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

Study of Interplanetary Magnetic Field with Ground State Alignment

We demonstrate a new way of studying interplanetary magnetic field -- Ground State Alignment (GSA). Instead of sending thousands of space probes, GSA allows magnetic mapping with any ground telescope facilities equipped with spectropolarimeter. The polarization of spectral lines that are pumped by the anisotropic radiation from the Sun is influenced by the magnetic realignment, which happens for magnetic field (<1G). As a result, the linear polarization becomes an excellent tracer of the embedded magnetic field. The method is illustrated by our synthetic observations of the Jupiter's Io and comet Halley. Polarization at each point was constructed according to the local magnetic field detected by spacecrafts. Both spatial and temporal variations of turbulent magnetic field can be traced with this technique as well. The influence of magnetic field on the polarization of scattered light is discussed in detail. For remote regions like the IBEX ribbons discovered at the boundary of interstellar medium, GSA provides a unique diagnostics of magnetic field.Comment: 11 pages, 19 figures, published in Astrophysics and Space Scienc

Physiological stress response, reflex impairment and delayed mortality of white sturgeon Acipenser transmontanus exposed to simulated fisheries stressors

White sturgeon (Acipenser transmontanus) are the largest freshwater fish in North America and a species exposed to widespread fishing pressure. Despite the growing interest in recreational fishing for white sturgeon, little is known about the sublethal and lethal impacts of angling on released sturgeon. In summer (July 2014, mean water temperature 15.3°C) and winter (February 2015, mean water temperature 6.6°C), captive white sturgeon (n = 48) were exposed to a combination of exercise and air exposure as a method of simulating an angling event. After the stressor, sturgeon were assessed for a physiological stress response, and reflex impairments were quantified to determine overall fish vitality (i.e. capacity for survival). A physiological stress response occurred in all sturgeon exposed to a fishing-related stressor, with the magnitude of the res

Linking canonical microcircuits and neuronal activity: Dynamic causal modelling of laminar recordings

Neural models describe brain activity at different scales, ranging from single cells to whole brain networks. Here, we attempt to reconcile models operating at the microscopic (compartmental) and mesoscopic (neural mass) scales to analyse data from microelectrode recordings of intralaminar neural activity. Although these two classes of models operate at different scales, it is relatively straightforward to create neural mass models of ensemble activity that are equipped with priors obtained after fitting data generated by detailed microscopic models. This provides generative (forward) models of measured neuronal responses that retain construct validity in relation to compartmental models. We illustrate our approach using cross spectral responses obtained from V1 during a visual perception paradigm that involved optogenetic manipulation of the basal forebrain. We find that the resulting neural mass model can distinguish between activity in distinct cortical layers – both with and without optogenetic activation – and that cholinergic input appears to enhance (disinhibit) superficial layer activity relative to deep layers. This is particularly interesting from the perspective of predictive coding, where neuromodulators are thought to boost prediction errors that ascend the cortical hierarchy

Migration and health: a study of effects of early life experiences and current socio-economic situation on mortality of immigrants in Sweden

Objectives. Previous research has demonstrated mortality differences between immigrants and natives living in Sweden. The aim of this study is to investigate the effects of early life conditions in the country of birth and current socio-economic conditions in adult life in Sweden on cardiovascular, cancer, all other cause and total mortality among immigrants and natives in Sweden. Design. The cohort data concerning individual demographic characteristics and socio-economic conditions stems from the Swedish Longitudinal Immigrant Database (SLI), a register-based representative database, and consists of individuals from 11 countries of birth, born between 1921 and 1939, who were residents in Sweden between 1980 and 2001. The associations between current socio-economic conditions as well as infant mortality rates (IMR) and Gross Domestic Product (GDP) per capita in the year and country of birth, and total, cardiovascular, cancer and 'all other' mortality in 1980-2001 were calculated by survival analysis using Cox proportional hazards regression to calculate hazard rate ratios. Results. The effects of current adult life socio-economic conditions in Sweden on mortality are both stronger and more straightforward than the effects of early life conditions in the sense that higher socio-economic status is significantly associated with lower mortality in all groups of diagnoses; however, we find associations between infant mortality rates (IMR) in the year and country of birth, and cancer mortality among men and women in the final model. Conclusions. Socioeconomic conditions in Sweden are more strongly associated with mortality than early life indicators IMR and GDP per capita in the year of birth in the country of origin. This finding has health policy and other policy implications

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

ЛЕЧЕНИЕ ПЕРЕЛОМОВ НАДКОЛЕННИКА С ИСПОЛЬЗОВАНИЕМ АППАРАТОВ ВНЕШНЕЙ ФИКСАЦИИ

The authors of the article suggest way of surgical treatment of patella fracture by means of external fixation. Such approach provides reduction ofrehabilitation period and reduces risk of complication