Related papers: On a "replicating character string" model
A further generalization of the stochastic replicator dynamic derived by Fudenberg and Harris \cite{FH92} is considered. In particular, a Poissonian integral is introduced to the fitness to simulate the affects of anomalous events. For the…
We study a one-dimensional spatial population model where the population sizes at each site are chosen according to a translation invariant and ergodic distribution and are uniformly bounded away from 0 and infinity. We suppose that the…
We study the relation between the persistent homology and the spectral sequence of a filtered chain complex over a field. Our method is based on a decomposition of the persistent homology. We demonstrate that, under fairly general…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…
The accuracy of the recombination estimation method of Padhukasahasram et al. 2006 can be improved by including additional informative summary statistics in the rejection scheme and by simulating datasets under a fixed segregating sites…
We study the stochastic dynamics of sequences evolving by single site mutations, segmental duplications, deletions, and random insertions. These processes are relevant for the evolution of genomic DNA. They define a universality class of…
This paper presents the construction of a particle filter, which incorporates elements inspired by genetic algorithms, in order to achieve accelerated adaptation of the estimated posterior distribution to changes in model parameters.…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of…
Stochastic kinetic models of genetic expression are able to describe protein fluctuations. A comparative study of the canonical and a feedback model is given here by using stochastic simulation methods. The feedback model is skeleton model…
In order to achieve deep natural language understanding, syntactic constituent parsing is a vital step, highly demanded by many artificial intelligence systems to process both text and speech. One of the most recent proposals is the use of…
Chinese Remainder Theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to…
Natural selection explains how life has evolved over millions of years from more primitive forms. The speed at which this happens, however, has sometimes defied formal explanations when based on random (uniformly distributed) mutations.…
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…
We study the statistical properties of the stationary firing-rate states of a neural network model with quenched disorder. The model has arbitrary size, discrete-time evolution equations and binary firing rates, while the topology and the…
This paper studies fixed-rate randomized vector quantization under the constraint that the quantizer's output has a given fixed probability distribution. A general representation of randomized quantizers that includes the common models in…
Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this…
Evolutionary analyses of large populations commonly incorporate stochasticity through temporal variation in selection while treating genetic transmission as fixed. Much less attention has been given to stochasticity in transmission itself.…
For a given unconstrained dynamical system, input redundancy has been recently redefined as the existence of distinct inputs producing identical output for the same initial state. By directly referring to signals, this definition readily…