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For any graph X with the adjacency matrix A , the transition matrix of the continuous-time quantum walk at time t is given by the matrix-valued function H X (t) = e i t A. We say that there is perfect state transfer in X from the vertex u to the vertex v at time τ if | H X (τ) u , v | = 1. It is an important problem to determine whether perfect state transfers can happen on a given family of graphs. In this paper we characterize all the graphs in the Johnson scheme which have this property. Indeed, we show that the Kneser graph K (2 k , k) is the only class in the scheme which admits perfect state transfers. We also show that, under some conditions, some of the unions of the graphs in the Johnson scheme admit perfect state transfer. [ABSTRACT FROM AUTHOR]

Centralized optimization methods have been widely used to manage the operation of distribution systems. However, these methods have some restrictions, such as the high computational cost, the reliance on a centralized computer system, and the lack of data privacy. To overcome these limitations, decentralized optimization methods have been proposed in recent years. Decentralized methods divide the control variables of the centralized optimization problem over several controllers, and each controller solves its own subproblem independently. This paper presents a multi-objective optimization framework for managing the operation of distribution systems. The primary objective of the proposed method is to optimize the tap positions of voltage regulators and charging and discharging powers for energy storage devices locally through a decentralized coordination process. The used objective functions take into account the voltage profile within the network, the lifetime of the devices, and the energy losses in the systems. Two decentralized methods, based on the Advanced Arithmetic Optimizer algorithm and the Profile Steering approach, are proposed to address the limitations of centralized optimization methods. The decentralized methods aim to improve the reliability and efficiency of the optimization process, while also minimizing communication and computational costs. The proposed methods are evaluated and compared to a centralized approach using the IEEE 33 and 69 bus systems. The results demonstrate that the proposed decentralized methods can effectively resolve voltage problems, minimize energy losses, and find high-quality solutions with improved computational efficiency compared to the centralized approach. • New objective function for voltage violations and asset lifetime maximization. • New objective function for minimizing energy losses and maximizing asset lifetime. • Investigation of decentralized methods for ESD operation with VRs to eliminate voltage deviations. • Investigating decentralized vs. centralized approach for optimizing objective function. • Development of AAO algorithm for MINLP with improved convergence and better solutions. [ABSTRACT FROM AUTHOR]

The use of energy storage systems (ESS) and distributed generators (DGs) to improve reliability is one of the solutions that has received much attention from researchers today. In this study, we utilize a multi-objective optimization method for optimal planning of distributed generators in electric distribution networks from the perspective of multi-objective optimization. The objective is to improve the reliability of the network while reducing the annual cost and network losses. A modified version of the multi-objective sine–cosine algorithm is used to determine the optimal size, location, and type of DGs and the optimal capacity, location, and operation strategy of the ESS. Three case studies of IEEE 33-bus, 69-bus and 141-bus test systems with Turkish DG and load data were conducted to validate the effectiveness of the proposed approach. The distribution of the Pareto front solutions and the optimal objective functions are compared with the other known algorithms. The simulation results show that the average energy not supplied and annual energy losses for the test systems are reduced by up to 68% and 64%, respectively. Moreover, the Pareto fronts of the proposed method show a better distribution and dominate those obtained by MOGWO, MOSMA, NSGA-II, MOPSO and MOEA-D according to three different Pareto optimization metrics. Finally, the computational effort result shows faster convergence of MOSCA compared to MOGWO, MOSMA, NSGA-II, MOPSO and MOEAD. • Optimal DER planning and ESS management in EDNs using a three-dimensional multiobjective optimization framework • DN Reliability improvement together with power losses and annual cost minimization. • 72 h optimization period to account the seasonal characteristics of the load and the DGs. • Real load curve and wind and solar radiation data of Turkish territory. • Multi objective sine–cosine algorithm providing better Pareto fronts according to two performance indices. [ABSTRACT FROM AUTHOR]

Abstract: A subset of the alternating group on points is intersecting if for any pair of permutations in , there is an element such that . We prove if and is intersecting, then . Also, we prove that provided that , then the only sets that meet this bound are the cosets of the stabilizer of a point of . These two results were first proven by Ku and Wong (2007), the proof given in this paper uses an algebraic method that is very different from the original proof. [Copyright &y& Elsevier]

A vertex coloring of a graph G is called distinguishing (or symmetry breaking) if no non-identity automorphism of G preserves it, and the distinguishing number, shown by D (G) , is the smallest number of colors required for such a coloring. This paper is about counting non-equivalent distinguishing colorings of graphs with k colors. A parameter, namely Φ k (G) , which is the number of non-equivalent distinguishing colorings of a graph G with at most k colors, is shown here to have an application in calculating the distinguishing number of the lexicographic product and the X -join of graphs. We study this index (and some other similar indices) which is generally difficult to calculate. Then, we show that if one knows the distinguishing threshold of a graph G , which is the smallest number of colors θ (G) so that, for k ≥ θ (G) , every k -coloring of G is distinguishing, then, in some special cases, counting the number of distinguishing colorings with k colors is very easy. We calculate θ (G) for some classes of graphs including the Kneser graph K (n , 2). We then turn to vertex partitioning by studying the distinguishing coloring partition of a graph G ; a partition of vertices of G which induces a distinguishing coloring for G. There, we introduce Ψ k (G) as the number of non-equivalent distinguishing coloring partitions with at most k cells, which is a generalization to its distinguishing coloring counterpart. [ABSTRACT FROM AUTHOR]

• The periodicity intensity factor is used for detecting the bearing degradation starting point. • The new hybrid fault – sensitive feature extraction technique is introduced using signal processing methods. • The new hybrid feature is able to detect the moment of the fault occurrence in the run-to-failure test. In this article, a new approach has been presented in which novel hybrid features are introduced to detect the time of the beginning of the bearing degradation in the run-to-failure test. At first, the ensemble empirical mode decomposition (EEMD) method and the wavelet packet decomposition (WPD) are used in signal decomposition. The conventional frequency and time domain features, the envelope harmonic-to-noise ratio (EHNR) and the recently introduced periodicity intensity factor (PIF) are utilized for constructing the features matrix. Consequently, the most sensitive feature is identified using the compensation distance evaluation technique. The results show that the hybrid features obtained by the PIF, the EEMD and WPD methods can determine the exact moment of degradation. Also, the new hybrid features are superior to the features introduced in other studies in the early fault detection. [ABSTRACT FROM AUTHOR]