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The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…

We provide an elementary approach to integrable systems associated with hyperelliptic curves of infinite genus. In particular, we explore the extent to which the classical Burchnall-Chaundy theory generalizes in the infinite genus limit,…

Generalised parton distributions are instrumental to study both the three-dimensional structure and the energy-momentum tensor of the nucleon, and motivate numerous experimental programmes involving hard exclusive measurements. Based on a…

We propose an unexplored quantization method. It is based on the assumption of dynamical space-time intrinsic periodicities for relativistic fields, which in turn can be regarded as dual to extra-dimensional fields. As a consequence we…

We establish a matrix generalization of the ultradiscrete fourth Painlev\'e equation (ud-PIV). Well-defined multicomponent systems that permit ultradiscretization are obtained using an approach that relies on a group defined by constraints…

The thermodynamical properties of heterogeneous DNA sequences are computed by path integral techniques applied to a nonlinear model Hamiltonian. The base pairs relative displacements are interpreted as time dependent paths whose amplitudes…

We studied how the inhomogeneity of a sequence affects the phase transition that takes place at DNA melting. Unlike previous works, which considered thermodynamic quantities averaged over many different inhomogeneous sequences, we focused…

The Transfer-Integral (TI) operator is a powerful method to investigate the statistical physics of 1-dimensional models, like those used to describe DNA denaturation. At the cost of a certain number of approximations, the TI equation can be…

We introduce a Langevin equation describing the pinning-depinning phase transition experienced by Kardar-Parisi-Zhang interfaces in the presence of a bounding ``lower-wall''. This provides a continuous description for this universality…

The contributions to non-singlet evolution kernels $P(z)$ for the DGLAP equation and $V(x,y)$ for the Brodsky-Lepage evolution equation are calculated for certain classes of diagrams which include the renormalon chains. Closed expressions…

We adapt a technique of Kisin to construct and study crystalline deformation rings of $G_K$ for a finite extension $K/\mathbb{Q}_p$. This is done by considering a moduli space of Breuil--Kisin modules, satisfying an additional Galois…

We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer…

The total-evidence approach to divergence-time dating uses molecular and morphological data from extant and fossil species to infer phylogenetic relationships, species divergence times, and macroevolutionary parameters in a single coherent…

Coarse-grained (CG) models play a crucial role in the study of protein structures, protein thermodynamic properties, and protein conformation dynamics. Due to the information loss in the coarse-graining process, backmapping from CG to…

We study deformation theory of mod $p$ Galois representations of $p$-adic fields with values in generalised tori, such as $L$-groups of (possibly non-split) tori. We show that the corresponding deformation rings are formally smooth over a…

The small longitudinal polarization fractions (50%) of $B \to \phi K^*$ measured by B factories contradict with the naive theoretical counting rules. We review the current theoretical status of the $B\to VV$ decay studies and calculate many…

We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Levy (jump-diffusion) processes. These equations are fully non-linear, degenerate parabolic integro-PDEs interpreted in the sense of viscosity…

We review the theoretical status of b to s hadronic penguin decays in the Standard Model and beyond. We summarize the main theoretical tools to compute Branching Ratios and CP asymmetries for b to s penguin dominated nonleptonic decays, and…

In this paper, we consider deformations of singular complex curves on complex surfaces. Despite the fundamental nature of the problem, little seems to be known for curves on general surfaces. Let $C\subset S$ be a complete integral curve on…

A notion of degeneration of elements in groups is introduced. It is used to parametrize the orbits in a finite abelian group under its full automorphism group by a finite distributive lattice. A pictorial description of this lattice leads…