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Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the context of a rapidly growing data science that requires new mathematical tools for discrete data. Toward this goal, the classical theory for connection matrices has been adapted to combinatorial frameworks that facilitate computation. We develop an efficient persistence-like algorithm to compute a connection matrix from a given combinatorial (multi) vector field on a simplicial complex. This algorithm requires a single pass, improving upon a known algorithm that runs an implicit recursion executing two passes at each level. Overall, the new algorithm is more simple, direct, and efficient than the state-of-the-art. Because of the algorithm's similarity to the persistence algorithm, one may take advantage of various software optimizations from topological data analysis. [ABSTRACT FROM AUTHOR]

The hybrid dc–dc converter family has desirable features to fulfil the performance matrix requirements of point-of-load converters. However, there are no well-established methods for synthesizing single and dual-path converters addressing design specifications. The existing connection matrix-based approaches are not helpful because they give rise to nonrealizable, redundant, and degenerative solutions. Therefore, a design-oriented and low-entropy equation-based single-path hybrid converter synthesis method is proposed in this article. To this end, general structures for the single- and multi-inductor converters have been proposed. They are based on the switched-capacitor cells. Therefore, a set of guidelines have been provided in this article to decompose a voltage gain polynomial for identifying the switched-capacitor cells. Moreover, a structured method to derive and approximate a converter gain polynomial has been presented in the article. The usefulness of the proposed method is validated by synthesizing a converter for a selected application and verifying its operation using experimental results. [ABSTRACT FROM AUTHOR]

Electrical substations are critical elements of a power grid, enabling the transmission and distribution of electric power from power generators to the end‐users. Experiences from previous earthquakes have shown that electrical substations can be damaged due to ground shaking, reducing their functionality and potentially preventing the generated electric power from reaching end‐users. To assess the seismic vulnerability of a substation, a modular quantitative assessment method is proposed. In this method, the relation between the functionality state of a substation and the damage state of its components was established through the connection matrix technique. A substation is viewed as a network system, whose topology is defined by the connections among various pieces of electrical equipment (i.e., the components), represented in the connection matrix. The maximum allowable power transmission capacity of the substation after an earthquake is adopted as the system functionality metric, which is jointly determined by the power input, transform, and output capacity of the substation. The seismic vulnerability of an electrical substation is quantified by probabilistically calculating its postearthquake functionality when exposed to various earthquake intensities using Monte Carlo sampling. Finally, the risk of substation functionality loss is quantified by integrating the seismic hazard curve with the seismic vulnerability model of the substation. Two realistic case studies on a distribution substation and a transmission substation, with the same equipment configuration but different power delivery paths, were performed using the proposed method. Furthermore, a sensitivity analysis regarding the equipment fragility parameters is conducted, providing a risk‐informed basis for improving the seismic performance of the substation system. [ABSTRACT FROM AUTHOR]

To enhance the reliability of converters, many fault-tolerant converters have been proposed in the literature. However, the design rule is seldom proposed. The converter is usually a switch circuit that can be described by the matrix; therefore, the design of a fault-tolerant converter can be transformed to the matrix design. The fault tolerance of a circuit is mainly determined by its alternative loops. In this study, minus-1 Boolean determinant is defined to establish a relationship between the matrix and the alternative loop. Then, the following proposition is proven: for a connection matrix of a circuit, the minus-1 Boolean determinant represents the sum of loops in the circuit, where each term of the minus-1 Boolean determinant represents a loop of the circuit. The asymmetric half bridge converter is the most commonly used converter of the switched reluctance motor (SRM). According to its connection matrix, its candidate fault-tolerant converters are listed, and with the proposition, their alternative loops are obtained, their fault tolerance performance is evaluated, and the optimal one is selected. Furthermore, the fault tolerance performance of the derived converter is tested by simulations and experiments on a 12/8 SRM. [ABSTRACT FROM AUTHOR]

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A mathematical model is established using the space coordinates of nodes and vector matrix of components to study the construction method and lightweight nature of single-layer tensegrity structures on the basis of their geometric parameters. Connection matrix and configuration of the single-layer tensegrity structures are built using MATLAB software. The force balance equations of nodes of a three-bar tensegrity structure are established by introducing the force–density method, and the force–density relationship amongst the components is analysed. Thus, the configuration principle of single-layer tensegrity structure is verified. The force–density relationship between the components in the single-layer tensegrity structure is obtained. The change rule of the force–density relationship in different single-layer tensegrity structures is also analysed. Notably, p-1 stable configurations are present in the p-bar tensegrity structure. The force–density relationships of these p-1 configurations are in symmetrical distribution, that is, the j-th and (p-j)th configurations have the same force–density relationship. The lightweight nature of the structure is studied using the force–density relationship between the components, and the optimal structural parameter relationship is obtained when the structure has the lightest mass.

The aim of this paper is to find the reasons for traffic congestion problem and its solution using Neutrosophic Cognitive Maps (NCMs) and Fuzzy Cognitive Maps (FCMs). Fuzzy theory only measures the grade of membership but fuzzy theory has failed to characteristic the perception when the relations between concepts in problems are indeterminate. Addition of concepts of indeterminate situation with fuzzy logic forms the neutrosophic logic. Since, some of the reasons for traffic congestions are indeterminate we use Neutrosophic Cognitive Maps to find a solution. The discussion is based on Indian road scenario. [ABSTRACT FROM AUTHOR]

Jacobi polynomials are frequently used in scientific and engineering applications, and often times, one needs to use the so-called Jacobi-Jacobi transforms which are transforms between two Jacobi expansions with different indices. In this paper, we develop a fast structured algorithm for Jacobi-Jacobi transforms. The algorithm is based on two main ingredients. (i) Derive explicit formulas for connection matrices of two Jacobi expansions with arbitrary indices. In particular, if the indices have integer differences, the connection matrices are relatively sparse or highly structured. The benefit of simultaneous promotion or demotion of the indices is shown. (ii) If the indices have non-integer differences, we explore analytically or numerically a low-rank property hidden in the connection matrices. Combining these two ingredients, we develop a fast structured Jacobi-Jacobi transform with nearly linear complexity, after a one-time precomputation with quadratic complexity, between coefficients of two Jacobi expansions with arbitrary indices. An important byproduct of the fast Jacobi-Jacobi transform is the fast Jacobi transform between the function values at a set of Chebyshev-Gauss-type points and coefficients of the Jacobi expansion with arbitrary indices. Ample numerical results are presented to illustrate the computational efficiency and accuracy of our algorithm. [ABSTRACT FROM AUTHOR]

Method for the analysis of the recyclability of building structures This publication introduces a method to analyse the ability of structures to be recycled. It has the objective to develop the recyclability of structures at the beginning and to secure this ability till the end of the life cycle. Structural compositions are described by recycling graphs. The components represent on the one hand material elements and on the other hand the connections between them. Materials are classified in terms of their recyclability, their ability to be incinerated and the harmfulness of their deposition. The connections are evaluated regarding their ability to be disassembled and the compatibility of the materials connected. The structures are translated into connection matrixes and the aspects of the evaluation are assessed individually and in combination. They are classified regarding their ability to be recycled (modularity and compatibility of materials). Further evaluation aspects are discussed for the potential extension of the method. The method has been implemented in a prototype of a modelling environment and is demonstrated and described for the analysis of four wall structures relevant to praxis. [ABSTRACT FROM AUTHOR]