Wai-Tong Louis Fan
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View article: Time Averaged Statistics of the 3D Stochastic Ladyzenskaya-Smagorinsky Equations
Time Averaged Statistics of the 3D Stochastic Ladyzenskaya-Smagorinsky Equations Open
Due to the chaotic nature of turbulence, statistical quantities are often more informative than pointwise characterizations. In this work, we consider the stochastic Ladyzhenskaya-Smagorinsky equation driven by space-time Gaussian noise on…
View article: A conditional coalescent for diploid exchangeable population models given the pedigree
A conditional coalescent for diploid exchangeable population models given the pedigree Open
We study coalescent processes conditional on the population pedigree under the exchangeable diploid bi-parental population model of \citet{BirknerEtAl2018}. While classical coalescent models average over all reproductive histories, thereby…
View article: Strong convergence with error estimates for a stochastic compartmental model of electrophysiology
Strong convergence with error estimates for a stochastic compartmental model of electrophysiology Open
This paper presents a rigorous mathematical analysis, alongside simulation studies, of a spatially extended stochastic electrophysiology model, the Hodgkin-Huxley model of the squid giant axon being a classical example. Although most studi…
View article: Intertwining the Busemann process of the directed polymer model
Intertwining the Busemann process of the directed polymer model Open
View article: Conditional gene genealogies given the population pedigree for a diploid Moran model with selfing
Conditional gene genealogies given the population pedigree for a diploid Moran model with selfing Open
We introduce a stochastic model of a population with overlapping generations and arbitrary levels of self-fertilization versus outcrossing. We study how the global graph of reproductive relationships, or population pedigree, influences the…
View article: Joint identifiability of ancestral sequence, phylogeny and mutation rates under the TKF91 model
Joint identifiability of ancestral sequence, phylogeny and mutation rates under the TKF91 model Open
We consider the problem of identifying jointly the ancestral sequence, the phylogeny and the parameters in models of DNA sequence evolution with insertion and deletion (indel). Under the classical TKF91 model of sequence evolution, we obta…
View article: Inconsistency of parsimony under the multispecies coalescent
Inconsistency of parsimony under the multispecies coalescent Open
While it is known that parsimony can be statistically inconsistent under certain models of evolution due to high levels of homoplasy, the consistency of parsimony under the multispecies coalescent (MSC) is less well studied. Previous studi…
View article: Joint Identifiability of Ancestral Sequence, Phylogeny and Mutation Rates Under the Tkf91 Model
Joint Identifiability of Ancestral Sequence, Phylogeny and Mutation Rates Under the Tkf91 Model Open
View article: Correlation of coalescence times in a diploid Wright-Fisher model with recombination and selfing
Correlation of coalescence times in a diploid Wright-Fisher model with recombination and selfing Open
The correlation among the gene genealogies at different loci is crucial in biology, yet challenging to understand because such correlation depends on many factors including genetic linkage, recombination, natural selection and population s…
View article: Bursts of coalescence within population pedigrees whenever big families occur
Bursts of coalescence within population pedigrees whenever big families occur Open
We consider a simple diploid population-genetic model with potentially high variability of offspring numbers among individuals. Specifically, against a backdrop of Wright-Fisher reproduction and no selection there is an additional probabil…
View article: Correlation of coalescence times in a diploid Wright-Fisher model with recombination and selfing
Correlation of coalescence times in a diploid Wright-Fisher model with recombination and selfing Open
The correlation among the gene genealogies at different loci is crucial in biology, yet challenging to understand because such correlation depends on many factors including genetic linkage, recombination, natural selection and population s…
View article: Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles
Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles Open
Defective interfering particles (DIPs) are virus-like particles that occur naturally during virus infections. These particles are defective, lacking essential genetic materials for replication, but they can interact with the wild-type viru…
View article: Quasi-stationary behavior of the stochastic FKPP equation on the circle
Quasi-stationary behavior of the stochastic FKPP equation on the circle Open
We consider the stochastic Fisher-Kolmogorov-Petrovsky-Piscunov (FKPP) equation on the circle $\mathbb{S}$, \begin{equation*} \partial_t u(t,x) \,= \fracα{2}Δu +β\,u(1-u) + \sqrt{γ\,u(1-u)}\,\dot{W}, \qquad (t,x)\in(0,\infty)\times \mathbb…
View article: A new path method for exponential ergodicity of Markov processes on $\mathbb Z^d$, with applications to stochastic reaction networks
A new path method for exponential ergodicity of Markov processes on $\mathbb Z^d$, with applications to stochastic reaction networks Open
This paper provides a new path method that can be used to determine when an ergodic continuous-time Markov chain on $\mathbb Z^d$ converges exponentially fast to its stationary distribution in $L^2$. Specifically, we provide general condit…
View article: Latent mutations in the ancestries of alleles under selection
Latent mutations in the ancestries of alleles under selection Open
We consider a single genetic locus with two alleles A 1 and A 2 in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and have…
View article: Latent mutations in the ancestries of alleles under selection
Latent mutations in the ancestries of alleles under selection Open
We consider a single genetic locus with two alleles $A_1$ and $A_2$ in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and …
View article: Recurrent mutation in the ancestry of a rare variant
Recurrent mutation in the ancestry of a rare variant Open
Recurrent mutation produces multiple copies of the same allele which may be co-segregating in a population. Yet, most analyses of allele-frequency or site-frequency spectra assume that all observed copies of an allele trace back to a singl…
View article: Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles
Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles Open
Defective interfering particles (DIPs) are virus-like particles that occur naturally during virus infections. These particles are defective, lacking essential genetic materials for replication, but they can interact with the wild-type viru…
View article: Constrained Langevin approximation for the Togashi-Kaneko model of autocatalytic reactions
Constrained Langevin approximation for the Togashi-Kaneko model of autocatalytic reactions Open
The Togashi Kaneko model (TK model), introduced by Togashi and Kaneko in 2001, is a simple stochastic reaction network that displays discreteness-induced transitions between meta-stable patterns. Here we study a constrained Langevin approx…
View article: Recurrent mutation in the ancestry of a rare variant
Recurrent mutation in the ancestry of a rare variant Open
Recurrent mutation produces multiple copies of the same allele which may be co-segregating in a population. Yet most analyses of allele-frequency or site-frequency spectra assume that all observed copies of an allele trace back to a single…
View article: Sensitivity of Tropical Cyclone Intensity Variability to Different Stochastic Parameterization Methods
Sensitivity of Tropical Cyclone Intensity Variability to Different Stochastic Parameterization Methods Open
Proper representations of stochastic processes in tropical cyclone (TC) models are critical for capturing TC intensity variability in real-time applications. In this study, three different stochastic parameterization methods, namely, rando…
View article: Constrained Langevin approximation for the Togashi-Kaneko model of autocatalytic reactions
Constrained Langevin approximation for the Togashi-Kaneko model of autocatalytic reactions Open
The Togashi Kaneko model (TK model) is a simple stochastic reaction network that displays discreteness-induced transitions between meta-stable patterns. Here we study a constrained Langevin approximation (CLA) of this model. This CLA, deri…
View article: Modeling atmospheric data and identifying dynamics Temporal data-driven modeling of air pollutants
Modeling atmospheric data and identifying dynamics Temporal data-driven modeling of air pollutants Open
View article: Stochastic PDEs on graphs as scaling limits of discrete interacting systems
Stochastic PDEs on graphs as scaling limits of discrete interacting systems Open
Stochastic partial differential equations (SPDE) on graphs were introduced by Cerrai and Freidlin [Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 865-899]. This class of stochastic equations in infinite dimensions provides a minimal fra…
View article: Wave Propagation for Reaction-Diffusion Equations on Infinite Random Trees
Wave Propagation for Reaction-Diffusion Equations on Infinite Random Trees Open
View article: Impossibility of phylogeny reconstruction from $k$-mer counts
Impossibility of phylogeny reconstruction from $k$-mer counts Open
We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed $k$ no statistically consistent…
View article: Modeling Atmospheric Data and Identifying Dynamics: Temporal Data-Driven Modeling of Air Pollutants
Modeling Atmospheric Data and Identifying Dynamics: Temporal Data-Driven Modeling of Air Pollutants Open
Atmospheric modeling has recently experienced a surge with the advent of deep learning. Most of these models, however, predict concentrations of pollutants following a data-driven approach in which the physical laws that govern their behav…
View article: Impossibility of Consistent Distance Estimation from Sequence Lengths Under the TKF91 Model
Impossibility of Consistent Distance Estimation from Sequence Lengths Under the TKF91 Model Open
View article: Impossibility of consistent distance estimation from sequence lengths\n under the TKF91 model
Impossibility of consistent distance estimation from sequence lengths\n under the TKF91 model Open
We consider the problem of distance estimation under the TKF91 model of\nsequence evolution by insertions, deletions and substitutions on a phylogeny.\nIn an asymptotic regime where the expected sequence lengths tend to infinity,\nwe show …
View article: Genealogies in expanding populations
Genealogies in expanding populations Open
The goal of this paper is to prove rigorous results for the behavior of genealogies in a one-dimensional long range biased voter model introduced by Hallatschek and Nelson [