595 research outputs found
The peripatric coalescent
We consider a dynamic metapopulation involving one large population of size N
surrounded by colonies of size \varepsilon_NN, usually called peripheral
isolates in ecology, where N\to\infty and \varepsilon_N\to 0 in such a way that
\varepsilon_NN\to\infty. The main population periodically sends propagules to
found new colonies (emigration), and each colony eventually merges with the
main population (fusion). Our aim is to study the genealogical history of a
finite number of lineages sampled at stationarity in such a metapopulation. We
make assumptions on model parameters ensuring that the total outer population
has size of the order of N and that each colony has a lifetime of the same
order. We prove that under these assumptions, the scaling limit of the
genealogical process of a finite sample is a censored coalescent where each
lineage can be in one of two states: an inner lineage (belonging to the main
population) or an outer lineage (belonging to some peripheral isolate).
Lineages change state at constant rate and inner lineages (only) coalesce at
constant rate per pair. This two-state censored coalescent is also shown to
converge weakly, as the landscape dynamics accelerate, to a time-changed
Kingman coalescent.Comment: 17 pages,1 figur
Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling
We introduce a class of interest rate models, called the -CIR model,
which gives a natural extension of the standard CIR model by adopting the
-stable L{\'e}vy process and preserving the branching property. This
model allows to describe in a unified and parsimonious way several recent
observations on the sovereign bond market such as the persistency of low
interest rate together with the presence of large jumps at local extent. We
emphasize on a general integral representation of the model by using random
fields, with which we establish the link to the CBI processes and the affine
models. Finally we analyze the jump behaviors and in particular the large
jumps, and we provide numerical illustrations
On the hitting times of continuous-state branching processes with immigration
We study the two-dimensional joint distribution of the first hitting time of
a constant level by a continuous-state branching process with immigration and
their primitive stopped at this time. We show an explicit expression of its
Laplace transform. Using this formula, we study the polarity of zero and
provide a necessary and sufficient criterion for transience or recurrence. We
follow the approach of Shiga, T. (1990) [A recurrence criterion for Markov
processes of Ornstein-Uhlenbeck type. Probability Theory and Related Fields,
85(4), 425-447], by finding some -invariant functions for the
generator
Limit theorems for continuous-state branching processes with immigration
We prove and extend some results stated by Mark Pinsky: Limit theorems for continuous state branching processes with immigration [Bull. Amer. Math. Soc. 78(1972), 242--244]. Consider a continuous-state branching process with immigration with branching mechanism and immigration mechanism (CBI for short). We shed some light on two different asymptotic regimes occurring when or . We first observe that when , supercritical CBIs have a growth rate dictated by the branching dynamics, namely there is a renormalization , only depending on , such that converges almost-surely to a finite random variable. When , it is shown that the immigration overwhelms the branching dynamics and that no linear renormalization of the process can exist. Asymptotics in the second regime are studied in details for all non-critical CBI processes via a nonlinear time-dependent renormalization in law. Three regimes of weak convergence are then exhibited, where a misprint in Pinsky's paper is corrected. CBI processes with critical branching mechanisms subject to a regular variation assumption are also studied
Visual Question Answering with Memory-Augmented Networks
In this paper, we exploit a memory-augmented neural network to predict
accurate answers to visual questions, even when those answers occur rarely in
the training set. The memory network incorporates both internal and external
memory blocks and selectively pays attention to each training exemplar. We show
that memory-augmented neural networks are able to maintain a relatively
long-term memory of scarce training exemplars, which is important for visual
question answering due to the heavy-tailed distribution of answers in a general
VQA setting. Experimental results on two large-scale benchmark datasets show
the favorable performance of the proposed algorithm with a comparison to state
of the art.Comment: CVPR 201
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