Constrained Hardy Space Approximation II: Numerics

We consider the problem of minimizing the distance kf − kLp(K), where K is a subset of the complex unit circle @D and ∈ C(K), subject to the constraint that f lies in the Hardy space Hp(D) and |f| ≤ g for some positive function g. This problem occurs in the context of filter design for causal LTI systems. We show that the optimization problem has a unique solution, which satisfies an extremal property similar to that for the Nehari problem. Moreover, we prove that the minimum of the optimization problem can be approximated by smooth functions. This makes the problem accessible for numerical solution, with which we deal in a follow-up paper

Constrained Hardy Space Approximation

We consider the problem of minimizing the distance kf − kLp(K), where K is a subset of the complex unit circle @D and ∈ C(K), subject to the constraint that f lies in the Hardy space Hp(D) and |f| ≤ g for some positive function g. This problem occurs in the context of filter design for causal LTI systems. We show that the optimization problem has a unique solution, which satisfies an extremal property similar to that for the Nehari problem. Moreover, we prove that the minimum of the optimization problem can be approximated by smooth functions. This makes the problem accessible for numerical solution, with which we deal in a follow-up paper

Bounds for optimization of the reflection coefficient by constrained optimization in hardy spaces

The purpose of this book is twofold. Our starting point is the design of layered media with a prescribed reflection coefficient. In the first part of this book we show that the space of physically realizable reflection coefficients is rather restricted by a number of properties. In the second part we consider a constrained approximation problem in Hardy spaces. This can be viewed as an optimization problem for the frequency response of a causal LTI system with limited gain

Investigating the performance of SPSA in simulation-optimization approaches to transportation problems

While optimization models play a key role in transportation analysis, the objective function to be optimized, however, cannot be defined analytically. It is therefore necessary to resort to non-differentiable optimization methods that usually pivot on evaluating the objective function. Special cases of particular interest are those in Dynamic OD Estimation, which cannot evaluate the objective function analytically and thus the formulation falls in the computational framework of Simulation-Optimization. SPSA is not limited to the inputs from conventional traffic counts and can be easily extended to account for the measurements of traffic variables supplied by emerging sensors exploiting Information and Communication Technologies (ICT). Numerical experiments have been conducted, and the results have been analyzed from two different perspectives: performance and solution quality. This allows understanding the behavior of the SPSA algorithm and new variants, which altogether contribute to the aim of adding ICT measures in the future. Their sensitivity to the initial values, the effect of bounding the variables and scaling techniques are analyzed. This paper will report on the results of the numerical experiments, their analyses, conclusions and further research.Peer ReviewedPostprint (published version

Studying the Potential of Multi-Target Classification to Characterize Combinations of Classes with Skewed Distribution

The identification of subpopulations with particu-lar characteristics with respect to a disease is important for personalized diagnostics and therapy design. For some diseases, the outcome is described by more than one target variable. An example is tinnitus: the perceived loudness of the phantom signal and the level of distress caused by it are both relevant targets for diagnosis and therapy. In this work, we study the potential of multi-target classification for the identification of those screening variables, which separate best among the different subpopula-tions of patients, paying particular attention to subpopulations with discordant value combinations of loudness and distress. We analyse the screening data of 1344 tinnitus patients from the University Hospital Regensburg, including questions from 7 questionnaires, and report on the performance of our workflow in target separation and in ranking the questionnaires’ variables on their discriminative power

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Bounds for optimization of the reflection coefficient by constrained optimization in hardy spaces

The purpose of this book is twofold. Our starting point is the design of layered media with a prescribed reflection coefficient. In the first part of this book we show that the space of physically realizable reflection coefficients is rather restricted by a number of properties. In the second part we consider a constrained approximation problem in Hardy spaces. This can be viewed as an optimization problem for the frequency response of a causal LTI system with limited gain