Related papers: Unique mechanisms from finite two-state trajectori…
The signal from many single molecule experiments monitoring molecular processes, such as enzyme turnover via fluorescence and opening and closing of ion channel via the flux of ions, consists of a time series of stochastic on and off (or…
Deducing an underlying multi-substate on-off kinetic scheme (KS) from the statistical properties of a two-state trajectory is the aim from many experiments in biophysics and chemistry, such as, ion channel recordings, enzymatic activity and…
Trajectories of on-off events are the output of many single molecule experiments. Usually, one describes the underlying mechanism that generates the trajectory using a kinetic scheme, and by analyzing the trajectory aims at deducing this…
We develop an general formalism of single enzyme kinetics in two dimension where substrates diffuse stochastically on a square lattice in presence of disorder. The dynamics of the model could be decoupled effectively to two stochastic…
Paper is devoted to maintaining the simple objective: We want to provide Hamiltonian canonical form for autonomous dynamical system reducible to even-dimensional one. Along the road we construct new class of conserved quantities, called…
A time trajectory of an observable that fluctuates between two values (say, on and off), stemming from some unknown multi-substate kinetic scheme, is the output of many single molecule experiments. Here we show that when all successive…
Phenomena in chemistry, biology and neuroscience are often modelled using ordinary differential equations (ODEs) in which the right-hand-side is comprised of terms which correspond to individual 'processes' or 'fluxes'. Frequently, these…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
Trajectories of a signal that fluctuates between two states which originate from single molecule activities have become ubiquitous. Common examples are trajectories of ionic flux through individual membrane-channels, and of photon counts…
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…
Chemical kinetic models in terms of ordinary differential equations correspond to finite dimensional dissipative dynamical systems involving a multiple time scale structure. Most dimension reduction approaches aimed at a slow…
The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. In this paper I present a simple model,…
The characterization of quantum processes is a key tool in quantum information processing tasks for several reasons: on one hand, it allows to acknowledge errors in the implementations of quantum algorithms; on the other, it allows to…
We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software.…
We consider multiple k-essence sources and obtain the conditions their kinetic functions must satisfy so that purely kinetic k-essences lead to models with phantom barrier crossing. After that, we show that polynomial kinetic functions…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by…
Ensemble control, an emerging research field focusing on the study of large populations of dynamical systems, has demonstrated great potential in numerous scientific and practical applications. Striking examples include pulse design for…