Related papers: Abstract DNA-type systems
We introduce the concept of an abstract evolution system, which provides a convenient framework for studying generic mathematical structures and their properties. Roughly speaking, an evolution system is a category endowed with a selected…
The connection between domain relaxations at individual scales and the collective heterogeneous response in non-equilibrium systems is a topic of profound interest in recent times. In a model sys- tem of constantly driven oppositely charged…
The notion of ontological states is introduced here with reference to the Cellular Automaton Interpretation of Quantum Mechanics proposed by G.'t Hooft. A class of discrete deterministic "Hamiltonian" Cellular Automata is defined that has…
The algebraic matrix hierarchy approach based on affine Lie $sl (n)$ algebras leads to a variety of 1+1 soliton equations. By varying the rank of the underlying $sl (n)$ algebra as well as its gradation in the affine setting, one…
Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in…
The theoretical study of deformability of special sequence of DNA double helix TATA-box is presentated. The paper elaborates on the mechanisms of abnormal deformation of DNA TATA-box double helix that cannot be explained using the standard…
In this paper mathematical models for the evolutionary conserved Notch-Delta pathway are developed and analyzed in order to better understand how two neighboring biological cells can become different. We pursue a structure-based…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
There is a lack of knowledge about the topological invariants of non-linear $d$-dimensional systems with a periodic potential. We study these systems through a classification of the linearized NLS/GP equation around their soliton solutions.…
We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order…
We introduce a new class of nonlinear equations admitting a representation in terms of Darboux-covariant compatibility conditions. Their special cases are, in particular, (i) the "general" von Neumann equation $i\dot\rho=[H,f(\rho)]$, with…
In the framework of algebraic topology the closed sequence of 4-dimensional polyhedra (algebraic polytopes) was defined. This sequence is started by the polytope {240}, discovered by Coxeter, and is determined by the second coordination…
It is shown that a set of functions which characterise the Lax hierarchy of non-linear equations may be represented in terms of the eigenstates of the potential which satisfies the generalised KdV equation. Such a representation leads to…
Using a bidifferential graded algebra approach to integrable partial differential or difference equations, a unified treatment of continuous, semi-discrete (Ablowitz-Ladik) and fully discrete matrix NLS systems is presented. These equations…
A recent development in the derivation of soliton solutions for initial-boundary value problems through Darboux transformations, motivated to reconsider solutions to the nonlinear Schr\"odinger (NLS) equation on two half-lines connected via…
This paper shows that various relevant dynamical systems can be described as vector fields associated to smooth functions via a bracket that defines what we call a Leibniz structure. We show that gradient flows, some dissipative systems,…
We study the dynamics of non-adiabatic transitions in non-Hermitian multi-level parabolic models where the separations of the diabatic energies are quadratic function of time. The model Hamiltonian has been used to describe the…
The collective response of a system is profoundly shaped by the interaction dynamics between its constituent elements. In physics, tailoring these interactions can enable the observation of unusual phenomena that are otherwise inaccessible…
We consider the continuum version of an elastic chain supporting topological and non-topological degrees of freedom; this generalizes a model for the dynamics of DNA recently proposed and investigated by ourselves. In a certain limit, the…
Liquids in equilibrium exhibit two types of disorder, simple and complex. Typical simple disorder liquid are liquid nitrogen, or weakly polar liquids. Complex liquids concern those who can form long lived local assemblies, and cover a large…