A problem of a new physical model test given observed experimental data is a typical one for modern experiments of high energy physics (HEP). A solution of the problem may be provided with two ...alternative statistical formalisms, namely frequentist and Bayesian, which are widely spread in contemporary HEP searches. A characteristic experimental situation is modeled from general considerations and both the approaches are utilized in order to test a new model. The results are juxtaposed, what demonstrates their consistency in this work. An effect of a systematic uncertainty treatment in the statistical analysis is also considered.
We consider the problem of constructing suboptimal filters (lower-order optimal filters, i.e., filters for linear vector functionals of the system state vector) for stochastic multivariable ...multicriteria plants. The method for constructing such filters is presented in the Luenberger canonical basis. Using a numerical example of a seventh-order system, we show that the proposed approach improves the optimality of filters compared to filters based on scalar observers.
We consider the problem of constructing functional filters (optimal functional observers, i.e., observers for linear functionals of the state vector) for linear time-invariant control systems in ...which the inhomogeneity contains additive white noise as a term in addition to control. The output of the system is linear in the state vector and also contains additive white noise as a term. With the help of canonical representations, a comparative analysis of the second- and third-order filters by the mean square observation error in the steady state is carried out. An example of a fourth-order system is given, showing that with an increase in the dynamic order of the filter, the optimality by a quadratic criterion increases.
The problem of constructing optimum observers (filters) of different dynamic orders is considered for stochastic control objects in discrete time. Analytical expressions are obtained for the transfer ...functions of filters,which allow us to calculate the quadratic optimality criterion. With an example of a fourth-order system, the constructed filters are compared by the mean-square observation error in the steady state.
The technique of ensuring of interoperability for Grid-systems and systems of cloud computing is provided. The technique is constructed on a basis of the uniform approach of ensuring interoperability ...for systems of the wide class offered by authors and recorded in the national Russian Federation standard.
Three problems closely related to the classical unbiased optimal filtration problem: an unbiased optimal filtration problem without a control in the system,a biased optimal filtration problem where ...the bias does not exceed a given value, and the joint problem of stabilization and optimal filtration. It is proposed these problems be reduced to ones of nonlinear optimization. For unbiased filtration with no control, conditions are provided that allow the one for classical unbiasedness to be weakened or excluded for the filter. A new estimate of the bias of the mean filtration error is proposed.
There are observations that right after total quarantine measures were introduced, there was no growth in number of suicides, but a situation remains unclear when it comes down to new waves in the ...pandemic development. Our research goal was to estimate risks of suicide in heterogeneous population groups in 2020, that is, from the pandemic start and up to the second wave rise. We analyzed data on completed suicides in Saint Petersburg, Udmurtia Republic (Russia), and Odessa region (Ukraine), 6,375 cases overall among population groups with total number of people being equal to 9,216 thousand starting from January 01, 2016 to December 31, 2020. Confidence intervals for frequencies as per months (per 100,000 people) in 2020 were calculated as per Wilson and compared with average ones calculated for 2016–2019. There was a decrease in frequency of completed suicides in all three population groups during a period when the strictest quarantine measures were valid; by the mid-summer the trend normalized or there was even a slight increase. When the second pandemic wave came, changes were multidirectional; in particular, in Saint Petersburg there was another decrease by the end of the year, the most apparent and statistically significant among men whereas there were short-term rises in Udmurtia and Odessa. Our comparison performed for population groups with initially different levels of suicides confirms that right after a crisis starts, suicidal behavior becomes less frequent among people; however, as a response to the second pandemic wave, we can expect both falls and rises in number of suicides and it requires more intense preventive activities.
The goal of this investigation was to overcome limitations of a persistency analysis, introduced by Benoit Mandelbrot for monofractal Brownian processes: nondifferentiability, Brownian nature of ...process, and a linear memory measure. We have extended a sense of a Hurst factor by consideration of a phase diffusion power law. It was shown that precatastrophic stabilization as an indicator of bifurcation leads to a new minimum of momentary phase diffusion, while bifurcation causes an increase of the momentary transport. An efficiency of a diffusive analysis has been experimentally compared to the Reynolds stability model application. An extended Reynolds parameter has been introduced as an indicator of phase transition. A combination of diffusive and Reynolds analyses has been applied for a description of a time series of Dow Jones Industrial weekly prices for the world financial crisis of 2007–2009. Diffusive and Reynolds parameters showed extreme values in October 2008 when a mortgage crisis was fixed. A combined R/D description allowed distinguishing of market evolution short-memory and long-memory shifts. It was stated that a systematic large scale failure of a financial system has begun in October 2008 and started fading in February 2009.
The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a nonstationary diffusion has been ...derived and used for chaos analysis. An anomalous transport turned out to be natural property of this equation. A nonlinear dispersion of the considered motion allowed us to find a principal consequence: a chaotic system with uniform dynamic properties tends to instable clustering. Small fluctuations of particles density increase by time and form attractors and stochastic islands even if the initial transport properties have uniform distribution. It was shown that an instability of phase trajectories leads to the nonlinear dispersion law and consequently to a space instability. A fixed boundary system was considered, using a standard Fokker-Planck equation. We have derived that such a type of dynamic systems has a discrete diffusive and energy spectra. It was shown that phase space diffusion is the only parameter that defines a dynamic accuracy in this case. The uncertainty relations have been obtained for conjugate phase space variables with account of transport properties. Given results can be used in the area of chaotic systems modelling and turbulence investigation.
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