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We present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…
We study the Brodsky-Lepage evolution equation for the nucleon and construct an eigenfunction basis by including contributions of up to polynomial order $9$. By exployting the permutation symmetry $P_{13}$ of these eigenfunctions, a basis…
Cells actively regulate their size during the cell cycle to maintain volume homeostasis across generations. While various mathematical models of cell size regulation have been proposed to explain how this is achieved, relating these models…
The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and…
In solution, DNA is a highly charged macromolecule which bears a unit of negative charge on each phosphate of its sugar-phosphate backbone. Although partially compensated by counterions adsorbed at or condensed near it, DNA still produces a…
Background: In Escherichia coli, overlapping rounds of DNA replication allow the bacteria to double in faster times than the time required to copy the genome. The precise timing of initiation of DNA replication is determined by a regulatory…
Unusually high bending flexibility has been recently reported for DNA on short length scales. We use atomic force microscopy (AFM) in solution to obtain a direct estimate of DNA bending statistics for scales down to one helical turn. It…
What is the size of the atomic nucleus? This deceivably simple question is difficult to answer. While the electric charge distributions in atomic nuclei were measured accurately already half a century ago, our knowledge of the distribution…
We present a new non-Archimedean model of evolutionary dynamics, in which the genomes are represented by p-adic numbers. In this model the genomes have a variable length, not necessarily bounded, in contrast with the classical models where…
We show, that the specific distribution of gene's length, which is observed in natural genomes, might be a result of a growth process, in which a single length scale $L(t)$ develops that grows with time as $t^{1/3}$. This length scale could…
We introduce a simple model for DNA evolution. Using the method of Peng et al.$^1$, we investigate the fractal properties of the system. For small chains and chains of intermediate size we find a fractal exponent that indicates the…
Stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with growing $N$ the system approaches a deterministic limit indicating…
The evolution in coding DNA sequences brings new flexibility and freedom to the codon words, even as the underlying nucleotides get significantly ordered. These curious contra-rules of gene organisation are observed from the distribution of…
A hypothesis of the evolution of the genetic code is proposed, the leading mechanism of which is the nucleotide spontaneous damage leading to AT-enrichment of the genome. The hypothesis accounts for stability of the genetic code towards…
DNA-coated colloids can self-assemble into an incredible diversity of crystal structures, but applications of this technology are limited by poor understanding and control over the dynamical crystallization pathways. To address this…
DNA is subject to large deformations in a wide range of biological processes. Two key examples illustrate how such deformations influence the readout of the genetic information: the sequestering of eukaryotic genes by nucleosomes, and DNA…
A proper understanding of the links between varying gene expression levels and complex trait adaptation is still lacking, despite recent advances in sequencing techniques leading to new insights on their importance in some evolutionary…
Among the genetic algorithms generally used for optimization problems in the recent decades, quantum-inspired variants are known for fast and high-fitness convergence and small resource requirement. Here the application to the patient…
The vacuum expectation value of the evolution operator for a general class of Hamiltonians used in quantum field theory and statistical physics and which include unstable particles is considered. An exact formula which describes the large…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…