Extending assortativity: An application to weighted social networks

Assortativity by degree for complex networks is quantified by the Newman coefficient, and it describes a tendency for nodes to be connected to others with a similar degree. A generalization of the assortativity index has been proposed in the literature for undirected and unweighted networks, analysing the correlation between vertices that are not necessarily adjacent, but connected through paths, shortest paths and random walks. The aim of this study is to define a new class of higher-order assortativity measures for weighted networks. The effectiveness of these measures is evident in social networks, where both weights and connections are significant. Applications to Facebook and co-authorship networks are provided, analysing the assortativity beyond the nearest neighbours

Increased facilitation of the primary motor cortex following 1 Hz repetitive transcranial magnetic stimulation of the contralateral cerebellum in normal humans

Connections between the cerebellum and the contralateral motor cortex are dense and important, but their physiological significance is difficult to measure in humans. We have studied a group of 10 healthy subjects to test whether a modulation of the excitability of the left cerebellum can affect the excitability of the contralateral motor cortex. We used repetitive transcranial magnetic stimulation (rTMS) at 1 Hz frequency to transiently depress the excitability of the left cerebellar cortex and paired-pulse TMS testing of intracortical inhibition (ICI) and intracortical facilitation (ICF) to probe the excitability of cortico-cortical connections in the right motor cortex. The cortical silent period was also measured before and after cerebellar rTMS. Motor evoked potentials (MEPs) were significantly larger after than before conditioning rTMS trains (p < 0.01). Moreover, left cerebellar rTMS increased the ICF of the right motor cortex as measured with paired-pulses separated by an interstimulus interval (ISI) of 15 ms. The effect lasted for up to 30 min afterward and was specific for the contralateral (right) motor cortex. The cortical silent period was unaffected by cerebellar rTMS. The implication is that rTMS of the cerebellar cortex can shape the flowing of inhibition from Purkinje cells toward deep nuclei, thereby increasing the excitability of interconnected brain areas

The use of transcranial magnetic stimulation in spatial cognition

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Modulation of excitatory and inhibitory circuits for visual awareness in the human right parietal cortex

The balance of specific patterns of excitation and inhibition in critical regions of both hemispheres could be relevant in orienting attention over the extrapersonal space. In the present study a group of normal subjects had to detect small rectangular stimuli presented briefly on a computer screen in three different conditions: unilateral presentation either to left or right visual periphery or bilateral simultaneous presentation. Paired transcranial magnetic stimulation (TMS), was applied over the right parietal cortex 150 ms after the presentation of the visual stimuli with different inter-stimulus intervals (ISIs: 1, 3,5 and 10 ms). When paired TMS was applied 150 ms, but not 100 ms, after simultaneous visual presentation, the number of failures in detecting left targets increased compared to the single-pulse condition if the ISI was 3 ms; on the contrary, it decreased if the ISI was 5 ms. No effects were seen when paired pulses of the same intensity were delivered. These findings provide evidence of a supramodal-specific pattern of excitability of the right posterior parietal cortex in processing visuospatial information

The use of transcranial magnetic stimulation in spatial cognition

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Modulation of excitatory and inhibitory circuits for visual awareness in the human right parietal cortex

The balance of specific patterns of excitation and inhibition in critical regions of both hemispheres could be relevant in orienting attention over the extrapersonal space. In the present study a group of normal subjects had to detect small rectangular stimuli presented briefly on a computer screen in three different conditions: unilateral presentation either to left or right visual periphery or bilateral simultaneous presentation. Paired transcranial magnetic stimulation (TMS), was applied over the right parietal cortex 150 ms after the presentation of the visual stimuli with different inter-stimulus intervals (ISIs: 1, 3,5 and 10 ms). When paired TMS was applied 150 ms, but not 100 ms, after simultaneous visual presentation, the number of failures in detecting left targets increased compared to the single-pulse condition if the ISI was 3 ms; on the contrary, it decreased if the ISI was 5 ms. No effects were seen when paired pulses of the same intensity were delivered. These findings provide evidence of a supramodal-specific pattern of excitability of the right posterior parietal cortex in processing visuospatial information

Betweenness Centrality: Extremal Values and Structural Properties

In this paper we investigate the structural properties of betweenness centrality and determine some cases in which betweenness reaches its extremal values. Special attention is paid to Star(G), the set of vertices adjacent to all other vertices in a graph and we prove several results about the betweenness of the elements of this set. We introduce the new concept of total betweenness and relate it to group betweenness. We prove a necessary and sufficient condition for the two measures to coincide. Next we consider cutsets and cutvertices and we find a lower bound for their betweenness; in particular for a cutvertex this lower bound is the cutting number. Finally we apply the previous results to trees, proving an alternative formula for betweenness based on cutvertex properties