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Dependent types can be used to capture useful properties about programs at compile time. However, developing dependently typed programs can be difficult in current systems. Capturing interesting program properties usually requires the user to write proofs, where constructing the latter can be both a difficult and tedious process. Additionally, finding and fixing errors in program scripts can be challenging. This thesis concerns ways in which functional programming with dependent types can be made easier. In particular, we focus on providing help for developing programs that incorporate user-defined types and user-defined functions. For the purpose of supporting dependently typed programming, we have designed a framework that provides improved proof automation and error feedback. Proof automation is provided with the use of heuristic based tactics that automate common patterns of proofs that arise when programming with dependent types. In particular, we use heuristics for generalising goals and employ the rippling heuristic for guiding inductive and non-inductive proofs. The automation we describe includes features for caching and reusing lemmas proven during proof search and, whenever proof search fails, the user can assist the prover by providing high-level hints. We concentrate on providing improved feedback for the errors that occur when there is a mismatch between the specification of a program, described with the use of dependent types, and the behaviour of the program. We employ a QuickCheck-like testing tool for automatically identifying these forms of errors, where the counter examples generated are used as error messages. To demonstrate the effectiveness of our framework for supporting dependently typed programming, we have developed a prototype based around the Coq theorem prover. We demonstrate that the framework as a whole makes program development easier by conducting a series of case studies. In these case studies, which involved verifying properties of tail recursive functions, sorting functions and a binary adder, a significant number of the proofs required were automated.

Goal Due to the development of medical technology, implementation of national health insurance (NHI) program and population aging, the increasing of ventilator-dependent patients are significant within these years. Patients with the catastrophic illness certification spent about 26.2% NHI medical resource. Oncology, hemodialysis and ventilator-dependent patients were thought to be the most resource utilized ones. The objective of this study was to find the possible risk of reintubation on those ventilator-dependent patients. So, that we may reduce the reintubation rate and shorten their hospital stays. Method This study was a retrospective study based on the database of a local teaching hospital. During 2005 and 2010, patients aged older than 17 years old and required more than 3 weeks of mechanical ventilation support were selected. Here were total 313 cases include 247 successful weaning and 66 reintubation. Statistical analysis included descriptive statistic, Chi-square test and logistic regression by SPSS® for windows. Risk factors included their demographic features, acute physiology and chronic health evaluation (APACHE) II scoring system as well as laboratory data. Results The ages of successful weaning and reintubation patients were 72¡Ó15 vs. 76¡Ó15, p=0.092 years old, respectively. APACH II score (17¡Ó8 vs. 22¡Ó8, p<0.001), BUN (33.2¡Ó26 vs. 43.0¡Ó33 mg/dL, p=0.033), K+ (3.8¡Ó0.8 vs. 4.2¡Ó0.9 mmol/L, p=0.002), Ca+ (8.0¡Ó0.8 vs. 8.6¡Ó0.9 mmol/L, p=0.007), WBC (13880¡Ó7270 vs. 17720¡Ó9540, p=0.003), Hb (11.8¡Ó2.5 g/dL vs. 10.3¡Ó1.4 g/dL, p<0.001), Platelet (224400¡Ó106310 vs. 284570¡Ó119160,p=0.001). However, Logistic regression found two significant factors were APACHE II (odds ratio [OR], 2.97), Hb (OR, 0.701). By means of ROC curves, we derived the critical values of reintubation risk due to Hb as 11.3 g/dL respectively. Conclusion Based on the results, we inference that the reintubation risk increases up to 1.2 per unit APACHE II score while decreases 45% per unit Hb. It is suggested that if clinical physician could keep Hb of patients above 11.3 g/dL respectively, the reintubation rate may be significantly reduced.

In this thesis, we focus on the study of dependent arcs of acyclic orientations of graphs. Given an acyclic orientation D of G, Edelman cite{West} defined an arc to be {em dependent} if its reversal creates a cycle in D; otherwise, it is independent. Let d(D) and i(D) be the numbers of dependent arcs and independent arcs in D, respectively. And, let d_{max}(G)(d_{min}(G)) and i_{max}(G) (i_{min}(G)) be the maximum (minimum) numbers of dependent arcs and independent arcs over all acyclic orientations of G, respectively. Edelman cite{Fisher} showed that if G is connected, then d_{max}(G)=||G||-|G|+1. A graph G is said to satisfy the {em interpolation property} (or G is fully orientable) if $G$ has an acyclic orientation with exactly k dependent arcs for every k with d_{min}(G) leq k leq d_{max}(G). West established the interpolation property for complete bipartite graphs cite{West}. We obtain the minimum numbers of dependent arcs of the outerplane graphs and show that the outerplane graphs satisfy the interpolation property. Let N(G) be the set { i(D)| D is an acyclic orientation of G }. N(G) is called the independent-arc spectra of G. For complete k-partite graphs G, we obtain i_{max}(G) and discuss the independent-arc spectra for some classes. On the other hand, we consider the cover problem. A cover graph is the underlying graph of the Hasse diagram of a finite partially ordered set. The cover problem is that whether a given graph is a cover graph. It is easy to see that a graph G is a cover graph if and only if d_{min}(G)=0. We show that the generalized Mycielski graphs M_m(C_{2t+1}) of an odd cycle, Kneser graphs KG(n,k), and Schrijver graphs SG(n,k) are not cover graphs when m geq 1, t geq 1, k geq 3 and n geq 2k+2.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Introduction: Historically, type 2 diabetes (T2DM) has been regarded as a progressive and degenerative disease and only minority of patients can have disease remission with conventional treatment. It was noticed that gastrointestinal surgery could induce complete remission of T2DM in most of morbidly obese patients. Compared to the West, the development of bariatric and metabolic surgery is slow in Hong Kong. It is unknown whether the knowledge and attitudes of medical doctors and patients towards surgical treatment for T2DM have impacts on the development in this field. The novel procedure sleeve gastrectomy (SG) had been shown to be effective in inducing T2DM remission in obese human. Duodenal jejunal bypass (DJB) and ileal transposition (IT) were reported to be effective for ameliorating T2DM in non-obese diabetic animal model. The anti-diabetic potency of DJB and IT is unknown in comparing to SG particularly in non-obese subjects. Currently, SG is the main procedure for morbidly obese patients with or without T2DM in the authors’ institution. Aims: The aims of the present thesis were to investigate the knowledge and attitudes of medical doctors and patients toward using surgery as a treatment for T2DM, to compare the anti-diabetic effect of SG, DJB and IT in non-obese T2DM animal model, and lastly, to review of outcomes of morbidly obese patients who underwent SG in authors’ institution. Methods: Survey was conducted using questionnaire for interview of both doctors and patients to investigate their knowledge and attitudes toward surgical treatment of T2DM. The anti-diabetic effects of novel surgical procedures SG, DJB and IT were compared using non-obese T2DM animal model (Goto Kakizaki rats). The outcomes were evaluation by measuring fasting glucose and glycosylated haemoglobin (HbA1c) levels. Other parameters including alteration in gut hormones and lipid profile were also analyzed. The outcomes of morbidly obese patients who underwent laparoscopic SG in last 5 years in the authors’ institution were retrospectively reviewed. Results: The knowledge of bariatric and metabolic surgery was inadequate both in medical doctors and patients. The attitude and pattern of referral from medical doctors depends on the amount of knowledge. Patients’ attitudes were positive and they accept surgery as a treatment option for T2DM as long as they were provided with adequate information. This implies that tremendous educational works are required both for medical doctors and patients for the development of bariatric and metabolic surgery in Hong Kong. All 3 procedures (SG, DJB and IT) significantly improved glucose homeostasis and the effect was more potent and durable in DJB and IT than SG. The improved glucose homeostasis in IT was resulted from increased GLP-1 and PYY secretion (hindgut theory). In DJB, GIP, GLP-1 and PYY were raised and the anti-diabetic effect could be explained both by the foregut and hindgut theories. SG reduced the diet triglyceride absorption. DJB reduced cholesterol absorption whereas IT reduced cholesterol but increase triglyceride absorption. The outcomes of SG for T2DM for morbidly obese patients were promising. More than 90% patients had T2DM ameliorated and 70% had complete remission. SG can effectively control the body weight of morbidly obese patients. Conclusion: Education, both to doctors and patients, was crucial to overcome the potential obstacles for the development of this newly specialty. The anti-diabetic effects of DJB and IT were more potent than SG in non-obese diabetic animal model. The lipid absorption varied in different surgical procedures. Application of these procedures in non-obese T2DM patients warrants individual consideration and further investigation. SG in the authors’ institution was effective to induce T2DM remission in morbidly obese patients. / published_or_final_version / Surgery / Doctoral / Doctor of Philosophy