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The Kerr metric is considered in a synchronous frame of reference obtained by using proper time and initial conditions for particles that freely move along a certain set of trajectories as coordinates. Modifying these coordinates in a…
We propose a new and easy-to-use method for identifying cointegrated components of nonstationary time series, consisting of an eigenanalysis for a certain non-negative definite matrix. Our setting is model-free, and we allow the…
The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of…
With assumption that an optical element is described by a Mueller matrix of the Lorentzian type, a method to find a 3-dimensional complex vector parameter for a corresponding Mueller matrix from results of four specially chosen polarization…
In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$-sparse vector $x \in \mathbb{R}^n$ given access to…
The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of…
Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical…
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…
For a graph consisting of parallel connected subgraphs we express the characteristic function of the boundary value problem with generalized Neumann conditions at both joining points via characteristic functions of different boundary…
This paper presents a nonlinear approach to measurements a general framework for dealing with variations of environmental conditions. My method may prove promising to extensions beyond classical physics, economics, and other sciences. I…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…
This paper is a modified chapter of the author's Ph.D. thesis. We introduce the notions of sequentially approximated types and sequentially approximated Keisler measures. As the names imply, these are types which can be approximated by a…
Classical linear regression is considered for a case when regression parameters depend on the external random environment. The last is described as a continuous time Markov chain with finite state space. Here the expected sojourn times in…
Quantitative recurrence indicators are defined by measuring the first entrance time of the orbit of a point $x$ in a decreasing sequence of neighborhoods of another point $y$. It is proved that these recurrence indicators are a.e. greater…
Time-series classification is an important domain of machine learning and a plethora of methods have been developed for the task. In comparison to existing approaches, this study presents a novel method which decomposes a time-series…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…