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Accurate estimates of subnational populations are important for policy formulation and monitoring population health indicators. For example, estimates of the number of women of reproductive age are important to understand the population at…
In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described by condition numbers or pseudospectra. However, the…
We investigate the problem of estimating the distribution of the individual reproduction number governing the COVID-19 pandemic. Under the assumption that this random variable follows a Negative Binomial distribution, we focus on…
In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models…
Reproduction data collected through standard bioassays are classically analyzed by regression in order to fit exposure-response curves and estimate ECx values (x% Effective Concentration). But regression is often misused on such data,…
Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…
In this work first we consider a physiologically structured population model with a distributed recruitment process. That is, our model allows newly recruited individuals to enter the population at all possible individual states, in…
We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a testbed for investigating the computational complexity of…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
Low rank matrix recovery problems appear widely in statistics, combinatorics, and imaging. One celebrated method for solving these problems is to formulate and solve a semidefinite program (SDP). It is often known that the exact solution to…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…
Population protocols are a relatively novel computational model in which very resource-limited anonymous agents interact in pairs with the goal of computing predicates. We consider the probabilistic version of this model, which naturally…
In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a…
Although a generalized spike population model has been actively studied in random matrix theory, its application to real data has been rarely explored. We find that most methods for determining the number of spikes based on the Johnstone's…
Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for…
The structured $\varepsilon$-stability radius is introduced as a quantity to assess the robustness of transient bounds of solutions to linear differential equations under structured perturbations of the matrix. This applies to general…
We consider the problem of estimating the reproduction number $R_t$ of an epidemic for populations where the probability of detection of cases depends on a known covariate. We argue that in such cases the normal empirical estimator can fail…
We develop a class of nonlocal delay Reaction-Diffusion (RD) models in a circular domain. Previous modeling efforts include RD population models with respect to one-dimensional unbounded domain, unbounded strip and rectangular spatial…
This work addresses the optimal birth control problem for invasive species in a spatial environment. We apply the method of semigroups to qualitatively analyze a size-structured population model in which individuals occupy a position in a…
The recently developed matrix based Renyi's entropy enables measurement of information in data simply using the eigenspectrum of symmetric positive semi definite (PSD) matrices in reproducing kernel Hilbert space, without estimation of the…