On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure

Tau Be or not Tau Be? - A Perspective on Service Compatibility and Substitutability

One of the main open research issues in Service Oriented Computing is to propose automated techniques to analyse service interfaces. A first problem, called compatibility, aims at determining whether a set of services (two in this paper) can be composed together and interact with each other as expected. Another related problem is to check the substitutability of one service with another. These problems are especially difficult when behavioural descriptions (i.e., message calls and their ordering) are taken into account in service interfaces. Interfaces should capture as faithfully as possible the service behaviour to make their automated analysis possible while not exhibiting implementation details. In this position paper, we choose Labelled Transition Systems to specify the behavioural part of service interfaces. In particular, we show that internal behaviours (tau transitions) are necessary in these transition systems in order to detect subtle errors that may occur when composing a set of services together. We also show that tau transitions should be handled differently in the compatibility and substitutability problem: the former problem requires to check if the compatibility is preserved every time a tau transition is traversed in one interface, whereas the latter requires a precise analysis of tau branchings in order to make the substitution preserve the properties (e.g., a compatibility notion) which were ensured before replacement.Comment: In Proceedings WCSI 2010, arXiv:1010.233

Low-threshold analysis of CDMS shallow-site data

Data taken during the final shallow-site run of the first tower of the Cryogenic Dark Matter Search (CDMS II) detectors have been reanalyzed with improved sensitivity to small energy depositions. Four ~224 g germanium and two ~105 g silicon detectors were operated at the Stanford Underground Facility (SUF) between December 2001 and June 2002, yielding 118 live days of raw exposure. Three of the germanium and both silicon detectors were analyzed with a new low-threshold technique, making it possible to lower the germanium and silicon analysis thresholds down to the actual trigger thresholds of ~1 keV and ~2 keV, respectively. Limits on the spin-independent cross section for weakly interacting massive particles (WIMPs) to elastically scatter from nuclei based on these data exclude interesting parameter space for WIMPs with masses below 9 GeV/c^2. Under standard halo assumptions, these data partially exclude parameter space favored by interpretations of the DAMA/LIBRA and CoGeNT experiments' data as WIMP signals, and exclude new parameter space for WIMP masses between 3 GeV/c^2 and 4 GeV/c^2.Comment: 18 pages, 12 figures, 5 table

Spatial imaging of charge transport in silicon at low temperature

We present direct imaging measurements of charge transport across a 1 cm × 1 cm × 4 mm crystal of high purity silicon (∼20 kΩ cm) at temperatures between 500 mK and 5 K. We use these data to determine the intervalley scattering rate of electrons as a function of the electric field applied along the ⟨111⟩ crystal axis, and we present a phenomenological model of intervalley scattering which explains the constant scattering rate seen at low-voltage for cryogenic temperatures. We also demonstrate direct imaging measurements of effective hole mass anisotropy, which is strongly dependent on both temperature and electric field strength. The observed effects can be explained by a warping of the valence bands for carrier energies near the spin-orbit splitting energy in silicon

Spatial Imaging of Charge Transport in Silicon at Low Temperature

We present direct imaging measurements of charge transport across a 1 cm$\times$ 1 cm$\times$ 4 mm crystal of high purity silicon ($\sim$20 k$\Omega$cm) at temperatures between 500 mK and and 5 K. We use these data to determine the intervalley scattering rate of electrons as a function of the electric field applied along the $\langle 111 \rangle$ crystal axis, and we present a phenomenological model of intervalley scattering that explains the constant scattering rate seen at low-voltage for cryogenic temperatures. We also demonstrate direct imaging measurements of effective hole mass anisotropy, which is strongly dependent on both temperature and electric field strength. The observed effects can be explained by a warping of the valence bands for carrier energies near the spin-orbit splitting energy in silicon.Comment: 5 Pages, 5 Figures. Submitted to Applied Physics Letter