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

Gravitational chiral anomaly and anomalous transport for fields with spin 3/2

In a fluid with vorticity and acceleration, an axial current arises in the third order of gradient expansion, called the kinematical vortical effect (KVE). While existing in the absence of gravitational fields, it is nevertheless associated with effects in curved space-time, namely with the gravitational chiral quantum anomaly. In this paper, the KVE transport coefficients were found using the Zubarev quantum-statistical density operator for the Rarita-Schwinger-Adler theory, which includes fields with spins 3/2 and 1/2. A prediction is made about the possible form of the transport coefficients for massless fields with arbitrary spin.Comment: 10 page

Novel phase transition at the Unruh temperature

In recent years, the theory of quantum phase transitions has rapidly developed. These are transitions at a zero temperature which are associated with a change of the theory parameters like couplings. In contrast, the classical phase transitions occur ``within'' the same theory (in particular, with the same couplings) and are associated with a change in temperature. Within the framework of a simple model of Dirac fields in the Euclidean Rindler space, we establish an intermediate case when the phase transition occurs at a finite temperature, but the temperature itself is of a quantum origin (the Unruh temperature). Moreover, the phase transition point is uniquely associated with the behavior of individual levels, namely at the Unruh temperature the two lowest Matsubara modes become singular on the Rindler horizon. This provides a new manifestation of the duality between the thermodynamic description and the geometric approach (the behavior of the quantum levels of particles living on a nontrivial geometric manifold). Although the considered example refers to the physics of black holes, we note the formal similarity of the Unruh temperature with the parameter characterizing quantum transitions in the theory of condensed matter.Comment: 11 pages, 2 figure

Effects of cholesterol- or 7-ketocholesterol-containing liposomes on colony-forming ability of cultured cells

AbstractExperiments with cultured Chinese hamster cells showed that incubation of the cells with (phosphatidylcholine + cholesterol + 7-ketocholesterol)-containing liposomes (4:3:1 by weight) during two hours led to a decrease in the colony-forming ability of cells down to zero, while (phosphatidylcholine + cholesterol)-containing liposomes (1:1 by weight) reduce this parameter by 90%. Furthermore, the cholesterol-containing liposomes (without 7-ketocholesterol) induce a decrease in the number of the maximal-site colonies accompanied by the corresponding increase in the number of the middle-size colonies

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

Correlation investigation of the brightness of GDE-grams using the methods of computer graphics and direct measurements

There are two methods of measuring the glow of a liquid under the conditions of gas-discharge imaging. This is a investigation of the brightness of GD-grams - a digital image of streamers created under these conditions, and a direct measurement of brightness using a luminometer, which is carried out during the formation of a streamer during a gas discharge. In the first case, the digital image is analyzed using computer graphics methods and certain software. In the second, the results of direct measurement are analyzed. We have analyzed these two methods using the example of the glow of water under the conditions of gas-discharge visualization. It is shown that with direct measurements the brightness values ​​are higher than when investigating the brightness of a digital image of the same streamer obtained in the same time period. Namely 1.5 cd/m2 and 1.7 cd/m2. The difference is 13% and significantly exceeds the measurement error of the brightness meter (± 7%). According to the results of our research, we suggest that, at the very least, when calibrating the devices that create the GDV-grams, use direct measurements of the glow of the liquid in photometric units. For example, in brightness units

Phenomenological theory of phase transitions in highly piezoelectric perovskites

Recently discovered fine structure of the morphotropic phase boundaries in highly piezoelectric mixture compounds PZT, PMN-PT, and PZN-PT demonstrates the importance of highly non-linear interactions in these systems. We show that an adequate Landau-type description of the ferroelectric phase transitions in these compounds is achieved by the use of a twelfth-order expansion of the Landau potential in terms of the phenomenological order parameter. Group-theoretical and catastrophe-theory methods are used in constructing the appropriate Landau potential. A complete phase diagram is calculated in phenomenological parameter space. The theory describes both PZT and PZN-PT types of phase diagrams, including the newly found monoclinic and orthorhombic phases. Anomalously large piezoelectric coefficients are predicted in the vicinity of the phase transition lines.Comment: RevTex4, 8 pages, 2 figures. Dramatically changed after referees' Comments, to appear in Phys. Rev. B, 1 April 200