Related papers: A Skorokhod Map on Measure-Valued Paths with Appli…
Zeroth-order optimization addresses problems where gradient information is inaccessible or impractical to compute. While most existing methods rely on first-order approximations, incorporating second-order (curvature) information can, in…
The St\v{r}eda formula establishes a fundamental connection between the topological invariants characterizing the bulk of topological matter and the presence of gapless edge modes. In this work, we extend the St\v{r}eda formula to…
Resource allocation and scheduling are a common problem in various distributed systems. Although widely studied, the state-of-the-art solutions either do not scale or lack the expressive power to capture the most complex instances of the…
Data-driven reduced-order models of the dynamics of complex flows are important for tasks related to design, understanding, prediction, and control. Many flows obey symmetries, and the present work illustrates how these can be exploited to…
Graph-structured data is prevalent in domains such as social networks, financial transactions, brain networks, and protein interactions. As a result, the research community has produced new databases and analytics engines to process such…
This paper presents a comprehensive overview of monotone priority queues, focusing on their evolution and application in shortest path algorithms. Monotone priority queues are characterized by the property that their minimum key does not…
We introduce a class of self-similar Gaussian processes and provide sufficient and necessary conditions for a member of the class to admit a unique small scale limit in the Skorokhod space. The class includes several well known processes.…
Stochastic processes on topological vector spaces over non-Archimedean fields and with transition measures having values in non-Archimedean fields are defined and investigated. For this the non-Archimedean analog of the Kolmogorov theorem…
Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In…
Optimal Markov Decision Process policies for problems with finite state and action space are identified through a partial ordering by comparing the value function across states. This is referred to as state-based optimality. This paper…
To better understand the flows of ideas or information through social and biological systems, researchers develop maps that reveal important patterns in network flows. In practice, network flow models have implied memoryless first-order…
A path integral formalism has been proposed recently for non-equilibrium statistical physics applications by the author. In this contribution we outline an efficient method for its numerical evaluation. The method used is based on the…
In this paper, we consider planning in stochastic shortest path (SSP) problems, a subclass of Markov Decision Problems (MDP). We focus on medium-size problems whose state space can be fully enumerated. This problem has numerous important…
We address the task of estimating multiple trajectories from unlabeled data. This problem arises in many settings, one could think of the construction of maps of transport networks from passive observation of travellers, or the…
We solve the Skorokhod embedding problem for a class of stochastic processes satisfying an inhomogeneous stochastic differential equation (SDE) of the form $d A_t =\mu (t, A_t) d t + \sigma(t, A_t) d W_t$. We provide sufficient conditions…
In the foreseeable future, toolchains for quantum computing should offer automatic means of transforming a high level problem formulation down to a hardware executable form. Thereby, it is crucial to find (multiple) transformation paths…
We introduce and analyze Structured Stochastic Zeroth order Descent (S-SZD), a finite difference approach that approximates a stochastic gradient on a set of $l\leq d$ orthogonal directions, where $d$ is the dimension of the ambient space.…
We construct an aggregated version of the value processes associated with stochastic control problems, where the criterion to optimise is given by solutions to semi-martingale backward stochastic differential equations (BSDEs). The results…
Quantum computing promises exponential acceleration for fluid flow simulations, yet the measurement overhead required to extract flow features from quantum-encoded flow field data fundamentally undermines this advantage--a critical…
We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular…