Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction diffusion equations

Using spatial domain techniques developed by the authors and Myunghyun Oh in the context of parabolic conservation laws, we establish under a natural set of spectral stability conditions nonlinear asymptotic stability with decay at Gaussian rate of spatially periodic traveling-waves of systems of reaction diffusion equations. In the case that wave-speed is identically zero for all periodic solutions, we recover and slightly sharpen a well-known result of Schneider obtained by renormalization/Bloch transform techniques; by the same arguments, we are able to treat the open case of nonzero wave-speeds to which Schneider's renormalization techniques do not appear to appl

Late Propagation in Near-Miss Clones: An Empirical Study

If two or more code fragments in the code-base of a software system are exactly or nearly similar to one another, we call them code clones. It is often important that updates (i.e., changes) in one clone fragment should be propagated to the other similar clone fragments to ensure consistency. However, if there is a delay in this propagation because of unawareness, the system might behave inconsistently. This delay in propagation, also known as late propagation, has been investigated by a number of existing studies. However, the existing studies did not investigate the intensity as well as the effect of late propagation in different types of clones separately. Also, late propagation in Type 3 clones is yet to investigate. In this research work we investigate late propagation in three types of clones (Type 1, Type 2, and Type 3) separately. According to our experimental results on six subject systems written in three programming languages, late propagation is more intense in Type 3 clones compared to the other two clone-types. Block clones are mostly involved in late propagation instead of method clones. Refactoring of block clones can possibly minimize late propagation. If not refactorable, then the clones that often need to be changed together consistently should be placed in close proximity to one another

Active Clones: Source Code Clones at Runtime

Code cloning is a common programming practice, and there have been aconsiderable amount of research that investigated the implications of code clones onsoftware maintenance using static analysis. However, little has been done to investigatethe runtime implications of code cloning. In this paper we investigate sourcecode clones at runtime, referring to clones as ‘active clones’ if they are invokedwhen a software system is in use. For example, if a particular use u of a systemresults in a clone c being invoked, we say that clone c is active with respect to useu. From this definition and given a set of uses fu1;u2; :::g and clones fc1;c2; :::gwe are able to identify the extent clones are active at runtime and analyze activeclone resource use (e.g., CPU time) and define and calculate a set of active clonemetrics to provide insights into source code cloning implications at runtime. We developeda hybrid static and dynamic analysis technique for detecting and analysingactive clones, and conducted an empirical study on five software systems (HSQLDB,JHotDraw, RText, jEdit and UniCentaoPOS) to validate our approach. We found asmall portion of clones are active during a typical use of a software system, and thatactive clones have the potential for guiding a software developer’s code inspectionactivity during a software maintenance task