Related papers: Phylogenetic invariants for stationary base compos…
Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
We study the evolution of an inverted spin ensemble coupled to a cavity. The inversion itself presents an inherent instability of the system; however, the inhomogeneous broadening of spin-resonance frequencies presents a stabilizing…
Complex periodic structures inherit spectral properties from the constituent parts of their unit cells, chiefly their spectral band gaps. Exploiting this intuitive principle, which is made precise in this work, means spectral features of…
Although the role of lateral gene transfer is well recognized in the evolution of bacteria, it is generally assumed that it has had less influence among eukaryotes. To explore this hypothesis we compare the dynamics of genome evolution in…
Cryptic genetic sequences have attenuated effects on phenotypes. In the classic view, relaxed selection allows cryptic genetic diversity to build up across individuals in a population, providing alleles that may later contribute to…
The secular evolution process, which slowly transforms the morphology of a galaxy over its lifetime, could naturally account for observed properties of the great majority of physical galaxies if both stellar and gaseous accretion processes…
Analysis of experimental kinetic dependences and results of the computer modeling of pairwise interactions in the heterogeneous system have shown that a character of its fractal property variation in the evolution process would be different…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
A phylogeny describes the evolutionary history of an evolving population. Evolutionary search algorithms can perfectly track the ancestry of candidate solutions, illuminating a population's trajectory through the search space. However,…
In higher organisms, all cells share the same genome, but every cell expresses only a limited and specific set of genes that defines the cell type. During cell division, not only the genome, but also the cell type is inherited by the…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
Diversity is an important factor in evolutionary algorithms to prevent premature convergence towards a single local optimum. In order to maintain diversity throughout the process of evolution, various means exist in literature. We analyze…
Consider a bisexual population such that the set of females can be partitioned into finitely many different types indexed by $\{1,2,\dots,n\}$ and, similarly, that the male types are indexed by $\{1,2,\dots,\nu \}$. Recently an evolution…
One of the basic questions of phylogenomics is how gene function evolves, whether among species or inside gene families. In this chapter, we provide a brief overview of the problems associated with defining gene function in a manner which…
Phylogenetic inference, grounded in molecular evolution models, is essential for understanding the evolutionary relationships in biological data. Accounting for the uncertainty of phylogenetic tree variables, which include tree topologies…
The affine group scheme of automorphisms of an evolution algebra that is equal to its square, is shown to lie in an exact sequence, such that the other terms depend solely on the directed graph associated to the algebra. As a consequence,…
Complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. Here we study this phenomenon using a mathematical model of a system that evolves under…
Machine learning methods can be unreliable when deployed in domains that differ from the domains on which they were trained. There are a wide range of proposals for mitigating this problem by learning representations that are ``invariant''…
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…