a network suited for displaying emergent intelligence from simple rules.

cond-mat.dis-nn↗

arXiv2024

Memristive Linear Algebra

The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the potential of memristive crossbars in implementing matrix inversion algorithms. We explore both static and dynamic approaches, emphasizing the advantages of analog and in-memory computing for matrix operations beyond multiplication. Our results demonstrate that memristive arrays can significantly reduce computational complexity and power consumption compared to traditional digital methods for certain matrix tasks. Furthermore, we address the challenges of device variability, precision, and scalability, providing insights into the practical implementation of these algorithms.

cond-mat.mes-hall↗

arXiv2024

Neuromorphic on-chip reservoir computing with spiking neural network architectures

Reservoir computing is a promising approach for harnessing the computational power of recurrent neural networks while dramatically simplifying training. This paper investigates the application of integrate-and-fire neurons within reservoir computing frameworks for two distinct tasks: capturing chaotic dynamics of the Hénon map and forecasting the Mackey-Glass time series. Integrate-and-fire neurons can be implemented in low-power neuromorphic architectures such as Intel Loihi. We explore the impact of network topologies created through random interactions on the reservoir's performance. Our study reveals task-specific variations in network effectiveness, highlighting the importance of tailored architectures for distinct computational tasks. To identify optimal network configurations, we employ a meta-learning approach combined with simulated annealing. This method efficiently explores the space of possible network structures, identifying architectures that excel in different scenarios. The resulting networks demonstrate a range of behaviors, showcasing how inherent architectural features influence task-specific capabilities. We study the reservoir computing performance using a custom integrate-and-fire code, Intel's Lava neuromorphic computing software framework, and via an on-chip implementation in Loihi. We conclude with an analysis of the energy performance of the Loihi architecture.

cs.NE↗

arXiv2024

Boundary-induced classical Generalized Gibbs Ensemble with angular momentum

We investigate the impact of the boundary shape on the thermalization behavior of a confined system of classical hard disks at low packing fraction and thus in the gas regime. We use both analytical calculations and numerical simulations, and leveraging on the insights from the maximum entropy principle, we explore how the geometry of the boundary influences the thermal equilibration process in such systems. Our simulations involve hard disks confined within varying boundary shapes, using both event-driven and time-driven simulations, ranging from conventional square boundaries to circular boundaries, showing that the two converge to different ensembles. The former converges to the Gibbs Ensemble, while the latter converges to the Generalized Gibbs Ensemble (GGE), with angular momentum as the extra conserved quantity. We introduce an order parameter to characterize the deviations from the Gibbs ensemble, and show that the GGE is not time-reversal invariant, it violates ergodicity and leads to a near-boundary condensation phenomenon. Because of this, we argue that Monte Carlo methods should include angular momentum in this situation. We conclude by discussing how these results lead to peculiar violations of the Bohr-van Leeuwen theorem.

cond-mat.stat-mech↗

arXiv2024

Quantum graph models for transport in filamentary switching

The formation of metallic nanofilaments bridging two electrodes across an insulator is a mechanism for resistive switching. Examples of such phenomena include atomic synapses, which constitute a distinct class of memristive devices whose behavior is closely tied to the properties of the filament. Until recently, experimental investigation of the low-temperature regime and quantum transport effects has been limited. However, with growing interest in understanding the true impacts of the filament on device conductance, comprehending quantum effects has become crucial for quantum neuromorphic hardware. We discuss quantum transport resulting from filamentary switching in a narrow region where the continuous approximation of the contact is not valid, and only a few atoms are involved. In this scenario, the filament can be represented by a graph depicting the adjacency of atoms and the overlap between atomic orbitals. Using quantum graphs, we calculate the scattering amplitude of charge carriers on this graph and explore the interplay between filamentary formation and quantum transport effects.

cond-mat.mes-hall↗

arXiv2024

Network analysis of memristive device circuits: dynamics, stability and correlations

Networks with memristive devices are a potential basis for the next generation of computing devices. They are also an important model system for basic science, from modeling nanoscale conductivity to providing insight into the information-processing of neurons. The resistance in a memristive device depends on the history of the applied bias and thus displays a type of memory. The interplay of this memory with the dynamic properties of the network can give rise to new behavior, offering many fascinating theoretical challenges. But methods to analyze general memristive circuits are not well described in the literature. In this paper we develop a general circuit analysis for networks that combine memristive devices alongside resistors, capacitors and inductors and under various types of control. We derive equations of motion for the memory parameters of these circuits and describe the conditions for which a network should display properties characteristic of a resonator system. For the case of a purely memresistive network, we derive Lyapunov functions, which can be used to study the stability of the network dynamics. Surprisingly, analysis of the Lyapunov functions show that these circuits do not always have a stable equilibrium in the case of nonlinear resistance and window functions. The Lyapunov function allows us to study circuit invariances, wherein different circuits give rise to similar equations of motion, which manifest through a gauge freedom and node permutations. Finally, we identify the relation between the graph Laplacian and the operators governing the dynamics of memristor networks operators, and we use these tools to study the correlations between distant memristive devices through the effective resistance.

cond-mat.dis-nn↗

arXiv2024

Distribution of centrality measures on undirected random networks via cavity method

The Katz centrality of a node in a complex network is a measure of the node's importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like and undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its "global" character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-cavity algorithm to solve linear systems on a tree-like structure, we show that (i) the Katz centrality of a single instance can be computed recursively in a very fast way, and (ii) the probability $P(K)$ that a random node in the ensemble of undirected random graphs has centrality $K$ satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and scale-free networks in the locally tree-like regime, with excellent agreement. The distributions display a crossover between multimodality and unimodality as the mean degree increases, where distinct peaks correspond to the contribution to the centrality coming from nodes of different degrees. We also provide an approximate formula based on a rank-$1$ projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way.

physics.soc-ph↗

arXiv2024

Upstreamness and downstreamness in input-output analysis from local and aggregate information

Ranking sectors and countries within global value chains is of paramount importance to estimate risks and forecast growth in large economies. However, this task is often non-trivial due to the lack of complete and accurate information on the flows of money and goods between sectors and countries, which are encoded in Input-Output (I-O) tables. In this work, we show that an accurate estimation of the role played by sectors and countries in supply chain networks can be achieved without full knowledge of the I-O tables, but only relying on local and aggregate information, e.g., the total intermediate demand per sector. Our method, based on a rank-$1$ approximation to the I-O table, shows consistently good performance in reconstructing rankings (i.e., upstreamness and downstreamness measures for countries and sectors) when tested on empirical data from the World Input-Output Database. Moreover, we connect the accuracy of our approximate framework with the spectral properties of the I-O tables, which ordinarily exhibit relatively large spectral gaps. Our approach provides a fast and analytical tractable framework to rank constituents of a complex economy without the need of matrix inversions and the knowledge of finer intersectorial details.

physics.soc-ph↗

arXiv2023

Ergodicity, lack thereof, and the performance of reservoir computing with memristive networks

Networks composed of nanoscale memristive components, such as nanowire and nanoparticle networks, have recently received considerable attention because of their potential use as neuromorphic devices. In this study, we explore the connection between ergodicity in memristive and nanowire networks, showing that the performance of reservoir devices improves when these networks are tuned to operate at the edge between two global stability points. The lack of ergodicity is associated with the emergence of memory in the system. We measure the level of ergodicity using the Thirumalai-Mountain metric, and we show that in the absence of ergodicity, two memristive systems show improved performance when utilized as reservoir computers (RC). In particular, we highlight that it is also important to let the system synchronize to the input signal in order for the performance of the RC to exhibit improvements over the baseline.

cond-mat.dis-nn↗