Static Analysis of Run-Time Errors in Embedded Real-Time Parallel C Programs

We present a static analysis by Abstract Interpretation to check for run-time errors in parallel and multi-threaded C programs. Following our work on Astr\'ee, we focus on embedded critical programs without recursion nor dynamic memory allocation, but extend the analysis to a static set of threads communicating implicitly through a shared memory and explicitly using a finite set of mutual exclusion locks, and scheduled according to a real-time scheduling policy and fixed priorities. Our method is thread-modular. It is based on a slightly modified non-parallel analysis that, when analyzing a thread, applies and enriches an abstract set of thread interferences. An iterator then re-analyzes each thread in turn until interferences stabilize. We prove the soundness of our method with respect to the sequential consistency semantics, but also with respect to a reasonable weakly consistent memory semantics. We also show how to take into account mutual exclusion and thread priorities through a partitioning over an abstraction of the scheduler state. We present preliminary experimental results analyzing an industrial program with our prototype, Th\'es\'ee, and demonstrate the scalability of our approach

Approximation for Bessel functions and their application in the computation of Hankel transforms

AbstractWe present rational approximations of the Bessel functions Jv(x), v=0,1,…,10, which can be used to simplify the computation of the Hankel transform to the computation of two Fourier transforms

Effects of P-wave Annihilation on the Angular Power Spectrum of Extragalactic Gamma-rays from Dark Matter Annihilation

We present a formalism for estimating the angular power spectrum of extragalactic gamma-rays produced by dark matter annihilating with any general velocity-dependent cross section. The relevant density and velocity distribution of dark matter is modeled as an ensemble of smooth, universal, rigid, disjoint, spherical halos with distribution and universal properties constrained by simulation data. We apply this formalism to theories of dark matter with p-wave annihilation, for which the relative-velocity-weighted annihilation cross section is \sigma v=a+bv^2. We determine that this significantly increases the gamma-ray power if b/a >> 10^6. The effect of p-wave annihilation on the angular power spectrum is very similar for the sample of particle physics models we explored, suggesting that the important effect for a given b/a is largely determined by the cosmic dark matter distribution. If the dark matter relic from strong p-wave theories is thermally produced, the intensities of annihilation gamma-rays are strongly p-wave suppressed, making them difficult to observe. If an angular power spectrum consistent with a strong p-wave were to be observed, it would likely indicate non-thermal production of dark matter in the early Universe.Comment: 20 pages, 3 figure

Computation of Fourier and Laplace transforms of singular functions using modified moments

AbstractIn this paper a recurrence formula for the computation of Mk = ∫−1+1 (1 − x)α(1 + x)β exp[−a/(1+x)]Tk(x)dx is presented. The numerical stability is discussed. The starting values are confluent hypergeometric functions which can be evaluated using Luke's results on Chebyshev series expansions and Padé approximations of hypergeometric functions. Applications of this recurrence relation are the evaluation of the Fourier transform of singular functions by modified Clenshaw-Curtis integration, the construction of Gaussian quadrature formulae for Fourier integrals and the numerical inversion of the Laplace transform

Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants

We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat non-numerical values of the integrand, how they deal with improper divergent integrals and how they estimate the integration error. The main focus of these improvements is to increase the reliability of the algorithms without significantly impacting their efficiency. Both algorithms are implemented in Matlab and tested using both the "families" suggested by Lyness and Kaganove and the battery test used by Gander and Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases less efficient, than other commonly-used adaptive integrators.Comment: 32 pages, submitted to ACM Transactions on Mathematical Softwar

A hybrid memory kernel approach for condensed phase non-adiabatic dynamics

The spin-boson model is a simplified Hamiltonian often used to study non-adiabatic dynamics in large condensed phase systems, even though it has not been solved in a fully analytic fashion. Herein, we present an exact analytic expression for the dynamics of the spin-boson model in the infinitely slow bath limit and generalize it to approximate dynamics for faster baths. We achieve the latter by developing a hybrid approach that combines the exact slow-bath result with the popular NIBA method to generate a memory kernel that is formally exact to second order in the diabatic coupling but also contains higher-order contributions approximated from the second order term alone. This kernel has the same computational complexity as NIBA, but is found to yield dramatically superior dynamics in regimes where NIBA breaks down---such as systems with large diabatic coupling or energy bias. This indicates that this hybrid approach could be used to cheaply incorporate higher order effects into second order methods, and could potentially be generalized to develop alternate kernel resummation schemes

Numerically improved computational scheme for the optical conductivity tensor in layered systems

The contour integration technique applied to calculate the optical conductivity tensor at finite temperatures in the case of layered systems within the framework of the spin-polarized relativistic screened Korringa-Kohn-Rostoker band structure method is improved from the computational point of view by applying the Gauss-Konrod quadrature for the integrals along the different parts of the contour and by designing a cumulative special points scheme for two-dimensional Brillouin zone integrals corresponding to cubic systems.Comment: 17 pages, LaTeX + 4 figures (Encapsulated PostScript), submitted to J. Phys.: Condensed Matter (19 Sept. 2000

Typing Copyless Message Passing

We present a calculus that models a form of process interaction based on copyless message passing, in the style of Singularity OS. The calculus is equipped with a type system ensuring that well-typed processes are free from memory faults, memory leaks, and communication errors. The type system is essentially linear, but we show that linearity alone is inadequate, because it leaves room for scenarios where well-typed processes leak significant amounts of memory. We address these problems basing the type system upon an original variant of session types.Comment: 50 page