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In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are…
Recent work on approximate linear programming (ALP) techniques for first-order Markov Decision Processes (FOMDPs) represents the value function linearly w.r.t. a set of first-order basis functions and uses linear programming techniques to…
An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…
This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…
Recent advances in nonlinear dynamical systems theory provide a new insight into numerical properties of discrete algorithms developed to solve nonlinear initial value problems. Basic features like accuracy and stability are well pointed…
Object oriented constraint programs (OOCPs) emerge as a leading evolution of constraint programming and artificial intelligence, first applied to a range of industrial applications called configuration problems. The rich variety of…
We study the problem of Out-of-Distribution (OOD) detection, that is, detecting whether a learning algorithm's output can be trusted at inference time. While a number of tests for OOD detection have been proposed in prior work, a formal…
Automatically detecting anomalies in event data can provide substantial value in domains such as healthcare, DevOps, and information security. In this paper, we frame the problem of detecting anomalous continuous-time event sequences as…
The obstacle problem is a class of free boundary problems which finds applications in many disciplines such as porous media, financial mathematics and optimal control. In this paper, we propose two operator-splitting methods to solve the…
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…
Solving partial differential equations (PDEs) by learning the solution operators has emerged as an attractive alternative to traditional numerical methods. However, implementing such architectures presents two main challenges: flexibility…
Although synthetic test problems are widely used for the performance assessment of evolutionary multi-objective optimization algorithms, they are likely to include unrealistic properties which may lead to overestimation/underestimation. To…
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…
The `equation-free toolbox' empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable you to immediately use microscopic simulators to perform macro-scale system level tasks and analysis, because…
The evolution of programming languages from low-level assembly to high-level abstractions demonstrates a fundamental principle: by constraining how programmers express computation and enriching semantic information at the language level, we…
A one-time program (OTP) works as follows: Alice provides Bob with the implementation of some function. Bob can have the function evaluated exclusively on a single input of his choosing. Once executed, the program will fail to evaluate on…
Solving linear systems and quadratic programming (QP) problems are both ubiquitous tasks in the engineering and computing fields. Direct methods for solving systems, such as Cholesky, LU, and QR factorizations, exhibit data-independent time…
EXPODE is a MATLAB toolbox for exponential time integration. It supports exponential Runge-Kutta- and Rosenbrock-methods, linearized and non-linearized multistep-methods and the EXP4. We support evaluation of the arising matrix functions…
Solving constrained nonlinear optimization problems (CNLPs) is a longstanding problem that arises in various fields, e.g., economics, computer science, and engineering. We propose optimization-informed neural networks (OINN), a deep…
\textit{DPLib} is an open-source MATLAB-based benchmark library created to support research and development in distributed and decentralized power system analysis and optimization. Distributed and decentralized methods offer scalability,…