相关论文: The irregular (integer) tetrahedron as a warehouse…

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…

In this work it is shown that 20 canonical amino acids (AAs) within genetic code appear to be a whole system with strict AAs positions; more exactly, with AAs ordinal number in three variants; first variant 00-19, second 00-21 and third…

Different novel organic-chemical possibilities for tetrahedral building units are considered, with attention to their utility in constructing different super-structures. As a representative construction we consider the use of sets of 20…

In the real world, most objects and data have multiple types of attributes and inter-connections. Such data structures are named "Heterogeneous Information Networks" (HIN) and have been widely researched. Biological systems are also…

What are proteins made from, as the working parts of the living cells protein machines? To answer this question, we need a technology to disassemble proteins onto elementary func-tional details and to prepare lumped description of such…

In the present work, 16 genetic code doublets and their cognate amino acids in the genetic code are fitted into a polyhedron model. Based on the structural regularity in nucleobases, and by using a series of common-sense topological…

Mathematical and computational approaches in chemistry and biochemistry fill a gap in respect to the analysis of the physicochemical features of compounds and their functionality and provide an overview of known as well as yet unknown, but…

Group theoretical concepts are invoked in a specific model to explain how only twenty amino acids occur in nature out of a possible sixty four. The methods we use enable us to justify the occurrence of the recently discovered twenty first…

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…

Upon the covalent-bonding hybrid of the nitrogen atoms taken as a measure for the structural regularity in nucleobases, it can be identified that the internal relation within the 20 amino acids follows a cooperative vector-in-space addition…

We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this problem is considerably more difficult than the corresponding…

Explainable and interpretable unsupervised machine learning helps understand the underlying structure of data. We introduce an ensemble analysis of machine learning models to consolidate their interpretation. Its application shows that…

We propose a predictive building-up of tetrahedral molecules, based on a previously derived chirality index, which characterizes a tetrahedral molecule, with n chiral centers, as achiral, diastereoisomer, or enantiomer as a function of the…

The discovery of new materials has a documented history of propelling human progress for centuries and more. The behaviour of a material is a function of its composition, structure, and properties, which further depend on its processing and…

On the basis of empirical Fischer projections, we developed an algebraic approach to central molecular chirality of tetrahedral molecules. The elements of such an algebra are obtained from the 24 projections which a single chiral…

In nature the three-dimensional structure of a protein is encoded in the corresponding gene. In this paper we describe a new method for encoding the three-dimensional structure of a protein into a binary sequence. The feature of the method…

Dense polyhedron packings are useful models of a variety of condensed matter and biological systems and have intrigued scientists mathematicians for centuries. Recently, organizing principles for the types of structures associated with the…

A representation of the genetic code as a six-dimensional Boolean hypercube is proposed. It is assumed here that this structure is the result of the hierarchical order of the interaction energies of the bases in codon-anticodon recognition.…

This paper presents a simple extension of the binary heap, the List Heap. We use List Heaps to demonstrate the idea of adaptive heaps: heaps whose performance is a function of both the size of the problem instance and the disorder of the…

A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…