Exponentially Fitted Element-Free Galerkin Approach for Nonlinear Singularly Perturbed Problems

As it is well recognized that conventional numerical schemes are inefficient in approximating the solutions of the singularly perturbed problems (SPP) in the boundary layer region, in the present work, an effort has been made to propose a robust and efficient numerical approach known as element-free Galerkin (EFG) technique to capture these solutions with a high precision of accuracy. Since a lot of weight functions exist in the literature which plays a crucial role in the moving least square (MLS) approximations for generating the shape functions and hence affect the accuracy of the numerical solution, in the present work, due emphasis has been given to propose a robust weight function for the element-free Galerkin scheme for SPP. The key feature of nonrequirement of elements or node connectivity of the EFG method has also been utilized by proposing a way to generate nonuniformly distributed nodes. In order to verify the computational consistency and robustness of the proposed scheme, a variety of linear and nonlinear numerical examples have been considered and L ∞ errors have been presented. Comparison of the EFG solutions with those available in the literature depicts the superiority of the proposed scheme.

Inside Information: Systematic within-node connectivity changes observed across tasks or groups

Mapping the human connectome and understanding its relationship to brain function holds tremendous clinical potential. The connectome has two fundamental components: the nodes and the connections between them. While much attention has been given to deriving atlases and measuring the connections between nodes, there have been no studies examining the networks within nodes. Here we demonstrate that each node contains significant connectivity information, that varies systematically across task-induced states and subjects, such that measures based on these variations can be used to classify tasks and identify subjects. The results are not specific for any particular atlas but hold across different atlas resolutions. To date, studies examining changes in connectivity have focused on edge changes and assumed there is no useful information within nodes. Our findings illustrate that for typical atlases, within-node changes can be significant and may account for a substantial fraction of the variance currently attributed to edge changes.

Hybrid Genetic Algorithm With Haar Wavelet for Maximum Target Coverage Node Deployment in Wireless Sensor Networks

Wireless sensor networks (WSNs) are used in industrial applications and focused on target coverage and node connectivity based WSNs. The set of sensors and targets is placed in optimal position the target coverage and node connectivity achieving maximum with limited senor nodes. To resolve this problem, the proposed hybrid genetic algorithm combined with lifting wavelet multi-resolution principles for recognizing optimal position for sensors to cover entire targets present in the fields. The hybrid genetic algorithm randomly identifies each sensor position and 2D Haar lifting wavelet transform to improve the quality of target coverage by adjusting node position. The 2D Haar lifting decomposes the population matrix into the optimal position of sensors. Experimental results show the performance of the proposed hybrid genetic algorithm and fast local search method compared with available algorithms improves the target coverage and the number of nodes with varying and fixed sensing ranges with a different region.

Quantitative effects of network connectivity on epidemics

Epidemics are affected by the connectivity of nodes in networks in addition to the cooperation of infection transmission. We investigate quantitatively the effects of node connectivity on transmission dynamics by comparing epidemic diffusion in null models with gradual connection strength. Results show that: (1) the inhomogeneity of network connectivity accelerates the spreading of epidemics, this phenomenon is more significant in the early stage of propagation; (2) the enhancement of connectivity of homogenous nodes restrains epidemic spreading, and the spreading speed correlates negatively with connection strength; (3) the spreading speed of epidemics does not change linearly with the strength of rich-club property, which means that the connectivity among hub nodes does not appreciably affect disease diffusion.

Efficient computation of optimal temporal walks under waiting-time constraints

Node connectivity plays a central role in temporal network analysis. We provide a broad study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but arc sets changing over time. Taking into account the temporal aspect leads to a rich set of optimization criteria for “shortest” walks. Extending and broadening state-of-the-art work of Wu et al. [IEEE TKDE 2016], we provide an algorithm for computing shortest walks that is capable to deal with various optimization criteria and any linear combination of these. It runs in O(|V|+|E|log|E|) time where |V| is the number of vertices and |E| is the number of time-arcs. A central distinguishing factor to Wu et al.’s work is that our model allows to, motivated by real-world applications, respect waiting-time constraints for vertices, that is, the minimum and maximum waiting time allowed in intermediate vertices of a walk. Moreover, other than Wu et al. our algorithm also allows to search for walks that pass multiple subsequent time-arcs in one time step, and it can deal with a richer set of optimization criteria. Our experimental studies indicate that our richer modeling can be achieved without significantly worsening the running time when compared to Wu et al.’s algorithms.

Network Structures of Symptoms From the Zung Depression Scale

The Self-rating Depression Scale (SDS) is a psychometric tool composed of 20 items used to assess depression symptoms. The aim of this work is to perform a network analysis of this scale in a large sample composed of 1090 French-speaking Belgian university students. We estimated a regularized partial correlation network and a Directed Acyclic Graph for the 20 items of the questionnaire. Node predictability (shared variance with surrounding nodes in the network) was used to assess the connectivity of items. The network comparison test was performed to compare networks from female and male students. The network composed of items from the SDS is overall positively connected, although node connectivity varies. Item 11 (“My mind is as clear as it used to be”) is the most interconnected item. Networks from female and male students did not differ. DAG reported directed edges among items. Network analysis is a useful tool to explore depression symptoms and offers new insight as to how they interact. Further studies may endeavor to replicate our findings in different samples, including clinical samples to replicate the network structures and determine possible viable targets for clinical intervention.

Network structures of symptoms from the Zung Depression Scale

The Self-rating Depression Scale (SDS) is a psychometric tool composed of 20 items used to assess depression symptoms. The aim of this work is to perform a network analysis of this scale in a large sample composed of 1090 French-speaking Belgian university students. We estimated a regularized partial correlation network and a Directed Acyclic Graph for the 20 items of the questionnaire. Node predictability (shared variance with surrounding nodes in the network) was used to assess the connectivity of items. The network comparison test was performed to compare networks from female and male students. The network composed of items from the SDS is overall positively connected, although node connectivity varies. Item 11 (“My mind is as clear as it used to be”) is the most interconnected item. Networks from female and male students did not differ. DAG reported directed edges among items. Network analysis is a useful tool to explore depression symptoms and offers new insight as to how they interact. Further studies may endeavor to replicate our findings in different samples, including clinical samples to replicate the network structures and determine possible viable targets for clinical intervention.