Automatische Erzeugung von Verifikations- und Falsifikationsbedingungen sequentieller Programme

The aim of program verification is to prove the correctness of a program S with respect to a formal specification, that consists of a pre- and a postcondition V and N. In other words: are program S and specification (V, N) consistent? -- V S -- N Program S is correct, if S starts in a state that fulfills V and terminates in state that fulfills N. The form al definition of correctness is S is correct wrt. (V, N) if [V => wp(S, N)]. wp(S, N) is the wea kest precondition, that guarantees termination in a state fulfilling N. For the purpose of program verification the axiomatic or relational semantics is necessary. These two kinds of formal semantics are equivalent. Axiomatic semantics uses the wp-function, that works on the complete lattice of predicates. Relational semantics uses the LP (largest preset)-function, that works on the complete lattice of state sets. These two lattices are isomorph thru the characteristic predicate function of a set. In order to work efficiently with the wp-function some properties of that function are necessary and useful. Two new properties are shown: strong disjunctivity for comparable predicates and the substitution lemma for wp. Furthermore it turns out, t hat all properties of the wp-function are easily provable in the lattice of state sets with elementary set theory. A VC is defined to be a condition that implies correctness, formally [VC => [V => wp(S, N)]. A distinction is made between exact and ap proximate VCs. The major results of the thesis are verifying loops without an invariant and falsification conditions. In order to verify loops without a given invariant, two strategies are possible: 1. generate the invariant or 2. compute the wp-function for the loop Strategy 1 is used to compute invariants for for-loops. The invariant is generated by substituting a constant in the postcondition by a variable, more exactly the upper limit of the loop is substituted by the loop variable. In gener al the upper limit is not a variable. Therefore the loop is transformed into a semantically equivalent loop. Strategy 2 is used to compute the wp of while-loops by a new method that uses E-unification. Falsification conditions (FCs) are very useful i n practical program verification. They explicitly prove the incorrectness of a program and facilitate a localization of program errors. FCs are defined in an analog way as VCs: an FC implies the incorrectness of a program, formally [FC => not [V => w p(S, N)]. FCs are reduced to constraint programming problems (cpp) or, in the case of integer types, to integer programming problems (ipp). ipp also arise in data dependence analysis. Therefore similar methods can be applied

NLO Cross Sections for the LHC using GOLEM: Status and Prospects

In this talk we review the GOLEM approach to one-loop calculations and present an automated implementation of this technique. This method is based on Feynman diagrams and an advanced reduction of one-loop tensor integrals which avoids numerical instabilities. We have extended our one-loop integral library golem95 with an automated one-loop matrix element generator to compute the virtual corrections of the process $q\bar{q}\to b\bar{b}b\bar{b}$. The implementation of the virtual matrix element has been interfaced with tree-level Monte Carlo programs to provide the full result for the above process.Comment: 8 pages, 1 figure, contribution to the proceedings of the 9th International Symposium on Radiative Corrections (RADCOR 2009), October 25-30 2009, Ascona, Switzerlan

Modern Feynman Diagrammatic One-Loop Calculations

In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast evaluation of the amplitude while monitoring the numerical stability of the calculation. In phase space regions close to singular kinematics we use a method avoiding spurious Gram determinants in the calculation. As an application of our approach we report on the status of the calculation of the amplitude for the process $pp\to b\bar{b}b\bar{b}+X$.Comment: 10 pages, 2 figures; contribution to the proceedings of the CPP2010 Workshop, 23-25 Sep. 2010, KEK, Tsukuba, Japa

Recent Progress in the Golem Project

We report on the current status of the Golem project which aims at the construction of a general one-loop evaluator for matrix elements. We construct the one-loop matrix elements from Feynman diagrams in a highly automated way and provide a library for the reduction and numerically stable evaluation of the tensor integrals involved in this approach. Furthermore, we present applications to physics processes relevant for the LHC.Comment: 7 pages, 4 figures, contrib. to proceedings of "Loops and Legs in Quantum Field Theory", 10th DESY Workshop on Elementary Particle Theory, 25-30 April 2010, Woerlitz, German

Novel CACNA1A mutation(s) associated with slow saccade velocities

Mutations in the voltage-gated Cav2.1 P/Q-type calcium channel (CACNA1A) can cause a wide spectrum of phenotypes, including the episodic ataxia type 2. Beside the growing number of descriptions of novel CACNA1A mutations with episodic ataxia type 2 phenotype; there are only rare reports on interictal oculomotor signs other than nystagmus. We describe a novel CACNA1A mutation and an unclassified CACNA1A in-frame variant in a Swiss family presenting as the episodic ataxia type 2 phenotype associated with reduced saccade velocity. In this case series interictal clinical examination showed only minimal neurological findings as mild limb ataxia and nystagmus, but most interestingly saccade analysis of all three affected individuals demonstrated reduced mean saccade velocity. Genetic testing of CACNA1A revealed a de novo frame-shift mutation (c.2691dupC/p.Thyr898Leufs*170) in the index patient in addition to an unclassified in-frame variant (c.6657_6659dupCCA/p.His2220dup) segregating in all three affected individuals. The de novo frame-shift CACNA1A mutation and the unclassified in-frame CACNA1A variant were associated with the episodic ataxia type 2 phenotype and reduced mean saccade velocity, which suggests involvement of brainstem or neural pathways connecting brainstem and the cerebellum in this diseas

Multi-messenger searches via IceCube’s high-energy neutrinos and gravitational-wave detections of LIGO/Virgo

We summarize initial results for high-energy neutrino counterpart searches coinciding with gravitational-wave events in LIGO/Virgo\u27s GWTC-2 catalog using IceCube\u27s neutrino triggers. We did not find any statistically significant high-energy neutrino counterpart and derived upper limits on the time-integrated neutrino emission on Earth as well as the isotropic equivalent energy emitted in high-energy neutrinos for each event

In-situ estimation of ice crystal properties at the South Pole using LED calibration data from the IceCube Neutrino Observatory

The IceCube Neutrino Observatory instruments about 1 km3 of deep, glacial ice at the geographic South Pole using 5160 photomultipliers to detect Cherenkov light emitted by charged relativistic particles. A unexpected light propagation effect observed by the experiment is an anisotropic attenuation, which is aligned with the local flow direction of the ice. Birefringent light propagation has been examined as a possible explanation for this effect. The predictions of a first-principles birefringence model developed for this purpose, in particular curved light trajectories resulting from asymmetric diffusion, provide a qualitatively good match to the main features of the data. This in turn allows us to deduce ice crystal properties. Since the wavelength of the detected light is short compared to the crystal size, these crystal properties do not only include the crystal orientation fabric, but also the average crystal size and shape, as a function of depth. By adding small empirical corrections to this first-principles model, a quantitatively accurate description of the optical properties of the IceCube glacial ice is obtained. In this paper, we present the experimental signature of ice optical anisotropy observed in IceCube LED calibration data, the theory and parametrization of the birefringence effect, the fitting procedures of these parameterizations to experimental data as well as the inferred crystal properties.</p