37 citations · 68 across the 11 of their papers we have counts for
11 papers
Map enumeration from a dynamical perspective
Nicholas Ercolani, Joceline Lega, Brandon Tippings
This contribution summarizes recent work of the authors that combines methods from dynamical systems theory (discrete Painlevé equations) and asymptotic analysis of orthogonal poly…
Non-recursive Counts of Graphs on Surfaces
Nicholas Ercolani, Joceline Lega, Brandon Tippings
The problem of map enumeration concerns counting connected spatial graphs, with a specified number of vertices, that can be embedded in a compact surface of genus in such a…
Multiple Scale Asymptotics of Map Enumeration
Nicholas Ercolani, Joceline Lega, Brandon Tippings
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…
Dynamics of Non-polar Solutions to the Discrete Painlevé I Equation
Nicholas Ercolani, Joceline Lega, Brandon Tippings
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 int…
EpiCovDA: a mechanistic COVID-19 forecasting model with data assimilation
Hannah R. Biegel, Joceline Lega
We introduce a minimalist outbreak forecasting model that combines data-driven parameter estimation with variational data assimilation. By focusing on the fundamental components of…
Aedes-AI: Neural Network Models of Mosquito Abundance
Adrienne C. Kinney, Sean Current, Joceline Lega
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 re…
Epidemics from the Eye of the Pathogen
Faryad Darabi Sahneh, William Fries, Joseph C. Watkins +1
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 incid…
Parameter Estimation from ICC curves
Joceline Lega
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 mo…
On collisions times of self-sorting interacting particles in one-dimension with random initial positions and velocities
Joceline Lega, Sunder Sethuraman, Alexander L Young
We investigate a one-dimensional system of particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is s…
Derivation and Equilibrium Analysis of a Regularized Model for Electrostatic MEMS
A. E. Lindsay, J. Lega, K. B. Glasner
In canonical models of Micro-Electro Mechanical Systems (MEMS), an event called touch- down whereby the electrical components of the device come into contact, is characterized by a…
Multiple Quenching Solutions of a Fourth Order Parabolic PDE with a singular nonlinearity modelling a MEMS Capacitor
Alan Lindsay, Joceline Lega
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 fie…