25 citations · 81 across the 31 of their papers we have counts for
32 papers · 1 filter
Poisson approximation by coupling
Rinaldo B. Schinazi
It is well known that a binomial can be approximated by a Poisson distribution with parameter . The typical approach in undergraduate probability texts is to show a con…
How far from the edge need a population be to survive? A probability model
Rinaldo B. Schinazi
Let be a natural number. We consider a population which lives on . Each individual gives birth at rate on each of its neighboring sites and die…
An elementary proof of existence and uniqueness of stationary distributions for irreducible Markov chains
Rinaldo B. Schinazi
Consider an matrix with the following properties. All entries in are positive or , the sum of each row is 1 and for all and in there…
Can a rudderless species survive?
Rinaldo B. Schinazi
Some species of salmon and sea turtle are famously good at finding their birth place to reproduce after having travelled vast expanses of ocean. In contrast, imagine now a species…
Does genetic diversity help survival?
Luiz Renato Fontes, Fabio P. Machado, Rinaldo B. Schinazi
We introduce the following model for the evolution of a population. At every discrete time exactly one individual is introduced in the population and is assigned a death…
Can a single migrant per generation rescue a dying population?
Iddo Ben-Ari, Rinaldo B. Schinazi
We introduce a population model to test the hypothesis that even a single migrant per generation may rescue a dying population. Let be a sequence of real numbers in …
Null recurrence and transience for a binomial catastrophe model in random environment
Luiz Renato Fontes, Fabio P. Machado, Rinaldo B. Schinazi
We consider a discrete time population model for which each individual alive at time survives independently of everybody else at time with probability . The sequence…
Collective behavior under catastrophes
Rinaldo B. Schinazi
We introduce the following discrete time model. Each natural number represents an ecological niche and is assigned a fitness in . All the sites are updated simultaneously at…
Self-similarity in an exchangeable site-dynamics model
Iddo Ben-Ari, Rinaldo B. Schinazi
We consider a model for which every site of is assigned a fitness in . At every discrete time all the sites are updated and each site samples a uniform on $[0,1…
Randomness versus selection in genome evolution
Rinaldo B. Schinazi
We propose a Markov chain approach for the evolution of a genealogical line of genomes. Our idealized genome has sites and each site can be in state or . At each time st…
Metastability of a random walk with catastrophes
Luiz Renato Fontes, Rinaldo B. Schinazi
We consider a random walk with catastrophes which was introduced to model population biology. It is known that this Markov chain gets eventually absorbed at for all parameter v…
Implosion of a pure death process
Luiz Renato Fontes, Rinaldo B. Schinazi
We study a pure death process. At each discrete time every individual dies or not independently of each other with a constant probability. We give examples showing that in a certai…
A random walk with catastrophes
Iddo Ben-Ari, Alexander Roitershtein, Rinaldo B. Schinazi
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In…
Survival in locally and globally changing environments
Rinaldo B. Schinazi
We consider branching like models in local, global and fixed environments. We show that survival is more likely in a locally changing environment than in a fixed environment and th…
Colonization and Collapse
Fábio Prates Machado, Alejandro Roldán-Correa, Rinaldo B. Schinazi
Many species live in colonies that thrive for a while and then collapse. Upon collapse very few individuals survive. The survivors start new colonies at other sites that thrive unt…
Does random dispersion help survival?
Rinaldo B. Schinazi
Many species live in colonies that prosper for a while and then collapse. After the collapse the colony survivors disperse randomly and found new colonies that may or may not make…
The waiting time for a second mutation: an alternative to the Moran model
Rinaldo B. Schinazi
The appearance of cancer in a tissue is thought to be the result of two or more successive mutations. We propose a stochastic model that allows for an exact computation of the dist…
An inhomogeneous contact process model for speciation
Rinaldo B. Schinazi
We propose the following model for speciation and extinction. Birth and deaths occur according to spatially inhomogeneous contact rates. We assume that the ratio of the birth rate…
A stochastic model for the evolution of the influenza virus
J. T. Cox, R. B. Schinazi
Consider a birth and death chain to model the number of types of a given virus. Each type gives birth to a new type at rate and dies at rate 1. Each type is also assigned a fit…
A spatial stochastic model for rumor transmission
Cristian F. Coletti, Pablo M. Rodriguez, Rinaldo B. Schinazi
We consider an interacting particle system representing the spread of a rumor by agents on the -dimensional integer lattice. Each agent may be in any of the three states belongi…
A Branching Process for Virus Survival
J. Theodore Cox, Rinaldo B. Schinazi
Quasispecies theory predicts that there is a critical mutation probability above which a viral population will go extinct. Above this threshold the virus loses the ability to repli…
Bacterial persistence: a winning strategy?
Olivier Garet, Regine Marchand, Rinaldo B. Schinazi
It has long been known that antibiotic treatment will not completely kill off a bacteria population. For many species a small fraction of bacteria is not sensitive to antibiotics.…
Strength in numbers? Not always!
Rinaldo B. Schinazi
We propose a simple model to compute the probability of success under a quorum sensing strategy. We show that a quorum sensing strategy has a higher probability of success than an…
Will the swine strain crowd out the seasonal influenza strain?
Rinaldo B. Schinazi
We use spatial and non spatial models to argue that competition alone may explain why two influenza strains do not usually coexist. The more virulent strain is likely to crowd out…