Smooth analysis of the condition number and the least singular value

Let \a be a complex random variable with mean zero and bounded variance. Let $N_{n}$ be the random matrix of size $n$ whose entries are iid copies of \a and $M$ be a fixed matrix of the same size. The goal of this paper is to give a general estimate for the condition number and least singular value of the matrix $M + N_{n}$, generalizing an earlier result of Spielman and Teng for the case when \a is gaussian. Our investigation reveals an interesting fact that the "core" matrix $M$ does play a role on tail bounds for the least singular value of $M+N_{n}$. This does not occur in Spielman-Teng studies when \a is gaussian. Consequently, our general estimate involves the norm $\|M\|$. In the special case when $\|M\|$ is relatively small, this estimate is nearly optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR

Relationship of edge localized mode burst times with divertor flux loop signal phase in JET

A phase relationship is identified between sequential edge localized modes (ELMs) occurrence times in a set of H-mode tokamak plasmas to the voltage measured in full flux azimuthal loops in the divertor region. We focus on plasmas in the Joint European Torus where a steady H-mode is sustained over several seconds, during which ELMs are observed in the Be II emission at the divertor. The ELMs analysed arise from intrinsic ELMing, in that there is no deliberate intent to control the ELMing process by external means. We use ELM timings derived from the Be II signal to perform direct time domain analysis of the full flux loop VLD2 and VLD3 signals, which provide a high cadence global measurement proportional to the voltage induced by changes in poloidal magnetic flux. Specifically, we examine how the time interval between pairs of successive ELMs is linked to the time-evolving phase of the full flux loop signals. Each ELM produces a clear early pulse in the full flux loop signals, whose peak time is used to condition our analysis. The arrival time of the following ELM, relative to this pulse, is found to fall into one of two categories: (i) prompt ELMs, which are directly paced by the initial response seen in the flux loop signals; and (ii) all other ELMs, which occur after the initial response of the full flux loop signals has decayed in amplitude. The times at which ELMs in category (ii) occur, relative to the first ELM of the pair, are clustered at times when the instantaneous phase of the full flux loop signal is close to its value at the time of the first ELM

DNA Aptamers Derived from HIV-1 RNase H Inhibitors are Strong Anti-integrase Agents

International audienceHIV-1 integrase, the retroviral-encoded enzyme involved in the integration of the retrotranscribed viral genome into the host nuclear DNA, is an attractive and still unexploited target. To date, very few inhibitors of this enzyme with a potential therapeutic value have been described. During the search for new HIV-1 targets, we recently described DNA oligodeoxynucleotide aptamers (ODN 93 and ODN 112) that are strong inhibitors of the RNase H activity associated with HIV-1 reverse transcriptase. The striking structural homology between RNase H and integrase led us to study the effect of the RNase H inhibitors on the integrase. Shorter DNA aptamers derived from ODNs 93 and 112 (ODNs 93del and 112del) were able to inhibit HIV-1 integrase in the nanomolar range. They had G-rich sequences able to form G-quartets stabilized by the presence of K(+). The presence of these ions increased the inhibitory efficiency of these agents dramatically. Inhibition of enzymatic activities by ODN 93del and ODN 112del was observed in a cell-free assay system using a recombinant integrase and HIV-1 replication was abolished in infected human cells. Moreover, cell fusion assays showed that these agents do not block viral cell entry at concentrations where viral replication is stopped