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Quantum systems are modelled as different mathematical structures, depending on their nature and complexity. This chapter considers one of the simplest (discrete-time) models of quantum systems, namely quantum automata. It introduces a way of describing linear-time (dynamic) properties of quantum systems and presents several algorithms for checking certain linear-time properties of quantum automata, for example, invariants and reachability.
Model checking is an algorithmic technique for verification of computing and communication hardware and software. This book extends the technique of model checking for quantum systems. As preliminaries, this chapter introduces basics of model checking for both classical non-probabilistic and probabilistic systems.
This chapter develops model-checking techniques for a much larger class of quantum systems modelled as quantum Markov chains or more generally, quantum Markov decision processes. The differences between quantum automata and quantum Markov systems require us to develop algorithms for the latter that are fundamentally different from those for the former.
This chapter is intended to introduce some basic notions of quantum theory needed in the subsequent chapters for the reader who is not familiar with them. Quantum mechanics is a fundamental physics subject that studies the phenomena at the atomic and subatomic scales. This chapter introduces the required mathematical tools and presents the postulates mainly through their mathematical formalisms. The physics interpretation of these is only very briefly discussed.
This chapter is devoted to studying a class of even more complex quantum systems modelled as so-called super-operator-valued Markov chains (SVMCs). This new model is particularly useful in modelling the high-level structure of quantum programs and quantum communication protocols. Several algorithms for checking SVMCs are presented in this chapter.
This is the concluding chapter of the book. It briefly discusses several possible directions for the further development, including the problem of state space explosion in model checking quantum systems, possible applications in verification and analysis of quantum circuits, quantum cryptographic protocols, and more generally, quantum programs.
Model checking is one of the most successful verification techniques and has been widely adopted in traditional computing and communication hardware and software industries. This book provides the first systematic introduction to model checking techniques applicable to quantum systems, with broad potential applications in the emerging industry of quantum computing and quantum communication as well as quantum physics. Suitable for use as a course textbook and for self-study, graduate and senior undergraduate students will appreciate the step-by-step explanations and the exercises included. Researchers and engineers in the related fields can further develop these techniques in their own work, with the final chapter outlining potential future applications.
Previous studies suggested that a disturbance of the dopamine system underlies the pathophysiology of bipolar disorder (BD). In addition, the therapeutic action of medications for treating BD, such as valproate (VPA), might modulate dopamine system activity, but it remains unclear. Here, we aimed to investigate the role of the striatal dopamine transporter (DAT) in BD patients and in social defeat (SD) mice treated with VPA.
We enrolled community-dwelling controls (N = 18) and BD patients (N = 23) who were treated with VPA in a euthymic stage. The striatal DAT availabilities were approached by TRODAT-1 single photon emission computed tomography. We also established a chronic SD mouse model and treated mice with 350 mg/kg VPA for 3 weeks. Behavioral tests were administered, and striatal DAT expression levels were determined.
In humans, the level of striatal DAT availability was significantly higher in euthymic BD patients (1.52 ± 0.17 and 1.37 ± 0.23, p = 0.015). Moreover, the level of striatal DAT availability was also negatively correlated with the VPA concentration in BD patients (r = −0.653, p = 0.003). In SD mice, the expression of striatal DAT significantly increased (p < 0.001), and the SD effect on DAT expression was rescued by VPA treatment.
The striatal DAT might play a role in the pathophysiology of BD and in the therapeutic mechanism of VPA. The homeostasis of DAT might represent a new therapeutic strategy for BD patients.
To assess the association between total alcohol intake, specific alcoholic beverages and sleep quality in a community-based cohort.
A cross-sectional study.
The Kailuan community, China.
Included were 11 905 participants who were free of a history of CVD, cancer, Parkinson’s disease, dementia and head injury in or prior to 2012. Alcohol consumption (amount and frequency intake) and alcoholic beverage type were collected in 2006 (baseline) and 2012. Participants were grouped into non-, light- (women: 0–0·4 serving/d; men: 0–0·9 serving/d), moderate- (women: 0·5–1·0 serving/d; men: 1·0–2·0 servings/d) and heavy- (women: >1·0 servings/d; men: >2·0 servings/d) drinkers. Overall sleep quality was measured in 2012 and included four sleep parameters (insomnia, daytime sleepiness, sleep duration, snoring/obstructive sleep apnoea).
We observed a dose–response association between higher alcohol consumption in 2006 and worse sleep quality in 2012 (Ptrend < 0·001), after adjusting for age, sex, socio-economic status, smoking status, physical activity, obesity, plasma lipid profiles, diabetes and hypertension. A similar association was observed when alcohol consumption in 2012 was used as exposure. Alcohol was associated with higher odds of having short sleep duration (adjusted OR for heavy- v. non-drinkers = 1·31; 95 % CI: 1·09, 1·57) and snoring (adjusted OR for heavy- v. non-drinkers: 1·38; 95 % CI: 1·22, 1·57). Consumption of hard liquor, but not beer or wine, was significantly associated with poor sleep quality.
Higher alcohol consumption was associated with poorer sleep quality and higher odds of having snoring and short sleep duration.
The upsurge in the number of people affected by the COVID-19 is likely to lead to increased rates of emotional trauma and mental illnesses. This article systematically reviewed the available data on the benefits of interventions to reduce adverse mental health sequelae of infectious disease outbreaks, and to offer guidance for mental health service responses to infectious disease pandemic. PubMed, Web of Science, Embase, PsycINFO, WHO Global Research Database on infectious disease, and the preprint server medRxiv were searched. Of 4278 reports identified, 32 were included in this review. Most articles of psychological interventions were implemented to address the impact of COVID-19 pandemic, followed by Ebola, SARS, and MERS for multiple vulnerable populations. Increasing mental health literacy of the public is vital to prevent the mental health crisis under the COVID-19 pandemic. Group-based cognitive behavioral therapy, psychological first aid, community-based psychosocial arts program, and other culturally adapted interventions were reported as being effective against the mental health impacts of COVID-19, Ebola, and SARS. Culturally-adapted, cost-effective, and accessible strategies integrated into the public health emergency response and established medical systems at the local and national levels are likely to be an effective option to enhance mental health response capacity for the current and for future infectious disease outbreaks. Tele-mental healthcare services were key central components of stepped care for both infectious disease outbreak management and routine support; however, the usefulness and limitations of remote health delivery should also be recognized.