Related papers: A Skorokhod Map on Measure-Valued Paths with Appli…
Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Gal\'{a}n recently introduced a novel stochastic shielding…
We develop a class of pathwise inequalities of the form $H(B_t)\ge M_t+F(L_t)$, where $B_t$ is Brownian motion, $L_t$ its local time at zero and $M_t$ a local martingale. The concrete nature of the representation makes the inequality useful…
Asynchronous parallel optimization received substantial successes and extensive attention recently. One of core theoretical questions is how much speedup (or benefit) the asynchronous parallelization can bring us. This paper provides a…
We modify the global Skorokhod topology, on the space of cadlag paths, by localising with respect to space variable, in order to include the eventual explosions. The tightness of families of probability measures on the paths space endowed…
Optimal sensor scheduling with applications to networked estimation and control systems is considered. We model sensor measurement and transmission instances using jumps between states of a continuous-time Markov chain. We introduce a cost…
To ensure the effective and objective development of transportation networks, it is crucial to identify performance limitations across various subsystems. A timetable-independent assessment of infrastructure capacity at railway junctions is…
A single-server queuing model is considered with customers that have deadlines. If a customer's deadline elapses before service is offered, the customer abandons the system (customers do not abandon while being served). When the server…
The increasing computational and memory demands in deep learning present significant challenges, especially in resource-constrained environments. We introduce a zero-order quantized optimization (ZOQO) method designed for training models…
We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…
Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the integrability of many probabilistic systems,…
We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge…
While dealing with matching shapes to their parts, we often apply a tool known as functional maps. The idea is to translate the shape matching problem into "convenient" spaces by which matching is performed algebraically by solving a least…
A reflection map, induced by the deterministic Skorohod problem on the nonnegative orthant, is applied to an $\mathbb{R}^n$ valued function $X$ on $[0,\infty)$ and then to $a+X$, where $a$ is a nonnegative constant vector. A question that…
We investigate fluid scaling of single server queueing systems under the shortest job first with aging (SJFA) scheduling policy. We use the measure-valued Skorokhod map to characterize the fluid limit for SJFA queues with a general aging…
Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…
Shellsort is a sorting method that is attractive due to its simplicity, yet it takes effort to analyze its efficiency. The heart of the algorithm is the gap sequence chosen a priori and used during sorting. The selection of this gap…
We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path…
We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking…
We study a single server queue operating under the shortest remaining processing time (SRPT) scheduling policy; that is, the server preemptively serves the job with the shortest remaining processing time first. In this work we are…
Ergodic exploration has spawned a lot of interest in mobile robotics due to its ability to design time trajectories that match desired spatial coverage statistics. However, current ergodic approaches are for continuous spaces, which require…