Zero Components Research Articles

Variable selection of partially functional linear spatial autoregressive model with a diverging number of parameters

In this article, we consider variable selection of partially functional linear spatial autoregressive model with a diverging number of parameters, in which the explanatory variables include infinite dimensional predictor procedure, treated as functional data, and multiple real valued scalar variate. By combining series approximation method, two-stage least squares method and a class of non convex penalty function, we propose a variable selection method to simultaneously select significant explanatory variables in the parametric component and estimate the corresponding parameter related to spatial lag of the response variable. Under appropriate conditions, we derive the rate of convergence of the series estimator of the functional and parametric component, and show that the proposed variable selection method processes the oracle property. That is, it can estimate the zero components as exact zero with high probability, and estimate the non zero components as efficiently as if the true model was known beforehand. Simulation result show that our proposed variable selection method has better finite sample property.Notably, in the case where the correlation among the explanatory variables in the parametric component is low, the proposed variable selection method performs well. An application of the proposed variable selection method serves as a practical illustration.

A novel Short-time Fourier transform-based algorithm for detection of wandering in the patients with Alzheimer’s disease

ABSTRACT As the elderly population rises, the growth rate of age-related diseases such as Alzheimer’s disease and cognitive impairments increases. Wandering is one of the first and the most progressive and challenging behaviors; that manifest with certain patterns in the mobility behavior of the patients in the early stages of the disease. Timely diagnosis of wandering can prevent irreparable damages, including the risk of losing the patient, severe physical injuries caused by accidents, and even death. So far, numerous studies have focused on the development of wandering detection algorithms. Most of these mainly rely on two approaches of extracting features from patients’ trajectory history and estimating the path complexity. Motion signal processing methods have rarely been used in this area. An important consideration for these patients is the instability in their movement behaviors, which has received limited attention in previous research, leading to less compatibility of models with this feature. Therefore, this paper proposes an algorithm based on motion signal processing using the Short-time Fourier transform (STFT). This algorithm detects wandering patterns only by using the patient’s trajectory data and changes in their zero and non-zero frequency components. The efficiency of the proposed algorithm has been evaluated using the Geolife open-source dataset, considering the macro-average of metrics such as accuracy, precision, specificity, recall, and F-score, achieving respective values of 96.38%, 94.89%, 96.36%, 96.36%, and 95.58%. The results have validated the proposed algorithm’s strong performance in diagnosing wandering behavior, which, on one hand, helps prevent adverse consequences and, on the other hand, aids in the diagnosis and predicting the progression of the disease to severe Alzheimer’s stage.

Characteristics and Parameters of a Three-Phase, Three-Wire Balanced Circuit with Non-Linear Load

The existing non-linear load in a three-phase circuit limits the possibilities of using the symmetrical components method to analyse it. This paper presents a method for analysing such a circuit when only the zero and positive components are present. Nonlinear loading in a circuit limits the applicability of the symmetrical components method in the analysis of a three-phase circuit. When there is only a zero component and a positive component, it is possible to carry out the analysis as presented in this article. The analysed circuit is balanced. An equal nonlinear load with a voltage described by a signum function of the current is considered in three phases. This load, through equal series RL elements, is supplied from a symmetrical three-phase voltage source. For a steady state with unbroken current flows, the equations of the circuit are solved symbolically. In the broader scope of the equation, solutions obtained using MATLAB-Simulink R2021b were used. The matching of the symbolic and simulation solutions was obtained. The current and voltage harmonic content coefficients of the receiver, the equivalent resistance and inductance of the nonlinear load, and the distribution of active and reactive power in the circuit were determined. The reactive power analysis shows that the considered load nonlinearity when generating higher harmonics, increases the reactive power of the circuit and the inductance of the circuit, which is seen from the terminals of the power source.

Study of Special Unbalanced Load Modes of New Double-Autotransformer of the Flexible Alternating Current Link

The purpose of the work is study of special asymmetric modes of new three-phase autotransformer device for flexible connection of alternative current power systems. The universal model was developed for the device, containing two autotransformers - the main phase-shifting and the additional regulating autotransformer. The model allows studying both symmetric and almost any asymmetric modes of the considered circuit. It became possible to connect asymmetrically the loads in different phases of the regulating autotransformer, as well as arbitrary connect the regulating autotransformer itself to the hexagon taps. According to the calculated values of currents, voltages and magnetic fluxes of the device the visual vectorial diagrams were constructed for the main and the regulating autotransformer, explaining specific of considered operating modes. It was shown that device’ currents in such modes contain symmetrical components of both zero and negative sequences. Also, at asymmetric connection of the regulating autotransformer, the relative magnetic flux of the legs of the main and regulating autotransformers are asymmetrical, but in main autotransformer their sum is approximately equal to zero and magnetic flux practically does not escape into the surrounding space. Radically different situation is observed in the regulating autotransformer. The significant zero-sequence fluxes arise with the release of significant (about 50%) magnetic flux into the surrounding space. This re-quires special measures to be taken to limit its harmful effects on the operation of the autotransformer.

Credible and comprehensive? Comparing policy mixes for Local Energy Systems in England, Scotland and Wales

Credible and comprehensive? Comparing policy mixes for Local Energy Systems in England, Scotland and Wales

Barzilai–Borwein-like rules in proximal gradient schemes for ℓ1-regularized problems

We propose a novel steplength selection rule in proximal gradient methods for minimizing the sum of a differentiable function plus an ℓ 1 -norm penalty term. The proposed rule modifies one of the classical Barzilai–Borwein steplength, extending analogous results obtained in the context of gradient projection methods for constrained optimization. We analyse the spectral properties of the Barzilai–Borwein-like steplength when the differentiable part is quadratic, showing that its reciprocal lies in the spectrum of the submatrix of the Hessian that depends on both the nonzero and the nonoptimal zero components of the current iterate, allowing for acceleration effects when the optimal zero components start to be identified. Furthermore, we insert the modified rule into a proximal gradient method with a nonmonotone line search, for which we prove global convergence towards a stationary point. Numerical experiments show the ability of the proposed rule to sweep the spectrum of the reduced Hessian on a series of quadratic ℓ 1 -regularized problems, as well as its effectiveness in recovering the ground truth in a least squares regularized problem arising in image restoration.

Heyde Theorem on Locally Compact Abelian Groups with the Connected Component of Zero of Dimension 1

Heyde Theorem on Locally Compact Abelian Groups with the Connected Component of Zero of Dimension 1

Algebraic independence of the partial derivatives of certain functions with arbitrary number of variables

Algebraic independence of the partial derivatives of certain functions with arbitrary number of variables

The Functor $K_{0}^{\operatorname {gr}}$ is Full and only Weakly Faithful

The Graded Classification Conjecture states that the pointed $K_{0}^{\operatorname {gr}}$ -group is a complete invariant of the Leavitt path algebras of finite graphs when these algebras are considered with their natural grading by $\mathbb {Z}$ . The strong version of this conjecture states that the functor $K_{0}^{\operatorname {gr}}$ is full and faithful when considered on the category of Leavitt path algebras of finite graphs and their graded homomorphisms modulo conjugations by invertible elements of the zero components. We show that the functor $K_{0}^{\operatorname {gr}}$ is full for the unital Leavitt path algebras of countable graphs and that it is faithful (modulo specified conjugations) only in a certain weaker sense.

Estimation of high-dimensional vector autoregression via sparse precision matrix

Summary We consider the problem of estimating sparse vector autoregression (VAR) via penalized precision matrices. This matrix is the output of the underlying directed acyclic graph of the VAR process, whose zero components correspond to the zero coefficients of the graphical representation of the VAR. The sparsity-based precision matrix estimator is deduced from the D-trace loss with convex and nonconvex penalty functions. We establish the consistency of the penalized estimator and provide the conditions for which all true zero entries of the precision matrix are actually estimated as zero with probability tending to one. The relevance of the method is supported by simulated experiments and a real data application.

Stochastic Stability of Markovian Neural Networks With Generally Hybrid Transition Rates.

This article studies the problem of the stability for Markovian neural networks (MNNs) with time delay. The transition rate is considered to be generally hybrid, which treats those existing ones as its special cases. The introduced generally hybrid transition rates (GHTRs) make these systems more general and practical. Apropos of the GHTRs, a double-boundary approach rather than the traditional estimation method is introduced to make full use of the error information in GHTRs. In order to fully capture system information, a parameter-type-delay-dependent-matrix (PTDDM) approach is proposed, in which the PTDDM approach removes some zero components on slack matrices in previous works. Thus, the PTDDM approach can fully link the relationship among time delay and state-related vectors. Based on these ingredients, a novel stochastic stability condition is proposed for MNNs with GHTRs. A numerical example is illustrated to demonstrate the effectiveness of the proposed approaches.

Negative cohomology and the endomorphism ring of the trivial module

Let k be a field of characteristic p > 0 and let H be a finite group or group scheme. We show that the negative Tate cohomology ring H ˆ ≤ 0 ( H , k ) can be realized as the endomorphism ring of the trivial module in a Verdier localization of the stable category of kG -modules for G an extension of H . This means in some cases that the endomorphism ring of the trivial module is a local ring with infinitely generated radical with square zero. This stands in stark contrast to some known calculations in which the endomorphism ring of the trivial module is the degree zero component of a localization of the cohomology ring of the group.

Stability and bifurcations in a general Cournot duopoly model with distributed time delays

This paper is devoted to the analysis of a Cournot game, described by a nonlinear mathematical model with four distributed time delays, modelling the behavior of two interacting firms on the market. For each firm, a delay for its own production and one for the production of the competitor are introduced. The analysis of the stability of the four equilibrium points is accomplished. The three equilibria with at least one zero component are shown to be unstable, regardless of the choice of time delays. For the stability and bifurcation analysis of the positive equilibrium, four scenarios are considered to highlight the role played by the time delays: only competitor's delays for both players, equal delays for both players, no delays for one player and only own delays for both players. Numerical simulations are performed to illustrate the theoretical results.

Complete analysis of dislocations in single crystal diamonds

In this study, we applied dislocation analysis to X-ray topography images to identify the complete dislocation information for two typical high-pressure high-temperature diamond crystals, IIa and Ib. Almost all dislocation line vectors of both crystals were identified for the first time. For IIa crystal, it was confirmed that up to 84% of the dislocations have 〈101〉 vectors. For Ib crystal, up to 71% of the dislocations have 〈112〉, 〈121〉, and 〈211〉 vectors. Both [110] and [1-10] with zero components of the c-axis are the major Burgers vectors. Regarding the types of dislocation, the major types were edge types, which were approximately 47% and 65% for IIa and Ib crystals, respectively. In addition, screw, 60° and 73° type on the IIa, and 30°, 35°, and 73° type on Ib were identified. Complete analysis of dislocations will give important information for the diamond growth and reduction of the dislocations.

An Ultra-High-Speed Algorithm for Fault Classification in Double Circuit Transmission Lines Using Only the First Group of Received Current Traveling Waves

• Fault detection and classification based on traveling wave • Lightning and fault classification with current traveling wave • Ultra high speed protection of double circuit transmission line using wavelet transform • Very fast algorithm for fault classification of parallel transmission line with single phase tripping This paper presents a new and very fast fault detection (FD), fault classification (FC), and fault phase selection (FPS) method, which is just based on the first group of current traveling waves (cTW) in double circuit transmission lines (DCTLs). All internal, inter-circuit faults and lightning strikes on transmission line (TL) phases and shield wires are reviewed. By the proposed algorithm, FC and FPS are performed in the shortest possible time. In this study, wavelet transform (WT) is used to extract the traveling wave (TW) caused by the fault from the current signal of one DCTL terminal, and only the first group of these waves is used for FC and PFS to increase velocity. To classify various fault types, the zero components of TWs of the two lines, which can be calculated using the conventional modal transforms and another modal transform of 6*6 dimensions defined on all six phases of the DCTL, is used. All simulations are performed in PSCAD on a 230kV grid and a DCTL of 200km length. Also, the performance of the proposed algorithm is tested under various fault and lightning conditions in the presence of white noise with different incidence angles and various fault resistances. .

Classification of multi-stage voltage sags and calculation of phase angle jump based on Clarke components ellipse

Multi-stage voltage sag is one of the problems in the power system that requires classification and separation of stages to recognize this phenomenon. An algorithm for classification of multi-stage voltage sags based on the ellipse drawn by Clarke's transformation components is presented in this paper. The proposed algorithm has the ability to detect if the voltage sag is single-stage or multi-stage, and separates the various stages of multi-stage voltage sag using the point-on-wave of initiation and recovery parameters that is the novelty of this paper. Also a new method for calculation the phase angle jump by considering the zero Clarke component in drawing an ellipse is presented. The proposed method has a better accuracy than the previous method, which did not consider the zero component of the Clarke's transform. For validation, the method is tested with real data provided by the Department of Energy and the Electric Power Research Institute and compared with the previous method. A 12-bus distribution network has also been used to evaluate the performance of the multi-stage voltage sags classification algorithm accurately. This 33 kV network has distributed generation sources and various types of multi-stage voltage sags have been created in this network that show the efficiency of the algorithm. The results show that the proposed algorithm is able to classify any type of multi-stage voltage sag.

Admissibility analysis of Takagi–Sugeno fuzzy descriptor systems with time-varying delay via nonorthogonal free-matrix-based inequality

This paper studies the admissibility of Takagi–Sugeno (T-S) fuzzy descriptor systems with time-varying delay. To analyze the admissibility, various free-matrix-based inequalities (FMIs) are used in the existing works, since they directly produce bounds for integral terms without time-varying delay in denominator. However, the slack matrices in these inequalities are incomplete with some zero components, which may lead to incomplete coupling system information. In this case, conservatism is unavoidable. To remove the issue, a nonorthogonal FMI (NFMI) is proposed by constructing nonorthogonal polynomials with auxiliary scalars and auxiliary vectors, which includes some existing FMIs as its special cases. Based on the NFMI, a less conservative admissibility criterion is obtained for T-S fuzzy descriptor system. Two examples are illustrated to demonstrate the effectiveness of the obtained results.

Vitamin D is directly associated with favorable glycemic, lipid, and inflammatory profiles in individuals with at least one component of metabolic syndrome irrespective of total adiposity: Pró-Saúde Study, Brazil

Vitamin D insufficiency has been suggested as a risk factor for several metabolic disorders. The objective of the study was to investigate the association between serum 25 hydroxyvitamin D [25(OH)D] and metabolic health markers of Brazilian individuals with normal-weight, overweight or obesity. We hypothesized that serum 25(OH)D would be inversely associated with glycemic, lipid and inflammatory markers indicative of metabolic abnormality. Data of 511 individuals (33-79 years), recruited from a longitudinal investigation (Pró-Saúde Study), were analyzed cross-sectionally. Anthropometric, biochemical, body composition, socio-demographic and lifestyle data were collected. Based on body mass index (BMI; normal weight, overweight, obesity) and metabolic health (metabolically healthy (MH) and metabolically unhealthy (MU)) categories, the participants were classified into 6 phenotypes. Individuals having zero components of the metabolic syndrome were considered as "MH". MH obesity was frequent in 2.0% of the participants and 56.0% exhibited vitamin D insufficiency (<20 ng/mL). In the subgroups of the same BMI category, there were no significant differences in 25(OH)D concentrations between individuals classified as MH and MU. After adjustments (including %body fat and BMI), an inverse association was observed between 25(OH)D and visceral adipose tissue (B=-6.46, 95% confidence interval, CI: -12.87, -0.04), leptin (B=-0.09, 95% confidence interval, CI: -0.14, -0.03), insulin (B=-0.21, 95%CI: -0.34, -0.07), HOMA-IR (B=-0.06, 95%CI: -0.10, -0.02), triglycerides (B=-2.44, 95%CI: -3.66, -1.22), and TNF-α (B=-0.12, 95%CI: -0.24, -0.005) only in MU individuals. Our results indicate that the association of 25(OH)D concentrations with a favorable biochemical profile (glycemic, lipidic and inflammatory) seems to depend on the individual's overall metabolic health, suggesting more benefits from higher serum vitamin D in MU individuals, regardless of their adiposity.

Component selection for exponential power mixture models

ABSTRACT Exponential Power (EP) family is a much flexible distribution family including Gaussian family as a sub-family. In this article, we study component selection and estimation for EP mixture models and regressions. The assumption on zero component mean in [X. Cao, Q. Zhao, D. Meng, Y. Chen, and Z. Xu, Robust low-rank matrix factorization under general mixture noise distributions, IEEE. Trans. Image. Process. 25 (2016), pp. 4677–4690.] is relaxed. To select components and estimate parameters simultaneously, we propose a penalized likelihood method, which can shrink mixing proportions to zero to achieve components selection. Modified EM algorithms are proposed, and the consistency of estimated component number is obtained. Simulation studies show the advantages of the proposed methods on accuracies of component number selection, parameter estimation, and density estimation. Analysis of value at risk of SHIBOR and a climate change data are given as illustration.

Sparse nonnegative tensor decomposition using proximal algorithm and inexact block coordinate descent scheme

Nonnegative tensor decomposition is a versatile tool for multiway data analysis, by which the extracted components are nonnegative and usually sparse. Nevertheless, the sparsity is only a side effect and cannot be explicitly controlled without additional regularization. In this paper, we investigated the nonnegative CANDECOMP/PARAFAC (NCP) decomposition with the sparse regularization item using l_1-norm (sparse NCP). When high sparsity is imposed, the factor matrices will contain more zero components and will not be of full column rank. Thus, the sparse NCP is prone to rank deficiency, and the algorithms of sparse NCP may not converge. In this paper, we proposed a novel model of sparse NCP with the proximal algorithm. The subproblems in the new model are strongly convex in the block coordinate descent (BCD) framework. Therefore, the new sparse NCP provides a full column rank condition and guarantees to converge to a stationary point. In addition, we proposed an inexact BCD scheme for sparse NCP, where each subproblem is updated multiple times to speed up the computation. In order to prove the effectiveness and efficiency of the sparse NCP with the proximal algorithm, we employed two optimization algorithms to solve the model, including inexact alternating nonnegative quadratic programming and inexact hierarchical alternating least squares. We evaluated the proposed sparse NCP methods by experiments on synthetic, real-world, small-scale, and large-scale tensor data. The experimental results demonstrate that our proposed algorithms can efficiently impose sparsity on factor matrices, extract meaningful sparse components, and outperform state-of-the-art methods.