286 research outputs found
Quantum Zeno-like effect and spectra of particles in cascade transition
Shr\"odinger equation for two-step spontaneous cascade transition in a
three-level quantum system is solved by means of Markovian approximation for
non-Markovian integro-differential evolution equations for amplitudes of
states. It is shown that both decay constant and radiation shift of initial
level are affected by instability of intermediate level of the cascade. These
phenomena are interpreted as the different manifestations of quantum Zeno-like
effect. The spectra of particles emitted during the cascade transition are
calculated in the general case and, in particular, for an unusual situation
when the initial state is lower than the intermediate one. It is shown that the
spectra of particles do not have a peak-like shape in the latter case.Comment: 13 pages, no figures, to be published in Physica
General equation for Zeno-like effects in spontaneous exponential decay
It was shown that different mechanisms of perturbation of spontaneous decay
constant: inelastic interaction of emitted particles with particle detector,
decay onto an unstable level, Rabi transition from the final state of decay
(electromagnetic field domination) and some others are really the special kinds
of one general effect - perturbation of decay constant by dissipation of the
final state of decay. Such phenomena are considered to be Zeno-like effects and
general formula for perturbed decay constant is deduced.Comment: LaTeX 2.09 file, 11 pages, no figures. Accepted in Physics Letters
Selective Nonparametric Regression via Testing
Prediction with the possibility of abstention (or selective prediction) is an
important problem for error-critical machine learning applications. While
well-studied in the classification setup, selective approaches to regression
are much less developed. In this work, we consider the nonparametric
heteroskedastic regression problem and develop an abstention procedure via
testing the hypothesis on the value of the conditional variance at a given
point. Unlike existing methods, the proposed one allows to account not only for
the value of the variance itself but also for the uncertainty of the
corresponding variance predictor. We prove non-asymptotic bounds on the risk of
the resulting estimator and show the existence of several different convergence
regimes. Theoretical analysis is illustrated with a series of experiments on
simulated and real-world data
Deeper Connections between Neural Networks and Gaussian Processes Speed-up Active Learning
Active learning methods for neural networks are usually based on greedy
criteria which ultimately give a single new design point for the evaluation.
Such an approach requires either some heuristics to sample a batch of design
points at one active learning iteration, or retraining the neural network after
adding each data point, which is computationally inefficient. Moreover,
uncertainty estimates for neural networks sometimes are overconfident for the
points lying far from the training sample. In this work we propose to
approximate Bayesian neural networks (BNN) by Gaussian processes, which allows
us to update the uncertainty estimates of predictions efficiently without
retraining the neural network, while avoiding overconfident uncertainty
prediction for out-of-sample points. In a series of experiments on real-world
data including large-scale problems of chemical and physical modeling, we show
superiority of the proposed approach over the state-of-the-art methods
HERO (High Energy Ray Observatory) optimization and current status
The High-Energy Ray Observatory (HERO) is a space experiment based on a heavy
ionization calorimeter for direct study of cosmic rays. The effective
geometrical factor of the apparatus varies from 12 to 60 msr for protons
depending on the weight of the calorimeter from 10 to 70 tons. During the
exposure for 5 years this mission will make it possible to measure energy
spectra of all abundant cosmic ray nuclei in the knee region (3 PeV) with
individual resolution of charges with energy resolution better than 30\% and
provide useful information to solve the puzzle of the cosmic ray knee origin.
HERO mission will make it also possible to measure energy spectra of cosmic
rays nuclei for energies 1-1000 TeV with very high precision and energy
resolution (up to 3\% for calorimeter 70 tons) and study the fine structure of
the spectra. The planned experiment launch is no earlier than 2029.Comment: LaTeX,25 pages, 19 figure
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