The Hermitian Kirchhoff Index and Robustness of Mixed Graph

Large-scale social graph data poses significant challenges for social analytic tools to monitor and analyze social networks. The information-theoretic distance measure, namely, resistance distance, is a vital parameter for ranking influential nodes or community detection. The superiority of resistance distance and Kirchhoff index is that it can reflect the global properties of the graph fairly, and they are widely used in assessment of graph connectivity and robustness. There are various measures of network criticality which have been investigated for underlying networks, while little is known about the corresponding metrics for mixed networks. In this paper, we propose the positive walk algorithm to construct the Hermitian matrix for the mixed graph and then introduce the Hermitian resistance matrix and the Hermitian Kirchhoff index which are based on the eigenvalues and eigenvectors of the Hermitian Laplacian matrix. Meanwhile, we also propose a modified algorithm, the directed traversal algorithm, to select the edges whose removal will maximize the Hermitian Kirchhoff index in the general mixed graph. Finally, we compare the results with the algebraic connectivity to verify the superiority of the proposed strategy.

Thermal Resistance Matrix Extraction from Finite-Element Analysis for High-Frequency Magnetic Components

The thermal management of magnetic components for power electronics is crucial to ensure their reliability. However, conventional thermal models for magnetic components are known to have either poor accuracy or excessive complexity. Contrary to these models, the use of Thermal Resistance Matrices is proposed in this paper instead, which combine both accuracy and simplicity. They are usually used to characterize semiconductor devices, but not for magnetic components. The guidelines to apply Thermal Resistance Matrices for magnetic components are discussed in detail. The accuracy of this model is validated by 3D FEA simulations and experimental results, showing an absolute error lower than 5 ∘C and a relative error between −6.4% and 3.9%, which is outstanding compared to the carried-out literature review.

Practical Structural Design Approach of Multiconfiguration Planar Single-Loop Metamorphic Mechanism with a Single Actuator

As a type of multiconfiguration mechanism that can operate in an under-actuated state, metamorphic mechanisms were proposed more than two decades ago and attracted significant interest. Studies on structural synthesis of metamorphic mechanisms tend to focus more on metamorphic techniques and the structural synthesis of source mechanisms for metamorphic mechanisms. By designing different constraint architectures of metamorphic joints, multistructures can be obtained from the same source metamorphic mechanism. To determine the constraint architectures of metamorphic joints and their different assembly combinations, a kinematic status matrix and a corresponding constraint status matrix are constructed based on the metamorphic cyclogram of a source mechanism. According to the equivalent resistance gradient model and the constraint status matrix, an equivalent resistance matrix for the metamorphic joints is proposed. A structural synthesis matrix of the metamorphic mechanism is then obtained from the equivalent resistance matrix by deducing the constraint form vectors of the metamorphic joints. Furthermore, a kinematic diagram synthesis of the source metamorphic mechanism of a planar single-loop metamorphic mechanism is proposed, which is based on only the 14 one- or zero-degrees-of-freedom linkage groups. The entire structural design method of a metamorphic mechanism is based on the structural synthesis matrix and is presented as a systematic process. Finally, the proposed structural design approach is illustrated by two examples to verify its feasibility and practicality. This study provides an effective method for designing a practical multi-mobility and multiconfiguration planar single-loop metamorphic mechanism with a single actuator.

Structure Synthesis of Multi-DOF Planar Metamorphic Mechanisms With a Single Driver

This paper approaches the type synthesis of multi-degree of freedom planar metamorphic mechanisms with a single driver in a systematic process. The process is facilitated by implementing a constraint status matrix and a equivalent resistance matrix as a method for identifying an appropriate structure of planar metamorphic mechanisms with a single driver. Multi-structures can be obtained from the same source metamorphic mechanism by designing different constraint architectures of metamorphic joints. To determine the constraint architectures of metamorphic joints and their different assembly combinations, the constraint status matrix is built based on the task-based metamorphic cyclogram of a source mechanism. According to the equivalent resistance gradient model and the constraint status matrix, an equivalent resistance matrix for the metamorphic joints is proposed. A structural synthesis matrix of the metamorphic mechanism is then obtained from the equivalent resistance matrix by deducing the constraint-form vectors of the metamorphic joints. Furthermore, an effective kinematic diagram synthesis of the source mechanism of the planar metamorphic mechanism is proposed which is based only on the 14 one or zero degree-of-freedom (DOF) linkage groups. The entire structural design method of a metamorphic mechanism is based on the structural synthesis matrix and given in steps. Finally, a proposed structural design approach is illustrated by two examples.

Application of management matrix models for strategic planning of enterprise activities

The importance of strategic planning enterprise activity is substantiated in the article. Detailed analysis of the management classic matrix models strategic planning, namely the Boston Consulting Group (BCG) method, the McKinsey method, and the Arthur D. Little method. Allowed to form a system basic models of strategic analysis. Which, unlike the existing ones, is built on the systematization of well-known matrix models of “packet management” in terms of tools, level of universalism and level of application. The article proposes an advanced strategic planning process for an enterprise with the application and combination of different types, methods, matrices and models, which includes three consecutive stages of analysis and planning. The authors of the article have also formulated and summarized the characteristics of matrices that are widely used in life and, above all, in the analysis of management activities. These are the change-resistance matrix and the Control Grid. The authors prove the importance and relevance of applying matrix methods in conjunction with the Blue Ocean strategy. The main instrument of the Blue Ocean Strategy is the Strategic Canvas - to diagnose and build such a strategy. In order to build an "outline strategy" for a company, it is necessary to identify the key characteristics of the products - theirs and their competitors. Analyzing a "strategic outline" allows the company to determine how well its market strategy is similar to that of its competitors. The creation of the "blue oceans" not only contributes to the strong growth and increase profits of enterprises, this strategic step has a serious positive effect on the consolidation of the existing brand the company in creating customers.

HOW TO MEASURE THE INFLUENCE OF LANDSCAPE ON POPULATION GENETIC STRUCTURE: DEVELOPING RESISTANCE SURFACES USING A PATTERN-ORIENTED MODELING APPROACH

There are several approaches to understand how a landscape, with its several components, affects the genetic population structure by imposing resistance to gene flow. Here we propose the creation of resistance surfaces using a Pattern-Oriented Modeling approach to explain genetic differentiation, estimated by pairwise FST, among “Baruzeiro” populations (Dipteryx alata), a tree species widely distributed in Brazilian Cerrado. To establish the resistance surface, we used land use layers from the area in which the 25 “Baruzeiro” populations were sampled, generating 10000 resistance surfaces. To establish the resistance surface, we used land use layers from the area in which the 25 “Baru” populations were sampled, generating 10000 resistance surfaces. We randomized the cost values for each landscape component between 0 and 100. We use these surfaces to calculate pairwise matrices of the effective resistance among populations. Mantel test revealed a correlation of pairwise FST with a geographical distance equal to r = 0.48 (P < 0.001), whereas the Mantel correlations between pairwise FST and the generated resistance matrices ranged between r = −0.2019 and r= 0.6736. Partial regression on distance matrices was used to select the resistance matrix that provided the highest correlation with pairwise FST, based on the AIC criterion. The selected models suggest that the areas with lower resistance are characterized as natural savanna habitats of different forms, mainly arboreal dense savannas. In contrast, roads, big rivers, and agricultural lands cause higher resistance to gene flow.