相关论文: Similarity of general population matrices and pseu…
The application of Leslie matrices in demographic research is considered in this paper. The Leslie matrix is first proposed in the 1940s and gained popularity in the mid-1960s, becoming fundamental tool for predicting population dynamics.…
We introduce a new predator-prey model by replacing the growth and predation constant by a square matrix, and the population density as a population vector. The classical Lotka-Volterra model describes a population that either modulates or…
Infinite Leslie matrices, introduced by Demetrius forty years ago are mathematical models of age-structured populations defined by a countable infinite number of age classes. This article is concerned with determining solutions of the…
When the process underlying DNA substitutions varies across evolutionary history, the standard Markov models underlying standard phylogenetic methods are mathematically inconsistent. The most prominent example is the general time reversible…
In this paper, we present a technique for parameterizing Leslie transition matrices from simple age and sex population counts, using an implementation of "Wood's Method" [wood]; these matrices can forecast population by age and sex (the…
Generalized entropies are studied as Lyapunov functions for the Master equation (Markov chains). Three basic properties of these Lyapunov functions are taken into consideration: universality (independence of the kinetic coefficients),…
Pedigrees are directed acyclic graphs that represent ancestral relationships between individuals in a population. Based on a schematic recombination process, we describe two simple Markov models for sequences evolving on pedigrees - Model R…
We study the problem of solvability of linear differential systems with small coefficients in the Liouvillian sense (or, by generalized quadratures). For a general system, this problem is equivalent to that of solvability of the Lie algebra…
Many of today's problems require techniques that involve the solution of arbitrarily large systems $A\mathbf{x}=\mathbf{b}$. A popular numerical approach is the so-called Greedy Rank-One Update Algorithm, based on a particular tensor…
Recent work has discussed the importance of multiplicative closure for the Markov models used in phylogenetics. For continuous-time Markov chains, a sufficient condition for multiplicative closure of a model class is ensured by demanding…
This paper introduces a neural network approach for fitting the Lee-Carter and the Poisson Lee-Carter model on multiple populations. We develop some neural networks that replicate the structure of the individual LC models and allow their…
The general linear model is a universally accepted method to conduct and test multiple linear regression models. Using this model one has the ability to simultaneously regress covariates among different groups of data. Moreover, there are…
In the hidden Markov process, there is a possibility that two different transition matrices for hidden and observed variables yield the same stochastic behavior for the observed variables. Since such two transition matrices cannot be…
On the universal seesaw mass matrix model, which is a promising model of the unified description of the quark and lepton mass matrices, the behaviors of the gauge coupling constants and intermediate energy scales in the SO(10)_L\times…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees. Substitutions in sequences are modelled through a continuous-time Markov process, characterised by an instantaneous rate matrix, which standard…
Two types of population models are well known -- the continuous and the discrete types.The two have very different characteristics and methods of solutions and analysis.In this note, we point out that an iterative technique when applied to…
We demonstrate that, for every grand unified model based on a conventional type I seesaw mechanism leading to a normal light neutrino mass hierarchy, one can easily generate a corresponding model with an inverted hierarchy which yields the…
We study a seesaw-type extension of the Standard Model in which the symmetry group is enlarged by a global U(1). We introduce adequate scalar and fermion representations which naturally explain the smallness of neutrino masses. With the…
We analyse sequential Markov coalescent algorithms for populations with demographic structure: for a bottleneck model, a population-divergence model, and for a two-island model with migration. The sequential Markov coalescent method is an…
We compare two approaches for determining the generation of lepton asymmetry during production and decay of quasi-degenerate neutrinos, namely the density matrix formalism and a recent proposal which does not involve any counting of…