arXiv subjects

Feng Yu

Publications and source records attributed to Feng Yu.

122 records · Page 7Linked to original sources

arXiv2013

Computing Traversal Times on Dynamic Markovian Paths

In source routing, a complete path is chosen for a packet to travel from source to destination. While computing the time to traverse such a path may be straightforward in a fixed, static graph, doing so becomes much more challenging in dynamic graphs, in which the state of an edge in one time slot (i.e., its presence or absence) is random, and may depend on its state in the previous time step. The traversal time is due to both time spent waiting for edges to appear and time spent crossing them once they become available. We compute the expected traversal time (ETT) for a dynamic path in a number of special cases of stochastic edge dynamics models, and for three edge failure models, culminating in a surprisingly challenging yet realistic setting in which the initial configuration of edge states for the entire path is known. We show that the ETT for this "initial configuration" setting can be computed in quadratic time, by an algorithm based on probability generating functions. We also give several linear-time upper and lower bounds on the ETT.

cs.NI↗

arXiv2010

Asymptotic behavior of the rate of adaptation

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 regardless of mutation rates, as long as the proportion of beneficial mutations is strictly positive, the adaptation rate is at least $\mathcal{O}(\log^{1-δ}N)$ where $δ$ can be any small positive number, if the population size is sufficiently large. This shows that if the genome is modeled as continuous, there is no limit to natural selection, that is, the rate of adaptation grows in $N$ without bound.

math.PR↗

arXiv2008

Fixation Probability for Competing Selective Sweeps

We consider a biological population in which a beneficial mutation is undergoing a selective sweep when a second beneficial mutation arises at a linked locus and we investigate the probability that both mutations will eventually fix in the population. Previous work has dealt with the case where the second mutation to arise confers a smaller benefit than the first. In that case population size plays almost no role. Here we consider the opposite case and observe that, by contrast, the probability of both mutations fixing can be heavily dependent on population size. Indeed the key parameter is $ρN$, the product of the population size and the recombination rate between the two selected loci. If $ρN$ is small, the probability that both mutations fix can be reduced through interference to almost zero while for large $ρN$ the mutations barely influence one another. The main rigorous result is a method for calculating the fixation probability of a double mutant in the large population limit.

math.PR↗

arXiv2007

Stationary distribution for dioecious branching particle systems with rapid stirring

We study dioecious (i.e., two-sex) branching particle system models, where there are two types of particles, modeling the male and female populations, and where birth of new particles requires the presence of both male and female particles. We show that stationary distributions of various dioecious branching particle models are nontrivial under certain conditions, for example, when there is sufficiently fast stirring.

math.PR↗

arXiv2007

Stationary distributions of a model of sympatric speciation

This paper deals with a model of sympatric speciation, that is, speciation in the absence of geographical separation, originally proposed by U. Dieckmann and M. Doebeli in 1999. We modify their original model to obtain a Fleming--Viot type model and study its stationary distribution. We show that speciation may occur, that is, the stationary distribution puts most of the mass on a configuration that does not concentrate on the phenotype with maximum carrying capacity, if competition between phenotypes is intense enough. Conversely, if competition between phenotypes is not intense, then speciation will not occur and most of the population will have the phenotype with the highest carrying capacity. The length of time it takes speciation to occur also has a delicate dependence on the mutation parameter, and the exact shape of the carrying capacity function and the competition kernel.

math.PR↗

arXiv2007

Equilibrium States of Two Stochastic Models in Mathematical Ecology

This work deals with two problems arising in mathematical ecology. The first problem is concerned with diploid branching particle models and its behavior when rapid stirring is added to the interaction. The particle models involve two types of particles, male and female, and branching can only occur when both types of particles are present. We show that if the branching rate is sufficiently large, this particle model has a nontrivial stationary distribution, i.e. one that does not concentrate all weight on the all-0 state, using a comparison argument due to R. Durrett. We also show extinction for small branching rates, thereby establishing the existence of a phase transition. We then add two different rapid stirring mechanisms to the interactions and show that for the particle models with rapid stirring, there also exist nontrivial stationary distribution(s); for this, we analyze the limiting PDE and establish a condition on the PDE that guarantees existence of nontrivial stationary distributions for sufficient fast stirring. The second problem deals with a model of sympatric speciation, i.e. speciation in the absence of geographical separation, originally proposed by U. Dieckmann and M. Doebeli in 1999. We modify their original model to obtain several constant-population particle models. We concentrate on a continuous-time model that converges to a deterministic dynamical system as the number of particles becomes large. We establish various results regarding whether speciation occurs by studying the existence of bimodal stationary distributions for the limiting dynamical system.

math.PR↗

arXiv1993

Many Boson Realizations of Universal Nonlinear $W_{\infty}$-Algebras

An infinite number of free field realizations of the universal nonlinear $\hat{W}_{\infty}^{(N)}$ ($\hat{W}_{1+\infty}^{(N)}$) algebras, which are identical to the KP Hamiltonian structures, are obtained in terms of $p$ plus $q$ scalars of different signatures with $p-q=N$. They are generalizations of the Miura transformation, and naturally give rise to the modified KP hierarchies via corresponding realizations of the latter. Their characteristic Lie-algebraic origin is shown to be the graded $SL(p,q)$.

hep-th↗

arXiv1992

D>2 Topological String

A $D>2$ topological string is presented by coupling the $2d$ topological gravity with the twisted version of the $N=2$ superconformal matter with $c=3k/(k-2)$. The latter is shown to admit $k+1$ chiral primary fields from the $SL(2,R)_{k}/U(1)$ unitary irreducible representations. The analysis of topological contact interactions along with the consistency requirement lead to recursion relations of correlation functions, that are convertable to the Virasoro constraints on the perturbed partition function. It is further expected to satisfy the nonlinear $\hat{W}^{(k-2)}_{\infty}$ constraints associated with the graded algebra $SL(k,2)$, and thus the model is completely solvable at arbitrary genus of the surface.

hep-th↗

arXiv1992

On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model --- The Classical and Quantum Cases

We give a unified description of our recent results on the the inter-relationship between the integrable infinite KP hierarchy, nonlinear $\hat{W}_{\infty}$ current algebra and conformal noncompact $SL(2,R)/U(1)$ coset model both at the classical and quantum levels. In particular, we present the construction of a quantum version of the KP hierarchy by deforming the second KP Hamiltonian structure through quantizing the $SL(2,R)_k/U(1)$ model and constructing an infinite set of commuting quantum $\hat{W}_{\infty}$ charges (at least at $k$=1).

hep-th↗

arXiv1992

On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model: I. The Classical Case

In this paper we study the inter-relationship between the integrable KP hierarchy, nonlinear $\hat{W}_{\infty}$ algebra and conformal noncompact $SL(2,R)/U(1)$ coset model at the classical level. We first derive explicitly the Possion brackets of the second Hamiltonian structure of the KP hierarchy, then use it to define the $\hat{W}_{1+\infty}$ algebra and its reduction $\hat{W}_{\infty}$. Then we show that the latter is realized in the $SL(2,R)/U(1)$ coset model as a hidden current algebra, through a free field realization of $\hat{W}_{\infty}$, in closed form for all higher-spin currents, in terms of two bosons. An immediate consequence is the existence of an infinite number of KP flows in the coset model, which preserve the $\hat{W}_{\infty}$ current algebra.

hep-th↗

arXiv1992

On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model: II. The Quantum Case

This paper is devoted to constructing a quantum version of the famous KP hierarchy, by deforming its second Hamiltonian structure, namely the nonlinear $\hat{W}_{\infty}$ algebra. This is achieved by quantizing the conformal noncompact $SL(2,R)_{k}/U(1)$ coset model, in which $\hat{W}_{\infty}$ appears as a hidden current algebra. For the quantum $\hat{W}_{\infty}$ algebra at level $k=1$, we have succeeded in constructing an infinite set of commuting quantum charges in explicit and closed form. Using them a completely integrable quantum KP hierarchy is constructed in the Hamiltonian form. A two boson realization of the quantum $\hat{W}_{\infty}$ currents has played a crucial role in this exploration.

hep-th↗

arXiv1992

An Infinite Number of Commuting Quantum $\hat{W}_{\infty}$ Charges in the $SL(2,R)/U(1)$ Coset Model

The conformal non-compact $SL(2,R)/U(1)$ coset model in two dimensions has been recently shown to embody a nonlinear $\hat{W}_\infty$ current algebra, consisting of currents of spin $\geq 2$ including the energy-momentum tensor. In this letter we explicitly construct an infinite set of commuting quantum $\hat{W}_\infty$ charges in the model with $k=1$. These commuting quantum charges generate a set of infinitely many compatible flows (quantum KP flows), which maintain the nonlinear $\hat{W}_\infty$ current algebra invariant.

hep-th↗

arXiv1991

Nonlinear $\hat{W}_{\infty}$ Current Algebra in the SL(2,R)/U(1) Coset Model

Previously we have established that the second Hamiltonian structure of the KP hierarchy is a nonlinear deformation, called $\hat{W}_{\infty}$, of the linear, centerless $W_{\infty}$ algebra. In this letter we present a free-field realization for all generators of $\hat{W}_{\infty}$ in terms of two scalars as well as an elegant generating function for the $\hat{W}_{\infty}$ currents in the classical conformal $SL(2,R)/U(1)$ coset model. After quantization, a quantum deformation of $\hat{W}_{\infty}$ appears as the hidden current algebra in this model. The $\hat{W}_{\infty}$ current algebra results in an infinite set of commuting conserved charges, which might give rise to $W$-hair for the 2d black hole arising in the corresponding string theory at level $k=9/4$.

hep-th↗

arXiv1991

Bi-Hamiltonian Sturcture of Super KP Hierarchy

We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the even super KP operator $Λ= θ^{2} + \sum^{\infty}_{i=-2}U_{i} θ^{-i-1}$, as a supersymmetric extension of the ordinary KP bi-Hamiltonian structure. It is expected to give rise to a universal super $W$-algebra incorporating all known extended superconformal $W_{N}$ algebras by reduction. We also construct the super BKP hierarchy by imposing a set of anti-self-dual constraints on the super KP hierarchy.

hep-th↗