Clusters Of Vertices Research Articles

Experimental and Computational 77Se NMR Spectroscopic Study on Selenaborane Cluster Compounds.

Calculated and measured 77Se nuclear magnetic resonance (NMR) chemical shift data on a diverse collection of 13 selenaborane cluster compounds, containing a total of 19 selenium centers, reveals a correlation between chemical shifts and the intracluster coordination of selenium atoms within their borane frameworks. A plot of the measured against calculated 77Se NMR chemical shifts shows an approximately linear relationship that can serve as a predictive tool in assessing the chemical shift range in which a selenium vertex from a particular compound might be expected to be found, thereby reducing expensive experimental time. Furthermore, the relative chemical shifts between selenium vertices in clusters containing more than one selenium atom are consistent across the range, thus allowing the assignment of the selenium resonances with a high degree of confidence even in relatively low-level density functional theory calculations. A new macropolyhedral 20-vertex selenaborane Se2B18H20 (A) is also reported.

Efficient Registration for Human Surfaces Via Isometric Regularization on Embedded Deformation.

3D registration is a fundamental step to obtain the correspondences between surfaces. Traditional mesh alignment methods tackle this problem through non-rigid deformation, mostly accomplished by applying ICP-based (Iterative Closest Point) optimization. The embedded deformation method is proposed for the purpose of acceleration, which enables various real-time applications. However, it regularizes on an underlying simplified structure, which could be problematic for intricate cases when the simplified graph doesn't fully represent the surface attributes. Moreover, without elaborate parameter-tuning, deformation usually performs suboptimally, leading to slow convergence or a local minimum if all regions on the surface are assumed to share the same rigidity during the optimization. In this paper, we propose a novel solution that decouples regularization from the underlying deformation model by explicitly managing the rigidity of vertex clusters. We further design an efficient two-step solution that alternates between isometric deformation and embedded deformation with cluster-based regularization. Our method can easily support region-adaptive regularization with cluster refinement and execute efficiently. Extensive experiments demonstrate the effectiveness of our approach for mesh alignment tasks even under large-scale deformation and imperfect data. Our method outperforms state-of-the-art methods both numerically and visually.

Automated deviation-aware landmark selection for freeform product accuracy qualification in 3D printing

Landmarks are essential in non-rigid shape registration for identifying the correspondence between designs and actual products. In 3D printing, manual selection of landmarks becomes labor-intensive, due to complex product geometries and their non-uniform shape deviations. Automatic selection, however, has to pinpoint landmarks indicative of geometric regions prone to deviations for accuracy qualification. Existing automatic landmarking methods often generate clustered and redundant landmarks for prominent features with high curvatures, compromising the balance between global and local registration errors. To address these issues, we propose an automatic landmark selection method through deviation-aware segmentation and landmarking. As opposed to segmentation for semantic feature identification, deviation-aware segmentation partitions a freeform product for high-curvature region identification. Prone to deviation, these regions are generated through curvature-sensitive remeshing to extract vertices of high curvature and automatic clustering of vertices based on vertex density. Within each segment or high-curvature region, a curvature-weighted function is tailored for the Gaussian process landmarking to sequentially select landmarks with the highest local curvatures. Furthermore, we propose a new evaluation criterion to assess the effectiveness of selected landmarks through registration. The proposed approach is tested through automatic landmarking of printed dental models.

Note on the finite vertex-based partitioning of supramolecular chain in Dialkyltin

ABSTRACT Complex networks are difficult to understand and deal with, yet building a graph of any complex and huge structure, whether chemical or computer-related, is quite straightforward. In the form of a graph theory view, it becomes simple to design networks. Each component's recognition is aided by the ease of its production in the form of graph theory. Finding a vertex (node or atom) in a structure is similarly difficult; in this instance, resolvability parameters come into play. This technique plays a significant role in managing or allowing access to each vertex in relation to some chosen vertices called a resolving set that shapes an entire cluster of vertices into a unique form and every single vertex is easy to recognise or locate, whether the small or large the structure. This article contributes the bounds on the parameter of partition dimension of chemical complexes in dialkyltin of supramolecular chain from N-Salicylidene-L-Valine. We supposed the complexes of chains from 2,3,4 and another chemical network, and we demonstrated that the number of vertices has a significant impact on the composition of resolving partition sets.

Statistical power, accuracy, reproducibility and robustness of a graph clusterability test

Not all graphs are clusterable. Not all graphs have a clustered structure and can be meaningfully summarized through vertex clustering. Clusterable graphs are characterized by pockets of densely connected vertices that are only sparsely connected to the remaining graph. In this article, we re-introduce a very simple and intuitive, yet highly informative, statistical hypothesis test for graph clusterability that is based on vertex and neighborhood samples. The goal of this test is to determine if a graph meets the necessary structural conditions to be summarized meaningfully through vertex clusters. Our test is based on the hypothesis that a clusterable graph will display, on average, a local neighborhood induced subgraph density that is greater than the graph’s overall density. The test is also applied to graph comparisons, to test whether one graph has a stronger clustered structure than another. Significance is assessed using the t-statistic. Since it is based on sampling, we provide a focused examination of our test’s sensitivity to sample size. The main contribution of this article is a detailed examination of our test’s accuracy, sensitivity to sample size, conclusion reproducibility and robustness. Our empirical results remain consistent with our earlier conclusions and demonstrate the almost perfect accuracy of our test, even with very small samples of the graph. They also reveal that our test remains robust even under severe departures from the null hypothesis.

Extent ‐ A Global Spatial Distribution Measure to Estimate Progression and Demonstrate Treatment Effect in Flortaucipir Scans

AbstractBackgroundWe previously reported that donanemab slows global and regional increase in flortaucipir standardized uptake value ratios (SUVRs)1. In addition to SUVR, a method to estimate spatial distribution of flortaucipir (FTP) uptake might provide valuable and complementary information. Here, we apply the previously developed Extent method to estimate the spread of FTP uptake in PET images and present comparisons against neocortical SUVR for the measurement of treatment effect in the TRAILBLAZER‐ALZ trial. We performed vertex‐wise statistical comparisons.MethodSubjects in the phase 2 TRAILBLAZER‐ALZ study completed FTP and florbetapir PET scans and MRIs at baseline and 18‐months. Flortaucipir images were processed using standard techniques2 and normalized to the cerebellum crustaneous reference region3. Each FTP image was converted to a z‐score image relative to sixteen young cognitively normal (YCN) subjects. Clusters with z‐scores smaller than a false discovery rate corrected p‐value of 0.01 were retained within a predefined neocortical mask. The neocortical mask and thresholds were selected based on previous data to maximize signal to noise ratio in 18‐month change of mild AD subjects. Extent is the ratio of voxels in this predefined mask that have abnormally elevated tau, defined as at least 2.32*SD above the mean of YCNs (values range between 0‐1). The primary outcome was 18‐month change in Extent and MUBADA2 SUVR between placebos and donanemab treated subjects. We performed vertex‐wise group comparisons to capture the differences in tau burden.ResultBoth Extent and MUBADA showed significant difference between treated and placebo subjects (Figure 1). The 18‐month change (SUVR and Extent) surface maps of the treated and placebo groups show larger spread of FTP in the superior, middle and medial orbito‐frontal regions (Figure 2 & 3). The difference and p‐value maps show clusters of vertices in the inferior temporal, parahippocampal, supramarginal, middle, medial and superior frontal regions as being significantly different.ConclusionSubjects treated with donanemab have significantly lesser flortaucipir distribution by Extent compared to placebo, and differences in surface maps of intensity and spread of FTP. Clusters in temporal, parietal, and frontal regions were significantly different. In addition to intensity differences, spatial distribution was different between treatment groups.

Cutting-plane algorithms and solution whitening for the vertex-cover problem.

The phase-transition behavior of the NP-hard vertex-cover (VC) combinatorial optimization problem is studied numerically by linear programming (LP) on ensembles of random graphs. As the basic Simplex (SX) algorithm suitable for such LPs may produce incomplete solutions for sufficiently complex graphs, the application of cutting-plane (CP) methods is sought. We consider Gomory and {0,1/2} cuts. We measure the probability of obtaining complete solutions with these approaches as a function of the average node degree c and observe transition between typically complete and incomplete phase regions. While not generally complete solutions are obtained for graphs of arbitrarily high complexity, the CP approaches still advance the boundary in comparison to the pure SX algorithm, beyond the known replica-symmetry breaking (RSB) transition at c=e≈2.718. In fact, our results provide evidence for another algorithmic transition at c≈2.90(2). Besides this, we quantify the transition between easy and hard solvability of the VC problem also in terms of numerical effort. Further we study the so-called whitening of the solution, which is a measure for the degree of freedom that single vertices experience with respect to degenerate solutions. Inspection of the quantities related to clusters of white vertices reveals that whitening is affected, only slightly but measurably, by the RSB transition.

On Spectral Algorithms for Community Detection in Stochastic Blockmodel Graphs With Vertex Covariates

In network inference applications, it is often desirable to detect community structure, namely to cluster vertices into groups, or blocks, according to some measure of similarity. Beyond mere adjacency matrices, many real networks also involve vertex covariates that carry key information about underlying block structure in graphs. To assess the effects of such covariates on block recovery, we present a comparative analysis of two model-based spectral algorithms for clustering vertices in stochastic blockmodel graphs with vertex covariates. The first algorithm uses only the adjacency matrix, and directly estimates the block assignments. The second algorithm incorporates both the adjacency matrix and the vertex covariates into the estimation of block assignments, and moreover quantifies the explicit impact of the vertex covariates on the resulting estimate of the block assignments. We employ Chernoff information to analytically compare the algorithms' performance and derive the information-theoretic Chernoff ratio for certain models of interest. Analytic results and simulations suggest that the second algorithm is often preferred: we can often better estimate the induced block assignments by first estimating the effect of vertex covariates. In addition, real data examples also indicate that the second algorithm has the advantages of revealing underlying block structure and taking observed vertex heterogeneity into account in real applications. Our findings emphasize the importance of distinguishing between observed and unobserved factors that can affect block structure in graphs.

Community detection using Local Group Assimilation

Clustering of vertices in complex networks to detect communities is an open challenge due to its unknown and hidden properties and broad areas. Complex networks occur in various areas and interdisciplinary fields be it biological, social, chemical, electrical or any other. Numerous methods have been proposed with significant contributions to detect communities but still its nature of properties, throw us a challenge in detecting meaningful communities in real networks. Communities are built through nodes and each node has its own significance. Similarity among nodes through their neighbors suggests common interest of those nodes. The idea is to identify small groups of similar nodes locally and gradually built communities using global information. Moreover, we are not taking any seed nodes and consider each node an important player. The identification of local structures and demarcating their boundaries possess another challenge. Here, we propose Local Group Assimilation (LGA) algorithm that identifies clusters or communities in a network graph using both local and global structure information. The algorithm compares two adjacent nodes by neighborhood similarity measure and picks the highest value pair. The highest value pairs of nodes are grouped together in such a manner that it generates initial clusters of various sizes. The local groups are merged further in iterative manner that maximizes inter cluster edge density between them. Our algorithm detects small significant and relevant communities on real networks that assimilate into larger ones with promising results. We evaluated our algorithm in both real world networks and synthetic benchmark networks and compared it with most popular state-of-the-art community detection algorithms. Our experimental results show that the LGA algorithm detects significant communities in complex networks comparable to most popular algorithms and can be used in real networks to detect communities.

Teaching the Virtual Brain

As a complex three-dimensional organ, the inside of a human brain is difficult to properly visualize. Magnetic Resonance Imaging provides an accurate model of the brain of a patient, but its medical or educational analysis as a set of flat slices is not enough to fully grasp its internal structure. A virtual reality application has been developed to generate a complete three-dimensional model based on MRI data, which users can explore internally through random planar cuts and color cluster isolation. An indexed vertex triangulation algorithm has been designed to efficiently display large amounts of complex three-dimensional vertex clusters in simple mobile devices. Feedback from students suggests that the resulting application satisfactorily complements theoretical lectures, as virtual reality allows them to better observe different structures within the human brain.

Restriction of the Global IgM Repertoire in Antiphospholipid Syndrome.

The typical anti-phospholipid antibodies (APLA) in the anti-phospholipid syndrome (APS) are reactive with the phospholipid-binding protein β2GPI as well as a growing list of other protein targets. The relation of APLA to natural antibodies and the fuzzy set of autoantigens involved provoked us to study the changes in the IgM repertoire in APS. To this end, peptides selected by serum IgM from a 7-residue linear peptide phage display library (PDL) were deep sequenced. The analysis was aided by a novel formal representation of the Igome (the mimotope set reflecting the IgM specificities) in the form of a sequence graph. The study involved women with APLA and habitual abortions (n=24) compared to age-matched clinically healthy pregnant women (n=20). Their pooled Igomes (297 028 mimotope sequences) were compared also to the global public repertoire Igome of pooled donor plasma IgM (n=2 796 484) and a set of 7-mer sequences found in the J regions of human immunoglobulins (n=4 433 252). The pooled Igome was represented as a graph connecting the sequences as similar as the mimotopes of the same monoclonal antibody. The criterion was based on previously published data. In the resulting graph, identifiable clusters of vertices were considered related to the footprints of overlapping antibody cross-reactivities. A subgraph based on the clusters with a significant differential expression of APS patients’ mimotopes contained predominantly specificities underrepresented in APS. The differentially expressed IgM footprints showed also an increased cross-reactivity with immunoglobulin J regions. The specificities underexpressed in APS had a higher correlation with public specificities than those overexpressed. The APS associated specificities were strongly related also to the human peptidome with 1 072 mimotope sequences found in 7 519 human proteins. These regions were characterized by low complexity. Thus, the IgM repertoire of the APS patients was found to be characterized by a significant reduction of certain public specificities found in the healthy controls with targets representing low complexity linear self-epitopes homologous to human antibody J regions.

Sharp bounds on partition dimension of hexagonal Möbius ladder

Complex networks are not easy to decode and understand to work on it, similarly, the Möbius structure is also considered as a complex structure or geometry. But making a graph of every complex and huge structure either chemical or computer-related networks becomes easy. After making easy of its construction, recognition of each vertex (node or atom) is also not an easy task, in this context resolvability parameters plays an important role in controlling or accessing each vertex with respect to some chosen vertices called as resolving set or sometimes dividing entire cluster of vertices into further subparts (subsets) and then accessing each vertex with respect to build in subsets called as resolving partition set. In these parameters, each vertex has its own unique identification and is easy to access despite the small or huge structures. In this article, we provide a resolving partition of hexagonal Möbius ladder graph and discuss bounds of partition dimension of hexagonal Möbius ladder network.

Cortical complexity in world trade center responders with chronic posttraumatic stress disorder

Approximately 23% of World Trade Center (WTC) responders are experiencing chronic posttraumatic stress disorder (PTSD) associated with their exposures at the WTC following the terrorist attacks of 9/11/2001, which has been demonstrated to be a risk factor for cognitive impairment raising concerns regarding their brain health. Cortical complexity, as measured by analyzing Fractal Dimension (FD) from T1 MRI brain images, has been reported to be reduced in a variety of psychiatric and neurological conditions. In this report, we hypothesized that FD would be also reduced in a case-control sample of 99 WTC responders as a result of WTC-related PTSD. The results of our surface-based morphometry cluster analysis found alterations in vertex clusters of complexity in WTC responders with PTSD, with marked reductions in regions within the frontal, parietal, and temporal cortices, in addition to whole-brain absolute bilateral and unilateral complexity. Furthermore, region of interest analysis identified that the magnitude of changes in regional FD severity was associated with increased PTSD symptoms (reexperiencing, avoidance, hyperarousal, negative affect) severity. This study confirms prior findings on FD and psychiatric disorders and extends our understanding of FD associations with posttraumatic symptom severity. The complex and traumatic experiences that led to WTC-related PTSD were associated with reductions in cortical complexity. Future work is needed to determine whether reduced cortical complexity arose prior to, or concurrently with, onset of PTSD.

Metabolic Pathway Prediction Using Non-Negative Matrix Factorization with Improved Precision.

Machine learning provides a probabilistic framework for metabolic pathway inference from genomic sequence information at different levels of complexity and completion. However, several challenges, including pathway features engineering, multiple mapping of enzymatic reactions, and emergent or distributed metabolism within populations or communities of cells, can limit prediction performance. In this article, we present triUMPF (triple non-negative matrix factorization [NMF] with community detection for metabolic pathway inference), which combines three stages of NMF to capture myriad relationships between enzymes and pathways within a graph network. This is followed by community detection to extract a higher-order structure based on the clustering of vertices that share similar statistical properties. We evaluated triUMPF performance by using experimental datasets manifesting diverse multi-label properties, including Tier 1 genomes from the BioCyc collection of organismal Pathway/Genome Databases and low complexity microbial communities. Resulting performance metrics equaled or exceeded other prediction methods on organismal genomes with improved precision on multi-organismal datasets.

Permutation-based inference for spatially localized signals in longitudinal MRI data

Alzheimer’s disease is a neurodegenerative disease in which the degree of cortical atrophy in specific structures of the brain serves as a useful imaging biomarker. Recent approaches using linear mixed effects (LME) models in longitudinal neuroimaging have been powerful and flexible in investigating the temporal trajectories of cortical thickness. However, massive-univariate analysis, a simplified approach that obtains a summary statistic (e.g., a p-value) for every vertex along the cortex, is insufficient to model cortical atrophy because it does not account for spatial similarities of the signals in neighboring locations. In this article, we develop a permutation-based inference procedure to detect spatial clusters of vertices showing statistically significant differences in the rates of cortical atrophy. The proposed method, called SpLoc, uses spatial information to combine the signals adaptively across neighboring vertices, yielding high statistical power while controlling family-wise error rate (FWER) accurately. When we reject the global null hypothesis, we use a cluster selection algorithm to detect the spatial clusters of significant vertices. We validate our method using simulation studies and apply it to the Alzheimer’s Disease Neuroimaging Initiative (ADNI) data to show its superior performance over existing methods. An R package for implementing SpLoc is publicly available.

Multi-Objective Evolutionary Algorithms to Find Community Structures in Large Networks

Real-world complex systems are often modeled by networks such that the elements are represented by vertices and their interactions are represented by edges. An important characteristic of these networks is that they contain clusters of vertices densely linked amongst themselves and more sparsely connected to nodes outside the cluster. Community detection in networks has become an emerging area of investigation in recent years, but most papers aim to solve single-objective formulations, often focused on optimizing structural metrics, including the modularity measure. However, several studies have highlighted that considering modularityas a unique objective often involves resolution limit and imbalance inconveniences. This paper opens a new avenue of research in the study of multi-objective variants of the classical community detection problem by applying multi-objective evolutionary algorithms that simultaneously optimize different objectives. In particular, they analyzed two multi-objective variants involving not only modularity but also the conductance metric and the imbalance in the number of nodes of the communities. With this aim, a new Pareto-based multi-objective evolutionary algorithm is presented that includes advanced initialization strategies and search operators. The results obtained when solving large-scale networks representing real-life power systems show the good performance of these methods and demonstrate that it is possible to obtain a balanced number of nodes in the clusters formed while also having high modularity and conductance values.

Characterization of 2-Path Signed Network

A signed network is a network where each edge receives a sign: positive or negative. In this paper, we report our investigation on 2-path signed network of a given signed network Σ , which is defined as the signed network whose vertex set is that of Σ and two vertices in Σ 2 are adjacent if there exist a path of length two between them in Σ . An edge ab in Σ 2 receives a negative sign if all the paths of length two between them are negative, otherwise it receives a positive sign. A signed network is said to be if clusterable its vertex set can be partitioned into pairwise disjoint subsets, called clusters, such that every negative edge joins vertices in different clusters and every positive edge joins vertices in the same clusters. A signed network is balanced if it is clusterable with exactly two clusters. A signed network is sign-regular if the number of positive (negative) edges incident to each vertex is the same for all the vertices. We characterize the 2-path signed graphs as balanced, clusterable, and sign-regular along with their respective algorithms. The 2-path network along with these characterizations is used to develop a theoretic model for the study and control of interference of frequency in wireless communication networks.

Simultaneous Dimensionality and Complexity Model Selection for Spectral Graph Clustering

Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement while often outperforming more traditional clustering algorithms. However, there are two inherent model selection problems in spectral clustering, namely estimating both the embedding dimension and number of clusters. This article attempts to address the issue by establishing a novel model selection framework specifically for vertex clustering on graphs under a stochastic block model. The first contribution is a probabilistic model which approximates the distribution of the extended spectral embedding of a graph. The model is constructed based on a theoretical result of asymptotic normality for the informative part of the embedding, and on simulation results providing a conjecture for the limiting behavior of the redundant part of the embedding. The second contribution is a simultaneous model selection framework. In contrast with traditional approaches, our model selection procedure estimates embedding dimension and number of clusters simultaneously. Based on our conjectured distributional model, a theorem on the consistency of the estimates of model parameters is presented, providing support for the utility of our method. Algorithms for our simultaneous model selection (SMS) for vertex clustering are proposed, demonstrating superior performance in simulation experiments. We illustrate our method via application to a collection of brain graphs.

Concepts on Coloring of Cluster Hypergraphs with Application

Coloring of graph theory is widely used in different fields like the map coloring, traffic light problems, etc. Hypergraphs are an extension of graph theory where edges contain single or multiple vertices. This study analyzes cluster hypergraphs where cluster vertices too contain simple vertices. Coloring of cluster networks where composite/cluster vertices exist is done using the concept of coloring of cluster hypergraphs. Proper coloring and strong coloring of cluster hypergraphs have been defined. Along with these, local coloring in cluster hypergraphs is also provided. Such a cluster network, COVID19 affected network, is assumed and colored to visualize the affected regions properly.

Hierarchies in communities of UK stock market from the perspective of Brexit

Nowadays, increase of analyzing stock markets as complex systems lead graph theory to play a key role. For instance, detecting graph communities is an important task in the analysis of stocks, and as planar maximally filtered graphs let us to get important information for the topology of the market. In this study, we first obtain correlation network representation of UK's leading stock market network by using a novel threshold method. Then, we determine vertex clusters by using modularity and analyze clusters in planar maximally filtered graph substructures. Our analyze include a new measure called weighted Gini index for measuring the sparsity. The main goal of this paper is to study the hierarchical evolution of the market communities throughout the Brexit referendum, which is known as the stress period for the stock market. Hence, the overall sample is divided into two sub-periods of pre-referendum, and post-referendum to obtain communities and hierarchical structures. Our results indicate that financial companies are leading elements of the clusters. Moreover, the significant changes within the network topologies are observed for insurance, consumer goods, consumer services, mining, and technology sectors whereas oil and gas and health care sectors have not been affected by Brexit stress.