ProofPeer - A Cloud-based Interactive Theorem Proving System

ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented as a solution to the problem of sharing proof state among the users of ProofPeer. Chronicles are introduced as a way to organize and version contexts

Effect of CD40 silencing in MAV-1 infected MH-S cells

The murine alveolar macrophage cell line, MH-S, constitutively expresses the immunoregulatory antigen CD40. Previous experiments have demonstrated that CD40 expression is upregulated following infection with the DNA virus, mouse adenovirus 1 1 Obua (MA V-1 ), suggesting a role for CD40 in MA V-1 infection. The purpose of this experiment is to investigate the effect ofCD40 silencing on MA V-1 replication in MH-S cells. To elucidate the importance ofCD40 signaling in MA V-1 replication, CD40 expression was reduced using a short hairpin RNA (shRNA) RNAi system. Five CD40-silenced lines were generated using shRNA and showed between 26-79 percent reduction in cell surface CD40 expression from wild type. To assess the effect of MA V-1 infection on costimulatory markers, CD40 expression was compared between the silenced cell line that showed the greatest level of CD40 suppression (designated NPBS) and wild type cells at I-day post infection. Flow cytometry revealed CD40 expression was increased in both cell lines following infection with MA V-1. Infected CD40-silenced cultures expressed approximately 50% the level of CD40 as infected wild type cultures. Further characterization of CD40-deficient MH-S cells may reveal novel mechanisms through which MA V-1 infection alters host cell metabolism

Proving Bounds for Real Linear Programs in Isabelle/HOL

Linear programming is a basic mathematical technique for optimizing a linear function on a domain that is constrained by linear inequalities. We restrict ourselves to linear programs on bounded domains that involve only real variables. In the context of theorem proving, this restriction makes it possible for any given linear program to obtain certificates from external linear programming tools that help to prove arbitrarily precise bounds for the given linear program. To this end, an explicit formalization of matrices in Isabelle/HOL is presented, and how the concept of lattice-ordered rings allows for a smooth integration of matrices with the axiomatic type classes of Isabelle. As our work is a contribution to the Flyspeck project, we demonstrate that via reflection and with the above techniques it is now possible to prove bounds for the linear programs arising in the proof of the Kepler conjecture sufficiently fast

Abstraction Logic: A New Foundation for (Computer) Mathematics

Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as predicate logic plus operators and variable binding. We argue that abstraction logic is the best foundational logic possible because it maximises both simplicity and practical expressivity. This argument is supported by the observation that abstraction logic has simpler terms and a simpler notion of proof than all other general logics. At the same time, abstraction logic can formalise both intuitionistic and classical abstraction logic, and is sound and complete for these logics and all other logics extending deduction logic with equality

Syntax and Semantics of Babel-17

We present Babel-17, the first programming language for purely functional structured programming (PFSP). Earlier work illustrated PFSP in the framework of a toy research language. Babel-17 takes this earlier work to a new level by showing how PFSP can be combined with pattern matching, object oriented programming, and features like concurrency, lazy evaluation, memoization and support for lenses

A Cross-sectional study to assess the Level of Utilization of Immediate Postpartum Family Planning among Postnatal women in Lira Regional Referral Hospital.

Background:  Over 214 million women globally have an unmet need for family planning. The majority of these women are in the postpartum period. About 336 mothers per 1000 live births in Uganda die due to pregnancy-related causes most of which are preventable. The use of contraception can prevent unwanted pregnancies and unsafe abortions that normally lead to the loss of lives of these women. Immediate post-partum family planning services need to be emphasized, where these women should leave the hospital with a safe and effective method of contraception in place. Despite the accepted demand for postpartum family planning, many women do not intend to use modern methods of contraception in the immediate postpartum period.    Objective;  This study aimed to assess the use and perceptions of women on immediate postpartum family planning among postnatal women attending Lira Regional Referral Hospital. Methods: This was a cross-sectional study conducted on 300 conveniently selected postnatal women in LRRH. The data was obtained and entered, cleaned, and analyzed using SPSS version 23. Univariate analysis was done to determine frequencies and percentages of the study variables and bivariate analysis was done using binary logistic regression to determine associations  Results:   Of a total of 310 postnatal women invited to the study, 300(97%) participated in the study of which 13(4.3%) reported having utilized IPPFP services. Age (p=0.002), Religion, Counseling, and knowledge about IPPFP (p=0.000) respectively were found to be significantly associated with the use of IPPFP. There was also an association between the client’s poor perceptions of the use of IPPF with (P=0.005). Conclusions and recommendations:  The IPPFP use among postnatal women attending Lira Regional Referral Hospital is very low (4.3%). Recommendations Therefore, multi-pronged Interventions should be implemented to address the poor perceptions of these postnatal women toward the uptake of IPPFP