arXiv subjects

Joceline Lega

Publications and source records attributed to Joceline Lega.

12 recordsLinked to original sources

arXiv2025

RDA-PSO: A computational method to quantify the diffusive dispersal of insects

This article introduces a computational method, called "Recapture of Diffusive Agents & Particle Swarm Optimization" (RDA-PSO), designed to estimate the dispersal parameter of diffusive insects in mark-release-recapture (MRR) field experiments. In addition to describing the method, its properties are discussed, with particular focus on robustness in estimating the observed diffusion coefficient in the presence of uncertainty. It is shown that RDA-PSO provides a simple and reliable approach to quantify insect dispersal that can handle low recapture rates and uneven capture site distributions without the need for area corrections. Tests on synthetic data, for which the actual diffusion coefficient is known, show the method outperforms three techniques based on the solution of the diffusion equation, which are also introduced in this work. Examples of application to real field data for the yellow fever mosquito are provided.

q-bio.QM↗

arXiv2024

Rapid and accurate mosquito abundance forecasting with Aedes-AI neural networks

We present a method to convert weather data into probabilistic forecasts of Aedes aegypti abundance. The approach, which relies on the Aedes-AI suite of neural networks, produces weekly point predictions with corresponding uncertainty estimates. Once calibrated on past trap and weather data, the model is designed to use weather forecasts to estimate future trap catches. We demonstrate that when reliable input data are used, the resulting predictions have high skill. This technique may therefore be used to supplement vector surveillance efforts or identify periods of elevated risk for vector-borne disease outbreaks.

q-bio.PE↗

arXiv2023

Map enumeration from a dynamical perspective

This contribution summarizes recent work of the authors that combines methods from dynamical systems theory (discrete Painlev\'e equations) and asymptotic analysis of orthogonal polynomial recurrences, to address long-standing questions in map enumeration. Given a genus $g$, we present a framework that provides the generating function for the number of maps that can be realized on a surface of that genus. In the case of 4-valent maps, our methodology leads to explicit expressions for map counts. For general even or mixed valence, the number of vertices of the map specifies the relevant order of the derivatives of the generating function that needs to be considered. Beyond summarizing our own results, we provide context for the program highlighted in this article through a brief review of the literature describing advances in map enumeration. In addition, we discuss open problems and challenges related to this fascinating area of research that stands at the intersection of statistical physics, random matrices, orthogonal polynomials, and discrete dynamical systems theory.

math-ph↗

arXiv2023

Non-recursive Counts of Graphs on Surfaces

The problem of map enumeration concerns counting connected spatial graphs, with a specified number $j$ of vertices, that can be embedded in a compact surface of genus $g$ in such a way that its complement yields a cellular decomposition of the surface. As such this problem lies at the cross-roads of combinatorial studies in low dimensional topology and graph theory. The determination of explicit formulae for map counts, in terms of closed classical combinatorial functions of $g$ and $j$ as opposed to a recursive prescription, has been a long-standing problem with explicit results known only for very low values of $g$. In this paper we derive closed-form expressions for counts of maps with an arbitrary number of even-valent vertices, embedded in surfaces of arbitrary genus. In particular, we exhibit a number of higher genus examples for 4-valent maps that have not appeared prior in the literature.

math.CO↗

arXiv2022

Multiple Scale Asymptotics of Map Enumeration

We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two asymptotic expansions obtained from two different fields of mathematics: the Riemann-Hilbert analysis of orthogonal polynomials and the theory of discrete dynamical systems. By equating the coefficients of these expansions in a common region of uniform validity in their parameters, we recover known results and provide new expressions for generating functions associated with graphical enumeration on surfaces of genera 0 through 7. Although the body of the article focuses on 4-valent maps, the methodology presented here extends to regular maps of arbitrary even valence and to some cases of odd valence, as detailed in the appendices.

math-ph↗

arXiv2022

Epidemics from the Eye of the Pathogen

While a common trend in disease modeling is to develop models of increasing complexity, it was recently pointed out that outbreaks appear remarkably simple when viewed in the incidence vs. cumulative cases (ICC) plane. This article details the theory behind this phenomenon by analyzing the stochastic SIR (Susceptible, Infected, Recovered) model in the cumulative cases domain. We prove that the Markov chain associated with this model reduces, in the ICC plane, to a pure birth chain for the cumulative number of cases, whose limit leads to an independent increments Gaussian process that fluctuates about a deterministic ICC curve. We calculate the associated variance and quantify the additional variability due to estimating incidence over a finite period of time. We also illustrate the universality brought forth by the ICC concept on real-world data for Influenza A and for the COVID-19 outbreak in Arizona.

q-bio.PE↗

arXiv2021

Dynamics of Non-polar Solutions to the Discrete Painlevé I Equation

This manuscript develops a novel understanding of non-polar solutions of the discrete Painlevé I equation (dP1). As the non-autonomous counterpart of an analytically completely integrable difference equation, this system is endowed with a rich dynamical structure. In addition, its non-polar solutions, which grow without bounds as the iteration index $n$ increases, are of particular relevance to other areas of mathematics. We combine theory and asymptotics with high-precision numerical simulations to arrive at the following picture: when extended to include backward iterates, known non-polar solutions of dP1 form a family of heteroclinic connections between two fixed points at infinity. One of these solutions, the Freud orbit of orthogonal polynomial theory, is a singular limit of the other solutions in the family. Near their asymptotic limits, all solutions converge to the Freud orbit, which follows invariant curves of dP1, when written as a 3-D autonomous system, and reaches the point at positive infinity along a center manifold. This description leads to two important results. First, the Freud orbit tracks sequences of period-1 and 2 points of the autonomous counterpart of dP1 for large positive and negative values of $n$, respectively. Second, we identify an elegant method to obtain an asymptotic expansion of the iterates on the Freud orbit for large positive values of $n$. The structure of invariant manifolds emerging from this picture contributes to a deeper understanding of the global analysis of an interesting class of discrete dynamical systems.

math.DS↗

arXiv2021

EpiCovDA: a mechanistic COVID-19 forecasting model with data assimilation

We introduce a minimalist outbreak forecasting model that combines data-driven parameter estimation with variational data assimilation. By focusing on the fundamental components of nonlinear disease transmission and representing data in a domain where model stochasticity simplifies into a process with independent increments, we design an approach that only requires four core parameters to be estimated. We illustrate this novel methodology on COVID-19 forecasts. Results include case count and deaths predictions for the US and all of its 50 states, the District of Columbia, and Puerto Rico. The method is computationally efficient and is not disease- or location-specific. It may therefore be applied to other outbreaks or other countries, provided case counts and/or deaths data are available.

q-bio.PE↗

arXiv2021

Aedes-AI: Neural Network Models of Mosquito Abundance

We present artificial neural networks as a feasible replacement for a mechanistic model of mosquito abundance. We develop a feed-forward neural network, a long short-term memory recurrent neural network, and a gated recurrent unit network. We evaluate the networks in their ability to replicate the spatiotemporal features of mosquito populations predicted by the mechanistic model, and discuss how augmenting the training data with time series that emphasize specific dynamical behaviors affects model performance. We conclude with an outlook on how such equation-free models may facilitate vector control or the estimation of disease risk at arbitrary spatial scales.

q-bio.PE↗

arXiv2021

Parameter Estimation from ICC curves

Incidence vs Cumulative Cases (ICC) curves are introduced and shown to provide a simple framework for parameter identification in the case of the most elementary epidemiological model, consisting of susceptible, infected, and removed compartments. This novel methodology is used to estimate the basic reproduction ratio of recent outbreaks, including the ongoing COVID-19 epidemic.

q-bio.PE↗

arXiv2017

On collisions times of self-sorting interacting particles in one-dimension with random initial positions and velocities

We investigate a one-dimensional system of $N$ particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the $N$ particles do not interact and become sorted according to their velocities. When the collisions are elastic, we derive asymptotic distributions for the final collision time of a single particle and the final collision time of the system as the number of particles approaches infinity, under different assumptions for the initial distributions of the particles' positions and velocities. For comparison, a numerical investigation is carried out to determine how a non-elastic collision rule, which conserves neither momentum nor energy, affects the median collision time of a particle and the median final collision time of the system.

math-ph↗

arXiv2011

Multiple Quenching Solutions of a Fourth Order Parabolic PDE with a singular nonlinearity modelling a MEMS Capacitor

Finite time singularity formation in a fourth order nonlinear parabolic partial differential equation (PDE) is analyzed. The PDE is a variant of a ubiquitous model found in the field of Micro-Electro Mechanical Systems (MEMS) and is studied on a one-dimensional (1D) strip and the unit disc. The solution itself remains continuous at the point of singularity while its higher derivatives diverge, a phenomenon known as quenching. For certain parameter regimes it is shown numerically that the singularity will form at multiple isolated points in the 1D strip case and along a ring of points in the radially symmetric 2D case. The location of these touchdown points is accurately predicted by means of asymptotic expansions. The solution itself is shown to converge to a stable self-similar profile at the singularity point. Analytical calculations are verified by use of adaptive numerical methods which take advantage of symmetries exhibited by the underlying PDE to accurately resolve solutions very close to the singularity.

math.AP↗