Drought prediction based on an improved VMD-OS-QR-ELM model

To overcome the low accuracy, poor reliability, and delay in the current drought prediction models, we propose a new extreme learning machine (ELM) based on an improved variational mode decomposition (VMD). The model first redefines the output of the hidden layer of the ELM model with orthogonal triangular matrix decomposition (QR) to construct an orthogonal triangular ELM (QR-ELM), and then introduces an online sequence learning mechanism (OS) into the QR-ELM to construct an online sequence OR-ELM (OS-QR-ELM), which effectively improves the efficiency of the ELM model. The mutual information extension method was then used to extend both ends of the original signal to improve the VMD end effect. Finally, VMD and OS-QR-ELM were combined to construct a drought prediction method based on the VMD-OS-QR-ELM. The reliability and accuracy of the VMD-OS-QR-ELM model were improved by 86.19% and 93.20%, respectively, compared with those of the support vector regression model combined with empirical mode decomposition. Furthermore, the calculation efficiency of the OS-QR-ELM model was increased by 88.65% and 85.32% compared with that of the ELM and QR-ELM models, respectively.

ESTIMATING WITH A GIVEN ACCURACY OF THE COEFFICIENTS AT NONLINEAR TERMS OF UNIVARIATE POLYNOMIAL REGRESSION USING A SMALL NUMBER OF TESTS IN AN ARBITRARY LIMITED ACTIVE EXPERIMENT

We substantiate the structure of the efficient numerical axis segment an active experiment on which allows finding estimates of the coefficients fornonlinear terms of univariate polynomial regression with high accuracy using normalized orthogonal Forsyth polynomials with a sufficiently smallnumber of experiments. For the case when an active experiment can be executed on a numerical axis segment that does not satisfy these conditions, wesubstantiate the possibility of conducting a virtual active experiment on an efficient interval of the numerical axis. According to the results of the experiment, we find estimates for nonlinear terms of the univariate polynomial regression under research as a solution of a linear equalities system withan upper non-degenerate triangular matrix of constraints. Thus, to solve the problem of estimating the coefficients for nonlinear terms of univariatepolynomial regression, it is necessary to choose an efficient interval of the numerical axis, set the minimum required number of values of the scalarvariable which belong to this segment and guarantee a given value of the variance of estimates for nonlinear terms of univariate polynomial regressionusing normalized orthogonal polynomials of Forsythe. Next, it is necessary to find with sufficient accuracy all the coefficients of the normalized orthogonal polynomials of Forsythe for the given values of the scalar variable. The resulting set of normalized orthogonal polynomials of Forsythe allows us to estimate with a given accuracy the coefficients of nonlinear terms of univariate polynomial regression in an arbitrary limited active experiment: the range of the scalar variable values can be an arbitrary segment of the numerical axis. We propose to find an estimate of the constant and ofthe coefficient at the linear term of univariate polynomial regression by solving the linear univariate regression problem using ordinary least squaresmethod in active experiment conditions. Author and his students shown in previous publications that the estimation of the coefficients for nonlinearterms of multivariate polynomial regression is reduced to the sequential construction of univariate regressions and the solution of the correspondingsystems of linear equalities. Thus, the results of the paper qualitatively increase the efficiency of finding estimates of the coefficients for nonlinearterms of multivariate polynomial regression given by a redundant representation.

Triangular matrix coalgebras: Representation theory and recollement

For any triangular matrix coalgebra [Formula: see text], in this paper, we first examine some connections between coalgebra properties of [Formula: see text] and its constituent coalgebras [Formula: see text], [Formula: see text], which contain semiperfectness, computability and row/column-finiteness of their left Cartan matices. Then we devote to considering the coresolution dimensions of recollement of comodule categories by investigating covariantly finite subcategories.

Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean c0(N) Space

In the present paper, we propose to study generalized weighted backward shifts BB over non-Archimedean c0(N) spaces; here, B=(bij) is an upper triangular matrix with supi,j|bij|<∞. We investigate the sypercyclic and hypercyclic properties of BB. Furthermore, certain properties of the operator I+BB are studied as well. To establish the hypercyclic property of I+BB we have essentially used the non-Archimedeanity of the norm which leads to the difference between the real case.

Gorenstein-Projective Modules over Upper Triangular Matrix Artin Algebras

Gorenstein-projective module is an important research topic in relative homological algebra, representation theory of algebras, triangulated categories, and algebraic geometry (especially in singularity theory). For a given algebra A , how to construct all the Gorenstein-projective A -modules is a fundamental problem in Gorenstein homological algebra. In this paper, we describe all complete projective resolutions over an upper triangular Artin algebra Λ = A M B A 0 B . We also give a necessary and sufficient condition for all finitely generated Gorenstein-projective modules over Λ = A M B A 0 B .

Predicting delays in service operations

Delays constitute a key challenge in the management of service operations, causing substantial quality and cost issues. Delays in one service event can cause delays in another service event and so on, which creates challenges in the management of complex services. Assuming a lower-triangular matrix formalism, we develop a novel approach to modelling such chains of delays in complex service operations such as health care and software development. This approach can enable service managers to identify, understand, predict and control delays. Our research provides a novel theoretical contribution to the literature on service delays.

Relative Gorenstein Dimensions over Triangular Matrix Rings

Let A and B be rings, U a (B,A)-bimodule, and T=A0UB the triangular matrix ring. In this paper, several notions in relative Gorenstein algebra over a triangular matrix ring are investigated. We first study how to construct w-tilting (tilting, semidualizing) over T using the corresponding ones over A and B. We show that when U is relative (weakly) compatible, we are able to describe the structure of GC-projective modules over T. As an application, we study when a morphism in T-Mod is a special GCP(T)-precover and when the class GCP(T) is a special precovering class. In addition, we study the relative global dimension of T. In some cases, we show that it can be computed from the relative global dimensions of A and B. We end the paper with a counterexample to a result that characterizes when a T-module has a finite projective dimension.

Structure of Iso-Symmetric Operators

For a Hilbert space operator T∈B(H), let LT and RT∈B(B(H)) denote, respectively, the operators of left multiplication and right multiplication by T. For positive integers m and n, let ▵T∗,Tm(I)=(LT∗RT−I)m(I) and δT∗,Tn(I)=(LT∗−RT)m(I). The operator T is said to be (m,n)-isosymmetric if ▵T∗,TmδT∗,Tn(I)=0. Power bounded (m,n)-isosymmetric operators T∈B(H) have an upper triangular matrix representation T=T1T30T2∈B(H1⊕H2) such that T1∈B(H1) is a C0.-operator which satisfies δT1∗,T1n(I|H1)=0 and T2∈B(H2) is a C1.-operator which satisfies AT2=(Vu⊕Vb)|H2A, A=limt→∞T2∗tT2t, Vu is a unitary and Vb is a bilateral shift. If, in particular, T is cohyponormal, then T is the direct sum of a unitary with a C00-contraction.

Detection of an Autism EEG Signature Through a New Processing Method Based on a Topological Approach

A new pre-processing approach of EEG data to detect topological EEG features has been applied to a continuous segment of artifact-free EEG data lasting 10 minutes in ASCII format derived from 50 ASD children and 50 children with other Neuro-psychiatric disorders, matched for age and male/female ratios. Each EEG was manipulated using a Cin-Cin algorithm, based on an input vector characterized by a linear composition of city-block matrix distances among19 electrodes. From the resulting triangular matrix of 171 numbers expressing all of the one-by-one distances among the 19 electrodes a minimum spanning tree(MST) is calculated. Electrode identification serial codes, sorted according to the decreasing number of links in MST, and the number of links in MST are taken as input vectors for machine learning systems. With this method all the content of an EEG is transformed in 38 numbers which represent the input vectors for machine learning systems classifiers. Machine learning systems have been applied to build up a predictive model to distinguish between the two diagnostic classes. The best machine learning system (KNN algorithm) obtained a global accuracy of 93.2% (92.37 % sensitivity and 94.03 % specificity) in differentiating ASD subjects from NPD subjects. In conclusion the results obtained in this study suggest that the two new pre-processing methods introduced, in particular the MST algorithm, have great potential to allow a machine learning system to discriminate EEGs obtained from subjects with autism from EEGs obtained from subjects affected by other psychiatric disorders.