1,656 research outputs found
First Passage Time Densities in Resonate-and-Fire Models
Motivated by the dynamics of resonant neurons we discuss the properties of
the first passage time (FPT) densities for nonmarkovian differentiable random
processes. We start from an exact expression for the FPT density in terms of an
infinite series of integrals over joint densities of level crossings, and
consider different approximations based on truncation or on approximate
summation of this series. Thus, the first few terms of the series give good
approximations for the FPT density on short times. For rapidly decaying
correlations the decoupling approximations perform well in the whole time
domain.
As an example we consider resonate-and-fire neurons representing stochastic
underdamped or moderately damped harmonic oscillators driven by white Gaussian
or by Ornstein-Uhlenbeck noise. We show, that approximations reproduce all
qualitatively different structures of the FPT densities: from monomodal to
multimodal densities with decaying peaks. The approximations work for the
systems of whatever dimension and are especially effective for the processes
with narrow spectral density, exactly when markovian approximations fail.Comment: 11 pages, 8 figure
Experimental investigation of high-energy photon splitting in atomic fields
The new data analysis of the experiment, where the photon splitting in the
atomic fields has been observed for the first time, is presented. This
experiment was performed at the tagged photon beam of the ROKK-1M facility at
the VEPP-4M collider. In the energy region of 120-450 MeV, the statistics of
photons incident on the BGO target was collected. About 400
candidates to the photon splitting events were reconstructed. Within the
attained experimental accuracy, the experimental results are consistent with
the cross section calculated exactly in an atomic field. The predictions
obtained in the Born approximation significantly differ from the experimental
results.Comment: 11 pages, 6 figures, LaTe
Cavity evolution in relativistic self-gravitating fluids
We consider the evolution of cavities within spherically symmetric
relativistic fluids, under the assumption that proper radial distance between
neighboring fluid elements remains constant during their evolution (purely
areal evolution condition). The general formalism is deployed and solutions are
presented. Some of them satisfy Darmois conditions whereas others present
shells and must satisfy Israel conditions, on either one or both boundary
surfaces. Prospective applications of these results to some astrophysical
scenarios is suggested.Comment: 10 pages Revtex. To appear in Class. Quantum Grav
C-H/C-H COUPLING OF 4H-IMIDAZOLE-3 OXIDES WITH INDOLES IN THE SYNTHESIS OF BIFUNCTIONAL AZAHETEROCYCLIC DERIVATIVES
The study was carried out with the financial support of the Russian Science Foundation as a part of a research project 20-43-01004
The stability for the Cauchy problem for elliptic equations
We discuss the ill-posed Cauchy problem for elliptic equations, which is
pervasive in inverse boundary value problems modeled by elliptic equations. We
provide essentially optimal stability results, in wide generality and under
substantially minimal assumptions. As a general scheme in our arguments, we
show that all such stability results can be derived by the use of a single
building brick, the three-spheres inequality.Comment: 57 pages, review articl
Measurement of decay rate and parameters at KEDR
Using the inclusive photon spectrum based on a data sample collected at the
peak with the KEDR detector at the VEPP-4M collider, we
measured the rate of the radiative decay as well
as mass and width. Taking into account an asymmetric photon
lineshape we obtained keV, MeV/, MeV.Comment: 6 pages, 3 figure
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