Independent Random Coefficients Research Articles

Computational method of the cardiovascular diseases classification based on a generalized nonlinear canonical decomposition of random sequences

Decision support systems can seriously help medical doctors in the diagnosis of different diseases, especially in complicated cases. This article is devoted to recognizing and diagnosing heart disease based on automatic computer processing of the electrocardiograms (ECG) of patients. In the general case, the change of the ECG parameters can be presented as a random sequence of the signals under processing. Developing new computational methods for such signal processing is an important research problem in creating efficient medical decision support systems. Authors consider the possibility of increasing the diagnostic accuracy of cardiovascular diseases by implementing of the new proposed computational method of information processing. This method is based on the generalized nonlinear canonical decomposition of a random sequence of the change of cardiogram parameters. The use of a nonlinear canonical model makes it possible to significantly simplify the maximum likelihood criterion for classifying diseases. This simplification is provided by the transition from a multi-dimensional distribution density of cardiogram parameters to a product of one-dimensional distribution densities of independent random coefficients of a nonlinear canonical decomposition. The absence of any restrictions on the class of random sequences under study makes it possible to achieve maximum accuracy in diagnosing cardiovascular diseases. Functional diagrams for implementing the proposed method reflecting the features of its application are presented. The quantitative parameters of the core of the computational diagnostic procedure can be determined in advance based on the preliminary statistical data of the ECGs for different heart diseases. That is why the developed method is quite simple in terms of computation (computing complexity, accuracy, computing time, etc.) and can be implemented in medical computer decision systems for monitoring cardiovascular diseases and for their diagnosis in real time. The results of the numerical experiment confirm the high accuracy of the developed method for classifying cardiovascular diseases.

Mixed logistic model with two independent random coefficients for financial crisis prediction: Argentinean companies

The paper develops a mixed logistic financial distress prediction model with two independent random coefficients and validates it for public Argentinean companies. This study complements existing literature on bankruptcy prediction in emerging economies advancing the application of contemporary econometric methods (Caro et al., 2013). Anticipating bankruptcy risks increases portfolios' profitability. Emerging economies and frontier markets differ from developed economies in political, cultural, social and institutional terms. Given those differences, investors and lenders need specific bankruptcy and financial distress prediction models. The model developed achieves an excellent performance using financial statements from firms listed in the Buenos Aires Stock Exchange during 1993-2000 with ratios accepted in the literature (Altman, 1993; Jones and Hensher, 2004). Results show that profitability, assets turnover and cash flow from operations reduce the likelihood of financial distress while leverage increases it for companies operating in a frontier market such as Argentina.

Mixed logistic model with two independent random coefficients for financial crisis prediction: Argentinean companies

Mixed logistic model with two independent random coefficients for financial crisis prediction: Argentinean companies

The limit G-Law for the solutions of systems of linear algebraic equations with independent random coefficients under the G-Lindeberg condition

Abstract The limit G-Law for the solutions of the systems of linear algebraic equations with independent random coefficients is proven under the G-Lindeberg condition.

The Inverse Tangent Law for the solutions of systems of linear algebraic equations with independent random coefficients

Abstract The Inverse Tangent Law for the solutions of systems of linear algebraic equations with independent random coefficients is proven under Lindeberg’s condition.

The total external length of the evolving Kingman coalescent

The evolving Kingman coalescent is the tree-valued process which records the time evolution undergone by the genealogies of Moran populations. We consider the associated process of total external tree length of the evolving Kingman coalescent and its asymptotic behaviour when the number of leaves of the tree tends to infinity. We show that on the time-scale of the Moran model slowed down by a factor equal to the population size, the (centred and rescaled) external length process converges to a stationary Gaussian process with almost surely continuous paths and covariance function \(c(s,t)=\Big ( \frac{2}{2+|s-t|} \Big )^2\). A key role in the evolution of the external length is played by the internal lengths of finite orders in the coalescent at a fixed time which behave asymptotically in a multivariate Gaussian manner [see Dahmer and Kersting (Ann Appl Probab 25(3):1325–1348, 2015)]. A coupling of the Moran model with a critical branching process is used. We also derive a central limit result for normally distributed sums endowed with independent random coefficients.

Characterization of a medium by estimating the constituent components of its coherency matrix in polarization optics

In this work, an alternative route to analyze a set of coherency matrices associated to a medium is addressed by means of the Independent Component Analysis (ICA) technique. We highlight the possibility of extracting an underlying structure of the medium in relation to a model of constituent components. The medium is considered as a mixture of unknown constituent components weighted by unknown but statistically independent random coefficients of thickness. The ICA technique can determine the number of components necessary to characterize a set of sample of the medium. An estimate of the value of these components and their respective weights is also determined. Analysis of random matrices generated by multiplying random diattenuators and depolarizers is presented to illustrate the proposed approach and demonstrate its capabilities.

35 years of the Inverse Tangent Law

The distribution functions of the solutions of the systems of linear algebraic equations (SLAE) , in general, have a cumbersome form; the order of these systems in some practical problems is large, therefore, the asymptotic behavior of the solutions should be studied in increasing order n of the system to infinity. A general form of the limit theorems of solutions of the systems of linear algebraic equations with independent random coefficients and components , i, j 1, . . . , n , are given in this survey. By the tradition of choosing the names of laws in probability theory (Arcsine law, Law of iterated logarithm, etc.) we call the unusual behavior of the solutions of (SLAERC) as Inverse Tangent Law .

Multiresolution Hilbert Approach to Multidimensional Gauss-Markov Processes

The study of the multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-Markov processes, are ordinarily defined through the theory of stochastic integration. Here, inspired by the Lévy-Ciesielski construction of the Wiener process, we propose an alternative representation of multidimensional Gauss-Markov processes as expansions on well-chosen Schauder bases, with independent random coefficients of normal law with zero mean and unit variance. We thereby offer a natural multiresolution description of the Gauss-Markov processes as limits of finite-dimensional partial sums of the expansion, that are strongly almost-surely convergent. Moreover, such finite-dimensional random processes constitute an optimal approximation of the process, in the sense of minimizing the associated Dirichlet energy under interpolating constraints. This approach allows for a simpler treatment of problems in many applied and theoretical fields, and we provide a short overview of applications we are currently developing.

On convergence of complex power series with independent random coefficients

We find the domains of convergence and analyticity of Maclaurin and Laurent random power series.

Analyticity domains of complex power series with independent random coefficients

We consider a complex power series with independent random coefficients and investigate the possibility of analytic extension of its sum beyond the boundaries of the domain of convergence.

Real zeros of random algebraic polynomials

There are many known asymptotic estimates of the expected number of real zeros of algebraic polynomials with independent random coefficients of equal means. The present paper considers the case when the means of the coefficients are not all necessarily equal. The expected number of crossings of two algebraic polynomials with unequal degree flows from the results.

On the Average Number of Real Roots of a Random Algebraic Equation

There are many known asymptotic estimates of the expected number of zeros of a polynomial of degree $n$ with independent random coefficients, for $n \rightarrow \infty$. The present paper provides an estimate of the expected number of times that such a polynomial assumes the real value $K$, where $K$ is not necessarily zero. The coefficients are assumed to be normally distributed. It is shown that the results are valid even for $K \rightarrow \infty$, as long as $K = O(\sqrt n)$.

Probability of getting a lucky short-exposure image through turbulence*

In short-exposure imaging through turbulence, there is some probability that the image will be nearly diffraction limited because the instantaneous wave-front distortion over the aperture was negligible. A number of years ago in a rather brief paper, Hufnagel (1966) argued heuristically that the probability of getting a good image would decrease exponentially with aperture area. This paper undertakes a rigorous quantitative analysis of the probability. We find that the probability of obtaining a good short-exposure image is Prob ≈ 5.6 exp[−0.1557 (D/r0)2] (for D/r0 ≥ 3.5), where D is the aperture diameter and r0 is the coherence length of the distorted wave front, as defined by Fried (1967). A good image is taken to be one for which the squared wave-front distortion over the aperture is 1 rad2 or less. The analysis is based on the decomposition of the distorted wave front over the aperture, in an orthonormal series with randomly independent coefficients. The orthonormal functions used are the eigenfunctions of a Karhunen-Loeve integral equation. The integral equation is solved using a separation of variables into radial and azimuthal dependence. The azimuthal dependence was solved analytically and the radial, numerically. The first 569 radial eigenfunctions and eigenvalues were obtained. The probability of obtaining a good short-exposure image corresponds to a hyperspace integral in which the spatial dimensions are the independent random coefficients in the orthonormal series expansion. It is equal to the probability that a randomly chosen point in the hyperspace will lie within a hypersphere of unit radius, the points in the hyperspace being randomly chosen in accordance with the product of independent Gaussian probability distribution—one distribution for each dimension. The variance of these distrbutions is directly proportional to the eigenvalues of the Karhunen-Loeve equation. This hyperspace integral (involving up to several hundred dimensions) has been evaluated using Monte Carlo techniques.