Related papers: Some Comments on the Stochastic Eulerian Tour Prob…
In this paper we show that there are applications that transform the movement of a pendulum into movements in $\mathbb{R}^3$. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top…
This paper considers the problem of steering the state distribution of a nonlinear stochastic system from an initial Gaussian to a terminal distribution with a specified mean and covariance, subject to probabilistic path constraints. An…
The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the…
This paper examines an averaging technique in which the nonlinear flux term is expanded and the convective velocities are passed through a low-pass filter. It is the intent that this modification to the nonlinear flux terms will result in…
Supplements to Mehta & Normand (1997) are given, with regard to integrals involving Euclidean distances between n+1 random points in d-dimensional space, each visited once.
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…
How predictable are turbulent flows? Here we use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the non-uniqueness of the solutions to the Euler equation that is…
We study a new modification of the Arrival problem, which allows for nodes that exhibit random as well as controlled behaviour, in addition to switching nodes. We study the computational complexity of these extensions, building on existing…
Stochastic parametrisations of the interactions among disparate scales of motion in fluid convection are often used for estimating prediction uncertainty, which can arise due to inadequate model resolution, or incomplete observations,…
We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent…
In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient…
Two-dimensional turbulence in a rectangular domain self-organises into large-scale unidirectional jets. While several results are present to characterize the mean jets velocity profile, much less is known about the fluctuations. We study…
We consider the population Wasserstein barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. This leads to a complicated stochastic optimization problem where the…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
Stochastic Thermodynamics (ST) extends the notions of classical thermodynamics to trajectories taken from a nonequilibrium ensemble. This extension yields a simple approach to fluctuation relations in small systems. Multiple time- and…
The Eulerian variational formulation of the gyrokinetic system with electrostatic turbulence is presented in general spatial coordinates by extending our previous work [H. Sugama, {\it et al}., Phys.\ Plasmas {\bf 25}, 102506 (2018)]. The…
This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time horizon $[0,T]$ as $T\rightarrow\infty$. The so-called turnpike properties are established for such problems, under…
The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal…
The deterministic variant of the Lambert's problem was posed by Lambert in the 18th century and its solution for conic trajectory has been derived by many, including Euler, Lambert, Lagrange, Laplace, Gauss and Legendre. The solution…