Related papers: Mutation model for oligonucleotides fitting a Yule…
This work recollects a non-universal set of quantum gates described by higher-dimensional Spin groups. They are also directly related with matchgates in theory of quantum computations and complexity. Various processes of quantum state…
The exact one-to-one mapping between (spinless) Jordan-Wigner lattice fermions and (spin-1/2) spinons is established for all eigenstates of the one-dimensional s = 1=2 XX model on a lattice with an even or odd number N of lattice sites and…
The flexibility of short DNA chains is investigated via computation of the average correlation function between dimers which defines the persistence length. Path integration techniques have been applied to confine the phase space available…
We examine the elastic model of short circular DNA. We obtain analytic expressions for configurations, elastic energy, twist and linking number of our solutions. We find the onset of the plectonemic transition. We suggest ways to use our…
The site frequency spectrum describes variation among a set of n DNA sequences. Its i'th entry (i=1,2,...,n-1) is the number of nucleotide sites at which the mutant allele is present in i copies. Under selective neutrality, random mating,…
We have analyzed DNA sequences of known genes from 16 yeast chromosomes (Saccharomyces cerevisiae) in terms of oligonucleotides. We have noticed that the relative abundances of oligonucleotide usage in the genome follow a long-tail…
Recent studies reveal even the smallest genomes such as viruses evolve through complex and stochastic processes, and the assumption of independent alleles is not valid in most applications. Advances in sequencing technologies produce…
The form of the spectral curve for $4d$ $N=2$ supersymmetric Yang-Mills theory with matter fields in the fundamental representation of the gauge group suggests that its $1d$ integrable counterpart should be looked for among (inhomogeneous)…
Classically spinning B=1 Skyrmions can be regarded as approximations to nucleons with quantised spin. Here, we investigate nucleon-nucleon scattering through numerical collisions of spinning Skyrmions. We identify the dineutron/diproton and…
One of the main applications of balance indices is in tests of null models of evolutionary processes. The knowledge of an exact formula for a statistic of a balance index, holding for any number n of leaves, is necessary in order to use…
Neutral macroevolutionary models, such as the Yule model, give rise to a probability distribution on the set of discrete rooted binary trees over a given leaf set. Such models can provide a signal as to the approximate location of the root…
DNA cyclization is a powerful technique to gain insight into the nature of DNA bending. The worm-like chain model provides a good description of small to moderate bending fluctuations, but some experiments on strongly-bent shorter molecules…
Recent studies have revealed that for the majority of species the length distributions of duplicated sequences in natural DNA follow a power-law tail. We study duplication-mutation models for processes in natural DNA sequences and the…
Determining the trajectories of cells and their lineages or ancestries in live-cell experiments are fundamental to the understanding of how cells behave and divide. This paper proposes novel online algorithms for jointly tracking and…
Observables emitted from various spin states in compound U nuclei are investigated to validate usefulness of the surrogate reaction method. It was found that energy spectrum of cascading $\gamma$-rays and their multiplicities, spectrum of…
We look at the evolution through rewiring of the degree distribution of a network so the number edges is constant. This is exactly equivalent to the evolution of probability distributions in models of cultural transmission with drift and…
The nucleon is naturally viewed as a bipartite system of valence spin -- defined by its non-vanishing chiral charge -- and non-valence or sea spin. The sea spin can be traced over to give a reduced density matrix, and it is shown that the…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
Analytical expressions for the eigenvalues of certain inhomogeneous XY spin chains are computed. These models are rewritten in terms of free-fermion models using a well-known Jordan-Wigner transformation. Finding the spectrum of such models…
In a phylogenetic tree, we often don't have information about the time a speciation event (inner node) occured. Under a neutral model for speciation, I develop fast algorithms for calculating the probability that an inner node i is the k-th…