Correlation between centrality metrics and their application to the opinion model

In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a high-complexity centrality metric by a strongly correlated low-complexity metric, we first study the correlation between centrality metrics in terms of their Pearson correlation coefficient and their similarity in ranking of nodes. In addition to considering the widely used centrality metrics, we introduce a new centrality measure, the degree mass. The m order degree mass of a node is the sum of the weighted degree of the node and its neighbors no further than m hops away. We find that the B_{n}, the closeness, and the components of x_{1} are strongly correlated with the degree, the 1st-order degree mass and the 2nd-order degree mass, respectively, in both network models and real-world networks. We then theoretically prove that the Pearson correlation coefficient between x_{1} and the 2nd-order degree mass is larger than that between x_{1} and a lower order degree mass. Finally, we investigate the effect of the inflexible antagonists selected based on different centrality metrics in helping one opinion to compete with another in the inflexible antagonists opinion model. Interestingly, we find that selecting the inflexible antagonists based on the leverage, the B_{n}, or the degree is more effective in opinion-competition than using other centrality metrics in all types of networks. This observation is supported by our previous observations, i.e., that there is a strong linear correlation between the degree and the B_{n}, as well as a high centrality similarity between the leverage and the degree.Comment: 20 page

Parameterized Complexity of 1-Planarity

We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the parameterized complexity of the problem with respect to the vertex cover number, tree-depth, and cyclomatic number. For these parameters we construct fixed-parameter tractable algorithms. However, the problem remains NP-complete for graphs of bounded bandwidth, pathwidth, or treewidth.Comment: WADS 201

Ablation of lysophosphatidic acid receptor 1 attenuates hypertrophic cardiomyopathy in a mouse model.

Myocardial fibrosis is a key pathologic feature of hypertrophic cardiomyopathy (HCM). However, the fibrotic pathways activated by HCM-causing sarcomere protein gene mutations are poorly defined. Because lysophosphatidic acid is a mediator of fibrosis in multiple organs and diseases, we tested the role of the lysophosphatidic acid pathway in HCM. Lysphosphatidic acid receptor 1 (LPAR1), a cell surface receptor, is required for lysophosphatidic acid mediation of fibrosis. We bred HCM mice carrying a pathogenic myosin heavy-chain variant (403(+/-)) with Lpar1-ablated mice to create mice carrying both genetic changes (403(+/-) LPAR1(-/-)) and assessed development of cardiac hypertrophy and fibrosis. Compared with 403(+/-) LPAR1(WT), 403(+/-) LPAR1(-/-) mice developed significantly less hypertrophy and fibrosis. Single-nucleus RNA sequencing of left ventricular tissue demonstrated that Lpar1 was predominantly expressed by lymphatic endothelial cells (LECs) and cardiac fibroblasts. Lpar1 ablation reduced the population of LECs, confirmed by immunofluorescence staining of the LEC markers Lyve1 and Ccl21a and, by in situ hybridization, for Reln and Ccl21a. Lpar1 ablation also altered the distribution of fibroblast cell states. FB1 and FB2 fibroblasts decreased while FB0 and FB3 fibroblasts increased. Our findings indicate that Lpar1 is expressed predominantly by LECs and fibroblasts in the heart and is required for development of hypertrophy and fibrosis in an HCM mouse model. LPAR1 antagonism, including agents in clinical trials for other fibrotic diseases, may be beneficial for HCM

Abnormally Large Baseline P300 Amplitude Is Associated With Conversion to Psychosis in Clinical High Risk Individuals With a History of Autism: A Pilot Study

Psychosis rates in autism spectrum disorder (ASD) are 5–35% higher than in the general population. The overlap in sensory and attentional processing abnormalities highlights the possibility of related neurobiological substrates. Previous research has shown that several electroencephalography (EEG)-derived event-related potential (ERP) components that are abnormal in schizophrenia, including P300, are also abnormal in individuals at Clinical High Risk (CHR) for psychosis and predict conversion to psychosis. Yet, it is unclear whether P300 is similarly sensitive to psychosis risk in help-seeking CHR individuals with ASD history. In this exploratory study, we leveraged data from the North American Prodrome Longitudinal Study (NAPLS2) to probe for the first time EEG markers of longitudinal psychosis profiles in ASD. Specifically, we investigated the P300 ERP component and its sensitivity to psychosis conversion across CHR groups with (ASD+) and without (ASD–) comorbid ASD. Baseline EEG data were analyzed from 304 CHR patients (14 ASD+; 290 ASD–) from the NAPLS2 cohort who were followed longitudinally over two years. We examined P300 amplitude to infrequent Target (10%; P3b) and Novel distractor (10%; P3a) stimuli from visual and auditory oddball tasks. Whereas P300 amplitude attenuation is typically characteristic of CHR and predictive of conversion to psychosis in non-ASD sample, in our sample, history of ASD moderated this relationship such that, in CHR/ASD+ individuals, enhanced – rather than attenuated - visual P300 (regardless of stimulus type) was associated with psychosis conversion. This pattern was also seen for auditory P3b amplitude to Target stimuli. Though drawn from a small sample of CHR individuals with ASD, these preliminary results point to a paradoxical effect, wherein those with both CHR and ASD history who go on to develop psychosis have a unique pattern of enhanced neural response during attention orienting to both visual and target stimuli. Such a pattern stands out from the usual finding of P300 amplitude reductions predicting psychosis in non-ASD CHR populations and warrants follow up in larger scale, targeted, longitudinal studies of those with ASD at clinical high risk for psychosis

Drawing the AS graph in 2.5 dimensions

We propose a method for drawing AS graph data using 2.5D graph visualization. In order to bring out the pure graph structure of the AS graph we consider its core hierarchy. The k-cores are represented by 2D layouts whose interdependence for increasing k is displayed by the third dimension. For the core with maximum value a spectral layout is chosen thus emphasizing on the most important part of the AS graph. The lower cores are added iteratively by force-based methods. In contrast to alternative approaches to visualize AS graph data, our method illustrates the entire AS graph structure. Moreover, it is generic with regard to the hierarchy displayed by the third dimension