3,043 research outputs found
An exactly solved model for mutation, recombination and selection
It is well known that rather general mutation-recombination models can be
solved algorithmically (though not in closed form) by means of Haldane
linearization. The price to be paid is that one has to work with a multiple
tensor product of the state space one started from.
Here, we present a relevant subclass of such models, in continuous time, with
independent mutation events at the sites, and crossover events between them. It
admits a closed solution of the corresponding differential equation on the
basis of the original state space, and also closed expressions for the linkage
disequilibria, derived by means of M\"obius inversion. As an extra benefit, the
approach can be extended to a model with selection of additive type across
sites. We also derive a necessary and sufficient criterion for the mean fitness
to be a Lyapunov function and determine the asymptotic behaviour of the
solutions.Comment: 48 page
Haldane linearisation done right: Solving the nonlinear recombination equation the easy way
The nonlinear recombination equation from population genetics has a long
history and is notoriously difficult to solve, both in continuous and in
discrete time. This is particularly so if one aims at full generality, thus
also including degenerate parameter cases. Due to recent progress for the
continuous time case via the identification of an underlying stochastic
fragmentation process, it became clear that a direct general solution at the
level of the corresponding ODE itself should also be possible. This paper shows
how to do it, and how to extend the approach to the discrete-time case as well.Comment: 12 pages, 1 figure; some minor update
Modeling sequences and temporal networks with dynamic community structures
In evolving complex systems such as air traffic and social organizations,
collective effects emerge from their many components' dynamic interactions.
While the dynamic interactions can be represented by temporal networks with
nodes and links that change over time, they remain highly complex. It is
therefore often necessary to use methods that extract the temporal networks'
large-scale dynamic community structure. However, such methods are subject to
overfitting or suffer from effects of arbitrary, a priori imposed timescales,
which should instead be extracted from data. Here we simultaneously address
both problems and develop a principled data-driven method that determines
relevant timescales and identifies patterns of dynamics that take place on
networks as well as shape the networks themselves. We base our method on an
arbitrary-order Markov chain model with community structure, and develop a
nonparametric Bayesian inference framework that identifies the simplest such
model that can explain temporal interaction data.Comment: 15 Pages, 6 figures, 2 table
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