The tropical double description method

We develop a tropical analogue of the classical double description method allowing one to compute an internal representation (in terms of vertices) of a polyhedron defined externally (by inequalities). The heart of the tropical algorithm is a characterization of the extreme points of a polyhedron in terms of a system of constraints which define it. We show that checking the extremality of a point reduces to checking whether there is only one minimal strongly connected component in an hypergraph. The latter problem can be solved in almost linear time, which allows us to eliminate quickly redundant generators. We report extensive tests (including benchmarks from an application to static analysis) showing that the method outperforms experimentally the previous ones by orders of magnitude. The present tools also lead to worst case bounds which improve the ones provided by previous methods.Comment: 12 pages, prepared for the Proceedings of the Symposium on Theoretical Aspects of Computer Science, 2010, Nancy, Franc

IDEF5 Ontology Description Capture Method: Concept Paper

The results of research towards an ontology capture method referred to as IDEF5 are presented. Viewed simply as the study of what exists in a domain, ontology is an activity that can be understood to be at work across the full range of human inquiry prompted by the persistent effort to understand the world in which it has found itself - and which it has helped to shape. In the contest of information management, ontology is the task of extracting the structure of a given engineering, manufacturing, business, or logistical domain and storing it in an usable representational medium. A key to effective integration is a system ontology that can be accessed and modified across domains and which captures common features of the overall system relevant to the goals of the disparate domains. If the focus is on information integration, then the strongest motivation for ontology comes from the need to support data sharing and function interoperability. In the correct architecture, an enterprise ontology base would allow th e construction of an integrated environment in which legacy systems appear to be open architecture integrated resources. If the focus is on system/software development, then support for the rapid acquisition of reliable systems is perhaps the strongest motivation for ontology. Finally, ontological analysis was demonstrated to be an effective first step in the construction of robust knowledge based systems

A lens-coupled scintillation counter in cryogenic environment

In this work we present an elegant solution for a scintillation counter to be integrated into a cryogenic system. Its distinguishing feature is the absence of a continuous light guide coupling the scintillation and the photodetector parts, operating at cryogenic and room temperatures respectively. The prototype detector consists of a plastic scintillator with glued-in wavelength-shifting fiber located inside a cryostat, a Geiger-mode Avalanche Photodiode (G-APD) outside the cryostat, and a lens system guiding the scintillation light re-emitted by the fiber to the G-APD through optical windows in the cryostat shields. With a 0.8mm diameter multiclad fiber and a 1mm active area G-APD the coupling efficiency of the "lens light guide" is about 50%. A reliable performance of the detector down to 3K is demonstrated.Comment: 14 pages, 11 figure

Fracture driven by a Thermal Gradient

Motivated by recent experiments by Yuse and Sano (Nature, 362, 329 (1993)), we propose a discrete model of linear springs for studying fracture in thin and elastically isotropic brittle films. The method enables us to draw a map of the stresses in the material. Cracks generated by the model, imposing a moving thermal gradient in the material, can branch or wiggle depending on the driving parameters. The results may be used to compare with other recent theoretical work, or to design future experiments.Comment: RevTeX file (9 pages) and 5 postscript figure

Optimizing the double description method for normal surface enumeration

Many key algorithms in 3-manifold topology involve the enumeration of normal surfaces, which is based upon the double description method for finding the vertices of a convex polytope. Typically we are only interested in a small subset of these vertices, thus opening the way for substantial optimization. Here we give an account of the vertex enumeration problem as it applies to normal surfaces, and present new optimizations that yield strong improvements in both running time and memory consumption. The resulting algorithms are tested using the freely available software package Regina.Comment: 27 pages, 12 figures; v2: Removed the 3^n bound from Section 3.3, fixed the projective equation in Lemma 4.4, clarified "most triangulations" in the introduction to section 5; v3: replace -ise with -ize for Mathematics of Computation (note that this changes the title of the paper

Verifying Real-Time Systems using Explicit-time Description Methods

Timed model checking has been extensively researched in recent years. Many new formalisms with time extensions and tools based on them have been presented. On the other hand, Explicit-Time Description Methods aim to verify real-time systems with general untimed model checkers. Lamport presented an explicit-time description method using a clock-ticking process (Tick) to simulate the passage of time together with a group of global variables for time requirements. This paper proposes a new explicit-time description method with no reliance on global variables. Instead, it uses rendezvous synchronization steps between the Tick process and each system process to simulate time. This new method achieves better modularity and facilitates usage of more complex timing constraints. The two explicit-time description methods are implemented in DIVINE, a well-known distributed-memory model checker. Preliminary experiment results show that our new method, with better modularity, is comparable to Lamport's method with respect to time and memory efficiency

Theoretical description of deformed proton emitters: nonadiabatic coupled-channel method

The newly developed nonadiabatic method based on the coupled-channel Schroedinger equation with Gamow states is used to study the phenomenon of proton radioactivity. The new method, adopting the weak coupling regime of the particle-plus-rotor model, allows for the inclusion of excitations in the daughter nucleus. This can lead to rather different predictions for lifetimes and branching ratios as compared to the standard adiabatic approximation corresponding to the strong coupling scheme. Calculations are performed for several experimentally seen, non-spherical nuclei beyond the proton dripline. By comparing theory and experiment, we are able to characterize the angular momentum content of the observed narrow resonance.Comment: 12 pages including 10 figure

Microscopic description of light unstable nuclei with the stochastic variational method

The structure of the light proton and neutron rich nuclei is studied in a microscopic multicluster model using the stochastic variational method. This approach enables us to describe the weakly bound nature of these nuclei in a consistent way. Applications for various nuclei $^{6-9}$Li, $^7$Be, $^8$B, $^9$C, $^{9-10}$Be, $^{9-10}$B presented. The paper discusses the relation of this model to other models as well as the possible extension for p and sd shell nuclei.Comment: 11 pages, latex, no figures