Related papers: Maximum principle and mutation thresholds for four…
Mutation is one of the most important stages of the genetic algorithm because of its impact on the exploration of global optima, and to overcome premature convergence. There are many types of mutation, and the problem lies in selection of…
The curse of dimensionality is a widely known issue in reinforcement learning (RL). In the tabular setting where the state space $\mathcal{S}$ and the action space $\mathcal{A}$ are both finite, to obtain a nearly optimal policy with…
A phenomenological model based on the three-dimensional theory of nonlinear elasticity is developed to describe the phenomenon of overstretching in the force-extension curve for dsDNA. By using the concept of a material with multiple…
The experimenter must perform a legitimate search in the entire set of feasible censoring schemes to identify the optimal type II progressive censoring scheme, when applied to a life-testing experiment. Current recommendations are limited…
Feature screening for ultrahigh-dimension, in general, proceeds with two essential steps. The first step is measuring and ranking the marginal dependence between response and covariates, and the second is determining the threshold. We…
It is generally accepted that populations are useful for the global exploration of multi-modal optimisation problems. Indeed, several theoretical results are available showing such advantages over single-trajectory search heuristics. In…
Likelihood-based, or explicit, deep generative models use neural networks to construct flexible high-dimensional densities. This formulation directly contradicts the manifold hypothesis, which states that observed data lies on a…
We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon…
Let Delta F be the free energy difference between two equilibrium states of a system. An established method of numerically computing Delta F involves a single, long ``switching simulation'', during which the system is driven reversibly from…
Accurate estimation of evolutionary distances between taxa is important for many phylogenetic reconstruction methods. In the case of bacteria, distances can be estimated using a range of different evolutionary models, from single nucleotide…
This paper concerns with mesh restrictions that are needed to satisfy several important mathematical properties -- maximum principles, comparison principles, and the non-negative constraint -- for a general linear second-order elliptic…
We propose a new distance metric for DNA sequences, which can be defined on any evolutionary Markov model with infinitesimal generator matrix Q. That is the new metric can be defined under existing models such as Jukes-Cantor model,…
The mutational heterogeneity of tumours can be described with a tree representing the evolutionary history of the tumour. With noisy sequencing data there may be uncertainty in the inferred tree structure, while we may also wish to study…
We study error-correcting codes for permutations under the infinity norm, motivated by a novel storage scheme for flash memories call rank modulation. In this scheme, a set of $n$ flash cells are combined to create a single virtual…
Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. Here, we calculate optimal error thresholds for…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We…
We develop a generally covariant description of evolutionary dynamics that operates consistently in both genotype and phenotype spaces. We show that the maximum entropy principle yields a fundamental identification between the inverse…
In this paper, we explore the theory and expand upon the practice of fitness landscape analysis for optimization problems over the space of permutations. Many of the computational and analytical tools for fitness landscape analysis, such as…