arXiv subjects

Roberto Mulet

Publications and source records attributed to Roberto Mulet.

At least 19 recordsLinked to original sources

arXiv2026

The Swapping Mechanism for Interacting Diffusions: Framework, Comparison with Switching, and an Exactly Solvable Example

We develop a rigorous framework for the swapping mechanism for two interacting jump-diffusion processes: each particle evolves independently but their positions are exchanged at random times, providing a continuous-time description of the replica-exchange Monte Carlo. Under mild hypotheses we establish strong existence, pathwise uniqueness, and a forward Kolmogorov equation for the transition density. A symmetrisation identity links swapping to the more standard regime-switching: swapping densities are relabelled sums of switching sectors, so permutation-invariant observables of these processes coincide, while antisymmetric ones differ. We prove that under detailed balance and reversibility the swapping process never degrades the spectral gap, and that, under label invariance, the antisymmetric gap improves compared to the decoupled process. We also show that, for $N$ particles, swapping remains Markov on $\mathbb{R}^N$ with polynomial moment closures, whereas switching requires tracking the full symmetric group, highlighting a fundamental complexity difference. We conclude the work presenting an exactly solvable benchmark of two Brownian motions with constant drifts and swap rate. For this model we obtain closed-form transition densities in terms of modified Bessel functions, exact moments, and two-time correlations. The asymptotic analysis reveals persistent asymmetries, an effective diffusivity correction, and a convergence rate of order $s^{-1/2}$ in the fast-swap limit (where $s>0$ is the constant swap rate).

math.PR↗

arXiv2026

The Longest Increasing Subsequence Problem revisited

The Longest Increasing Subsequence problem - a classic combinatorial challenge with deep connections to statistical mechanics- exhibits a rich thermodynamic landscape. Introducing a temperature we identify two distinct energy scales: A Schottky-like crossover at T_cross and a condensation transition at T_cond, below which the number of maximum-length configurations becomes sub-exponential in system size. We also show that despite the existence of polynomial-time dynamic programming algorithms for the ground state, local Monte Carlo dynamics, after sudden quenches at low temperatures, become trapped in metastable state configurations displaying characteristic glassy signatures: two-step relaxation, persistent dynamical overlaps and aging. On the other hand, logarithmic annealing tracks equilibrium down to the ground state. These results establish that thermodynamic sparsity - not energetic barriers - can render local search dynamically intractable, positioning the LIS problem as a bridge between exactly solvable optimization and glassy spin-glass phenomenology.

cond-mat.dis-nn↗

arXiv2025

Sparse Interactions Reshape Stability in Random Lotka-Volterra Dynamics

Classical approaches to ecological stability rely on fully connected interaction models, yet real ecosystems are sparse and structured--a feature that qualitatively reshapes their collective dynamics. Here, we establish a thermodynamically exact stability phase diagram for generalized Lotka-Volterra dynamics on sparse random graphs, resolving how finite connectivity and interaction heterogeneity jointly govern ecosystem resilience. Using a small-coupling expansion of the dynamic cavity method, we derive an effective single-site stochastic process that is solvable via population dynamics. Our approach uncovers a topological phase transition--driven purely by the finite connectivity structure of the network--that leads to multi-stability. This instability is fundamentally distinct from the disorder-driven transitions induced by quenched randomness of the couplings. Our framework overcomes the considerable computational cost of direct simulations, offering a scalable and versatile analysis of stability, biodiversity, and alternative stable states in realistic, large-scale ecological ecosystems.

cond-mat.dis-nn↗

arXiv2025

Local equations describe unreasonably efficient stochastic algorithms in random K-SAT

Despite significant advances in characterizing the highly nonconvex landscapes of constraint satisfaction problems, the good performance of certain algorithms in solving hard combinatorial optimization tasks remains poorly understood. This gap in understanding stems largely from the lack of theoretical tools for analyzing their out-of-equilibrium dynamics. To address this challenge, we develop a system of approximate master equations that capture the behavior of local search algorithms in constraint satisfaction problems. Our framework shows excellent qualitative agreement with the phase diagrams of two paradigmatic algorithms: Focused Metropolis Search (FMS) and greedy-WalkSAT (G-WalkSAT) for random 3-SAT. The equations not only confirm the numerical observation that G-WalkSAT's algorithmic threshold is nearly parameter-independent, but also successfully predict FMS's threshold beyond the clustering transition. We also exploit these equations in a decimation scheme, demonstrating that the computed marginals encode valuable information about the local structure of the solution space explored by stochastic algorithms. Notably, our decimation approach achieves a threshold that surpasses the clustering transition, outperforming conventional methods like Belief Propagation-guided decimation. These results challenge the prevailing assumption that long-range correlations are always necessary to describe efficient local search dynamics and open a new path to designing efficient algorithms to solve combinatorial optimization problems.

cond-mat.dis-nn↗

arXiv2025

Looking into informal currency markets as Limit Order Books: impact of market makers

This study pioneers the application of the market microstructure framework to an informal financial market. By scraping data from websites and social media about the Cuban informal currency market, we model the dynamics of bid/ask intentions using a Limit Order Book (LOB). This approach enables us to study key characteristics such as liquidity, stability and volume profiles. We continue exploiting the Avellaneda-Stoikov model to explore the impact of introducing a Market Maker (MM) into this informal setting, assessing its influence on the market structure and the bid/ask dynamics. We show that the Market Maker improves the quality of the market. Beyond their academic significance, we believe that our findings are relevant for policymakers seeking to intervene informal markets with limited resources.

q-fin.TR↗

arXiv2024

Metabolic coordination and phase transitions in spatially distributed multi-cellular systems

During overflow metabolism, cells excrete glycolytic byproducts when growing under aerobic conditions in a seemingly wasteful fashion. While potentially advantageous for microbes with finite oxidative capacity, its role in higher organisms is harder to assess. Recent single-cell experiments suggest overflow metabolism arises due to imbalances in inter-cellular exchange networks. We quantitatively characterize this scenario by integrating spatial metabolic modeling with tools from statistical physics and experimental single-cell flux data. Our results provide a theoretical demonstration of how diffusion-limited exchanges shape the space of accessible multi-cellular metabolic states. Specifically, a phase transition from a balanced network of exchanges to an unbalanced, overflow regime occurs as mean glucose and oxygen uptake rates vary. Heterogeneous single-cell metabolic phenotypes occur near this transition. Time-resolved tumor-stroma co-culture data support the idea that overflow metabolism stems from failure of inter-cellular metabolic coordination. In summary, environmental control is an emergent multi-cellular property, rather than a cell-autonomous effect.

cond-mat.stat-mech↗

arXiv2023

Improved mean-field dynamical equations are able to detect the two-steps relaxation in glassy dynamics at low temperatures

We study the stochastic relaxation dynamics of the Ising p-spin model on a random graph, a well-known model with glassy dynamics at low temperatures. We introduce and discuss a new closure scheme for the master equation governing the continuous-time relaxation of the system, that translates into a set of differential equations for the evolution of local probabilities. The solution to these dynamical mean-field equations describes very well the out-of-equilibrium dynamics at high temperatures, notwithstanding the key observation that the off-equilibrium probability measure contains higher-order interaction terms, not present in the equilibrium measure. In the low-temperature regime, the solution to the dynamical mean-field equations shows the correct two-step relaxation (a typical feature of the glassy dynamics), but with a relaxation timescale too short. We propose a solution to this problem by identifying the range of energies where entropic barriers play a key role and defining a renormalized microscopic timescale for the dynamical mean-field solution. The final result perfectly matches the complex out-of-equilibrium dynamics computed through extensive Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2022

A closure for the Master Equation starting from the Dynamic Cavity Method

We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We introduce a new such method which can be derived in a more systematic manner, and which performs better on several important classes of problems.

cond-mat.stat-mech↗

arXiv2022

The mighty force: statistical inference and high-dimensional statistics

This is a review to appear as a contribution to the edited volume "Spin Glass Theory & Far Beyond - Replica Symmetry Breaking after 40 Years", World Scientific. It showcases a selection of contributions from the spin glass community at large to high-dimensional statistics, by focusing on three important graph-based models and methodologies having deeply impacted the field: inference of graphs (a.k.a. direct coupling analysis), inference from graphs (the community detection problem), and the dynamic cavity method, which in particular allows for inference from graphs encoding causal relations.

cond-mat.dis-nn↗

arXiv2021

Path-integral solution of MacArthur's resource-competition model for large ecosystems with random species-resources couplings

We solve MacArthur's resource-competition model with random species-resource couplings in the `thermodynamic' limit of infinitely many species and resources using dynamical path-integrals a la De Domincis. We analyze how the steady state picture changes upon modifying several parameters, including the degree of heterogeneity of metabolic strategies (encoding the preferences of species) and of maximal resource levels (carrying capacities), and discuss its stability. Ultimately, the scenario obtained by other approaches is recovered by analyzing an effective one-species-one-resource ecosystem that is fully equivalent to the original multi-species one. The technique used here can be applied for the analysis of other model ecosystems related to the version of MacArthur's model considered here.

q-bio.PE↗

arXiv2021

Ancestral Sequence Reconstruction for Co-evolutionary models

The ancestral sequence reconstruction problem is the inference, back in time, of the properties of common sequence ancestors from measured properties of contemporary populations. Standard algorithms for this problem assume independent (factorized) evolution of the characters of the sequences, which is generally wrong (e.g. proteins and genome sequences). In this work, we have studied this problem for sequences described by global co-evolutionary models, which reproduce the global pattern of cooperative interactions between the elements that compose it. For this, we first modeled the temporal evolution of correlated real valued characters by a multivariate Ornstein-Uhlenbeck process on a finite tree. This represents sequences as Gaussian vectors evolving in a quadratic potential, who describe selection forces acting on the evolving entities. Under a Bayesian framework, we developed a reconstruction algorithm for these sequences and obtained an analytical expression to quantify the quality of our estimation. We extend this formalism to discrete valued sequences by applying our method to a Potts model. We showed that for both continuous and discrete configurations, there is a wide range of parameters where, to properly reconstruct the ancestral sequences, intra-species correlations must be taken into account. We also demonstrated that, for sequences with discrete elements, our reconstruction algorithm outperforms traditional schemes based on independent site approximations.

cond-mat.dis-nn↗

arXiv2021

The quantum network as an environment

quantum system interacting with other quantum systems experiences these other systems asan effective environment. The environment is the result of integrating out all the other degrees of freedom in the network, and can be represented by a Feynman-Vernon influence functional (IF)acting on system of interest. A network is characterized by the constitutive systems, how they interact, and the topology of those interactions. Here we show that for networks having the topology of locally tree-like graphs, the Feynman-Vernon influence functional can be determined in a new version of the cavity or Belief Propagation (BP) method. In the BP update stage, cavity IFs are mapped to cavity IFs, while in the BP output stage cavity IFs are combined to output IFs. We compute the fixed point of of this version of BP for harmonic oscillator systems interacting uniformly. We discuss Replica Symmetry and the effects of disorder in this context.

quant-ph↗

arXiv2021

From random point processes to hierarchical Cavity Master Equations for the stochastic dynamics of disordered systems in Random Graphs: Ising models and epidemics

We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that generalize and improve the Cavity Master Equation (CME) recently obtained in other publications. Our derivation clarifies some of the hypotheses and approximations that originally lead to the CME, considered now as the first order of a more general technique. We tested the new scheme in the dynamics of three models defined over diluted graphs: the Ising ferromagnet, the Viana-Bray spin-glass and the susceptible-infectious-susceptible model for epidemics. In the first two, the new equations perform similarly to the best-known approaches in the literature. In the latter, they outperform the well-known Pair Quenched Mean-Field Approximation.

cond-mat.dis-nn↗

arXiv2020

The Quantum Cluster Variational Method and the Phase Diagram of the quantum ferromagnetic $J_1$-$J_2$ model

We exploit the Quantum Cluster Variational Method (QCVM) to study the $J_1$-$J_2$ model for quantum Ising spins. We first describe the QCVM and discuss how it is related to other Mean Field approximations. The phase diagram of the model is studied at the level of the Kikuchi approximation in square lattices as a function of the ratio between $g = J_2/J_1$ , the temperature and the longitudinal and transverse external fields. Our results show that quantum fluctuations may change the order of the transition and induce a gap between the ferromagnetic and the stripe phases. Moreover, when both longitudinal and transverse fields are present, thermal fluctuations and quantum effects contribute to the appearance of a nematic phase.

cond-mat.dis-nn↗

arXiv2019

Spin Glass Theory of Interacting Metabolic Networks

We cast the metabolism of interacting cells within a statistical mechanics framework considering both, the actual phenotypic capacities of each cell and its interaction with its neighbors. Reaction fluxes will be the components of high-dimensional spin vectors, whose values will be constrained by the stochiometry and the energy requirements of the metabolism. Within this picture, finding the phenotypic states of the population turns out to be equivalent to searching for the equilibrium states of a disordered spin model. We provide a general solution of this problem for arbitrary metabolic networks and interactions. We apply this solution to a simplified model of metabolism and to a complex metabolic network, the central core of the \emph{E. coli}, and demonstrate that the combination of selective pressure and interactions define a complex phenotypic space. Cells may specialize in producing or consuming metabolites complementing each other at the population level and this is described by an equilibrium phase space with multiple minima, like in a spin-glass model.

q-bio.MN↗

arXiv2019

Modeling functional resting-state brain networks through neural message passing on the human connectome

Understanding the relationship between the structure and function of the human brain is one of the most important open questions in Neurosciences. In particular, Resting State Networks (RSN) and more specifically the Default Mode Network (DMN) of the brain, which are defined from the analysis of functional data lack a definitive justification consistent with the anatomical structure of the brain. In this work, we show that a possible connection may naturally rest on the idea that information flows in the brain through a neural message-passing dynamics between macroscopic structures, like those defined by the human connectome (HC). In our model, each brain region in the HC is assumed to have a binary behavior (active or not), the strength of interactions among them is encoded in the anatomical connectivity matrix defined by the HC, and the dynamics of the system is defined by a neural message-passing algorithm, Belief Propagation (BP), working near the critical point of the human connectome. We show that in the absence of direct external stimuli the BP algorithm converges to a spatial map of activations that is similar to the DMN. Moreover, we computed, using Susceptibility Propagation (SP), the matrix of correlations between the different regions and show that the modules defined by a clustering of this matrix resemble several Resting States Networks determined experimentally. Both results suggest that the functional DMN and RSNs can be seen as simple consequences of the anatomical structure of the brain and a neural message-passing dynamics between macroscopic regions. We then show preliminary results indicating our predictions on how functional DMN maps change when the anatomical brain network suffers structural anomalies, like in Alzheimers Disease and in lesions of the Corpus Callosum.

q-bio.NC↗

arXiv2018

Maximum entropy and population heterogeneity in continuous cell cultures

Continuous cultures of mammalian cells are complex systems displaying hallmark phenomena of nonlinear dynamics, such as multi-stability, hysteresis, as well as sharp transitions between different metabolic states. In this context mathematical models may suggest control strategies to steer the system towards desired states. Although even clonal populations are known to exhibit cell-to-cell variability, most of the currently studied models assume that the population is homogeneous. To overcome this limitation, we use the maximum entropy principle to model the phenotypic distribution of cells in a chemostat as a function of the dilution rate. We consider the coupling between cell metabolism and extracellular variables describing the state of the bioreactor and take into account the impact of toxic byproduct accumulation on cell viability. We present a formal solution for the stationary state of the chemostat and show how to apply it in two examples. First, a simplified model of cell metabolism where the exact solution is tractable, and then a genome-scale metabolic network of the Chinese hamster ovary (CHO) cell line. Along the way we discuss several consequences of heterogeneity, such as: qualitative changes in the dynamical landscape of the system, increasing concentrations of byproducts that vanish in the homogeneous case, and larger population sizes.

q-bio.MN↗

arXiv2018

Cell population heterogeneity driven by stochastic partition and growth optimality

A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. Here we show that population bimodality can emerge even when biological processes are homogenous at the cell level and the environment is kept constant. Our model is based on the stochastic partitioning of a cell component with an optimal copy number. We show that the existence of unimodal or bimodal distributions depends on the variance of partition errors and the growth rate tolerance around the optimal copy number. In particular, our theory provides a consistent explanation for the maintenance of aneuploid states in a population. The proposed model can also be relevant for other cell components such as mitochondria and plasmids, whose abundances affect the growth rate and are subject to stochastic partition at cell division.

q-bio.MN↗