Related papers: Lie algebra solution of population models based on…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
Physical parameterizations are used as representations of unresolved subgrid processes within weather and global climate models or coarse-scale turbulent models, whose resolutions are too coarse to resolve small-scale processes. These…
A matrix Lie algebra is a linear space of matrices closed under the operation $ [A, B] = AB-BA $. The "Lie closure" of a set of matrices is the smallest matrix Lie algebra which contains the set. In the context of Markov chain theory, if a…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities,…
Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on an isomorphism between alignments and physical helix-coil models, we show in statistical mechanics that alignments with realistic laws for…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…
We show that each member of a broad class of Markovian population models induces a unique stochastic process on the space of genealogies. We construct this genealogy process and derive exact expressions for the likelihood of an observed…
Classical and exceptional Lie algebras and their representations are among the most important tools in the analysis of symmetry in physical systems. In this letter we show how the computation of tensor products and branching rules of…
We consider the significant class of holomorphically nondegenerate CR manifolds of finite type that are represented by some weighted homogeneous polynomials and we derive some useful features which enable us to set up a fast effective…
Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type…
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
This note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE's, physics or biology. The involved mathematical tools as…
The problem of selecting a model given a set of candidates remains a challenging one that pervades many scientific fields. We employ techniques from the theory of Lie groups to analyse the symmetries in differential equation models of…
Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple…
Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…
We apply the Lie algebraic method to reflecting optical systems with plane-symmetric freeform mirrors. Using analytical ray-tracing equations we construct an optical map. The expansion of this map gives us the aberration coefficients in…
In this paper, we consider statistical estimation of time-inhomogeneous aggregate Markov models. Unaggregated models, which corresponds to Markov chains, are commonly used in multi-state life insurance to model the biometric states of an…
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…