Related papers: An asymptotic maximum principle for essentially li…
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…
A four-state mutation-selection model for the evolution of populations of DNA-sequences is investigated with particular interest in the phenomenon of error thresholds. The mutation model considered is the Kimura 3ST mutation scheme, fitness…
We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…
We study the equilibrium behaviour of a deterministic four-state mutation-selection model as a model for the evolution of a population of nucleotide sequences in sequence space. The mutation model is the Kimura 3ST mutation scheme, and the…
We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is…
We study alternating minimization for matrix completion in the simplest possible setting: completing a rank-one matrix from a revealed subset of the entries. We bound the asymptotic convergence rate by the variational characterization of…
In this paper we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense…
We consider a model of asexually reproducing individuals with random mutations and selection. The rate of mutations is proportional to the population size, $N$. The mutations may be either beneficial or deleterious. In a paper by Yu,…
We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
In this paper, we develop asymptotic theories for a class of latent variable models for large-scale multi-relational networks. In particular, we establish consistency results and asymptotic error bounds for the (penalized) maximum…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
In this paper, we consider directly estimating the eigenvalues of precision matrix, without inverting the corresponding estimator for the eigenvalues of covariance matrix. We focus on a general asymptotic regime, i.e., the large dimensional…
Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…
We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is…
A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the…
We study the asymptotic behavior of the maximum degree in the evolving tree model with a choice based on both degree and fitness of a vertex. The tree is constructed in the following recursive way. Each vertex is assigned a parameter to it…
The stationary sampling distribution of a neutral decoupled Moran or Wright-Fisher diffusion with neutral mutations is known to first order for a general rate matrix with small but otherwise unconstrained mutation rates. Using this…
This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent…
We consider the accumulation of beneficial and deleterious mutations in large asexual populations. The rate of adaptation is affected by the total mutation rate, proportion of beneficial mutations and population size $N$. We show that…