Related papers: p-Adic numbers in bioinformatics: from genetic cod…
This paper proposes a new mathematical approach to characterize native protein structures based on the discrete differential geometry of tetrahedron tiles. In the approach, local structure of proteins is classified into finite types…
Ultrametric matrices have a rich structure that is not apparent from their definition. Notably, the subclass of strictly ultrametric matrices are covariance matrices of certain weighted rooted binary trees. In applications, these matrices…
Advances in bioinformatics are primarily due to new algorithms for processing diverse biological data sources. While sophisticated alignment algorithms have been pivotal in analyzing biological sequences, deep learning has substantially…
We introduce a technique for establishing and amplifying gaps between parameters of network coding and index coding. The technique uses linear programs to establish separations between combinatorial and coding-theoretic parameters and…
In order to associate complex traits with genetic polymorphisms, genome-wide association studies process huge datasets involving tens of thousands of individuals genotyped for millions of polymorphisms. When handling these datasets, which…
We introduce genetic algorithms as a means to analyze supernovae type Ia data and extract model-independent constraints on the evolution of the Dark Energy equation of state. Specifically, we will give a brief introduction to the genetic…
The generalized binary sequences of order 2 have been used to construct good binary cyclic codes [4]. The linear complexity of these sequences has been computed in [2]. The autocorrelation values of such sequences have been determined in…
The prediction of protein 3D structure from amino acid sequence is a computational grand challenge in biophysics, and plays a key role in robust protein structure prediction algorithms, from drug discovery to genome interpretation. The…
With its three independent parameters, the $ABCD$ matrix serves as the beam transfer matrix in optics. If it is transformed to an equi-diagonal form, the matrix has only two independent parameters determined by optical devices. It is shown…
We derive the amino acid assignment to one codon representation (typical 64-dimensional irreducible representation) of the basic classical Lie superalgebra osp(5|2) from biochemical arguments. We motivate the approach of mathematical…
Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist $p$-adic representation of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the…
The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the…
The standard genetic code is known to be much more efficient in minimizing adverse effects of misreading errors and one-point mutations in comparison with a random code having the same structure, i.e. the same number of codons coding for…
For many-electron systems, the second-order reduced density matrix (2-RDM) provides sufficient information for characterizing their properties of interests in physics and chemistry, ranging from total energy, magnetism, quantum correlation…
Advances in molecular "omics'" technologies have motivated new methodology for the integration of multiple sources of high-content biomedical data. However, most statistical methods for integrating multiple data matrices only consider data…
An important application of distance geometry to biochemistry studies the embeddings of the vertices of a weighted graph in the three-dimensional Euclidean space such that the edge weights are equal to the Euclidean distances between…
In this manuscript, an original numerical procedure for the nonlinear peridynamics on arbitrarily--shaped two-dimensional (2D) closed manifolds is proposed. When dealing with non parameterized 2D manifolds at the discrete scale, the problem…
We study the problem of polynomial identity testing (PIT) for depth 2 arithmetic circuits over matrix algebra. We show that identity testing of depth 3 (Sigma-Pi-Sigma) arithmetic circuits over a field F is polynomial time equivalent to…
Artificial Intelligence (AI) techniques are known for its ability in tackling problems found to be unyielding to traditional mathematical methods. A recent addition to these techniques are the Computational Intelligence (CI) techniques…
PLINK 1 is a widely used open-source C/C++ toolset for genome-wide association studies (GWAS) and research in population genetics. However, the steady accumulation of data from imputation and whole-genome sequencing studies has exposed a…