Approximation with Random Bases: Pro et Contra

In this work we discuss the problem of selecting suitable approximators from families of parameterized elementary functions that are known to be dense in a Hilbert space of functions. We consider and analyze published procedures, both randomized and deterministic, for selecting elements from these families that have been shown to ensure the rate of convergence in $L_2$ norm of order $O(1/N)$, where $N$ is the number of elements. We show that both randomized and deterministic procedures are successful if additional information about the families of functions to be approximated is provided. In the absence of such additional information one may observe exponential growth of the number of terms needed to approximate the function and/or extreme sensitivity of the outcome of the approximation to parameters. Implications of our analysis for applications of neural networks in modeling and control are illustrated with examples.Comment: arXiv admin note: text overlap with arXiv:0905.067

Hard production of a Z boson plus heavy flavor jets at LHC and the intrinsic charm content of a proton

The cross section of associated production of a Z boson with heavy flavor jets in $pp$ collisions is calculated using the SHERPA Monte Carlo generator and the analytical combined QCD approach based on kt-factorization at small x and conventional collinear QCD at large x. A satisfactory description of the ATLAS and CMS data on the $p_T$ spectra of Z bosons and c-jets in the whole rapidity, y, region is shown. Searching for the intrinsic charm (IC) contribution in these processes, which could be visible at large y > 1.5, we study observables very sensitive to non-zero IC contributions and less affected by theoretical QCD scale uncertainties. One of such observables is the so-called double ratio: the ratio of the differential cross section of Z + c production in the central region of |y| < 1.5 and in the forward region 1.5 < |y| < 2.5, divided by the same ratio for Z + b production. These observables could be more promising for the search of IC at LHC as compared to the observables considered earlier.Comment: 18 pages, 7 figure

Ultrasound picture of Cowper’s glands in adults

The results of ultrasonography Cowper’s glands (CG) using the rectal probe 5-9 MHz of 260 male volunteers aged 16 to 95 years of age, formed the control group and 253 patients with benign prostatic hyperplasia (BPH) are presented. In the control group, CG was visualized in 243 (93.5%) cases among patients with BPH - in 238 (94.1%). For CG were characterized by diaphragm-bulbar localization, ovoid form, clear and smooth contours, homogeneous structure, comparable in echogenicity with the echogenicity of the bulb of the penis and the urogenital diaphragm. Average dimensions of CG were as follows: length - 6.5 mm thick, and the width is 4 mm, the volume of each CG - 0.06 cm3. Vascular density in CG was equal to 0 -1. In the control group intraglandular blood flow was recorded only in 6 (2.3%) cases. Blood flow was highly resistant and low speed with maximum linear speed (V max) is less than 12 cm Is and the index of peripheral resistance (RI) is equal to 0.70. Age restructuring of CG began with 60 years of age and included the reduction of the dimensions of CG, enhancing their echogenicity, appearance of small retention cysts in the parenchyma of CG. The minor strength of the relationship, reflecting a decrease of the total volume of CG in elderly and senile age (r = - 0.13, p = 0.0093) was identified. Dimensions of CG in patients with BPH and men volunteers of the control group statistically differed (p < 0.05). The minor and a weak inverse correlations between CG dimensions and the size of the BPH host: for length of CG (r = - 0.24; p = 0.0017), the width of the CG (r = - 0.35; p = 0.0001), for the thickness of CG (r = - 0.32; p = 0.0001), total volume of CG (r = - 0.33; p = 0.0012) were identified. The ultrasound criteria for a normal CG were proposed.Представлены результаты ультразвукового исследования куперовых желез (КЖ) с применением ректального датчика 5-9 МГц у 260 мужчин-добровольцев в возрасте 16 - 95 лет, составивших контрольную группу, и у 253 пациентов с доброкачественной гиперплазией предстательной железы (ДГПЖ). В контрольной группе КЖ были визуализированы в 243 (93,5%) случаях, среди пациентов с ДГПЖ - в 238 (94,1%). Для КЖ были характерны диафрагма-бульбарная локализация, овоидная форма, четкие и ровные контуры, однородная структура, сопоставимая по эхогенности с эхогенностью луковицы полового члена или мочеполовой диафрагмы. Средние размеры КЖ составили: длина - 6,5 мм, толщина и ширина - по 4 мм, объем каждой КЖ - 0,06 см. Сосудистая плотность КЖ была равна 0 -1. В контрольной группе внутрижелезистый кровоток регистрировался только в 6 (2,3%) случаях и был высокорезистентным, низкоскоростным с максимальной линейной скоростью (V max) меньше 12 см/с и индексом периферического сосудистого сопротивления (RI) равном 0,70. Возрастная перестройка КЖ начиналась с 60-летнего возраста и включала уменьшение размеров КЖ, повышение их эхогенности, появление мелких ретенционных кист в паренхиме КЖ. Установлена незначительная по силе взаимосвязь, отражающая уменьшение суммарного объема КЖ в пожилом и старческом возрасте (r = - 0,13; р = 0,0093). Размеры КЖ у пациентов с ДГПЖ и мужчин-добровольцев группы контроля статистически различались (р < 0,05). Выявлены незначительные и слабые обратные корреляции между размерами КЖ и размерами узла ДГПЖ: для длины КЖ (r = - 0,24; р = 0,0017), для ширины КЖ (г = - 0,35; р = 0,0001), для толщины КЖ (r = - 0,32; р = 0,0001), для суммарного объема КЖ (r = - 0,33; р = 0,0012). Предложены ультразвуковые критерии нормальных КЖ

Unruh effect in curved space-time and hydrodynamics

We consider an accelerated relativistic fluid in four-dimensional (anti-)de Sitter space-time. Analyzing only hydrodynamic equations, we construct the equilibrium stress-energy tensor. We confirm that (A)dS vacuum corresponds to a thermal bath in the accelerated frame with a temperature, depending on the acceleration in a flat higher-dimensional (namely, five-dimensional) space, in which curved space-times are embedded. We develop the duality between hydrodynamics and gravity finding a direct relationship between the transport coefficients in flat and curved space-times

Trans-sonic propeller stage

We follow the approach used by Davies and Pringle (1981) and discuss the trans-sonic substage of the propeller regime. This substage is intermediate between the supersonic and subsonic propeller substages. In the trans-sonic regime an envelope around a magnetosphere of a neutron star passes through a kind of a reorganization process. The envelope in this regime consists of two parts. In the bottom one turbulent motions are subsonic. Then at some distance $r_\mathrm{s}$ the turbulent velocity becomes equal to the sound velocity. During this substage the boundary $r_\mathrm{s}$ propagates outwards till it reaches the outer boundary, and so the subsonic regime starts. We found that the trans-sonic substage is unstable, so the transition between supersonic and subsonic substages proceeds on the dynamical time scale. For realistic parameters this time is in the range from weeks to years.Comment: 8 pages with figures, submitted to Astron. Astroph. Transaction