On discretely structured growth models and their moments
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range from the ageing of individuals in a species to immune cell exhaustion by cancerous tissue. Through exploration of a range of concrete examples and a general analysis of polynomial kinetics, we derive necessary and sufficient conditions for the dependence of the kinetics on structure to result in closed, low-dimensional moment equations that are exact. Further, we showcase how coarse-grained moment information can be used to elucidate the details of structured dynamics, with immediate potential for model selection and hypothesis testing. This paper belongs to the special collection: Problems, Progress and Perspectives in Mathematical and Computational Biology.
Code (0)
등록된 구현이 없습니다.
Tasks
Model SelectionSimilar Papers 제목 키워드 기반
The Log Moment formula for implied volatility
We revisit the foundational Moment Formula proved by Roger Lee fifteen years ago. We show that when the underlying stock price martingale admits finite log-moments E[|log(S)|^q] for some positive q, the arbitrage-free gr…
Efficient Computation of the Quasi Likelihood function for Discretely Observed Diffusion Processes
We introduce a simple method for nearly simultaneous computation of all moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations commonly seen in finan…
AllNon-Existent Moments of Earnings Growth
The literature often employs moment-based earnings risk measures like variance, skewness, and kurtosis. However, under heavy-tailed distributions, these moments may not exist in the population. Our empirical analysis rev…
A Modeling Approach of Return and Volatility of Structured Investment Products with Caps and Floors
Popular investment structured products in Puerto Rico are stock market tied Individual Retirement Accounts (IRA), which offer some stock market growth while protecting the principal. The performance of these retirement s…
Preservation Is Not Enough for Width Growth: Regime-Sensitive Selection of Dense LM Warm Starts
Width expansion offers a practical route to reuse smaller causal-language-model checkpoints, but selecting a widened warm start is not solved by zero-step preservation alone. We study dense width growth as a candidate-se…