Related papers: The genetic code invariance: when Euler and Fibona…
To reach a deeper understanding of the origin of elements in the periodic table, we construct Galactic chemical evolution (GCE) models for all stable elements from C (A=12) to U (A=238) from first principles, i.e., using theoretical…
An RNA sequence is a word over an alphabet on four elements $\{A,C,G,U\}$ called bases. RNA sequences fold into secondary structures where some bases match one another while others remain unpaired. Pseudoknot-free secondary structures can…
Fibonacci codes are self-synchronizing variable-length codes that are proven useful for their robustness and compression capability. Asymptotically, these codes provide better compression efficiency as the order of the underlying Fibonacci…
Odd electrons of benzenoid units and correlation of these electrons having different spins are the main concepts of the molecular theory of graphene. In contrast to the theory of aromaticity, the molecular theory is based on the fact that…
An equivalent definition of the Fibonacci numbers is that they are the unique sequence such that every integer can be written uniquely as a sum of non-adjacent terms. We can view this as we have bins of length 1, we can take at most one…
Topological quantum computing holding global anti-interference ability is realized by braiding some anyons, such as well-known Fibonacci anyons. Here, based on $SO(3)_2 $ theory we obtain a total of 6 anyon models utilizing…
We address the question, related with the origin of the genetic code, of why are there three bases per codon in the translation to protein process. As a followup to our previous work, we approach this problem by considering the…
A Poincare' covariant Faddeev equation is presented, which enables the simultaneous prediction of meson and baryon observables using the leading-order in a truncation of the Dyson-Schwinger equations that can systematically be improved. The…
One of the greatest challenges in biophysical models of translation is to identify coding sequences features that affect the rate of translation and therefore the overall protein production in the cell. We propose an analytic method to…
For an integer $n\geq 8$ divisible by $4$, let $R_n=\mathbb{Z}[\zeta_n,1/2]$ and let $\operatorname{U}_2(R_n)$ be the group of $2\times 2$ unitary matrices with entries in $R_n$. Set…
We present a bijective algorithm with which an arbitrary permutation decomposes canonically into elementary blocks which we call families, which are sets with a specified number of ascents and descents. We show that families, arranged in an…
Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution, which are characterized by successfully finding robust solutions for optimization problems. Here, we propose a subroutine-based quantum genetic…
Abundances of 18 chemical elements have been derived for 27 A/Am and 16 F stars members of the Pleiades and Coma Berenices open clusters. We have specifically computed, with the Montr\'eal code, a series of evolutionary models for two A…
We enumerate the number of RNA contact structures according to their genus, i.e. the topological character of their pseudoknots. By using a recently proposed matrix model formulation for the RNA folding problem, we obtain exact results for…
The toric code can be constructed as a gauge theory of finite groups on oriented two dimensional lattices. Here we construct analogous models with the gauge fields belonging to groupoids, which are categories where every morphism has an…
We propose a novel encoding scheme for algebraic codes such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed-Solomon codes and present numerical examples. We employ the recurrence from the Gr\"obner…
A brief review, from basic atomic constants to "Mendeleev Table" of leptons, quarks, fundamental bosons, and then to superunification of all forces and particles.
We describe rational knots with any of the possible combinations of the properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting number one (or higher), and determine exactly their number for a given number of crossings…
We give recurrence relations for the enumeration of symmetric elements within four classes of arc diagrams corresponding to certain involutions and set partitions whose blocks contain no consecutive integers. These arc diagrams are…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…