Related papers: Optimal crossover designs for the proportional mod…
Our main contribution in this article is the achievement of the turnpike property in its integral and exponential forms for parameter-dependent systems with averaged observations in the cost functional. Namely, under suitable assumptions…
The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have…
In computational inverse problems, the optimal experimental design (OED) problem seeks the best locations in time and space at which to take measurements. We investigate the nonlinear OED problem in the context of continuously-indexed…
There are several approaches to define an eigenvector decomposition of the finite Fourier Transform, which is in some sense unique, and at best resembles the eigenstates of the quantum harmonic oscillator. A solution given by Balian and…
We consider the general performance of the difference-in-means estimator in an equally-allocated two-arm randomized experiment under common experimental endpoints such as continuous (regression), incidence, proportion, count and uncensored…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
Complex Ornstein-Uhlenbeck (OU) processes have various applications in statistical modelling. They play role e.g. in the description of the motion of a charged test particle in a constant magnetic field or in the study of rotating waves in…
We propose a class of subspace ascent methods for computing optimal approximate designs that covers both existing as well as new and more efficient algorithms. Within this class of methods, we construct a simple, randomized exchange…
Response-adaptive clinical trial designs allow targeting a given objective by skewing the allocation of participants to treatments based on observed outcomes. Response-adaptive designs face greater regulatory scrutiny due to potential type…
We give some new explicit examples of putatively optimal projective spherical designs. i.e., ones for which there is numerical evidence that they are of minimal size. These form continuous families, and so have little apparent symmetry in…
This is part II of a two-part paper. Part I presented a universal Birkhoff theory for fast and accurate trajectory optimization. The theory rested on two main hypotheses. In this paper, it is shown that if the computational grid is selected…
The hybrid approach to experimental design aims to control frequentist operating characteristics of Bayesian decision procedures. These operating characteristics are assessed by simulating sampling distributions of posterior summaries under…
We propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special type. We propose some kind of "algebra" on different models and corresponding…
The proportional hazards model represents the most commonly assumed hazard structure when analysing time to event data using regression models. We study a general hazard structure which contains, as particular cases, proportional hazards,…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
Imbalance in covariate distributions leads to biased estimates of causal effects. Weighting methods attempt to correct this imbalance but rely on specifying models for the treatment assignment mechanism, which is unknown in observational…
Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is…
We generalize a well-known result of L. Caffarelli on Lipschitz estimates for optimal transportation $T$ between uniformly log-concave probability measures. Let $T : \R^d \to \R^d$ be an optimal transportation pushing forward $\mu =…
There is a movement in design of experiments away from the classic randomization put forward by Fisher, Cochran and others to one based on optimization. In fixed-sample trials comparing two groups, measurements of subjects are known in…
In a physical design problem, the designer chooses values of some physical parameters, within limits, to optimize the resulting field. We focus on the specific case in which each physical design parameter is the ratio of two field…