A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces

We propose a Nystr¨om/product integration method for a class of second kind integral equations on the real line which arise in problems of two-dimensional scalar and elastic wave scattering by unbounded surfaces. Stability and convergence of the method is established with convergence rates dependent on the smoothness of components of the kernel. The method is applied to the problem of acoustic scattering by a sound soft one-dimensional surface which is the graph of a function f, and superalgebraic convergence is established in the case when f is infinitely smooth. Numerical results are presented illustrating this behavior for the case when f is periodic (the diffraction grating case). The Nystr¨om method for this problem is stable and convergent uniformly with respect to the period of the grating, in contrast to standard integral equation methods for diffraction gratings which fail at a countable set of grating periods

Disentangling performance-monitoring signals encoded in feedback-related EEG dynamics

The feedback-related negativity (FRN) is a well-established electrophysiological correlate of feedback-processing. However, there is still an ongoing debate whether the FRN is driven by negative or positive reward prediction errors (RPE), valence of feedback, or mere surprise. Our study disentangles independent contributions of valence, surprise, and RPE on the feedback-related neuronal signal including the FRN and P3 components using the statistical power of a sample of N = 992 healthy individuals. The participants performed a modified time-estimation task, while EEG from 64 scalp electrodes was recorded. Our results show that valence coding is present during the FRN with larger amplitudes for negative feedback. The FRN is further modulated by surprise in a valence-dependent way being more positive-going for surprising positive outcomes. The P3 was strongly driven by both global and local surprise, with larger amplitudes for unexpected feedback and local deviants. Behavioral adaptations after feedback and FRN just show small associations. Results support the theory of the FRN as a representation of a signed RPE. Additionally, our data indicates that surprising positive feedback enhances the EEG response in the time window of the P3. These results corroborate previous findings linking the P3 to the evaluation of PEs in decision making and learning tasks

Activation dependent clustering of the erbB2 receptor tyrosine kinase detected by scanning near-field optical microscopy

ErbB2 (HER2, Neu), a member of the epidermal growth factor (EGF) receptor tyrosine kinase family, is often overexpressed in breast cancer and other malignancies, ErbB2 homodimerizes but also presents as a common auxiliary subunit of the EGF and heregulin receptors (erbB1 or EGFR; and erbB3-4, respectively), with which it heteroassociates, ErbB2 is generally regarded as an orphan (ligand-less) receptor with a very potent kinase domain activated either via its associated partners or constitutively as a consequence of discrete mutations. It follows that the extent and regulation of its cell surface interactions are of central importance. We have studied the large-scale association pattern of erbB2 in quiescent and activated cells labeled with fluorescent anti-erbB2 monoclonal antibodies using scanning near-field optical microscopy (SNOM), ErbB2 was found to be concentrated in irregular membrane patches with a mean diameter of approx. 0.5 mu m in nonactivated SKBR3 and MDA453 human breast tumor cells. The average number of erbB2 proteins in a single cluster on nonactivated SKBR3 cells was about 10(3). Activation of SKBR3 cells with EGF, heregulin as well as a partially agonistic anti-erbB2 monoclonal antibody led to an increase in the mean cluster diameter to 0.6-0.9 mu m, irrespective of the ligand, The EGF-induced increase in the erbB2 cluster size was inhibited by the EGFR-specific tyrosine kinase inhibitor PD153035, The average size of erbB2 clusters on the erbB2-transfected line of CHO cells (CB2) was similar to that of activated SKBR3 cells, a finding correlated with the increased base-line tyrosine phosphorylation of erbB2 in cells expressing only erbB2, We conclude that an increase in cluster size may constitute a general phenomenon in the activation of erbB2

The equivalence of fluctuation scale dependence and autocorrelations

We define optimal per-particle fluctuation and correlation measures, relate fluctuations and correlations through an integral equation and show how to invert that equation to obtain precise autocorrelations from fluctuation scale dependence. We test the precision of the inversion with Monte Carlo data and compare autocorrelations to conditional distributions conventionally used to study high-$p_t$ jet structure.Comment: 10 pages, 9 figures, proceedings, MIT workshop on correlations and fluctuations in relativistic nuclear collision

Gamma-widths, lifetimes and fluctuations in the nuclear quasi-continuum

Statistical $\gamma$-decay from highly excited states is determined by the nuclear level density (NLD) and the $\gamma$-ray strength function ($\gamma$SF). These average quantities have been measured for several nuclei using the Oslo method. For the first time, we exploit the NLD and $\gamma$SF to evaluate the $\gamma$-width in the energy region below the neutron binding energy, often called the quasi-continuum region. The lifetimes of states in the quasi-continuum are important benchmarks for a theoretical description of nuclear structure and dynamics at high temperature. The lifetimes may also have impact on reaction rates for the rapid neutron-capture process, now demonstrated to take place in neutron star mergers.Comment: CGS16, Shanghai 2017, Proceedings, 5 pages, 3 figure

Physics Analysis Expert PAX: First Applications

PAX (Physics Analysis Expert) is a novel, C++ based toolkit designed to assist teams in particle physics data analysis issues. The core of PAX are event interpretation containers, holding relevant information about and possible interpretations of a physics event. Providing this new level of abstraction beyond the results of the detector reconstruction programs, PAX facilitates the buildup and use of modern analysis factories. Class structure and user command syntax of PAX are set up to support expert teams as well as newcomers in preparing for the challenges expected to arise in the data analysis at future hadron colliders.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 7 pages, LaTeX, 10 eps figures. PSN THLT00

Determining the shape of defects in non-absorbing inhomogeneous media from far-field measurements

International audienceWe consider non-absorbing inhomogeneous media represented by some refraction index. We have developed a method to reconstruct, from far-field measurements, the shape of the areas where the actual index differs from a reference index. Following the principle of the Factorization Method, we present a fast reconstruction algorithm relying on far field measurements and near field values, easily computed from the reference index. Our reconstruction result is illustrated by several numerical test cases

The weak localization for the alloy-type Anderson model on a cubic lattice

We consider alloy type random Schr\"odinger operators on a cubic lattice whose randomness is generated by the sign-indefinite single-site potential. We derive Anderson localization for this class of models in the Lifshitz tails regime, i.e. when the coupling parameter $\lambda$ is small, for the energies $E \le -C \lambda^2$.Comment: 45 pages, 2 figures. To appear in J. Stat. Phy