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Background: The rate at which fitness declines as an organism's genome accumulates random mutations is an important variable in several evolutionary theories. At an intuitive level, it might seem natural that random mutations should tend to…
The understanding of how the arrangement of defects in photonic crystals impacts its photonic properties is cru-cial for the design of functional materials based thereon. By preparing photonic crystals with random missing scatterers we…
The chiral phase transition in the conventional random matrix model is the second order in the chiral limit, irrespective of the number of flavors N_f, because it lacks the U_A(1)-breaking determinant interaction term. Furthermore, it…
We show the expected order of RNA saturated secondary structures of size $n$ is $\log_4n(1+O(\frac{\log_2n}{n}))$, if we select the saturated secondary structure uniformly at random. Furthermore, the order of saturated secondary structures…
Subcritical catalytic branching random walk on d-dimensional lattice is studied. New theorems concerning the asymptotic behavior of distributions of local particles numbers are established. To prove the results different approaches are used…
The circuit complexity of time-evolved pure quantum states grows linearly in time for an exponentially long time. This behavior has been proven in certain models, is conjectured to hold for generic quantum many-body systems, and is believed…
Recently, the use of mathematical methods and computer science applications have got significant response among biochemists and biologists to modeling the biological systems. The computational and mathematical methods have enormous…
We consider a Hamiltonian system made of $N$ classical particles moving in two dimensions, coupled via an {\it infinite-range interaction} gauged by a parameter $A$. This system shows a low energy phase with most of the particles trapped in…
We report X-ray diffraction and magnetic susceptibility studies of the structural phase transition in $\alpha$-RuCl$_{3}$. By utilizing a single crystal sample with predominantly single twin domain, we show that $\alpha$-RuCl$_{3}$ goes…
Neutron scattering experiments have recently been performed in the superconducting state of UPt3 to determine the structure of the vortex lattice. The data show anomalous field dependence of the aspect ratio of the unit cell in the B phase.…
Many simple RNA viruses enclose their genetic material by a protein shell called the capsid. While the capsid structures are well characterized for most viruses, the structure of RNA inside the shells and the factors contributing to it…
Heterogeneous nucleation of a new bulk phase on a flat substrate can be associated with the surface phase transition called wetting transition. When this bulk heterogeneous nucleation occurs on a completely-wettable flat substrate with a…
We introduce mutations in replication systems in which the intact copying mechanism is performed by discrete iterations of a complex quadratic map in the family $f_c(z) = z^2+c$. More specifically, we consider a "correct" function $f_{c_1}$…
Exercising direct control over the unusual electronic structures arising from quantum confinement effects in graphene nanoribbons (GNRs) - atomically defined quasi one-dimensional (1D) strips of graphene - is intimately linked to geometric…
We have studied the transition in shape of two dimensional polyampholytes using Monte Carlo simulation. We observe that polymers with randomly charged monomers get into a globular shape at lower temperatures, provided that their total…
The transition from the quantum to the classical regime of the nucleation of the closed Robertson-Walker Universe with spacially homogeneous matter fields is investigated with a perturbation expansion around the sphaleron configuration. A…
We study numerically the behavior of RNA secondary structures under influence of a varying external force. This allows to measure the work $W$ during the resulting fast unfolding and refolding processes. Here, we investigate a medium-size…
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…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe…