Related papers: Disorder and Power-law Tails of DNA Sequence Self-…
The conformation of circular DNA molecules of various lengths adsorbed in a 2D conformation on a mica surface is studied. The results confirm the conjecture that the critical exponent $\nu$ is topologically invariant and equal to the SAW…
The advent of new experimental genomic technologies and the massive increase of DNA sequence information is helping researchers better understand how our genes work. Recently, experiments on mRNA abundance (gene expression) have revealed…
We introduce a model of DNA sequence evolution which can account for biases in mutation rates that depend on the identity of the neighboring bases. An analytic solution for this class of non-equilibrium models is developed by adopting…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
We study numerically the fully nonlinear gravitational collapse of a self-gravitating, minimally-coupled, massless scalar field in spherical symmetry. Our numerical code is based on double-null coordinates and on free evolution of the…
We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…
Cells attach to their environment by means of focal adhesions, which are molecular complexes that exhibit the remarkable ability to adapt to mechanical load by changing their size. Drawing from the biomolecular mechanisms underlying this…
We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's equations of coagulation for the solvable kernels $K(x,y)=2$, $x+y$ and $xy$. In addition to the known self-similar solutions with exponential tails, there…
The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of…
The influence of decoherence and bonding on the linear conductance of single double-stranded DNA molecules is examined by fitting a phenomenological statistical model developed recently (EPJB {\bf 68}, 237 (2009)) to experimental results.…
The numerical solutions of the non-linear evolution equation are shown to display the ``geometric'' scaling recently discovered in the experimental data. The phenomena hold both for proton and nucleus targets for all $x$ below $10^{-2}$ and…
We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density…
The deposition dynamics of particles (or the growth of a rigid crystal) on a disordered substrate at a finite deposition rate is explored. We begin with an equation of motion which includes, in addition to the disorder, the periodic…
Designing regulatory DNA sequences that achieve precise cell-type-specific gene expression is crucial for advancements in synthetic biology, gene therapy and precision medicine. Although transformer-based language models (LMs) can…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
Spontaneous symmetry breaking plays a fundamental role in many areas of condensed matter and particle physics. A fundamental problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory,…
The evolution of occupied volume under progressive fragmentation of granular matter is studied using a purely geometric model. Rather than modelling disorder directly, properties are investigated by analysing highly ordered reference…
A Self Consistent Field Theory description of equilibrium, but non uniform, configurations adopted by semi flexible liquid crystal molecules is presented. Two cases are considered, isotropic-nematic phase boundaries, and topological defects…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…