New bounds for the inhomogenous Burgers and the Kuramoto-Sivashinsky equations

We give a substantially simplified proof of near-optimal estimate on the Kuramoto-Sivashinsky equation from [F. Otto, "Optimal bounds on the Kuramoto-Sivashinsky equation", JFA 2009], at the same time slightly improving the result. The result in the above cited paper relied on two ingredients: a regularity estimate for capillary Burgers and an a novel priori estimate for the inhomogeneous inviscid Burgers equation, which works out that in many ways the conservative transport nonlinearity acts as a coercive term. It is the proof of the second ingredient that we substantially simplify by proving a modified K\'arm\'an-Howarth-Monin identity for solutions of the inhomogeneous inviscid Burgers equation. This gives a new interpretation of the results obtained in [F. Golse, B. Perthame "Optimal regularizing effect for scalar conservation laws", Rev. Mat. Iber., 2013]

Modular Termination Proofs of Recursive Java Bytecode Programs by Term Rewriting

In earlier work we presented an approach to prove termination of non-recursive Java Bytecode (JBC) programs automatically. Here, JBC programs are first transformed to finite termination graphs which represent all possible runs of the program. Afterwards, the termination graphs are translated to term rewrite systems (TRSs) such that termination of the resulting TRSs implies termination of the original JBC programs. So in this way, existing techniques and tools from term rewriting can be used to prove termination of JBC automatically. In this paper, we improve this approach substantially in two ways: (1) We extend it in order to also analyze recursive JBC programs. To this end, one has to represent call stacks of arbitrary size. (2) To handle JBC programs with several methods, we modularize our approach in order to re-use termination graphs and TRSs for the separate methods and to prove termination of the resulting TRS in a modular way. We implemented our approach in the tool AProVE. Our experiments show that the new contributions increase the power of termination analysis for JBC significantly

Clamping, COKAM, KADS, and OMOS : the construction and operationalization of a KADS conceptual model

For a simplified version of the clamping tool selection problem in mechanical engineering, the knowledge acquisition tool COKAM is applied to obtain an informal knowledge base and explanation structures from technical documents and previously solved cases. The output of COKAM is used to construct a three layered KADS conceptual model, which is then transformed into an operational model in the language OMOS. The OMOS formalization allows to verify the informal KADS conceptual model and to check the completeness of the domain knowledge. The results of this analysis are utilized in the next knowledge elicitation session with COKAM

Automated Termination Analysis of Java Bytecode by Term Rewriting

We present an automated approach to prove termination of Java Bytecode (JBC) programs by automatically transforming them to term rewrite systems (TRSs). In this way, the numerous techniques and tools developed for TRS termination can now be used for imperative object-oriented languages like Java, which can be compiled into JBC

Mechanosensitive Self-Replication Driven by Self-Organization

Self-replicating molecules are likely to have played an important role in the origin of life, and a small number of fully synthetic self-replicators have already been described. Yet it remains an open question which factors most effectively bias the replication toward the far-from-equilibrium distributions characterizing even simple organisms. We report here two self-replicating peptide-derived macrocycles that emerge from a small dynamic combinatorial library and compete for a common feedstock. Replication is driven by nanostructure formation, resulting from the assembly of the peptides into fibers held together by β sheets. Which of the two replicators becomes dominant is influenced by whether the sample is shaken or stirred. These results establish that mechanical forces can act as a selection pressure in the competition between replicators and can determine the outcome of a covalent synthesis.