Network partition methods for use in symbolic analysis by interpolation

A symbolic linear analyzer that integrates the analysis of both lumped and distributed networks is presented in this paper. This is achieved by implementing a consistent set of notations and a unified mathematical framework. The merits of sparse symbolic matrices are utilized to develop a complete symbolic sparse toolbox that includes all basic elements of electrical circuits. A new storage scheme called Row-Indexed Semi-Symetric (RISS) sparse is proposed and implemented for symbolic network matrices. Several existing and newly developed matrix solvers are implemented and their performances are compared. These solvers are used in the proposed symbolic solver to provide a multi-path analysis root that can be optimized for a particular problem. The overall performance of the proposed symbolic analyzer is assessed practically using several application examples. The obtained results are found in agreement with the results obtained from previously reported analyses and thus confirm validity of the adopted formula approximation method. A polynomial fitting shows that the time complexity of a variable size RC network is super-quadratic with the number of network sections. A substantial reduction in the analysis time of a large ladder RC network is demonstrated with the implementation of macromodeling techniques.KeywordsSymbolic analysissymbolic matrix storagelumped and distributed network analysisoptimal computer solution

Non-linear analysis of the heart rate variability in characterization of manic and euthymic phases of bipolar disorder

In this paper we present two numerical methods for the calculation of Gaussian field incident on a pinhole. The first method is based on Kirchhoff's Huygens aperture field method and the other on the spectrum of plane wave approach. Numerous calculations proved that Kirchhoff's Huygens method is faster and gives accurate results in the Fraunchofer region. The plane wave spectrum is the only one giving valid results ranging from the radiating aperture to, theoretically any distance, but the computational time is rapidly increasing for distances where the other method gives accurate and fast results.

A new approach to the problem of symbolic circuit analysis of large-scale circuits is presented. The methodology has been implemented in a computer program called SCAPP (symbolic circuit analysis program with partitioning). The method solves the problem by utilizing a hierarchical network approach and the sequence of expressions concept rather than a topological approach and the single expression idea which have dominated symbolic analysis in the past. The result is a linear growth in the number of terms in the symbolic solutions for the network approach versus the exponential growth exhibited by traditional methods. The analysis methodology introduces the concept of the RMNA (reduced modified nodal analysis) matrix. This allows the characterization of symbolic networks in terms of only a small subset of the network variables (external variables) rather than the complete set of variables. The analysis algorithm is most efficient when network partitioning is used. Partitioning results in a reduction in the number of terms in the symbolic solutions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nowadays, deep learning methods with high structural complexity and flexibility inevitably lean on the computational capability of the hardware. A platform with high-performance GPUs and large amounts of memory could support neural networks having large numbers of layers and kernels. However, naively pursuing high-cost hardware would probably drag the technical development of deep learning methods. In the article, we thus establish a new preprocessing method to reduce the computational complexity of the neural networks. Inspired by the band theory of solids in physics, we map the image space into a noninteraction physical system isomorphically and then treat image voxels as particle-like clusters. Then, we reconstruct the Fermi–Dirac distribution to be a correction function for the normalization of the voxel intensity and as a filter of insignificant cluster components. The filtered clusters at the circumstance can delineate the morphological heterogeneity of the image voxels. We used the BraTS 2019 datasets and the dimensional fusion U-net for the algorithmic validation, and the proposed Fermi–Dirac correction function exhibited comparable performance to other employed preprocessing methods. By comparing to the conventional z-score normalization function and the Gamma correction function, the proposed algorithm can save at least 38% of computational time cost under a low-cost hardware architecture. Even though the correction function of global histogram equalization has the lowest computational time among the employed correction functions, the proposed Fermi–Dirac correction function exhibits better capabilities of image augmentation and segmentation.

A comparison of stitching techniques to reconstruct large volume x-ray tomography of batteries

The increasing complexity, heterogeneity and unpredictability of networks make the task of managing these systems highly complex. The autonomic computing paradigm brings innovative solutions to the network management area with new adaptable and “clever” solutions which should consider a heterogeneous functionality in a wide variety of fields. One of the challenges involved in proposing autonomic solutions for QoS management consists of dealing with the inherent complexity and proposing solutions with feasible execution time. In brief, the autonomic solution effective response time should be fast enough so that it could be applied before any new important network state change. In this paper, a framework that uses self-partitioning methods is considered as the basis for evaluating a solution to the problem of dynamic LSPs setup allocation in a general MPLS network topology focusing on keeping a low complexity solution and aiming at achieving the best possible problem solution identification response time.KeywordsNetwork ManagementNetwork PartitioningSelf-sizing NetworksBandwidth AllocationAutonomic ComputingComputatio- nal ComplexityQuality of ServiceMPLSLSPs

Deep feed-forward networks, with high complexity, backpropagate the gradient of the loss function from final layers to earlier layers. As a consequence, the “gradient” may descend rapidly toward zero. This is known as the vanishing gradient phenomenon that prevents earlier layers from benefiting from further training. One of the most efficient techniques to solve this problem is using skip connection (shortcut) schemes that enable the gradient to be directly backpropagated to earlier layers. This paper investigates whether skip connections significantly affect the performance of deep neural networks of low complexity or whether their inclusion has little or no effect. The analysis was conducted using four Convolutional Neural Networks (CNNs) to predict four different multiscale basis functions for the mixed Generalized Multiscale Finite Element Method (GMsFEM). These models were applied to 249,375 samples. Three skip connection schemes were added to the base structure: Scheme 1 from the first convolutional block to the last, Scheme 2 from the middle to the last block, and Scheme 3 from the middle to the last and the second-to-last blocks. The results demonstrate that the third scheme is most effective, as it increases the coefficient of determination (R2) value by 0.0224–0.044 and decreases the Mean Squared Error (MSE) value by 0.0027–0.0058 compared to the base structure. Hence, it is concluded that enriching the last convolutional blocks with the information hidden in neighboring blocks is more effective than enriching using earlier convolutional blocks near the input layer.

In the electrical impedance imaging algorithms developed so far, the inverse problems involved are treated by using either iterative methods, which generate more accurate results but require large amounts of computation time, or non-iterative methods that are faster but produce less accurate results. In this paper, a new iterative procedure for electrical impedance imaging is presented. At each iteration step, the updated conductivity distribution is used to solve a forward problem and two-layer backpropagation neural networks with nonlinear activation functions are employed for solving an inverse problem. This allows for a smaller computation time with respect to other iterative methods and, at the same time, yields accurate images. Comparison with results obtained by applying an existing impedance tomography algorithm illustrates the efficiency of the proposed iterative method.

BackgroundInferring gene orders of ancestral genomes has the potential to provide detailed information about the recent evolution of species descended from them. Current popular tools to infer ancestral genome data (such as GRAPPA and MGR) are all parsimony-based direct optimization methods with the aim to minimize the number of evolutionary events. Recently a new method based on the approach of maximum likelihood is proposed. The current implementation of these direct optimization methods are all based on solving the median problems and achieve more accurate results than the maximum likelihood method. However, both GRAPPA and MGR are extremely time consuming under high rearrangement rates. The maximum likelihood method, on the contrary, runs much faster with less accurate results.ResultsWe propose a mixture method to optimize the inference of ancestral gene orders. This method first uses the maximum likelihood approach to identify gene adjacencies that are likely to be present in the ancestral genomes, which are then fixed in the branch-and-bound search of median calculations. This hybrid approach not only greatly speeds up the direct optimization methods, but also retains high accuracy even when the genomes are evolutionary very distant.ConclusionsOur mixture method produces more accurate ancestral genomes compared with the maximum likelihood method while the computation time is far less than that of the parsimony-based direct optimization methods. It can effectively deal with genome data of relatively high rearrangement rates which is hard for the direct optimization methods to solve in a reasonable amount of time, thus extends the range of data that can be analyzed by the existing methods.

The time dependent solution of the heat conduction equation is represented by expandingTin terms of eigenfunctions and eigenvalues (= inverse time constants). Once these are known, the time evolution ofTcan be computed readily for arbitrary heat sources. A method is presented for computing eigenfunctions and eigenvalues for a multilayer structure, where all layers have the same lateral extension and differ vertically in thickness and material parameters. Those structures are encountered in modeling IC packages and multichip modules in power electronic applications. Examples will be given for the temperature evolution calculated for the time dependent heat distribution in power converter applications. However, computation time and storage demands will be high if high spatial and temporal resolution for the temperature field is needed. Using effective time constants and functions the numerical effort can be reduced considerably

Medium-term wind power forecasting using reduced principal component analysis based random forest model

Recent methods in the literature to parallelize the traffic assignment problem consider partitioning a network into subnetworks to reduce the computation time. In this article, a partitioning method is sought that generates subnetworks minimizing the computation time of a decomposition approach for solving the traffic assignment (DSTAP). The aim is to minimize the number of boundary nodes, the interflow between subnetworks, and the computation time when the traffic assignment problem is solved in parallel on the subnetworks. Two different methods for partitioning are tested. The first is an agglomerative clustering heuristic that reduces the subnetwork boundary nodes. The second is a flow weighted spectral partitioning algorithm that uses the normalized graph Laplacian to partition the network. The performance of both algorithms is assessed on different test networks. The results indicate that the agglomerative heuristic generates subnetworks with a lower number of boundary nodes, which reduces the per iteration computation time of DSTAP. However, the partitions generated may be heavily imbalanced leading to a higher computation time when the subnetworks are solved in parallel separately at a particular DSTAP iteration. For the Austin network partitioned into four subnetworks, the agglomerative heuristic requires 3.5 times more computation time to solve the subnetworks in parallel. The results also show that the spectral partitioning method is superior for minimizing the interflow between subnetworks. This leads to a faster convergence rate of the DSTAP algorithm.

Algorithms used in the optimization of wireless deployments have computational time as one of their main drawbacks. This computational time is very dependent on the test points established to characterize a deployment scenario. The approach commonly used to define sample points is based on a regular grid, which leads to a remarkable number of sample points if accuracy is required. In this paper, a novel scenario-dependent sampling scheme based on mathematical morphology is presented. Its performance is evaluated and compared to regular sampling, outperforming typical schemes reducing computational time while maintaining very accurate results.

Translator Eccentricity Analysis in Tubular Linear Machines using Quasi-3D Finite Element Method Modeling