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Transmission-constrained problems in power systems can be cast as polynomial optimization problems whose coefficients vary over time. We consider the complications therein and suggest several approaches. On the example of the…
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…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
Generating function equation has been derived for the probability distribution of the number of nodes with $k \ge 0$ outgoing lines in randomly evolving special trees. The stochastic properties of end-nodes (k=0) have been analyzed, and it…
For any graph having a suitable uniform Poincare inequality and volume growth regularity, we establish two-sided Gaussian transition density estimates and parabolic Harnack inequality, for constant speed continuous time random walks…
We propose a proof of convergence of an adaptive method used in molecular dynamics to compute free energy profiles. Mathematically, it amounts to studying the long-time behavior of a stochastic process which satisfies a non-linear…
When a malfunction causes a control system to lose authority over a subset of its actuators, achieving a task may require spending additional energy in order to compensate for the effect of uncontrolled inputs. To understand this increase…
A rather simple random walk model on a one-dimensional lattice is put forward. The lattice as a whole switches randomly between two possible states which are spatially symmetric. Both lattice states are identical, but translated by one site…
We show that, for any graph optimization problem in which the feasible solutions can be expressed by a formula in monadic second-order logic describing sets of vertices or edges and in which the goal is to minimize the sum of the weights in…
In this paper, we study the problem of fast dynamic pointer following: given a directed graph $G$ where each vertex has outdegree $1$, efficiently support the operations of i) changing the outgoing edge of any vertex, and ii) find the…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
In standard textbooks of college physics, the Work Energy Theorem is usually presented for inertial frames of references and it is clear that energy is conserved when there is not net work of interaction forces. But what happens when energy…
We consider, on a temporal star graph, the problem of optimal damping a control system is considered for a generalized pantograph equation, which is a neutral-type equation with a time-proportional delay. The delay in the system propagates…
Properties of the turbulent cascade of kinetic energy are studied using direct numerical simulations of three-dimensional hydrodynamic decaying turbulence with a moderate Reynolds number and the initial Mach number $M=1$. Compressible and…
We introduce a simple but powerful technique to study processes driven by two or more reinforcement mechanisms in competition. We apply our method to two types of models: to non conservative zero range processes on finite graphs, and to…
On the rooted $k$-ary tree we consider a 0-1 kinetically constrained spin model in which the occupancy variable at each node is re-sampled with rate one from the Bernoulli(p) measure iff all its children are empty. For this process the…
The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
We consider a discrete-time dynamical process on graphs, firstly introduced in connection with a protocol for controlling large networks of spin 1/2 quantum mechanical particles [Phys. Rev. Lett. 99, 100501 (2007)]. A description is as…
We consider arbitrary trajectories subject to a coordinate-wise energy decrease: the sign of the derivative of each entry is never the same as that of the corresponding entry of the gradient of some energy function. We show that this simple…