The field of separate rippling transforms has been attracting substantial interest partially as a result of the rippling analysis being capable of modeling an indication into a specific set of basic functions equipped with sensible spectral properties. Rippling analysis has been accustomed observe system non-linearities by creating use of its localization feature. DWT-based multi-resolution ana...

We present an interpretable machine learning model to predict accurately the complex rippling deformations of multiwalled carbon nanotubes made millions atoms. Atomistic-physics-based models are accurate but computationally prohibitive for such large systems. To overcome this bottleneck, we have developed a that comprises novel dimensionality reduction technique and deep neural network-based in...

We present a method for integrating rippling-based rewriting into matrix-based theorem proving as a means for automating inductive specification proofs. The selection of connections in an inductive matrix proof is guided by symmetries between induction hypothesis and induction conclusion. Unification is extended by decision procedures and a rippling/reverse-rippling heuristic. Conditional subst...

Difference matching is a generalization of first-order matching where terms are made identical both by variable instantiation and by structure hiding. After matching, the hidden structure may be removed by a type of controlled rewriting, called rippling, that leaves the rest of the term unaltered. Rippling has proved highly successful in inductive theorem proving. Difference matching allows us ...

extremely optimistic about the future. There are two general categories for my enthusiasm: the tangible benefits that will be brought by financially invigorated research programs, and perhaps the more important intangible benefits to morale, image and outlook that will be brought by replacing political ideologues with responsible scientists. Even if I myself never see a single dollar in increas...

Myxococcus xanthus cells self-organize into periodic bands of traveling waves, termed ripples, during multicellular fruiting body development and predation on other bacteria. To investigate the mechanistic basis of rippling behavior and its physiological role during predation by this Gram-negative soil bacterium, we have used an approach that combines mathematical modeling with experimental obs...

1 This paper presents a methodology to guide equa-tional reasoning in a goal directed way. Suggested by rippling methods developed in the eld of inductive theorem proving we use attributes of terms and heuristics to determine bridge lemmas, i.e. lemmas which have to be used during the proof of the theorem. Once we have found such a bridge lemma we use the techniques of diierence uniication and ...

Spatial organization of cells is important for both multicellular development and tactic responses to a changing environment. We find that the social bacterium, Myxococcus xanthus utilizes a chemotaxis (Che)-like pathway to regulate multicellular rippling during predation of other microbial species. Tracking of GFP-labeled cells indicates directed movement of M. xanthus cells during the formati...