Related papers: Lower bounds on the maximum delay margin by analyt…
We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…
This paper describes the analysis of Lagrange interpolation errors on tetrahedrons. In many textbooks, the error analysis of Lagrange interpolation is conducted under geometric assumptions such as shape regularity or the (generalized)…
For stochastic approximation algorithms with discontinuous dynamics, it is shown that under suitable distributional assumptions, the interpolated iterates track a Fillipov solution of the limiting differential inclusion. In addition, we…
We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should…
We consider an overdetermined problem for Laplace equation on a disk with partial boundary data where additional pointwise data inside the disk have to be taken into account. After reformulation, this ill-posed problem reduces to a bounded…
We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradients must satisfy to ensure the existence of a global…
We study a delay-sensitive information flow problem where a source streams information to a sink over a directed graph G(V,E) at a fixed rate R possibly using multiple paths to minimize the maximum end-to-end delay, denoted as the…
This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled…
Intermodal logistics typically include the successive stages of intermodal shipment and last-mile delivery. We investigate this problem under a novel Logic-Based Benders Decomposition, which exploits the staged nature of the problem to…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…
A time-variant analogue of an interpolation problem equivalent to the relaxed commutant lifting problem is introduced and studied. In a somewhat less general form the problem already appears in the analysis of the set of all solutions to…
For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
We study methods for solving stochastic control problems of systems of forward-backward mean-field equations with delay, in finite or infinite horizon. Necessary and sufficient maximum principles under partial information are given. The…
This work presents a supervised learning based approach to the computer vision problem of frame interpolation. The presented technique could also be used in the cartoon animations since drawing each individual frame consumes a noticeable…
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…
In this paper, we provide explicit upper and lower bounds for the argument of the Riemann zeta-function and its antiderivatives in the critical strip under the assumption of the Riemann hypothesis. This extends the previously known bounds…
The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound…