Structure Aware Runge–Kutta Time Stepping for Spacetime Tents

We introduce a new class of Runge–Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge–Kutta methods, the new methods yield expected convergence properties when standard high order spatial (discontinuous Galerkin) discretizations are used. After presenting a derivation of nonstandard order conditions for these methods, we show numerical examples of nonlinear hyperbolic systems to demonstrate the optimal convergence rates. We also report on the discrete stability properties of these methods applied to linear hyperbolic equations

Lazy Decomposition for Distributed Decision Procedures

The increasing popularity of automated tools for software and hardware verification puts ever increasing demands on the underlying decision procedures. This paper presents a framework for distributed decision procedures (for first-order problems) based on Craig interpolation. Formulas are distributed in a lazy fashion, i.e., without the use of costly decomposition algorithms. Potential models which are shown to be incorrect are reconciled through the use of Craig interpolants. Experimental results on challenging propositional satisfiability problems indicate that our method is able to outperform traditional solving techniques even without the use of additional resources.Comment: In Proceedings PDMC 2011, arXiv:1111.006

Convergence analysis of some tent-based schemes for linear hyperbolic systems

Finite element methods for symmetric linear hyperbolic systems using unstructured advancing fronts (satisfying a causality condition) are considered in this work. Convergence results and error bounds are obtained for mapped tent pitching schemes made with standard discontinuous Galerkin discretizations for spatial approximation on mapped tents. Techniques to study semidiscretization on mapped tents, design fully discrete schemes, prove local error bounds, prove stability on spacetime fronts, and bound error propagated through unstructured layers are developed

Loop summarization using state and transition invariants

This paper presents algorithms for program abstraction based on the principle of loop summarization, which, unlike traditional program approximation approaches (e.g., abstract interpretation), does not employ iterative fixpoint computation, but instead computes symbolic abstract transformers with respect to a set of abstract domains. This allows for an effective exploitation of problem-specific abstract domains for summarization and, as a consequence, the precision of an abstract model may be tailored to specific verification needs. Furthermore, we extend the concept of loop summarization to incorporate relational abstract domains to enable the discovery of transition invariants, which are subsequently used to prove termination of programs. Well-foundedness of the discovered transition invariants is ensured either by a separate decision procedure call or by using abstract domains that are well-founded by construction. We experimentally evaluate several abstract domains related to memory operations to detect buffer overflow problems. Also, our light-weight termination analysis is demonstrated to be effective on a wide range of benchmarks, including OS device driver

SCNS: a graphical tool for reconstructing executable regulatory networks from single-cell genomic data.

Background Reconstruction of executable mechanistic models from single-cell gene expression data represents a powerful approach to understanding developmental and disease processes. New ambitious efforts like the Human Cell Atlas will soon lead to an explosion of data with potential for uncovering and understanding the regulatory networks which underlie the behaviour of all human cells. In order to take advantage of this data, however, there is a need for general-purpose, user-friendly and efficient computational tools that can be readily used by biologists who do not have specialist computer science knowledge. Results The Single Cell Network Synthesis toolkit (SCNS) is a general-purpose computational tool for the reconstruction and analysis of executable models from single-cell gene expression data. Through a graphical user interface, SCNS takes single-cell qPCR or RNA-sequencing data taken across a time course, and searches for logical rules that drive transitions from early cell states towards late cell states. Because the resulting reconstructed models are executable, they can be used to make predictions about the effect of specific gene perturbations on the generation of specific lineages. Conclusions SCNS should be of broad interest to the growing number of researchers working in single-cell genomics and will help further facilitate the generation of valuable mechanistic insights into developmental, homeostatic and disease processes.Research in the Gottgens lab is supported by infrastructure support funding from the Wellcome Trust to the Wellcome Trust and MRC Cambridge Stem Cell Institute. Steven Woodhouse is a postdoctoral researcher supported by Microsoft Researc