Formalization of Ring Theory in PVS

This paper presents a PVS development of relevant results of the theory of rings. The PVS theory includes complete proofs of the three classical isomorphism theorems for rings, and characterizations of principal, prime and maximal ideals. Algebraic concepts and properties are specified and formalized as generally as possible allowing in this manner their application to other algebraic structures. The development provides the required elements to formalize important algebraic theorems. In particular, the paper presents the formalization of the general algebraic-theoretical version of the Chinese remainder theorem (CRT) for the theory of rings, as given in abstract algebra textbooks, proved as a consequence of the first isomorphism theorem. Also, the PVS theory includes a formalization of the number-theoretical version of CRT for the structure of integers, which is the version of CRT found in formalizations. CRT for integers is obtained as a consequence of the general version of CRT for the theory of rings.

     

Application of the novel Droplet digital PCR technology for identification of meat species

The authenticity and traceability of meat products are issues of primary importance to ensure food safety. Unfortunately, food adulteration (e.g. the addition of inexpensive cuts to minced meat products) and mislabelling (e.g. the inclusion of meat from species other than those declared) happens frequently worldwide. The aim of this study was to apply a droplet digital PCR assay for the detection and quantification (copies μL⁻¹) of the beef, pork, horse, sheep, chicken and turkey in meat products. The analysis conducted on commercial meat showed the presence of traces of DNA from other animal species than those declared. We show that the method is highly sensitive, specific and accurate (accuracy = 100%). This method could be adopted by competent food safety authorities to verify compliance with the labelling of meat products and to ensure quality and safety throughout the meat supply chain, from primary production to consumption.     

Cell Sheet Comprised of Mesenchymal Stromal Cells Overexpressing Stem Cell Factor Promotes Epicardium Activation and Heart Function Improvement in a Rat Model of Myocardium Infarction

Cell therapy of the post-infarcted myocardium is still far from clinical use. Poor survival of transplanted cells, insufficient regeneration, and replacement of the damaged tissue limit the potential of currently available cell-based techniques. In this study, we generated a multilayered construct from adipose-derived mesenchymal stromal cells (MSCs) modified to secrete stem cell factor, SCF. In a rat model of myocardium infarction, we show that transplantation of SCF producing cell sheet induced activation of the epicardium and promoted the accumulation of c-kit positive cells in ischemic muscle. Morphometry showed the reduction of infarct size (16%) and a left ventricle expansion index (0.12) in the treatment group compared to controls (24–28%; 0.17–0.32). The ratio of viable myocardium was more than 1.5-fold higher, reaching 49% compared to the control (28%) or unmodified cell sheet group (30%). Finally, by day 30 after myocardium infarction, SCF-producing cell sheet transplantation increased left ventricle ejection fraction from 37% in the control sham-operated group to 53%. Our results suggest that, combining the genetic modification of MSCs and their assembly into a multilayered construct, we can provide prolonged pleiotropic effects to the damaged heart, induce endogenous regenerative processes, and improve cardiac function.