Related papers: A more comprehensive formulation of evolutionary e…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical…
A large class of initial-boundary value problems of linear evolution partial differential equations formulated on the half-line is analyzed via the unified transform method. In particular, explicit formulae are presented for the generalized…
Evolution formulas of the density operator, the photon number distribution, and the Wigner function are derived for the problem on the optical fields propagation in realistic environments. The method of deriving these formulas is novel and…
A central question in developmental biology is how size and position are determined. The genetic code carries instructions on how to control these properties in order to regulate the pattern and morphology of structures in the developing…
Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic, such that the dynamics becomes deterministic…
Evolution by natural selection, which is one of the most compelling themes of modern science, brought forth evolutionary algorithms and evolutionary computation, applying mechanisms of evolution in nature to various problems solved by…
Recent methodological advances are enabling better examination of speciation and extinction processes and patterns. A major open question is the origin of large discrepancies in species number between groups of the same age. Existing…
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…
The modelling of evolutionary game dynamics in finite populations requires microscopic processes that determine how strategies spread. The exact details of these processes are often chosen without much further consideration. Different types…
An autocatalytic pattern matching polymer system is studied as an abstract model for chemical ecosystem evolution. Highly ordered populations with particular sequence patterns appear spontaneously out of a vast number of possible states.…
This study presents the approach to analyzing the evolution of an arbitrary complex system whose behavior is characterized by a set of different time-dependent factors. The key requirement for these factors is only that they must contain an…
We introduce the Webworld model, which links together the ecological modelling of food web structure with the evolutionary modelling of speciation and extinction events. The model describes dynamics of ecological communities on an…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
The evolution model with parallel mutation-selection scheme is solved for the case when selection is accompanied by base substitutions, insertions, and deletions. The fitness is assumed to be either a single-peak function (i.e., having one…
We propose a simple cognitive model where qualitative and quantitative com- parisons enable animals to identify objects, associate them with their properties held in memory and make naive inference. Simple notions like equivalence re-…
This paper reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of of various approaches at building Riemannian spaces of shapes, with a special focus on the…
In this paper we explore the eco-evolutionary dynamics of a predator-prey model, where the prey population is structured according to a certain life history trait. The trait distribution within the prey population is the result of interplay…
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…
We incorporate the generic hierarchical architecture of foodwebs into a "{\it unified}" model that describes both "micro" and "macro" evolutions within a single theoretical framework. This model describes the "micro" -evolution in detail by…