Engineering a static verification tool for GPU kernels

We report on practical experiences over the last 2.5 years related to the engineering of GPUVerify, a static verification tool for OpenCL and CUDA GPU kernels, plotting the progress of GPUVerify from a prototype to a fully functional and relatively efficient analysis tool. Our hope is that this experience report will serve the verification community by helping to inform future tooling efforts. © 2014 Springer International Publishing

Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data

We study Newton type methods for inverse problems described by nonlinear operator equations $F(u)=g$ in Banach spaces where the Newton equations $F'(u_n;u_{n+1}-u_n) = g-F(u_n)$ are regularized variationally using a general data misfit functional and a convex regularization term. This generalizes the well-known iteratively regularized Gauss-Newton method (IRGNM). We prove convergence and convergence rates as the noise level tends to 0 both for an a priori stopping rule and for a Lepski{\u\i}-type a posteriori stopping rule. Our analysis includes previous order optimal convergence rate results for the IRGNM as special cases. The main focus of this paper is on inverse problems with Poisson data where the natural data misfit functional is given by the Kullback-Leibler divergence. Two examples of such problems are discussed in detail: an inverse obstacle scattering problem with amplitude data of the far-field pattern and a phase retrieval problem. The performence of the proposed method for these problems is illustrated in numerical examples

The orbit structure of Dynkin curves

Let G be a simple algebraic group over an algebraically closed field k; assume that Char k is zero or good for G. Let \cB be the variety of Borel subgroups of G and let e in Lie G be nilpotent. There is a natural action of the centralizer C_G(e) of e in G on the Springer fibre \cB_e = {B' in \cB | e in Lie B'} associated to e. In this paper we consider the case, where e lies in the subregular nilpotent orbit; in this case \cB_e is a Dynkin curve. We give a complete description of the C_G(e)-orbits in \cB_e. In particular, we classify the irreducible components of \cB_e on which C_G(e) acts with finitely many orbits. In an application we obtain a classification of all subregular orbital varieties admitting a finite number of B-orbits for B a fixed Borel subgroup of G.Comment: 12 pages, to appear in Math

Molecular analysis of HLA-DQB1 alleles in childhood common acute lymphoblastic leukaemia.

Epidemiological studies suggest that childhood common acute lymphoblastic leukaemia (c-ALL) may be the rare outcome of early post-natal infection with a common infectious agent. One of the factors that may determine whether a child succumbs to c-ALL is how it responds to the candidate infection. Since immune responses to infection are under the partial control of (human leucocyte antigen) HLA genes, an association between an HLA allele and c-ALL could provide support for an infectious aetiology. To define the limit of c-ALL susceptibility within the HLA region, we have compared HLA-DQB1 allele frequencies in a cohort of 62 children with c-ALL with 76 newborn controls, using group-specific polymerase chain reaction (PCR) amplification, and single-strand conformation polymorphism (SSCP) analysis. We find that a significant excess of children with c-ALL type for DQB1*05 [relative risk (RR): 2.54, uncorrected P=0.038], and a marginal excess with DQB1*0501 (RR: 2.18; P=0.095). Only 3 of the 62 children with c-ALL have the other susceptibility allele, DPB1*0201 as well as DQB1*0501, whereas 15 had one or the other allele. This suggests that HLA-associated susceptibility may be determined independently by at least two loci, and is not due to linkage disequilibrium. The combined relative risk of the two groups of children with DPB1*0201 and/or DQB1*0501 is 2.76 (P=0.0076). Analysis of amino acids encoded by exon 2 of DQB1 reveal additional complexity, with significant (P<0.05) or borderline-significant increases in Gly26, His30, Val57, Glu66-Val67 encoding motifs in c-ALL compared with controls. Since these amino acids are not restricted to DQB1*0501, our results suggest that, as with DPB1, the increased risk of c-ALL associated with DQB1 is determined by specific amino acid encoding motifs rather than by an individual allele. These results also suggest that HLA-associated susceptibility to c-ALL may not be restricted to the region bounded by DPB1 and DQB1

Auxiliary-level-assisted operations with charge qubits in semiconductors

We present a new scheme for rotations of a charge qubit associated with a singly ionized pair of donor atoms in a semiconductor host. The logical states of such a qubit proposed recently by Hollenberg et al. are defined by the lowest two energy states of the remaining valence electron localized around one or another donor. We show that an electron located initially at one donor site can be transferred to another donor site via an auxiliary molecular level formed upon the hybridization of the excited states of two donors. The electron transfer is driven by a single resonant microwave pulse in the case that the energies of the lowest donor states coincide or two resonant pulses in the case that they differ from each other. Depending on the pulse parameters, various one-qubit operations, including the phase gate, the NOT gate, and the Hadamard gate, can be realized in short times. Decoherence of an electron due to the interaction with acoustic phonons is analyzed and shown to be weak enough for coherent qubit manipulation being possible, at least in the proof-of-principle experiments on one-qubit devices.Comment: Extended version of cond-mat/0411605 with detailed discussion of phonon-induced decoherence including dephasing and relaxation; to be published in JET

Quantum phase retrieval of a Rydberg wave packet using a half-cycle pulse

A terahertz half-cycle pulse was used to retrieve information stored as quantum phase in an $N$-state Rydberg atom data register. The register was prepared as a wave packet with one state phase-reversed from the others (the "marked bit"). A half-cycle pulse then drove a significant portion of the electron probability into the flipped state via multimode interference.Comment: accepted by PR

Shape resonance for the anisotropic superconducting gaps near a Lifshitz transition: the effect of electron hopping between layers

The multigap superconductivity modulated by quantum confinement effects in a superlattice of quantum wells is presented. Our theoretical BCS approach captures the low-energy physics of a shape resonance in the superconducting gaps when the chemical potential is tuned near a Lifshitz transition. We focus on the case of weak Cooper-pairing coupling channels and strong pair exchange interaction driven by repulsive Coulomb interaction that allows to use the BCS theory in the weak-coupling regime neglecting retardation effects like in quantum condensates of ultracold gases. The calculated matrix element effects in the pairing interaction are shown to yield a complex physics near the particular quantum critical points due to Lifshitz transitions in multigap superconductivity. Strong deviations of the ratio $2\Delta/T_c$ from the standard BCS value as a function of the position of the chemical potential relative to the Lifshitz transition point measured by the Lifshitz parameter are found. The response of the condensate phase to the tuning of the Lifshitz parameter is compared with the response of ultracold gases in the BCS-BEC crossover tuned by an external magnetic field. The results provide the description of the condensates in this regime where matrix element effects play a key role.Comment: 12 pages, 6 figure

On the Influence of Pulse Shapes on Ionization Probability

We investigate analytical expressions for the upper and lower bounds for the ionization probability through ultra-intense shortly pulsed laser radiation. We take several different pulse shapes into account, including in particular those with a smooth adiabatic turn-on and turn-off. For all situations for which our bounds are applicable we do not find any evidence for bound-state stabilization.Comment: 21 pages LateX, 10 figure