Fast Computing Betweenness Centrality with Virtual Nodes on Large Sparse Networks

Betweenness centrality is an essential index for analysis of complex networks. However, the calculation of betweenness centrality is quite time-consuming and the fastest known algorithm uses time and space for weighted networks, where and are the number of nodes and edges in the network, respectively. By inserting virtual nodes into the weighted edges and transforming the shortest path problem into a breadth-first search (BFS) problem, we propose an algorithm that can compute the betweenness centrality in time for integer-weighted networks, where is the average weight of edges and is the average degree in the network. Considerable time can be saved with the proposed algorithm when , indicating that it is suitable for lightly weighted large sparse networks. A similar concept of virtual node transformation can be used to calculate other shortest path based indices such as closeness centrality, graph centrality, stress centrality, and so on. Numerical simulations on various randomly generated networks reveal that it is feasible to use the proposed algorithm in large network analysis

Betweenness Centrality – Incremental and Faster

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Potential-based bounded-cost search and Anytime Non-Parametric A *

This paper presents two new search algorithms: Potential Search (PTS) and Anytime Potential Search/Anytime Non-Parametric A* (APTS/ANA*). Both algorithms are based on a new evaluation function that is easy to implement and does not require user-tuned parameters. PTS is designed to solve bounded-cost search problems, which are problems where the task is to find as fast as possible a solution under a given cost bound. APTS/ANA* is a non-parametric anytime search algorithm discovered independently by two research groups via two very different derivations. In this paper, co-authored by researchers from both groups, we present these derivations: as a sequence of calls to PTS and as a non-parametric greedy variant of Anytime Repairing A*. We describe experiments that evaluate the new algorithms in the 15-puzzle, KPP-COM, robot motion planning, gridworld navigation, and multiple sequence alignment search domains. Our results suggest that when compared with previous anytime algorithms, APTS/ANA*: (1) does not require user-set parameters, (2) finds an initial solution faster, (3) spends less time between solution improvements, (4) decreases the suboptimality bound of the current-best solution more gradually, and (5) converges faster to an optimal solution when reachable. © 2014 Elsevier B.V

Survival, integration, and axon growth support of glia transplanted into the chronically contused spinal cord

Due to an ever-growing population of individuals with chronic spinal cord injury, there is a need for experimental models to translate efficacious regenerative and reparative acute therapies to chronic injury application. The present study assessed the ability of fluid grafts of either Schwann cells (SCs) or olfactory ensheathing glia (OEG) to facilitate the growth of supraspinal and afferent axons and promote restitution of hind limb function after transplantation into a 2-month-old, moderate, thoracic (T8) contusion in the rat. The use of cultured glial cells, transduced with lentiviral vectors encoding enhanced green fluorescent protein (EGFP), permitted long-term tracking of the cells following spinal cord transplantation to examine their survival, migration, and axonal association. At 3 months following grafting of 2 million SCs or OEG in 6 microl of DMEM/F12 medium into the injury site, stereological quantification of the three-dimensional reconstructed spinal cords revealed that an average of 17.1 +/- 6.8% of the SCs and 2.3 +/- 1.4% of the OEG survived from the number transplanted. In the OEG grafted spinal cord, a limited number of glia were unable to prevent central cavitation and were found in patches around the cavity rim. The transplanted SCs, however, formed a substantive graft within the injury site capable of supporting the ingrowth of numerous, densely packed neurofilament-positive axons. The SC grafts were able to support growth of both ascending calcitonin gene-related peptide (CGRP)-positive and supraspinal serotonergic axons and, although no biotinylated dextran amine (BDA)-traced corticospinal axons were present within the center of the grafts, the SC transplants significantly increased corticospinal axon numbers immediately rostral to the injury-graft site compared with injury-only controls. Moreover, SC grafted animals demonstrated modest, though significant, improvements in open field locomotion and exhibited less foot position errors (base of support and foot rotation). Whereas these results demonstrate that SC grafts survive, support axon growth, and can improve functional outcome after chronic contusive spinal cord injury, further development of OEG grafting procedures in this model and putative combination strategies with SC grafts need to be further explored to produce substantial improvements in axon growth and function

Transplantation of Schwann cells and/or olfactory ensheathing glia into the contused spinal cord: Survival, migration, axon association, and functional recovery

Schwann cells (SCs) and olfactory ensheathing glia (OEG) have shown promise for spinal cord injury repair. We sought their in vivo identification following transplantation into the contused adult rat spinal cord at 1 week post-injury by: (i) DNA in situ hybridization (ISH) with a Y-chromosome specific probe to identify male transplants in female rats and (ii) lentiviral vector-mediated expression of EGFP. Survival, migration, and axon-glia association were quantified from 3 days to 9 weeks post-transplantation. At 3 weeks after transplantation into the lesion, a 60-90% loss of grafted cells was observed. OEG-only grafts survived very poorly within the lesion (<5%); injection outside the lesion led to a 60% survival rate, implying that the injury milieu was hostile to transplanted cells and or prevented their proliferation. At later times post-grafting, p75(+)/EGFP(-) cells in the lesion outnumbered EGFP(+) cells in all paradigms, evidence of significant host SC infiltration. SCs and OEG injected into the injury failed to migrate from the lesion. Injection of OEG outside of the injury resulted in their migration into the SC-injected injury site, not via normal-appearing host tissue but along the pia or via the central canal. In all paradigms, host axons were seen in association with or ensheathed by transplanted glia. Numerous myelinated axons were found within regions of grafted SCs but not OEG. The current study details the temporal survival, migration, axon association of SCs and OEG, and functional recovery after grafting into the contused spinal cord, research previously complicated due to a lack of quality, long-term markers for cell tracking in vivo