Balanced Lethal Systems: An Evolutionary Mystery

When a female crested newt lays her clutch of about three-hundred eggs, half of these will never hatch. What an incredible waste! It turns out that these newts suffer from a deadly hereditary disease called a balanced lethal system. Here is how it works: in a balanced lethal system, there are two distinct versions of a particular chromosome. Newts need both to live. However, which version a fertilized newt egg gets from its father and mother is random. Therefore, there is a 50% chance that it receives the same version twice—and misses the other half of the critical pair. Hence, half of the eggs end up with the wrong chromosome combination and die. The newts are not the only example; balanced lethal systems are found in some plants and insects as well. Why something so disadvantageous as a balanced lethal system would ever evolve is still a big, evolutionary mystery!

Reliability Analysis of Critical Kinematic Pair of the RD-33 Engine

The article addressed the technological problem occurring in the RD-33 turbine engine on the kinematic pair between the accessory gearbox (AGB) and fuel regulator pump HP-59A (Polish: NR-59A). In the beginning, examples of operational problems were described. Then, the power balance for the accessory gearbox and strength calculations of gear and splines of a critical pair were presented. It was demonstrated that gear made from an original material complies with strength criteria and the observed operational problems with splines are created by other factors.

THE MAXIMUM SIZE OF -SUM-FREE SETS IN CYCLIC GROUPS

A subset$A$of a finite abelian group$G$is called$(k,l)$-sum-free if the sum of$k$(not necessarily distinct) elements of$A$never equals the sum of$l$(not necessarily distinct) elements of $A$. We find an explicit formula for the maximum size of a$(k,l)$-sum-free subset in$G$for all$k$and$l$in the case when$G$is cyclic by proving that it suffices to consider$(k,l)$-sum-free intervals in subgroups of $G$. This simplifies and extends earlier results by Hamidoune and Plagne [‘A new critical pair theorem applied to sum-free sets in abelian groups’,Comment. Math. Helv. 79(1) (2004), 183–207] and Bajnok [‘On the maximum size of a$(k,l)$-sum-free subset of an abelian group’,Int. J. Number Theory 5(6) (2009), 953–971].

Critical Pair Analysis in Nominal Rewriting

Nominal rewriting (Fernández, Gabbay & Mackie, 2004;Fernández & Gabbay, 2007) is a framework that extendsfirst-order term rewriting by a binding mechanismbased on the nominal approach (Gabbay & Pitts, 2002;Pitts, 2003). In this paper, we investigate confluenceproperties of nominal rewriting, following the study oforthogonal systems in (Suzuki et al., 2015), but herewe treat systems in which overlaps of the rewrite rulesexist. First we present an example where choice ofbound variables (atoms) of rules affects joinability ofthe induced critical pairs. Then we give a detailedproof of the critical pair lemma, and illustrate someof its applications including confluence results fornon-terminating systems.

A Specification and Detection Approach for Parallel Evolution Conflicts of Software Architectures

Software evolution has been a necessary part of the software development, while software architecture evolution is an important issue of software evolution. Software architecture evolution is generally realized through some evolution operations such as adding components or connectors, removing components or connectors. However, when some evolution operations are applied to the same software architecture in parallel, they sometimes make conflicting modifications, which will hinder the correctness of software architecture evolution. Although different approaches have been proposed to describe and analyze software architecture evolution, little work has been made to address evolution conflicts of software architectures. Focusing on parallel evolution conflicts of software architectures, firstly the paper establishes definitions and characterizations of parallel evolution conflicts of software architectures based on hypergraph morphisms and set theories, and describes parallel evolution conflicts of software architectures through these definitions and characterizations. Secondly the paper constructs the critical pair definition of parallel evolution conflicts of software architectures based on hypergraphs and hypergraph morphisms, analyzes the completeness of the critical pair, designs and optimizes an algorithm to detect efficiently parallel evolution conflicts of software architectures using the critical pair. Finally, a tool support is used to evaluate the effectiveness of the proposed method.