Computing

Some nonlinear methods for solving single ordinary differiential equations are generalized to solve systems of equations. To perform this, a new vector product, compatible with the Samelson inverse of a vector, is defined. Conditions for a given order are derived.

Piecewise cubic polynomial spline interpolation [3] or smoothing [4] often gives undesirable inflexion points. We describe a spline interpolation method that allows to avoid these inflexion points and contains cubic splines as special case. The method is a generalization of the work in [2]. The proof of the theorem motivating the use of exponential splines is simplified. An ALGOL procedure is presented that allows to mix piecewise cubic and exponential spline interpolation suitably.

The solution of Schrödinger's equation leads to a high number N of independent variables. Furthermore, the restriction to (anti)symmetric functions implies some complications. We propose a sparse-grid approximation which leads to a set of non-orthogonal basis. Due to the antisymmetry, scalar products are expressed by sums of N×N-determinants. Because of the sparsity of the sparse-grid approximation, these determinants can be reduced from N×N to a much smaller size K×K. The sums over all permutations reduce to the quantities det K (α1,…,α K ):=∑≤i 1,i 2,…,i K ≤Ndet(a iα ,i β (αβ))α,β=1,…, K to be determined, where a i , j (αβ) are certain one-dimensional scalar products involving (sparse-grid) basis functions ϕαβ. We propose a method to evaluate this expression such that the asymptotics of the computational cost with respect to N is O(N 3) for fixed K, while the storage requirements increase only with the factor N 2. Furthermore, we describe a parallel version (N processors) with full speed up.

New opportunities have been created for the management of critical situations utilizing the Internet of Things (IoT). However, one of the difficulties in providing services for critical situation management using IoT is that access will often be needed by users at the critical events, where access to data and resources is usually restricted by means of their normal roles. In Role-Based Access Control, these roles are organized in static hierarchies and users are authorized to play such roles in order to exercise their organizational functions. However, some of these roles cannot be organized in the same way in static hierarchies as the authorizations granted to such roles directly correspond to the dynamic contextual conditions (e.g., body sensors data). Users need to satisfy these conditions to exercise the functions of such dynamic contextual roles. These dynamic conditions can be effectively derived from the IoT devices in order to manage the critical situations. However, a large number of static roles and contextual conditions has led to the high administrative and processing overheads. In this paper, we present a formal approach to CAAC for dynamically specifying the contextual roles based on the relevant contextual conditions derived from information provided through IoT. We also introduce an ontology-based approach which models the dynamic contextual roles and its associated access control policies. We demonstrate the feasibility of our proposal by providing a walkthrough of the whole mechanism. We also carry out an experimental study on the performance of our approach compared to our previous approach.

In dieser Arbeit werden die quasilinearen RäumeQ mit dimQ≤2 charakterisiert und dadurch eine Sonderstellung, des quasilinearen Raumes I(R), des Raumes der kompakten Intervalle überR, aufgezeigt.

In wireless sensor networks (WSNs), balancing energy consumption is always a critical problem. Multi-hop data transmission may cause the nodes around the static sink to exhaust energy prematurely. It can be avoided by introducing the mobile sink (MS) in WSNs. The MS only needs to visit some specific nodes, such as cluster heads (CHs) in the clustering network, to collect data. In this paper, we propose an energy-adaptive clustering method based on Taguchi-based-GWO optimizer (EACM-TGWO). Different from the existing clustering protocols, we develop the optimal number of CHs according to the characteristic of energy consumption in MS-based WSNs. Afterwards, the fitness function is established by combining the residual energy and the average distance within clusters to select CHs. Meanwhile, an adaptive weight factor is introduced to dynamically tune the influence degree of the two factors on the clustering results. Furthermore, a novel meta-heuristic algorithm Taguchi-based grey wolf optimizer (TGWO) is used to search for the optimal CHs set. Compared with grey wolf optimizer (GWO) and some of its improved versions, TGWO is more excellent tested in CEC2017. We also make an elaborate comparison of EACM-TGWO with LEACH-C, EACM-GWO, MSECA, and GAOC. The simulation results indicate that EACM-TGWO is more powerful in terms of balancing energy consumption and saving network energy.

This paper presents methods for the time-oriented evaluation of special GERT networks. If every node of a GERT network has an exclusive-or entrance and a stochastic exit (so-called STEOR node), then a Markov renewal process can be assigned to this activity network. In this case, the quantities of interest in project scheduling may be determined from the renewal functions of the process. In addition, GERT networks containing “non-STEOR nodes” are treated where the non-STEOR nodes are allowed to occur only within special subnetworks, called basic element structures. Numerical tests have shown that in most cases the methods described consume less computing time than simulation.

The spectral portrait of a matrix is the picture of its ɛ-spectra forε ∈[ε 1,ε 2], where an ɛ-spectrum ofA is the union of all the eigenvalues of all the matricesA+Δ with ∥Δ∥2≤ε∥A∥2. The spectral portrait is, for example, useful to study the stability of various problems, or, as we illustrate in this paper, to visualize the condition number of an eigenvalue. Some methods to estimate the spectral portrait already exist, but only for small matrices. We propose here a new algorithm for non hermitian large sparse matrices.

As many engineering optimization problems are rather complicated, it is usually necessary to search the optimal solution in a complex and huge search space. When faced with these large-scale problems, conventional optimization algorithms need to traverse the entire search space and it is impossible for them to finish the search within polynomial time. Moreover, it can’t meet requirements in terms of computation velocity, convergence and sensitivity to initial value. So, it is very difficult to apply them to engineering optimization problems. Swarm intelligence methods simulate the collective behaviors of social creatures in the nature and they come from the relationship between the community formed by simple individuals and the environment as well as the interactions between the individuals. A single individual can only perform simple tasks, but the population formed by single individuals can fulfill complex tasks. Such intelligence presented by such population is called swarm intelligence. Due to the limitations of existing optimization algorithms, it is usually impractical to obtain excellent computational performance with only one optimization algorithm. In consideration of the jumping property of simulated annealing, it is not easy to get trapped into local minimum and it has strong local search capability near the optimal value and fast convergence velocity. This paper combines it with particle swarm optimization, proposes a cooperative particle swarm optimization with constriction factor based on simulated annealing (SA-CPSO), offers guidelines on selection of related parameters and dynamically adjusts the particle velocity according to its movement track. In this way, it improves the convergence velocity of the algorithm by improving the spatial search ability of the particle so as to make the particle accept the solution which makes the fitness of the objective function “better” as well as the solution that makes the said fitness “worse” at a certain probability during the flight of the particle. The experiment shows that the SA-CPSO improves the diversity of the particle and enhances its ability to get rid of locally optimal solutions. So, SA-CPSO is not easy to be trapped into local optimum and it has stronger ability of global optimization, a faster convergence velocity and higher convergence accuracy.