Enhancing network lifespan in wireless sensor networks using deep learning based Graph Neural Network

Inadequate energy of sensors is one of the most significant challenges in the development of a reliable wireless sensor network (WSN) that can withstand the demands of growing WSN applications. Implementing a sleep-wake scheduling scheme while assigning data collection and sensing chores to a dominant group of awake sensors while all other nodes are in a sleep state seems to be a potential way for preserving the energy of these sensor nodes. When the starting energy of the nodes changes from one node to another, this issue becomes more difficult to solve. The notion of a dominant set-in graph has been used in a variety of situations. The search for the smallest dominant set in a big graph might be time-consuming. Specifically, we address two issues: first, identifying the smallest possible dominant set, and second, extending the network lifespan by saving the energy of the sensors. To overcome the first problem, we design and develop a deep learning-based Graph Neural Network (DL-GNN). The GNN training method and back-propagation approach were used to train a GNN consisting of three networks such as transition network, bias network, and output network, to determine the minimal dominant set in the created graph. As a second step, we proposed a hybrid fixed-variant search (HFVS) method that considers minimal dominant sets as input and improves overall network lifespan by swapping nodes of minimal dominating sets. We prepared simulated networks with various network configurations and modeled different WSNs as undirected graphs. To get better convergence, the different values of state vector dimensions of the input vectors are investigated. When the state vector dimension is 3 or 4, minimum dominant set is recognized with high accuracy. The paper also presents comparative analyses between the proposed HFVS algorithm and other existing algorithms for extending network lifespan and discusses the trade-offs that exist between them. Lifespan of wireless sensor network, which is based on the dominant set method, is greatly increased by the techniques we have proposed.     

Eu掺杂量对锐钛矿相TiO2电子寿命和吸收光谱影响的第一性原理研究

采用基于密度泛函理论框架下的第一性原理平面波超软赝势方法,建立了不同Eu掺杂量的锐钛矿相TiO₂超胞模型,计算了其态密度、差分电荷密度、能带结构和吸收光谱.结果发现:掺杂后Eu在TiO₂的禁带中产生杂质能级.通过对比两种不同Eu掺杂量(1.39at%和2.08at%)下的锐钛矿TiO₂的能带结构,发现掺杂量越高,杂质能级越向深能级方向移动,说明电子复合率随杂质浓度增加而增加,即电子寿命变小,同时吸收光谱红移越显著,强度越强.根据实际需要,可在锐钛矿TiO₂中适量掺杂Eu,在适当减少电子寿命情况下,使吸收光谱红移.     

REMARKS ON THE LIFESPAN FOR THE SOLUTION TO NONLINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

The authors consider the Cauchy problem for the following nonlinear wave equationswhere x ∈ R3, t ≥ 0, ε > 0 is a small parameter, and obtain the sharp bounds for the lifespan of solution to (0.1). Specially, it is proved that there exist two constants C1 and C2, which are independent of ε, then the lifespan T(ε) satisfies the folowing inequalities     

Influence of target surface degradation on the properties of r.f. magnetron‐sputtered calcium phosphate coatings

This paper reports a detailed study of how repeated r.f. magnetron sputtering from a hydroxyapatite (HA) powder target affects the nature and reproducibility of a sequential series of thin‐film coatings deposited onto Ti6Al4V substrates. An evaluation of the effective lifespan of the HA sputter targets and the reproducibility of the calcium phosphate (CaP) coatings produced from them has been made from Fourier transform infrared spectroscopy, XPS and, as appropriate, atomic force microscopy and SEM/energy dispersive x‐ray analyses. The annulus region of the target surface, from which sputtering under r.f. magnetron conditions normally occurs, showed severe surface degradation after only one deposition run, as indicated by significant PO₄^3? and OH^? depletion. This deterioration continued after each subsequent deposition cycle but to a much lesser extent than that observed in the initial sputtering period. The layers produced from all of the sputter runs contained the expected Ca²⁺ and PO₄^3? species characteristic of a CaP system but were OH^? deficient in the as‐deposited state. However, the chemical and morphological properties of the coatings did not change significantly until after the third consecutive sputter cycle. Hence, these data indicate that, even though a significant level of degradation of the HA target occurs at the outset of the sputtering procedure, the general plasma conditions employed here have a dominant influence on the coating properties until a critical degradation condition is met. As such, the compacted HA powder targets of interest can have a life‐cycle greater than single usage without detriment to the chemistry and morphology of the coatings produced from them. Copyright © 2003 John Wiley & Sons, Ltd.     

Lower bound for the lifespan of solutions for a class of fourth order wave equations

This paper deals with blow-up solutions of a class of initial–boundary value problems for a fourth order semilinear wave equation. A lower bound for the lifespan of such solutions is derived.     

A zero-inventory production and distribution problem with a fixed customer sequence

In this paper, we study the zero-inventory production and distribution problem with a single transporter and a fixed sequence of customers. The production facility has a limited production rate, and the delivery truck has non-negligible traveling times between locations. The order in which customers may receive deliveries is fixed. Each customer requests a delivery quantity and a time window for receiving the delivery. The lifespan of the product starts as soon as the production for a customer’s order is finished, which makes the product expire in a constant time. Since the production facility and the shipping truck are limited resources, not all the customers may receive the delivery within their specified time windows and/or within product lifespan. The problem is then to choose a subset of customers from the given sequence to receive the deliveries to maximize the total demand satisfied, without violating the product lifespan, the production/distribution capacity, and the delivery time window constraints. We analyze several fundamental properties of the problem and show that these properties can lead to a fast branch and bound search procedure for practical problems. A heuristic lower bound on the optimal solution is developed to accelerate the search. Empirical studies on the computational effort required by the proposed search procedure comparing to that required by CPLEX on randomly generated test cases are reported.     

The asymptotic behaviour of solutions for a class of quasilinear wave equations with cubic nonlinearity in two space dimensions

For a class of quasilinear wave equations with small initial data, first we give the lower bound of lifespan of classical solutions, then we discuss the long time asymptotic behaviour of solutions away from the blowup time. This project is supported by the Tianyuan Foundation of China and Laburay of Mathematics for Nonlinear Problems, Fudan University.     

Remark on the Lifespan of Solutions to 3-D Anisotropic Navier Stokes Equations

The goal of this article is to provide a lower bound for the lifespan of smooth solutions to 3-D anisotropic incompressible Navier-Stokes system,which in particular extends a similar type of result for the classical 3-D incompressible Navier-S tokes system.