Necessary and sufficient conditions for the reachability and observability of the positive electrical circuits composed of resistors, coils, condensators and voltage sources are established. Definitions of the input-decoupling zeros, output-decoupling zeros and input-output decoupling zeros of the positive electrical circuits are proposed. Some properties of the decoupling zeros of positive electrical circuits are discussed.
Necessary and sufficient conditions for robust stability of the positive discrete-time interval system with time-delays are established.
It is shown that this system is robustly stable if and only if one well de?ned positive discrete-time system with time-delays is asymptotically stable. The considerations are illustrated by numerical example.
Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems with delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed conditions are compared with the suitable conditions for the standard systems. The considerations are illustrated by numerical examples.
Simple new necessary and sufficient conditions for asymptotic stability of the positive linear discrete-time systems with delays in states are established. It is shown that asymptotic stability of the system is equivalent to asymptotic stability of the corresponding positive discrete-time system without delays of the same size. The considerations are illustrated by numerical examples.
New equivalent conditions of the asymptotical stability and stabilization of positive linear dynamical systems are investigated in this paper. The asymptotical stability of the positive linear systems means that there is a solution for linear inequalities systems. New necessary and sufficient conditions for the existence of solutions of the linear inequalities systems as well as the asymptotical stability of the linear dynamical systems are obtained. New conditions for the stabilization of the resultant closed-loop systems to be asymptotically stable and positive are also presented. Both the stability and the stabilization conditions can be easily checked by the so-called I-rank of a matrix and by solving linear programming (LP). The proposed LP has compact form and is ready to be implemented, which can be considered as an improvement of existing LP methods. Numerical examples are provided in the end to show the effectiveness of the proposed method.
Positively invariant sets play an important role in the theory and applications of dynamical systems. The stability in the sense of Lyapunov of the equilibrium x = 0 is equivalent to the existence of the ellipsoidal positively invariant sets. The constraints on the state and control vectors of dynamical systems can be formulated as polyhedral positively invariant sets in practical engineering problems. Numerical checking method of positive invariance of polyhedral sets is addressed in this paper. The validation of the positively invariant sets can be done by solving LPs which can be easily done numerically. It is illustrated by examples that our checking method is effective. Compared with the now existing algebraic methods, numerical checking method is an attractive method in that it’s easy to be implemented.
This paper presents the current stage of the development of EA-MOSGWA – a tool for identifying causal genes in Genome Wide Association Studies (GWAS). The main goal of GWAS is to identify chromosomal regions which are associated with a particular disease (e.g. diabetes, cancer) or with some quantitative trait (e.g height or blood pressure). To this end hundreds of thousands of Single Nucleotide Polymorphisms (SNP) are genotyped. One is then interested to identify as many SNPs as possible which are associated with the trait in question, while at the same time minimizing the number of false detections.
The software package MOSGWA allows to detect SNPs via variable selection using the criterion mBIC2, a modified version of the Schwarz Bayesian Information Criterion. MOSGWA tries to minimize mBIC2 using some stepwise selection methods, whereas EA-MOSGWA applies some advanced evolutionary algorithms to achieve the same goal. We present results from an extensive simulation study where we compare the performance of EA-MOSGWA when using different parameter settings. We also consider using a clustering procedure to relax the multiple testing correction in mBIC2. Finally we compare results from EA-MOSGWA with the original stepwise search from MOSGWA, and show that the newly proposed algorithm has good properties in terms of minimizing the mBIC2 criterion, as well as in minimizing the misclassification rate of detected SNPs.
Given a linear discrete system with initial state x0 and output function yi , we investigate a low dimensional linear systemthat produces, with a tolerance index ǫ, the same output function when the initial state belongs to a specified set, called ǫ-admissible set, that we characterize by a finite number of inequalities. We also give an algorithm which allows us to determine an ǫ-admissible set.
For many years, a digital waveguide model is being used for sound propagation in the modeling of the vocal tract with the structured and uniform mesh of scattering junctions connected by same delay lines. There are many varieties in the formation and layouts of the mesh grid called topologies. Current novel work has been dedicated to the mesh of two-dimensional digital waveguide models of sound propagation in the vocal tract with the structured and non-uniform rectilinear grid in orientation. In this work, there are two types of delay lines: one is called a smaller-delay line and other is called a larger-delay line. The larger-delay lines are the double of the smaller delay lines. The scheme of using the combination of both smaller- and larger-delay lines generates the non-uniform rectilinear two-dimensional waveguide mesh. The advantage of this approach is the ability to get a transfer function without fractional delay. This eliminates the need to get interpolation for the approximation of fractional delay and give efficient simulation for sound wave propagation in the two-dimensional waveguide modeling of the vocal tract. The simulation has been performed by considering the vowels /ɔ/, /a/, /i/ and /u/ in this work. By keeping the same sampling frequency, the standard two-dimensional waveguide model with uniform mesh is considered as our benchmark model. The results and efficiency of the proposed model have compared with our benchmark model.
It is shown that in uncontrollable linear system ẋ = Ax + Bu it is possible to assign arbitrarily the eigenvalues of the closed-loop system with state feedbacks u = Kx, K ∈ ℜn⨉m if rank [A B] = n. The design procedure consists in two steps. In the step 1 a nonsingular matrix M ∈ ℜn⨉m is chosen so that the pair (MA,MB) is controllable. In step 2 the feedback matrix K is chosen so that the closed-loop matrix Ac = A − BK has the desired eigenvalues. The procedure is illustrated by simple example.
Statistical analysis is helpful for better understanding of the processes which take place in agricultural ecosystems. Particular attention should be paid to the processes of crops’ productivity formation under the influence of natural and anthropogenic factors. The goal of our study was to provide new theoretical knowledge about the dependence of vegetable crops’ productivity on water supply and heat income. The study was conducted in the irrigated conditions of the semi-arid cold Steppe zone on the fields of the Institute of Irrigated Agriculture of NAAS, Kherson, Ukraine. We studied the historical data of productivity of three most common in the region vegetable crops: potato, tomato, onion. The crops were cultivated by using the generally accepted in the region agrotechnology. Historical yielding and meteorological data of the period 1990–2016 were used to develop the models of the vegetable crops’ productivity. We used two approaches: development of pair linear models in three categories (“yield – water use”, “yield – sum of the effective air temperatures above 10°C”); development of complex linear regression models taking into account such factors as total water use, and temperature regime during the crops’ vegetation. Pair linear models of the crops’ productivity showed that the highest effect on the yields of potato and onion has the water use index (R2 of 0.9350 and 0.9689, respectively), and on the yield of tomato – temperature regime (R2 of 0.9573). The results of pair analysis were proved by the multiple regression analysis that revealed the same tendencies in the crop yield formation depending on the studied factors.