Multiple Roots Of Characteristic Equations Research Articles

Deep Markov models of multidimensional random fields

Abstract The paper discusses the use of a doubly stochastic random field model based on autoregressions with multiple roots of characteristic equations for solving the problem of image generation and segmentation. It was proposed to form an image taking into account hidden Markov parameter fields. In particular, the correlation coefficients of the model, as well as the average values and brightness variances, are realizations of random fields, the assessment of which in explicit form is not possible. In addition, a modification of a variational autoencoder for a doubly stochastic model is considered. Finally, based on the use of a modified variational auto encoder, classification and segmentation of satellite images is performed. The combined use of the developed segmentation algorithm with the Unet neural network provides an increase in segmentation accuracy of 3%.

Using probabilistic statistics to determine the parameters of doubly stochastic models based on autoregression with multiple roots

An important task when describing images using mathematical models is the identification of parameters from an real image. Such a task is of particular difficulty for combined mathematical models, which, among other things, make it possible to describe multidimensional spatially inhomogeneous signals. An example of such a model is a doubly stochastic model based on autoregression with multiple roots of characteristic equations, which has an important property of quasi-isotropy and allows describing a smooth change in the statistical and correlation properties of simulated images. This work is aimed at developing algorithms for identifying the parameters of this model based on the estimated probabilistic properties of the available image.

Determination of constraint stabilization parameters with multiple roots of characteristic equation

During a numerical integration of motion equations of a constrained mechanical system effect of deviations from initial data can be neglected with the help of Baumgarte stabilization method. According to this method first time derivatives of constraint equations are not considered as first integrals and are equated to an arbitrarily linear form of constraints themselves. The coefficients of these forms are called perturbation parameters. So, the problem of constraint stabilization is reduced to a problem of finding an appropriate range of perturbation parameters’ values. This problem can be solved by obtaining these values with the help of stability conditions. The procedure of evaluation is getting even more easier if the perturbation coefficients correspond to the multiple root case of its characteristic equation.

Developing a Filtering Algorithm for Doubly Stochastic Images Based on Models with Multiple Roots of Characteristic Equations

The properties of doubly stochastic models constructed using a combination of autoregression models with multiple roots of characteristic equations are studied. These models are demonstrated to be adequate to real multidimensional signals; the probabilistic and correlation properties of the simulated signals are studied. Based on the proposed models, a filtering algorithm is developed for doubly stochastic autoregression random fields generated by the models with multiple roots of the characteristic equations. The algorithm is compared to the alternative approaches.

Ensuring the effectiveness of the taxi order service by mathematical modeling and machine learning

We can’t imagine modern science without mathematical modeling. At the same time, ideas related to mathematical modeling find themselves in various fields. One of the interesting applications of mathematical modeling of random processes is the work of the taxi order service. The article describes the description of the operation of the taxi order service using autoregressive models with multiple roots of characteristic equations of different multiplicity. Also attempts were made to approximate and predict the time series of various important parameters of the taxi order service. Algorithms for identifying model parameters are proposed. Besides, we try to introduce machine learning methods to optimize work of taxi service.