Small-World Networks with Unitary Cayley Graphs for Various Energy Generation

Complex networks have been a prominent topic of research for several years,spanning a wide range of fields from mathematics to computer science and also to social and biological sciences.The eigenvalues of the Seidel matrix,Seidel Signless Laplacian matrix,Seidel energy,Seidel Signless Laplacian energy,Maximum and Minimum energy,Degree Sum energy and Distance Degree energy of the Unitary Cayley graphs[UCG]have been calculated.Low-power devices must be able to transfer data across long distances with low delay and reliability.To overcome this drawback a small-world network depending on the unitary Cayley graph is proposed to decrease the delay and increase the reliability and is also used to create and analyze network communication.Small-world networks based on the Cayley graph have a basic construction and are highly adaptable.The simulation result shows that the small-world network based on unitary Cayley graphs has a shorter delay and is more reliable.Furthermore,the maximum delay is lowered by 40%.

The Laplacian Energy of Hesitancy Fuzzy Graphs in Decision-Making Problems

Decision-making(DM)is a process in which several persons concur-rently engage,examine the problems,evaluate potential alternatives,and select an appropriate option to the problem.Technique for determining order preference by similarity to the ideal solution(TOPSIS)is an established DM process.The objective of this report happens to broaden the approach of TOPSIS to solve the DM issues designed with Hesitancy fuzzy data,in which evaluation evidence given by the experts on possible solutions is presents as Hesitancy fuzzy decision matrices,each of which is defined by Hesitancy fuzzy numbers.Findings:we represent analytical results,such as designing a satellite communication network and assessing reservoir operation methods,to demonstrate that our suggested thoughts may be used in DM.Aim:We studied a new testing method for the arti-ficial communication system to give proof of the future construction of satellite earth stations.We aim to identify the best one from the different testing places.We are alsofinding the best operation schemes in the reservoir.In this article,we present the concepts of Laplacian energy(LE)in Hesitancy fuzzy graphs(HFGs),the weight function of LE of HFGs,and the TOPSIS method technique is used to produce the hesitancy fuzzy weighted-average(HFWA).Also,consider practical examples to illustrate the applicability of thefinest design of satellite communication systems and also evaluation of reservoir schemes.

Directed Acyclic Graph Blockchain for Secure Spectrum Sharing and Energy Trading in Power IoT

Peer-to-peer(P2P)spectrum sharing and energy trading are promising solutions to locally satisfy spectrum and energy demands in power Internet of Things(IoT).However,implementation of largescale P2P spectrum sharing and energy trading confronts security and privacy challenges.In this paper,we exploit consortium blockchain and Directed Acyclic Graph(DAG)to propose a new secure and distributed spectrum sharing and energy trading framework in power IoT,named spectrum-energy chain,where a set of local aggregators(LAGs)cooperatively confirm the identity of the power devices by utilizing consortium blockchain,so as to form a main chain.Then,the local power devices verify spectrum and energy micro-transactions simultaneously but asynchronously to form local spectrum tangle and local energy tangle,respectively.Moreover,an iterative double auction based micro transactions scheme is designed to solve the spectrum and energy pricing and the amount of shared spectrum and energy among power devices.Security analysis and numerical results illustrate that the developed spectrum-energy chain and the designed iterative double auction based microtransactions scheme are secure and efficient for spectrum sharing and energy trading in power IoT.

NeurstrucEnergy:A bi-directional GNN model for energy prediction of neural networks in IoT

A significant demand rises for energy-efficient deep neural networks to support power-limited embedding devices with successful deep learning applications in IoT and edge computing fields.An accurate energy prediction approach is critical to provide measurement and lead optimization direction.However,the current energy prediction approaches lack accuracy and generalization ability due to the lack of research on the neural network structure and the excessive reliance on customized training dataset.This paper presents a novel energy prediction model,NeurstrucEnergy.NeurstrucEnergy treats neural networks as directed graphs and applies a bi-directional graph neural network training on a randomly generated dataset to extract structural features for energy prediction.NeurstrucEnergy has advantages over linear approaches because the bi-directional graph neural network collects structural features from each layer's parents and children.Experimental results show that NeurstrucEnergy establishes state-of-the-art results with mean absolute percentage error of 2.60%.We also evaluate NeurstrucEnergy in a randomly generated dataset,achieving the mean absolute percentage error of 4.83%over 10 typical convolutional neural networks in recent years and 7 efficient convolutional neural networks created by neural architecture search.Our code is available at https://github.com/NEUSoftGreenAI/NeurstrucEnergy.git.

Energy Economic Dispatch for Photovoltaic-Storage via Distributed Event-Triggered Surplus Algorithm

This paper presents a novel approach to economic dispatch in smart grids equipped with diverse energy devices.This method integrates features including photovoltaic(PV)systems,energy storage coupling,varied energy roles,and energy supply and demand dynamics.The systemmodel is developed by considering energy devices as versatile units capable of fulfilling various functionalities and playing multiple roles simultaneously.To strike a balance between optimality and feasibility,renewable energy resources are modeled with considerations for forecasting errors,Gaussian distribution,and penalty factors.Furthermore,this study introduces a distributed event-triggered surplus algorithm designed to address the economic dispatch problem by minimizing production costs.Rooted in surplus theory and finite time projection,the algorithm effectively rectifies network imbalances caused by directed graphs and addresses local inequality constraints.The algorithm greatly reduces the communication burden through event triggering mechanism.Finally,both theoretical proofs and numerical simulations verify the convergence and event-triggered nature of the algorithm.

The Energy and Operations of Graphs

Let G be a finite and undirected simple graph on n vertices, A(G) is the adjacency matrix of G, λ1,λ2,...,λn are eigenvalues of A(G), then the energy of G is . In this paper, we determine the energy of graphs obtained from a graph by other unary operations, or graphs obtained from two graphs by other binary operations. In terms of binary operation, we prove that the energy of product graphs is equal to the product of the energy of graphs G1 and G2, and give the computational formulas of the energy of Corona graph , join graph of two regular graphs G and H, respectively. In terms of unary operation, we give the computational formulas of the energy of the duplication graph DmG, the line graph L(G), the subdivision graph S(G), and the total graph T(G) of a regular graph G, respectively. In particularly, we obtained a lot of graphs pair of equienergetic.

The Distance Energy of Circulant Graphs

For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. In this note, we establish lower bounds for the distance energy of circulant graphs. In particular, we discuss upper bound of distance energy for the 4-circulant graph.

A Graph Theoretical Interpretation of Different Types of Energies of Elementary Particles, Atoms and Molecules

The present work illustrates a predictive method, based on graph theory, for different types of energy of subatomic particles, atoms and molecules, to be specific, the mass defect of the first thirteen elements of the periodic table, the rotational and vibrational energies of simple molecules (such as , H2, FH and CO) as well as the electronic energy of both atoms and molecules (conjugated alkenes). It is shown that such a diverse group of energies can be expressed as a function of few simple graph-theoretical descriptors, resulting from assigning graphs to every wave function. Since these descriptors are closely related to the topology of the graph, it makes sense to wonder about the meaning of such relation between energy and topology and suggests points of view helping to formulate novel hypotheses about this relation.

A Graph-Theoretical Approach to Calculate Vibrational Energies of Atomic and Subatomic Systems

One of the challenges still pending in string theory and other particle physics related fields is the accurate prediction of the masses of the elementary particles defined in the standard model. In this paper an original algorithm to assign graphs to each of these particles is proposed. Based on this mapping, we demonstrate that certain indices associated with the topology of the graph (graph theoretical indices) are very effective in predicting the masses of the particles. Specifically, the spectral moments of the graph adjacency matrix weighted by edge degrees play a key role in the excellent correlations found. Moreover, the same topological pattern is found in other well known quantum systems such as the particle in a box and the vibrational frequencies of diatomic molecules, such as hydrogen. The results shown here open a suggestive pathway for the use of graph-theoretical approaches in predicting properties of elementary particles and other physical systems, which seem to match similar topological patterns.

How graph features decipher the soot assisted pigmental energy transport in leaves?A laser-assisted thermal lens study in nanobiophotonics

The paper employs the principles of graph theory in nanobiophotonics, where the soot-assisted intra-pigmental energy transport in leaves is unveiled through the laser-induced thermal lens(TL) technique. Nanofluids with different soot concentrations are sprayed over Lablab purpureus(L) sweet leaves, and the extracted pigments are analyzed. The graph features of the constructed complex network from the TL signal of the samples are analyzed to understand their variations with optical absorbance. Besides revealing the presence of optimum soot concentration that can enhance photosynthesis,the study brings out the potential application of graph features in nanobiophotonics.

Ordering of Unicyclic Graphs with Perfect Matchings by Minimal Matching Energies

In 2012, Gutman and Wagner proposed the concept of the matching energy of a graph and pointed out that its chemical applications can go back to the 1970s. The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. Let u and v be the non-isolated vertices of the graphs G and H with the same order, respectively. Let wi?be a non-isolated vertex of graph Gi?where i=1, 2, …, k. We use Gu(k)?(respectively, Hv(k)) to denote the graph which is the coalescence of G (respectively, H) and G1, G2,…, Gk?by identifying the vertices u (respectively, v) and w1, w2,…, wk. In this paper, we first present a new technique of directly comparing the matching energies of Gu(k)?and Hv(k), which can tackle some quasi-order incomparable problems. As the applications of the technique, then we can determine the unicyclic graphs with perfect matchings of order 2n with the first to the ninth smallest matching energies for all n≥211.

On the Non-Common Neighbourhood Energy of Graphs

In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ,?,?NCN-energy for some standard graphs is obtained and an upper bound for ?is found when G is a strongly regular graph. Also the relation between common neigh-bourhood energy and non-common neighbourhood energy of a graph is established.

On the Spectral Properties of Graphs with Rank 4

Let G be a graph and A(G) the adjacency matrix of G. The spectrum of G is the eigenvalues together with their multiplicities of A(G). Chang et al. (2011) characterized the structures of all graphs with rank 4. Monsalve and Rada (2021) gave the bound of spectral radius of all graphs with rank 4. Based on these results as above, we further investigate the spectral properties of graphs with rank 4. And we give the expressions of the spectral radius and energy of all graphs with rank 4. In particular, we show that some graphs with rank 4 are determined by their spectra.

Judicious training pattern for superior molecular reorganization energy prediction model

Reorganization energy(RE)is closely related to the charge transport properties and is one of the important parameters for screening novel organic semiconductors(OSCs).With the rise of data-driven technology,accurate and efficient machine learning(ML)models for high-throughput screening novel organic molecules play an important role in the boom of material science.Comparing different molecular descriptors and algorithms,we construct a reasonable algorithm framework with molecular graphs to describe the compositional structure,convolutional neural networks to extract material features,and subsequently embedded fully connected neural networks to establish the mapping between features and predicted properties.With our well-designed judicious training pattern about feature-guided stratified random sampling,we have obtained a high-precision and robust reorganization energy prediction model,which can be used as one of the important descriptors for rapid screening potential OSCs.The root-meansquare error(RMSE)and the squared Pearson correlation coefficient(R^(2))of this model are 2.6 me V and0.99,respectively.More importantly,we confirm and emphasize that training pattern plays a crucial role in constructing supreme ML models.We are calling for more attention to designing innovative judicious training patterns in addition to high-quality databases,efficient material feature engineering and algorithm framework construction.

Laplacian Energies of Regular Graph Transformations

Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,+,-}. Some Laplacian equienergetic pairs of G^(xyz) for r = 2 and x,y,z∈{0,1, +,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.

The Correlation Coefficient of Hesitancy Fuzzy Graphs in Decision Making

The hesitancy fuzzy graphs(HFGs),an extension of fuzzy graphs,are useful tools for dealing with ambiguity and uncertainty in issues involving decision-making(DM).This research implements a correlation coefficient measure(CCM)to assess the strength of the association between HFGs in this article since CCMs have a high capacity to process and interpret data.The CCM that is proposed between the HFGs has better qualities than the existing ones.It lowers restrictions on the hesitant fuzzy elements’length and may be used to establish whether the HFGs are connected negatively or favorably.Additionally,a CCMbased attribute DM approach is built into a hesitant fuzzy environment.This article suggests the use of weighted correlation coefficient measures(WCCMs)using the CCM concept to quantify the correlation between two HFGs.The decisionmaking problems of hesitancy fuzzy preference relations(HFPRs)are considered.This research proposes a new technique for assessing the relative weights of experts based on the uncertainty of HFPRs and the correlation coefficient degree of each HFPR.This paper determines the ranking order of all alternatives and the best one by using the CCMs between each option and the ideal choice.In the meantime,the appropriate example is given to demonstrate the viability of the new strategies.

Photovoltaic energy balance estimation based on the building integration level

The photovoltaic module building integration level affects the module temperature and,consequently,its output power.In this work,a methodology has been proposed to estimate the influence of the level of architectural photovoltaic integration on the photovoltaic energy balance with natural ventilation or with forced cooling systems.The developed methodology is applied for five photovoltaic module technologies(m⁃Si,p⁃Si,a⁃Si,CdTe,and CIGS)on four characteristic locations(Athens,Davos,Stockholm,and Würzburg).To this end,a photovoltaic module thermal radiation parameter,PVj,is introduced in the characterization of the PV module technology,rendering the correlations suitable for building⁃integrated photovoltaic(BIPV)applications,with natural ventilation or with forced cooling systems.The results show that PVj has a significant influence on the energy balances,according to the architectural photovoltaic integration and climatic conditions.Keywords:Photovoltaic cooling;BIPV;Photovoltaic;Ventilation;Photovoltaic integration level in building【OA】(2)Graph⁃Based methodology for Multi⁃Scale generation of energy analysis models from IFC,by Asier Mediavilla,Peru Elguezabal,Natalia Lasarte,Article 112795 Abstract:Process digitalisation and automation is unstoppable in all industries,including construction.However,its widespread adoption,even for non⁃experts,demands easy⁃to⁃use tools that reduce technical requirements.BIM to BEM(Building Energy Models)workflows are a clear example,where ad⁃hoc prepared models are needed.This paper describes a methodology,based on graph techniques,to automate it by highly reducing the input BIM requirements found in similar approaches,being applicable to almost any IFC.This is especially relevant in retrofitting,where reality capture tools(e.g.,3D laser scanning,object recognition in drawings)are prone to create geometry clashes and other inconsistencies,posing higher challenges for automation.Another innovation presented is its multi⁃scale nature,efficiently addressing the surroundings impact in the energy model.The application to selected test cases has been successful and further tests are ongoing,considering a higher variety of BIM models in relation to tools and techniques used and model sizes.

压缩感知和图卷积神经网络相结合的宽频振荡扰动源定位方法

新能源并网引发的宽频振荡严重威胁电网安全,实现宽频振荡源的在线定位并及时采取抑制措施以保证系统安全稳定尤为必要。为此,提出一种压缩采样和图卷积神经网络相结合的宽频振荡源定位方法,该方法首先在子站对时序的振荡信号进行稀疏采样,获得其低维观测序列,作为节点的时序信息,然后在主站融合系统的拓扑结构捕捉各节点的邻接关系,综合考虑系统振荡的时空特性,运用图卷积神经网络实现振荡源定位。最后利用宽频振荡样本集进行仿真验证,结果表明所提方法在量测数据含有噪声、传输数据缺失以及传输数据偏差的情况下都有较高的定位准确度。

基于自适应图卷积和注意力池化的点云分类与分割

针对现有点云分类与分割方法使用最大池化聚合局部邻域特征,导致最大值以外的重要信息丢失的缺陷,提出一种结合自适应图卷积AdaptConv和注意力池化AP的点云分类与分割网络。首先,采用K近邻算法构建点云局部图结构,根据点的特征生成自适应卷积核,灵活精确地捕获点云的局部邻域特征;其次,为有效提高特征聚合能力,采用注意力池化定义能量函数得到权重值,加权并聚合出更具代表性的点云局部特征;最后,堆叠自适应图卷积和注意力池化逐层提取全局特征,提高网络的分类和分割精度。实验结果表明,相较基准方法,点云分类的平均类别精度提升0.9%,部件分割和语义分割的平均交并比分别提升0.8%和0.3%,证明所提方法可有效提升点云分类与分割的准确率,具有较高的鲁棒性。

考虑新能源随机性的新型电力系统图深度学习稳定指标概率分布评估模型

新型电力系统的新能源大规模随机性出力特点导致目前在线暂态稳定扫描结论面临失效风险,这一问题从元件建模精度、系统拓扑适应性和计算速度三个方面同时对现有方法提出挑战。因此提出了基于重概率化改进的置信带方法和图深度学习的稳定指标概率分布及置信带评估模型,通过图深度学习模型快速评估少量采样点,再由重概率化置信带方法扩增结果,利用标签共现知识引导时域仿真对准确率进行增强,最后使用置信带方法给出随机出力下的稳定概率分布和区间形式的评估结论。该方法优点在于利用了图深度学习的拓扑适应能力和快速计算特点,且不受元件建模精度限制,置信带计算结论具有可靠的理论背景,能够评估稳定概率分布。在IEEE-39和IEEE-300节点系统上的评估精度验证表明,所提方法能够高精度地预测指定方式暂态稳定指标,并给出可靠的概率评估结论。