Related papers: Harmonic problems arising from continuous time ran…
Multi-photon quantum walks in integrated optics are an attractive controlled quantum system, that can mimic less readily accessible quantum systems and exhibit behavior that cannot in general be accurately replicated by classical light…
The continuous time random walk (CTRW) model exhibits a non-ergodic phase when the average waiting time diverges. Using an analytical approach for the non-biased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a…
Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems.…
The usual random walk on a group (homogeneous both in time and in space) is determined by a probability measure on the group. In a random walk with random transition probabilities this single measure is replaced with a stationary sequence…
We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. Based on this fact is our method of group classification of potential symmetries of systems of…
We study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We establish a global well-posedness theory for the system with small smooth initial data. Additionally, we derive asymptotic emergent…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
In this paper we examine a mutual control problem for systems of two abstract evolution equations subject to a proportionality final condition. Related observability and semi-observability problems are discussed. The analysis employs a…
We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…
A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…
L\'evy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of…
We couple the issue of evolution in the laws of physics with that of violations of energy conservation. We define evolution in terms of time variables canonically dual to ``constants'' (such as $\Lambda$, the Planck mass or the…
We consider dynamic random walks where the nearest neighbour jump rates are determined by an underlying supercritical contact process in equilibrium. This has previously been studied by den Hollander and dos Santos and den Hollander, dos…
Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation,…
In this paper, we build a procedure that allows to establish regularity and controls in time for probabilistic solutions to PDEs. Probabilistic approaches to global wellposedness problems usually provide ensemble bounds on the solutions.…
We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…
The Continuous-Time Random Walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this article we will show how the random combination of two different unbiased CTRWs can give raise to a process with clear…
In this paper we introduce the notion of Random Walk in Changing Environment - a random walk in which each step is performed in a different graph on the same set of vertices, or more generally, a weighted random walk on the same vertex and…
Accurate tracking of planned trajectories in the presence of perturbations is an important problem in control and robotics. Symmetry is a fundamental mathematical feature of many dynamical systems and exploiting this property offers the…