992 research outputs found
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 norm of order
, where 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
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
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
Hydrodynamical duals of the gravitational axial anomaly and the cosmological constant
We construct the hydrodynamic expansion for a rotating and accelerated medium
in a curved space-time, and establish a duality between the currents related to
the cosmological constant and the acceleration. Then we consider the more
general case with a non-zero Weyl tensor, and show the relationship between the
current in flat space-time and the gravitational axial anomaly. This
generalizes the previous derivation to the case with a non-zero Ricci tensor.Comment: 15 page
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
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