We develop a continuous-time control approach to optimal trading in a Proof-of-Stake (PoS) blockchain, formulated as a consumption-investment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/tr...
We give a space-optimal algorithm with update time O(log^2(1/eps)loglog(1/eps)) for (1+eps)-approximating the pth frequency moment, 0 < p < 2, of a length-n vector updated in a data stream. This provides a nearly exponential improvement in the update...
We leverage second-order information for tuning of inverse optimal controllers for a class of discrete-time nonlinear input-affine systems. For this, we select the input penalty matrix, representing a tuning knob, to yield the Hessian of the Lyapunov...
In this paper, we investigate optimal control problems for Allen-Cahn variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator. The approach covers both the cases of distributed...
In this paper, we investigate optimal control problems for Allen-Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace-Beltrami operator. The approach covers both the cases of d...
Sepsis is one of the leading causes of death in Intensive Care Units (ICU). The strategy for treating sepsis involves the infusion of intravenous (IV) fluids and administration of antibiotics. Determining the optimal quantity of IV fluids is a challe...
We extend the signature-based primal and dual solutions to the optimal stopping problem recently introduced in [Bayer et al.: Primal and dual optimal stopping with signatures, to appear in Finance & Stochastics 2025], by integrating deep-signature an...
An optimal transport (OT) problem seeks to find the cheapest mapping between two distributions with equal total density, given the cost of transporting density from one place to another. Unbalanced OT allows for different total density in each distri...
The most commonly used model for battery energy storage systems (BESSs) in optimal BESS allocation problems is a constant-efficiency model. However, the charging and discharging efficiencies of BESSs vary non-linearly as functions of their state-of-c...
We study several optimal stopping problems that arise from trading a mean-reverting price spread over a finite horizon. Modeling the spread by the Ornstein-Uhlenbeck process, we analyze three different trading strategies: (i) the long-short strategy;...
The Benes network has been used as a rearrangeable network for over 40 years, yet the uniform $N(2 \log N-1)$ control complexity of the $N \times N$ Benes is not optimal for many permutations. In this paper, we present a novel $O(\log N)$ depth rea...
While the ultimate goal of solving computationally intractable problems is to find a provably optimal solutions, practical constraints of real-world scenarios often necessitate focusing on efficiently obtaining high-quality, near-optimal solutions. T...
We introduce a construction for families of 2n-dimensional arrays with asymptotically optimal pairwise cross-correlation. These arrays are constructed using a circulant array of n-dimensional Legendre arrays. We also introduce an application of these...
Conventional local planners frequently become trapped in a locally optimal trajectory, primarily due to their inability to traverse obstacles. Having a larger number of topologically distinctive paths increases the likelihood of finding the optimal t...
This paper presents a UAV-based optimal crop-dusting method to control anomalously diffusing infestation of crops. Two anomalous diffusion models are considered, which are, respectively, time-fractional order diffusion equation and space-fractional o...
The Sinkhorn algorithm has emerged as a powerful tool for solving optimal transport problems, finding applications in various domains such as machine learning, image processing, and computational biology. Despite its widespread use, the intricate str...
We study the sample complexity of learning an $\varepsilon$-optimal policy in an average-reward Markov decision process (MDP) under a generative model. For weakly communicating MDPs, we establish the complexity bound $\widetilde{O}(SA\frac{H}{\vareps...
The presentation covers prerequisite results from Topology and Measure Theory. This is then followed by an introduction into couplings and basic definitions for optimal transport. The Kantrorovich problem is then introduced and an existence theorem i...
We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their fluxes, and th...
We consider computing optimal k-norm preemptive schedules of jobs that arrive over time. In particular, we show that computing the optimal k-norm of flow schedule, is strongly NP-hard for k in (0, 1) and integers k in (1, infinity). Further we show t...