Related papers: Averaging method for systems with separatrix cross…
In this paper, we present an averaging method for obtaining quasi-periodic response solutions in perturbed, real analytic, quasi-periodic systems with Diophantine frequency vectors. Under the assumptions that the averaged system possesses a…
In mixture model-based clustering applications, it is common to fit several models from a family and report clustering results from only the `best' one. In such circumstances, selection of this best model is achieved using a model selection…
We consider general (not necessarily Hamiltonian) perturbations of Hamiltonian systems with one degree of freedom near separatrices of the unperturbed system. We present asymptotic formulas for change of slow variables at evolution across…
Sampling from a multimodal distribution is a fundamental and challenging problem in computational science and statistics. Among various approaches proposed for this task, one popular method is Annealed Importance Sampling (AIS). In this…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…
Crossover and mutation are the two main operators that lead to new solutions in evolutionary approaches. In this article, a new method of performing the crossover phase is presented. The problem of choice is evolutionary decision tree…
Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only $\sigma$-additivity in probability and continuity of the paths. It is proved that the averaging principle holds for…
The width of the distribution of species in a polydisperse system is employed in a small-variable expansion, to obtain a well-controlled and compact scheme by which to calculate phase equilibria in multi-phase systems. General and universal…
We consider the reconciliation problem, in which the task is to find a mapping of a gene tree into a species tree, so as to maximize the likelihood of such fitting, given the available data. We describe a model for the evolution of the…
Phase separation has emerged as an essential concept for the spatial organization inside biological cells. However, despite the clear relevance to virtually all physiological functions, we understand surprisingly little about what phases…
This paper considers the task of learning how to make a prognosis of a patient based on his/her micro-array expression levels. The method is an application of the aggregation method as recently proposed in the literature on theoretical…
We present an algebraic approach to evolutionary accumulation modelling (EvAM). EvAM is concerned with learning and predicting the order in which evolutionary features accumulate over time. Our approach is complementary to the more common…
A fundamental question in systems biology is what combinations of mean and variance of the species present in a stochastic biochemical reaction network are attainable by perturbing the system with an external signal. To address this…
An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged…
Calibration is a widely used method in survey sampling to adjust weights so that estimated totals of some chosen calibration variables match known population totals or totals obtained from other sources. When a large number of auxiliary…
We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to…
Given a random walk a method is presented to produce a matrix of transition probabilities that is consistent with that random walk. The method is a kind of reverse application of the usual ergodicity and is tested by using a transition…