Appendix: Conjectures Concerning Proof, Design, and Verification

This article focuses on an esoteric but practical use of automated reasoning that may indeed be new to many, especially those concerned primarily with verification of both hardware and software. Specifically, featured are a discussion and some methodology for taking an existing design -- of a circuit, a chip, a program, or the like--and refining and improving it in various ways. Although the methodology is general and does not require the use of a specific program, McCune's program OTTER does offer what is needed. OTTER has played and continues to play the key role in my research, and an interested person can gain access to this program in various ways, not the least of which is through the included CD-ROM in [3]. When success occurs, the result is a new design that may require fewer components, avoid the use of certain costly components, offer more reliability and ease of verification, and, perhaps most important, be more efficient in the contexts of speed and heat generation. Although the author has minimal experience in circuit design, circuit validation, program synthesis, program verification, and similar concerns, (at the encouragement of colleagues based on successes to be cited) he presents materials that might indeed be of substantial interest to manufacturers and programmers. He writes this article in part prompted by the recent activities of chip designers that include Intel and AMD, activities heavily emphasizing the proving of theorems. As for his research that appears to the author to be relevant, he has made an intense and most profitable study of finding proofs that are shorter [2,3], some that avoid the use of various types of term, some that are far less complex than previously known, and the like. Those results suggest to me a strong possible connection between more appealing proofs (in mathematics and in logic) and enhanced and improved design of both hardware and software. Here the author explores diverse conjectures that elucidate some of the possibly fruitful connections

Immunodepletion in xenotransplantation

Xenograft transplantation is perhaps the most immunologically difficult problem in transplantation today. An overwhelming hyperacute rejection reaction (HAR) occurs within minutes of organ implantation. Preformed antibodies are thought to initiate this process. We used a pig-to-dog renal xenograft transplant model and investigated methods of decreasing the severity of hyperacute rejection. Female pigs weighing 15-20 kg were used as donors. Recipients were mongrel dogs weighing 15-25 kg. Experimental dogs were all given a number of treatments of IgG depletion using an antibody removal system (Dupont-Excorim). This machine immunoadsorbs plasma against a column containing immobilized staphylococcal protein A, which is known to bind the IgG Fc receptor. An 84% reduction in the IgG levels and a 71% reduction in IgM levels was achieved. Postoperative assessment was made of urine output, time to onset of HAR, and histopathological examination of the rejected kidneys. Although cross-matches between donor lymphocytes and recipient sera remained strongly positive in the treated dogs, there was a two- to fourfold reduction in the titers. The time to onset of HAR was prolonged in the experimental group, and the urine output was increased slightly. The histopathologic changes in the experimental group generally showed signs of HAR, but of less intensity than in the nonimmunodepleted control group. © 1990 Informa UK Ltd All rights reserved: reproduction in whole or part not permitted

Trust and contextual engagement with the PEPPER system: The qualitative findings of a clinical feasibility study

Background and aims. PEPPER (Patient Empowerment through Predictive PERsonalised decision support) is an EU-funded research project which aims to improve self-management of type 1 diabetes (T1D). The system comprises an AI insulin bolus recommender, coupled with a safety system. The aim of the qualitative arm of this clinical feasibility study was to examine the context of participants’ interaction with the PEPPER system and identify incidents where bolus recommendations were trusted and accepted. Methods. This was a multicentre (UK and Spain) non-randomised open-labelled 6-week pilot study. Thirteen adults with T1D participated in weekly telephone interviews to explore the context of their interactions and responses to PEPPER. Data was thematically analysed through conceptual frameworks for engagement with healthcare digital behaviour change interventions. Results. Participants reported their key interactions as responding to PEPPER bolus recommendations, inputting carbohydrate values, interpreting continuous glucose monitoring (CGM) values through visualization of personal data and dealing with safety alarms. Two themes were associated with trust and engagement with the system; ‘feeling monitored’ and ‘feeling in control’. The incidents where participants trusted PEPPER also enhanced personal expertise of T1D through insights provided by the safety system such as low glucose basal insulin for pump users. Benefits were balanced against technical challenges of the system, which were used to improve the PEPPER application and enhance user experience. Conclusion. Some participants suggested that even access to PEPPER for a temporary period could positively influence self-management strategies. Contextual interviewing is a valuable tool in mobile application development for diabetes decision support systems

A method for finding new sets of axioms for classes of semigroups

We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices

Bilateral versus single internal-thoracic-artery grafts at 10 years

BACKGROUND Multiple arterial grafts may result in longer survival than single arterial grafts after coronary-artery bypass grafting (CABG) surgery. We evaluated the use of bilateral internal-thoracic-artery grafts for CABG. METHODS We randomly assigned patients scheduled for CABG to undergo bilateral or single internal-thoracic-artery grafting. Additional arterial or vein grafts were used as indicated. The primary outcome was death from any cause at 10 years. The composite of death from any cause, myocardial infarction, or stroke was a secondary outcome. RESULTS A total of 1548 patients were randomly assigned to undergo bilateral internal-thoracic-artery grafting (the bilateral-graft group) and 1554 to undergo single internal-thoracic-artery grafting (the single-graft group). In the bilateral-graft group, 13.9% of the patients received only a single internal-thoracic-artery graft, and in the single-graft group, 21.8% of the patients also received a radial-artery graft. Vital status was not known for 2.3% of the patients at 10 years. In the intention-to-treat analysis at 10 years, there were 315 deaths (20.3% of the patients) in the bilateral-graft group and 329 deaths (21.2%) in the single-graft group (hazard ratio, 0.96; 95% confidence interval [CI], 0.82 to 1.12; P=0.62). Regarding the composite outcome of death, myocardial infarction, or stroke, there were 385 patients (24.9%) with an event in the bilateral-graft group and 425 patients (27.3%) with an event in the single-graft group (hazard ratio, 0.90; 95% CI, 0.79 to 1.03). CONCLUSIONS Among patients who were scheduled for CABG and had been randomly assigned to undergo bilateral or single internal-thoracic-artery grafting, there was no significant between-group difference in the rate of death from any cause at 10 years in the intention-to-treat analysis. Further studies are needed to determine whether multiple arterial grafts provide better outcomes than a single internal-thoracic-artery graft. (Funded by the British Heath Foundation and others; Current Controlled Trials number, ISRCTN46552265.