相关论文: Efficient numerical computation of the basic repro…
What is called "numerical reproducibility" is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing…
We present an iteration for the computation of simple eigenvalues using a pseudospectrum approach. The most appealing characteristic of the proposed iteration is that it reduces the computation of a single eigenvalue to a small number of…
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
We consider the general character of the spatial distribution of a population that grows through reproduction and subsequent local resettlement of new population members. We present several simple one and two-dimensional point placement…
We introduce a supervised dimensionality reduction methodology for categorical (and discretized mixed-type) data based on a density-matrix construction induced by class-conditional frequencies. Given a labeled dataset encoded in a one-hot…
An important issue in theoretical epidemiology is the epidemic threshold phenomenon, which specify the conditions for an epidemic to grow or die out. In standard (mean-field-like) compartmental models the concept of the basic reproductive…
Statistical and computational methods are widely used in today's scientific studies. Using a female fertility potential in childhood cancer survivors as an example, we illustrate how these methods can be used to extract insight regarding…
Since the last century, deterministic compartmental models have emerged as powerful tools to predict and control epidemic outbreaks, in many cases helping to mitigate their impacts. A key quantity for these models is the so-called Basic…
In several fields such as statistics, machine learning, and bioinformatics, categorical variables are frequently represented as one-hot encoded vectors. For example, given 8 distinct values, we map each value to a byte where only a single…
This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by [17]. Moreover, its multiplicative structure and the multiplicative…
This chapter reviews some aspects of the theory of age-structured models of populations with finite maximum age. We formulate both the renewal equation for the birth rate and the partial differential equation for the age density, and show…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
A simplified method to compute $R_t$, the Effective Reproduction Number, is presented. The method relates the value of $R_t$ to the estimation of the doubling time performed with a local exponential fit. The condition $R_t = 1$ corresponds…
We present a computational model to reconstruct trees of ancestors for animals with sexual reproduction. Through a recursive algorithm combined with a random number generator, it is possible to reproduce the number of ancestors for each…
We introduce the boundary reproduction number, adapted from the next generation matrix method, to assess whether an infusion of species will persist or become exhausted in a chemical reaction system. Our main contributions are as follows:…
The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction contribute crucial knowledge on disease control, elimination, and mitigation…
Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
Matrix population models have proved popular and useful for studying stage-structured populations in quantitative ecology. The goal of this paper is to develop and analyze a general matrix population model that is applicable to the…
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…