arXiv subjects

Javier Aguilar

Publications and source records attributed to Javier Aguilar.

12 recordsLinked to original sources

arXiv2026

The Limits of Inference in Complex Systems: When Stochastic Models Become Indistinguishable

Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes to deliver reliable parameter estimation and model selection from coarsely sampled time series, without requiring analytical solutions. Crucially, we couple mechanistic stochastic models with their inference procedures to quantify how experimental design -specifically, sampling frequency and dataset size- governs estimator precision and model distinguishability. This analysis reveals optimal sampling regimes and sharp, resolution-dependent limits beyond which competing models become empirically indistinguishable. We validate the approach across four disparate systems -trajectories of optically trapped particles, human microbiome dynamics, social-media topic mentions, and forest population time series- recovering parameters and identifying when inference is fundamentally constrained by measurement resolution, thereby clarifying ongoing debates about dominant noise sources in these systems. Together, these results establish path-based Monte Carlo as a practical, general tool for inference and model discrimination in complex systems and provide principled guidelines for designing measurements that maximize information under real-world constraints.

cond-mat.stat-mech↗

arXiv2026

Unraveling the temporal dependence of ecological interaction measures

Identifying the network of species interactions is a fundamental step toward understanding ecosystem stability and biodiversity. However, the interpretability of empirical interaction measures remains a major challenge. Experimental estimates frequently exhibit puzzling temporal fluctuations, including sign shifts typically interpreted as transitions between competition and facilitation. Here, we analyze the temporal behavior of pairwise interaction measures to demonstrate that these fluctuations - and apparent shifts in ecological roles - can emerge intrinsically from standard population dynamics, without any underlying change in the actual ecological relationships. We show that inferred interactions are heavily distorted by experimental protocol choices, particularly the duration of observation and microbial growth constraints. By systematically evaluating interactions across timescales, we uncover a principled mechanism to mitigate these biases: short-term measurements reliably isolate direct, pairwise species couplings, whereas longer-term observations inevitably absorb indirect community feedbacks and systemic experimental constraints. By disentangling direct couplings from indirect network effects, our framework provides a robust, timescale-aware approach to interpreting empirical interaction matrices, offering critical quantitative guidance for experimental design and predictive ecosystem modeling.

q-bio.PE↗

arXiv2026

Noise-induced excitability: bloom, bust and extirpation in autotoxic population dynamics

Species populations often modify their environment as they grow. When environmental feedback operates more slowly than population growth, the system can undergo boom-bust dynamics, where the population overshoots its carrying capacity and subsequently collapses. In extreme cases, this collapse leads to total extinction. While deterministic models typically fail to capture these finite-time extinction events, we propose a stochastic framework, derived from an individual-based model, to describe boom-bust-extirpation dynamics. We identify a noise-driven, threshold-like behavior where, depending on initial conditions, the population either undergoes a ``boom'' or is extirpated before the expansion occurs. Furthermore, we characterize a transition between an excitable regime, where most trajectories are captured by the absorbing state immediately after the first bust, and a persistent regime, where most populations reach a metastable state. We show that this transition is governed by the noise strength and the ratio of environmental-to-population timescales. This framework provides a theoretical basis for understanding irreversible transitions in invasive species, plant succession, microbial dynamics, and the elimination of cancerous tumors.

q-bio.PE↗

arXiv2026

Numerical methods for quasi-stationary distributions

In stochastic processes with absorbing states, the quasi-stationary distribution provides valuable insights into the long-term behaviour prior to absorption. In this work, we revisit two well-established numerical methods for its computation. The first is an iterative algorithm for solving the non-linear equation that defines the quasi-stationary distribution. We generalise this technique to accommodate general Markov stochastic processes, either with discrete or continuous state space, and with multiple absorbing states. The second is a Monte Carlo method with resetting, for which we propose a novel single-trajectory approach that uses the trajectory's own history to perform resets after absorption. In addition to these methodological contributions, we provide a detailed analysis of implementation aspects for both methods. We also compare their accuracy and efficiency across a range of examples. The results indicate that the iterative algorithm is generally the preferred choice for problems with simple boundaries, while the Monte Carlo approach is more suitable for problems with complex boundaries, where the implementation of the iterative algorithm is a challenging task.

cond-mat.stat-mech↗

arXiv2025

Comparing temporal and aggregated network descriptions of fluid transport in the Mediterranean Sea

Ocean currents exhibit strong time dependence at all scales that influences physical and biochemical dynamics. Network approaches to fluid transport permit to address explicitly how connectivity across the seascape is affected by the spatiotemporal variability of currents. However, such temporal aspect is mostly neglected, relying on a static representation of the flow. We here investigate the role of current variability on networks describing physical transport across the Mediterranean basin. We first focus on degree distributions and community structure comparing ensembles of temporal networks that explicitly resolve time dependence and their aggregated, i.e. time-averaged, counterparts. Furthermore, we explore the implications of the two approaches in a simple reaction dispersal model for a generic tracer. Our analysis evidences that aggregation induces structural network changes that cannot be easily avoided, not even introducing a pruning of the aggregated adjacency matrix. We also highlight that, depending on the time scales considered, the importance of the temporal features of the networks can vary significantly. Finally, we find that the tracer evolution obtained from a temporal dispersal kernel cannot be always approximated by aggregated adjacency matrices, in particular during transients of the dynamics.

physics.soc-ph↗

arXiv2024

Optimal switching strategies in multi-drug therapies for chronic diseases

Antimicrobial resistance is a threat to public health with millions of deaths linked to drug resistant infections every year. To mitigate resistance, common strategies that are used are combination therapies and therapy switching. However, the stochastic nature of pathogenic mutation makes the optimization of these strategies challenging. Here, we propose a two-scale stochastic model that considers the effective evolution of therapies in a multidimensional efficacy space, where each dimension represents the efficacy of a specific drug in the therapy. The diffusion of therapies within this space is subject to stochastic resets, representing therapy switches. The boundaries of the space, inferred from coarser pathogen-host dynamics, can be either reflecting or absorbing. Reflecting boundaries impede full recovery of the host, while absorbing boundaries represent the development of antimicrobial resistance, leading to therapy failure. We derive analytical expressions for the average absorption times, accounting for both continuous and discrete genomic changes using the frameworks of Langevin and Master equations, respectively. These expressions allow us to evaluate the relevance of times between drug-switches and the number of simultaneous drugs in relation to typical timescales for drug resistance development. We also explore realistic scenarios where therapy constraints are imposed to the number of administered therapies and/or their costs, finding non-trivial optimal drug-switching protocols that maximize the time before antimicrobial resistance develops while reducing therapy costs.

q-bio.PE↗

arXiv2024

Analytic and Monte Carlo Approximations to the Distribution of the First Passage Time of the Drifted Diffusion with Stochastic Resetting and Mixed Boundary Conditions

This article introduces two techniques for computing the distribution of the absorption or first passage time of the drifted Wiener diffusion subject to Poisson resetting times, to an upper hard wall barrier and to a lower absorbing barrier. The first method, which we call ``Padé-partial fraction'' approximation, starts with the Padé approximation to the Laplace transform of the first passage time distribution, which is then exactly inverted by means of the partial fraction decomposition. The second method, which we call "multiresolution algorithm", is a Monte Carlo technique that exploits the properties of the Wiener process in order to generate Brownian bridges at increasing levels of resolution. Our numerical study reveals that the multiresolution algorithm has higher efficiency than standard Monte Carlo, whereas the faster Padé-partial fraction method is accurate in various circumstances and provides an analytical formula. Also, a closed-form exact expression for the expected first passage time is derived.

physics.comp-ph↗

arXiv2024

Biased versus unbiased numerical methods for stochastic simulations

Approximate numerical methods are one of the most used strategies to extract information from many-interacting-agents systems. In particular, numerical approximations are of extended use to deal with epidemic, ecological and biological models, since unbiased methods like the Gillespie algorithm can become unpractical due to high CPU time usage required. However, the use of approximations has been debated and there is no clear consensus about whether unbiased methods or biased approach is the best option. In this work, we derive scaling relations for the errors in approximations based on binomial extractions. This finding allows us to build rules to compute the optimal values of both the discretization time and number of realizations needed to compute averages with the biased method with a target precision and minimum CPU-time usage. Furthermore, we also present another rule to discern whether the unbiased method or biased approach is more efficient. Ultimately, we will show that the choice of the method should depend on the desired precision for the estimation of averages.

physics.soc-ph↗

arXiv2024

A unified perspective on exponential tilt and bridge algorithms for rare trajectories of discrete Markov processes

This article analyzes and compares two general techniques of rare event simulation for generating paths of Markov processes over fixed time horizons: exponential tilting and stochastic bridge. These two methods allow to accurately compute the probability that a Markov process ends within a rare region, which is unlikely to be attained. Exponential tilting is a general technique for obtaining an alternative or tilted sampling probability measure, under which the Markov process becomes likely to hit the rare region at terminal time. The stochastic bridge technique involves conditioning paths towards two endpoints: the terminal point and the initial one. The terminal point is generated from some appropriately chosen probability distribution that covers well the rare region. We show that both methods belong to the class of importance sampling procedures, by providing a common mathematical framework of these two conceptually different methods of sampling rare trajectories. We also conduct a numerical comparison of these two methods, revealing distinct areas of application for each Monte Carlo method, where they exhibit superior efficiency. Detailed simulation algorithms are provided.

cond-mat.stat-mech↗

arXiv2023

Endemic infectious states below the epidemic threshold and beyond herd immunity

In the recent COVID-19 pandemic we assisted at a sequence of epidemic waves intertwined by anomalous fade-outs with periods of low but persistent epidemic prevalence. These long-living epidemic states complicate epidemic control and challenge current modeling approaches as classical epidemic models fail to explain their emergence. Inspired by this phenomenon, we propose a simple mechanism able to reproduce several features observed in real data. Specifically, here we introduce a modification of the Susceptible-Infected-Recovered (SIR) model in a meta-population framework where a small inflow of infected individuals accounts for undetected internal or imported cases. Focusing on a regime where this external seeding is so small that cannot be detected from the analysis of epidemic curves, we find that outbreaks of finite duration percolate in time resulting in overall low but long-living epidemic states below and above the epidemic threshold. Using a two-state description of the local dynamics, we can extract analytical predictions for the phase space. The comparison with epidemic data demonstrates that our model is able to reproduce some critical signatures observed in COVID-19 spreading in England. Finally, our findings defy our understanding of the concept of epidemic threshold and its relationship with outbreaks survival for disease control.

physics.soc-ph↗

arXiv2022

Impact of urban structure on infectious disease spreading

The ongoing SARS-CoV-2 pandemic has been holding the world hostage for more than a year now. Mobility is key to viral spreading and its restriction is the main non-pharmaceutical interventions to fight the virus expansion. Previous works have shown a connection between the structural organization of cities and the movement patterns of their residents. This puts urban centers in the focus of epidemic surveillance and interventions. Here we show that the organization of urban flows has a tremendous impact on disease spreading and on the amenability of different mitigation strategies. By studying anonymous and aggregated intra-urban flows in a variety of cities in the United States and other countries, and a combination of empirical analysis and analytical methods, we demonstrate that the response of cities to epidemic spreading can be roughly classified in two major types according to the overall organization of those flows. Hierarchical cities, where flows are concentrated primarily between mobility hotspots, are particularly vulnerable to the rapid spread of epidemics. Nevertheless, mobility restrictions in such types of cities are very effective in mitigating the spread of a virus. Conversely, in sprawled cities which present many centers of activity, the spread of an epidemic is much slower, but the response to mobility restrictions is much weaker and less effective. Investing resources on early monitoring and prompt ad-hoc interventions in more vulnerable cities may prove helpful in containing and reducing the impact of future pandemics.

physics.soc-ph↗

arXiv2021

Sampling rare trajectories using stochastic bridges

The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have fixed start and end points (so-called stochastic bridges). We then show that by carefully choosing a set of such bridges and assigning an appropriate statistical weight to each bridge, one can focus more processing power on the rare events of a target stochastic process while faithfully preserving the statistics of these rate trajectories. Further, we also compare the stochastic bridges produced using our method to the Wentzel-Kramers-Brillouin (WKB) optimal paths of the target process, derived in the limit of low noise. We see that the paths produced using our method, encoding the full statistics of the process, collapse onto the WKB optimal path as the level of noise is reduced. We propose that our method can be used to judge the accuracy of the WKB approximation at finite levels of noise.

cond-mat.stat-mech↗