Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks proposed by Caldarelli et al. (2002). Power-law degree distributions, particularly with the dynamically stable scaling exponent 2, realistic clustering, and short path lengths are produced for many types of weight distributions. Thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2. It contrasts with the class of growth models with preferential attachment, which is marked by competitiveness and baseline scaling exponent 3.Comment: 5 figure

Rainbow domination and related problems on some classes of perfect graphs

Let $k \in \mathbb{N}$ and let $G$ be a graph. A function $f: V(G) \rightarrow 2^{[k]}$ is a rainbow function if, for every vertex $x$ with $f(x)=\emptyset$, $f(N(x)) =[k]$. The rainbow domination number $\gamma_{kr}(G)$ is the minimum of $\sum_{x \in V(G)} |f(x)|$ over all rainbow functions. We investigate the rainbow domination problem for some classes of perfect graphs

Separating Hierarchical and General Hub Labelings

In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An $s,t$ query computes the corresponding distance from the labels of $s$ and $t$ only, without looking at the input graph. Hub labels is a class of labels that has been extensively studied. Performance of the hub label query depends on the label size. Hierarchical labels are a natural special kind of hub labels. These labels are related to other problems and can be computed more efficiently. This brings up a natural question of the quality of hierarchical labels. We show that there is a gap: optimal hierarchical labels can be polynomially bigger than the general hub labels. To prove this result, we give tight upper and lower bounds on the size of hierarchical and general labels for hypercubes.Comment: 11 pages, minor corrections, MFCS 201

A SAT Approach to Clique-Width

Clique-width is a graph invariant that has been widely studied in combinatorics and computer science. However, computing the clique-width of a graph is an intricate problem, the exact clique-width is not known even for very small graphs. We present a new method for computing the clique-width of graphs based on an encoding to propositional satisfiability (SAT) which is then evaluated by a SAT solver. Our encoding is based on a reformulation of clique-width in terms of partitions that utilizes an efficient encoding of cardinality constraints. Our SAT-based method is the first to discover the exact clique-width of various small graphs, including famous graphs from the literature as well as random graphs of various density. With our method we determined the smallest graphs that require a small pre-described clique-width.Comment: proofs in section 3 updated, results remain unchange

Event-related alpha suppression in response to facial motion

This article has been made available through the Brunel Open Access Publishing Fund.While biological motion refers to both face and body movements, little is known about the visual perception of facial motion. We therefore examined alpha wave suppression as a reduction in power is thought to reflect visual activity, in addition to attentional reorienting and memory processes. Nineteen neurologically healthy adults were tested on their ability to discriminate between successive facial motion captures. These animations exhibited both rigid and non-rigid facial motion, as well as speech expressions. The structural and surface appearance of these facial animations did not differ, thus participants decisions were based solely on differences in facial movements. Upright, orientation-inverted and luminance-inverted facial stimuli were compared. At occipital and parieto-occipital regions, upright facial motion evoked a transient increase in alpha which was then followed by a significant reduction. This finding is discussed in terms of neural efficiency, gating mechanisms and neural synchronization. Moreover, there was no difference in the amount of alpha suppression evoked by each facial stimulus at occipital regions, suggesting early visual processing remains unaffected by manipulation paradigms. However, upright facial motion evoked greater suppression at parieto-occipital sites, and did so in the shortest latency. Increased activity within this region may reflect higher attentional reorienting to natural facial motion but also involvement of areas associated with the visual control of body effectors. © 2014 Girges et al

The Role of Gamma-Band Activity in the Representation of Faces: Reduced Activity in the Fusiform Face Area in Congenital Prosopagnosia

Congenital prosopagnosia (CP) describes an impairment in face processing that is presumably present from birth. The neuronal correlates of this dysfunction are still under debate. In the current paper, we investigate high-frequent oscillatory activity in response to faces in persons with CP. Such neuronal activity is thought to reflect higher-level representations for faces.Source localization of induced Gamma-Band Responses (iGBR) measured by magnetoencephalography (MEG) was used to establish the origin of oscillatory activity in response to famous and unknown faces which were presented in upright and inverted orientation. Persons suffering from congenital prosopagnosia (CP) were compared to matched controls.Corroborating earlier research, both groups revealed amplified iGBR in response to upright compared to inverted faces predominately in a time interval between 170 and 330 ms and in a frequency range from 50-100 Hz. Oscillatory activity upon known faces was smaller in comparison to unknown faces, suggesting a "sharpening" effect reflecting more efficient processing for familiar stimuli. These effects were seen in a wide cortical network encompassing temporal and parietal areas involved in the disambiguation of homogenous stimuli such as faces, and in the retrieval of semantic information. Importantly, participants suffering from CP displayed a strongly reduced iGBR in the left fusiform area compared to control participants.In sum, these data stress the crucial role of oscillatory activity for face representation and demonstrate the involvement of a distributed occipito-temporo-parietal network in generating iGBR. This study also provides the first evidence that persons suffering from an agnosia actually display reduced gamma band activity. Finally, the results argue strongly against the view that oscillatory activity is a mere epiphenomenon brought fourth by rapid eye-movements (micro saccades)