A metric space associated with probability space

For a complete probability space (Ω,∑,P), the set of all complete sub-σ-algebras of ∑, S(∑), is given a natural metric and studied. The questions of when S(∑) is compact or connected are awswered and the important subset consisting of all continuous sub-σ-algebras is shown to be closed. Connections with Christensen's metric on the von Neumann subalgebras of a Type II1-factor are briefly discussed

Completeness of the set of sub- σ

A new metric is introduced on the set of all sub-σ-algebras of a complete probability space from functional analysis point of view. In this note, we will show that the resulting metric space is complete

Asymptotic properties of bandit processes with geometric responses

Abstract Asymptotic properties of optimal strategies for two-armed bandit processes with geometrically distributed survival times are derived. These results provide asymptotic boundary conditions and further extend structure properties of optimal strategies for bandit processes with delayed responses

Research on the Influence of Switching Frequency on Low-Frequency Oscillation in the Voltage-Controlled Buck-Boost Converter

The influence of switching frequency on the low-frequency oscillation in the voltage-controlled buck-boost converter is studied in this paper. Firstly, the mathematical model of this system is derived. And then, a glimpse at the influence of switching frequency on the low-frequency oscillation in this system by MATLAB/Simulink is given. The improved averaged model of the system is established, and the corresponding theoretical analysis is presented. It is found that the switching frequency has an important influence on the low-frequency oscillation in the system, that is, the low-frequency oscillation is easy to occur when the switching frequency is low. Finally, the effectiveness of the improved averaged model and the theoretical analysis are confirmed by circuit experiment

Average and Small Signal Modeling of Negative-Output KY Boost Converter in CCM Operation

Negative-output KY Boost converter, which can obtain the negative output voltage and could be driven easily, is a good topology to overcome traditional Boost and Buck-Boost converters and it is believed that this converter will be widely used in engineering applications in the future. In this study, by using the averaging method and geometrical technique, the average and small signal model of the negative-output KY Boost converter are established. The DC equilibrium point and transfer functions of the system are derived and analyzed. Finally, the effectiveness of the established model and the correctness of the theoretical analysis are confirmed by the circuit experiment

Therapy by physician–pharmacist combination and economic returns for cancer pain management in China: a cost-effectiveness analysis

Objective: To examine whether joint management of cancer pain by physicians and pharmacists in clinics provides economic advantages from the perspective of the Chinese healthcare system.Methods: From February 2018 to March 2020, 100 patients who visited the joint cancer pain clinic at the Xiangya Hospital of Central South University were included. These patients were randomly assigned to either the control or intervention groups. The control group received regular outpatient services from a physician, while the intervention group received regular outpatient services from a physician and medication education provided by a pharmacist. The study considered various direct costs, including drug expenses, physician-pharmacist outpatient services, adverse event management, consultations, examinations, and readmissions. The outcome indicators considered were the cancer pain control rate and the reduction in pain scores. Decision tree modeling, single-factor sensitivity analysis, and probabilistic sensitivity analysis were performed to evaluate the cost-effectiveness of joint physician-pharmacist outpatient services compared to physician-alone outpatient services.Results: The intervention group showed a significantly higher cancer pain control rate than the control group (0.69 vs. 0.39, p = 0.03). In the decision tree model, the intervention group had a significantly lower pain score than the control group (0.23 vs. 0.14). The cost per person in the intervention group was $165.39, while it was$191.1 per person in the control group. The univariate sensitivity analysis showed that the cost of self-management for patients in the control group was identified as the primary sensitivity factor. Probabilistic sensitivity analysis indicated that the joint clinic group had a favorable incremental cost-effectiveness compared to the physician clinic group. In addition, the probabilistic sensitivity analysis demonstrated an absolute advantage in the incremental cost-effectiveness of the joint clinic group over the outpatient physician group.Conclusion: The participation of pharmacists in joint cancer pain clinic services led to improved pain management for patients, demonstrating a clear advantage in terms of cost-effectiveness

Play-the-Winner Rule and Adaptive Designs of Clinical Trials

In another paper, we have argued that the traditional randomized design of clinical trials is ethically infeasible in desperate medical situations and adaptive designs are morally required. We have also argued that in such situations, the appropriate designs must satisfy what we call the “Principle of interchangeability.” In this statistics paper, we show that the statistical model of bandit processes satisfies this principle of interchangeability. Moreover, we demonstrate that when such a model is used as an adaptive design, the total regret of successes lost is smaller when compared with simple randomization. We illustrate the results by the simple deterministic play-the-winner design