相关论文: An exactly solved model for mutation, recombinatio…
We introduce an age-structured asexual population model containing all the relevant features of evolutionary ageing theories. Beneficial as well as deleterious mutations, heredity and arbitrary fecundity are present and managed by natural…
Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient…
We expand the solutions of linearly coupled Mathieu equations in terms of infinite-continued matrix inversions, and use it to find the modes which diagonalize the dynamical problem. This allows obtaining explicitly the ('Floquet-Lyapunov')…
We simulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves 1) the structure of the ground state, 2) its thermodynamic stability and 3) its kinetic accessibility. All other…
Sampling the phase space of molecular systems -- and, more generally, of complex systems effectively modeled by stochastic differential equations -- is a crucial modeling step in many fields, from protein folding to materials discovery.…
Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local…
Exact inference for hidden Markov models requires the evaluation of all distributions of interest - filtering, prediction, smoothing and likelihood - with a finite computational effort. This article provides sufficient conditions for exact…
Modern datasets are becoming heterogeneous. To this end, we present in this paper Mixed-Variate Restricted Boltzmann Machines for simultaneously modelling variables of multiple types and modalities, including binary and continuous…
We consider a class of nonlocal reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. By using explicit changes of unknown function, we show that they are equivalent to the heat equation and,…
The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator…
In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
This contribution is concerned with mathematical models for the dynamics of the genetic composition of populations evolving under recombination. Recombination is the genetic mechanism by which two parent individuals create the mixed type of…
Machine learning (ML) in its current form implies that an answer to any problem can be well approximated by a function of a very peculiar form: a specially adjusted iteration of Heavyside theta-functions. It is natural to ask if the answers…
We analyze a replicator-mutator model arising in the context of directed evolution [23], where the selection term is modulated over time by the mean-fitness. We combine a Cumulant Generating Function approach [13] and a spatio-temporal…
This paper is addressed to the well-posedness of some linear and semilinear backward stochastic differential equations with general filtration, without using the Martingale Representation Theorem. The point of our approach is to introduce a…
We study a novel large dimensional approximate factor model with regime changes in the loadings driven by a latent first order Markov process. By exploiting the equivalent linear representation of the model, we first recover the latent…
We introduce an evolutionary algorithm called recombinator-$k$-means for optimizing the highly non-convex kmeans problem. Its defining feature is that its crossover step involves all the members of the current generation, stochastically…
We study the uniform boundedness of solutions to reaction-diffusion systems possessing a Lyapunov-like function and satisfying an {\it intermediate sum condition}. This significantly generalizes the mass dissipation condition in the…
This paper presents new theory and methodology for the Bayesian estimation of overfitted hidden Markov models, with finite state space. The goal is then to achieve posterior emptying of extra states. A prior configuration is constructed…