Related papers: Algebraic computation of genetic patterns related …
Group-based models appear in algebraic statistics as mathematical models coming from evolutionary biology, respectively the study of mutations of organisms. Both theoretically and in terms of applications, we are interested in determining…
This paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structure is a topological invariant that is characterized by the…
In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated…
Cell formation is a critical step in the design of cellular manufacturing systems. Recently, it was tackled using a cut-based-graph-partitioning model. This model meets real-life production systems requirements as it uses the actual amount…
Molecule generation is a very important practical problem, with uses in drug discovery and material design, and AI methods promise to provide useful solutions. However, existing methods for molecule generation focus either on 2D graph…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
In this short note, we describe the so-called homogeneous involution on finite-dimensional graded-division algebra over an algebraically closed field. We also compute their graded polynomial identities with involution. As pointed out by L.…
During cell migration, cells become polarized, change their shape, and move in response to various internal and external cues. Cell polarization is defined through the spatio-temporal organization of molecules such as PI3K or small GTPases,…
We give an efficient, deterministic algorithm to decide if two abelian varieties over a number field are isogenous. From this, we derive an algorithm to compute the endomorphism ring of an elliptic curve over a number field.
In this paper, we introduce Volterra evolution algebras which are evolution algebras whose structural matrices are described by skew symmetric matrices. A main result of the present paper gives a connection between such kind of algebras…
Algebraic properties of the genetic code are analyzed. The investigations of the genetic code on the basis of matrix approaches ("matrix genetics") are described. The degeneracy of the vertebrate mitochondria genetic code is reflected in…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
Using the syzygy method, established in our earlier paper, we characterize the combinatorial stratification of the variety of two-dimensional real generic algebras. We show that there exist exactly three different homotopic types of such…
Evolutionary transitions occur when previously-independent replicating entities unite to form more complex individuals. Such transitions have profoundly shaped natural evolutionary history and occur in two forms: fraternal transitions…
Given any arbitrary semi-algebraic set $X$, any two points in $X$ may be joined by a piecewise $C^2$ path $\gamma$ of shortest length. Suppose $\mathcal{A}$ is a semi-algebraic stratification of $X$ such that each component of $\gamma \cap…
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…
For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of…
We construct a sheaf-theoretic representation of quantum observables algebras over a base category equipped with a Grothendieck topology, consisting of epimorphic families of commutative observables algebras, playing the role of local…
The set of known dialects of the genetic code (GC) is analyzed from the viewpoint of the genetic octave Yin-Yang-algebra. This algebra was described in the previous author's publications. The algebra was discovered on the basis of…
The genetic code structure into distinct multiplet-classes as well as the numeric degeneracies of the latter are revealed by a two-step process. First, an empirical inventory of the degeneracies (of the shuffled multiplets) in two specific…