Spanning Tree Of Graph Research Articles

A multifaceted graph-wise network analysis of sector-based financial instruments’ price-based discrepancies with diverse statistical interdependencies

We explore discrepancies in financial networks, focusing on sector-based exchange-traded funds, through an in-depth analysis using statistical measures to validate interdependencies. By adopting methodologies such as the Minimum Spanning Tree, Average Linkage Minimum Spanning Tree, p-value-based networks, and Planar Maximally Filtered Graph, we investigate price-based discrepancies to uncover underlying network structures within financial data. Our key contribution is showing how employing a variety of measures and network analyses can offer diverse insights into financial markets. This approach enhances our understanding of market dynamics and provides a comprehensive framework for examining the intricate web of relationships that underpin the financial market.

Impact assessment of unsustainable airport development in the Himalayas using remote sensing: A case study of Pakyong Airport, Sikkim, India

Ground deformation is a widespread phenomenon that accelerates due to anthropogenic land development. Thus reclaimed/created land is more vulnerable to deformation and subsidence, especially in mountain areas. Advanced Differential Synthetic Aperture Radar Interferometry (A-DInSAR) can be used to monitor such projects. The Pakyong Airport is an engineering feat, constructed by cutting a mountain and converting it into a tabletop in a landslide-prone zone and seismically active region of the Sikkim Himalayas. The cutting of hill slopes for airport construction and other anthropogenic activities has increased slope instability in the region. This paper studies the slow-moving landslides in the airport neighbourhood using A-DInSAR on Sentinel-1 time series data consisting of 64 images of ascending track and 82 images of the descending track. The time period of monitoring was from October 2014 to April 2018 (43 months). The images have been connected using the Minimum Spanning Tree graph for interferogram generation for estimating deformation. The atmospheric noise was removed, and the results enabled the identification of deformation (in line-of-sight) on the airstrip as well as in the neighbouring area, both the upslope and downslope of the airport. The deformation rates estimated were up to ±90 mm/year in Pakyong from both tracks. We could successfully capture such land movement associated with the Pakyong Airport construction and help assess the impacts of infrastructure construction on the slope stability of the area. The controlling factors such as precipitation, seismicity, geology and others were analysed with respect to the deformation obtained. This study helps in assessing the land deformation after construction (cutting and filling of the slope) in the area. The deformation detected in this study needs to be addressed for the safety of the residents as well as for the infrastructure present in the area.

Reconstruction of Single-Cell Trajectories Using Stochastic Tree Search.

The recent advancement in single-cell RNA sequencing technologies enables the understanding of dynamic cellular processes at the single-cell level. Using trajectory inference methods, pseudotimes can be estimated based on reconstructed single-cell trajectories which can be further used to gain biological knowledge. Existing methods for modeling cell trajectories, such as minimal spanning tree or k-nearest neighbor graph, often lead to locally optimal solutions. In this paper, we propose a penalized likelihood-based framework and introduce a stochastic tree search (STS) algorithm aiming at the global solution in a large and non-convex tree space. Both simulated and real data experiments show that our approach is more accurate and robust than other existing methods in terms of cell ordering and pseudotime estimation.

Differential expression and cross-correlation between global regulator and pho regulon genes involved in decision-making under phosphate stress.

The differential gene expression under phosphate stress conditions leads to cross-talk between the global regulator, pho regulon, and metabolic genes. Promoter activity analysis of the selected 23 genes reveals the dynamic nature of real-time gene expression under different phosphate conditions. The expression profiles of the global regulator (rpoD, soxR, soxS, arcB, and fur), pho regulon (phoH, phoR, phoB, and ugpB), and metabolic genes (sdh, pfkA, ldh) varied significantly on phosphate level variation. Under stress conditions, soxR switches expression partners and co-expresses with rpoS instead of soxS. The partner-switching behavior of the genes under a challenging environment represents the intelligence of functional execution and ensures cell survival. The dynamic expression profile of the selected genes applies a time-lagged correlation to provide insight into the differential gene interaction between time-shifted expression profiles. Under different phosphate conditions, the minimum spanning tree graph revealed a different clustering pattern of selected genes depending on the computed distance and its proximity to other promoters.

Differences in Capital Market Network Structures under COVID-19

Abstract This paper analyses the structural changes of the underlying stock and currency markets as well as the industrial productions by using a minimum spanning tree graph on a Central and East European sample. The aim is to point out the similarities and differences of the COVID-19 pandemic compared to previous recessions, namely the Dot-com crisis in the early 2000s and the Subprime crisis around 2008. Focusing on the incidence, closeness, and betweenness properties of the graph, we are looking for the emergence of a shock-propagating hub. We identify such a hub during the Subprime crisis but not during the COVID-19 pandemic, which points to the higher efficiency of the economic policy to absorb the worst effects of the crisis.

High-frequency connectedness between Bitcoin and other top-traded crypto assets during the COVID-19 crisis

In this paper, we analyse co-movements and correlations between Bitcoin and thirty-one of the most-tradable crypto assets using high-frequency data for the period from January 2019 to December 2020. We apply the Diagonal-BEKK model to data from the pre-COVID and COVID-19 periods, and identify significant changes in patterns of co-movements and correlations during the pandemic period. We also employ the Minimum Spanning Tree (MST) and Planar Maximally Filtered Graph (PMFG) methods to study the changes of the crypto asset network structure after the COVID-19 outbreak. While the influential role of Bitcoin in the digital asset ecosystem has been confirmed, our novel findings reveal that due to recent developments in the blockchain ecosystem, crypto assets that can be categorised as dApps and protocols have become more attractive to investors than pure cryptocurrencies.

Altered brain network topology during speech tracking in developmental dyslexia

Developmental dyslexia is often accompanied by altered phonological processing of speech. Underlying neural changes have typically been characterized in terms of stimulus- and/or task-related responses within individual brain regions or their functional connectivity. Less is known about potential changes in the more global functional organization of brain networks. Here we recorded electroencephalography (EEG) in typical and dyslexic readers while they listened to (a) a random sequence of syllables and (b) a series of tri-syllabic real words. The network topology of the phase synchronization of evoked cortical oscillations was investigated in four frequency bands (delta, theta, alpha and beta) using minimum spanning tree graphs. We found that, compared to syllable tracking, word tracking triggered a shift toward a more integrated network topology in the theta band in both groups. Importantly, this change was significantly stronger in the dyslexic readers, who also showed increased reliance on a right frontal cluster of electrodes for word tracking. The current findings point towards an altered effect of word-level processing on the functional brain network organization that may be associated with less efficient phonological and reading skills in dyslexia.

End‐faithful spanning trees in graphs without normal spanning trees

AbstractSchmidt characterised the class of rayless graphs by an ordinal rank function, which makes it possible to prove statements about rayless graphs by transfinite induction. Halin asked whether Schmidt's rank function can be generalised to characterise other important classes of graphs. In this paper, we address Halin's question: we characterise an important class of graphs by an ordinal function. Another largely open problem raised by Halin asks for a characterisation of the class of graphs with an end‐faithful spanning tree. A well‐studied subclass is formed by the graphs with a normal spanning tree. We determine a larger subclass, the class of normally traceable graphs, which consists of the connected graphs with a rayless tree‐decomposition into normally spanned parts. Investigating the class of normally traceable graphs further we prove that, for every normally traceable graph, having a rayless spanning tree is equivalent to all its ends being dominated. Our proofs rely on a characterisation of the class of normally traceable graphs by an ordinal rank function that we provide.

High-Frequency Connectedness between Bitcoin and Other Top-Traded Crypto Assets during the COVID-19 Crisis

In this paper, we analyse co-movements and correlations between Bitcoin and thirty-one of the most-tradable crypto assets using high-frequency data for the period from January 2019 to December 2020. We apply the Diagonal-BEKK model to data from the pre-COVID and COVID-19 periods, and identify significant changes in patterns of co-movements and correlations during the pandemic period. We also employ the Minimum Spanning Tree (MST) and Planar Maximally Filtered Graph (PMFG) methods to study the changes of the crypto asset network structure after the COVID-19 outbreak. While the influential role of Bitcoin in the digital asset ecosystem has been confirmed, our novel findings reveal that due to recent developments in the blockchain ecosystem, crypto assets that can be categorised as dApps and Protocols have become more attractive to investors than pure cryptocurrencies, with dApps exhibiting the highest average degree of correlations with all crypto assets in the sample during the COVID-19 pandemic period.

Maximum Spanning Tree Graph Model: National Examination Data Analysis of Junior High School in Lampung Province

The purpose of this study is to determine the tendencies of learning in Lampung Province especially at junior high school level. Subjects of this study are all result of national examination data for junior high school in 2017 and 2018 in Lampung Province. The method of this study using model analysis of maximum spanning tree (MST) graph assisted by descriptive and inferential statistics technique. The data obtained are analysed using descriptive statistical analysis to find out the basic information of the data and inferential statistical analysis to get the value of coefficient correlation. Then, the MST graph is formed using Kruskal’s algorithm by interpreting the vertices as a subject and the edges as the value of coefficient correlation. The subject that have the closest relationship to any subject is a graph vertex with the greatest degree. Based on the MST graph model, the result of this study shows that the subject which has closest relationship with another subject is Science in 2017, while in 2018 are English and Mathematics. Based on these result and relevant research, the conclusion shows that Science and Mathematics to be the centre for the national examination of junior high school in 2017 and 2018 in Lampung Province.

Robust Consensus and Connectivity-maintenance under Edge-agreement-based Protocols for Directed Spanning Tree Graphs

We address the consensus problem with connectivity maintenance for networks of multi-agent systems interconnected over directed spanning tree graphs in the edge-agreement space and, for the first time in the literature, we provide a strict Lyapunov function. The importance of this contribution is that it allows to establish uniform global asymptotic stability of the consensus manifold for a multi-agent system subject to proximity constraints. Moreover, robustness in the sense of input-to-state stability with respect to external disturbances is also established. These properties have not been established before when dealing with state-dependent constraints, even for a class of directed graphs, because most often in the literature only non-uniform convergence to the consensus manifold is established.

Psychopathy is associated with shifts in the organization of neural networks in a large incarcerated male sample.

Psychopathy is a personality disorder defined by antisocial behavior paired with callousness, low empathy, and low interpersonal emotions. Psychopathic individuals reliably display complex atypicalities in emotion and attention processing that are evident when examining task performance, activation within specific neural regions, and connections between regions. Recent advances in neuroimaging methods, namely graph analysis, attempt to unpack this type of processing complexity by evaluating the overall organization of neural networks. Graph analysis has been used to better understand neural functioning in several clinical disorders but has not yet been used in the study of psychopathy. The present study applies a minimum spanning tree graph analysis to resting-state fMRI data collected from male inmates assessed for psychopathy with the Hare Psychopathy Checklist-Revised (n = 847). Minimum spanning tree analysis provides several metrics of neural organization optimality (i.e., the effectiveness, efficiency, and robustness of neural network organization). Results show that inmates higher in psychopathy exhibit a more efficiently organized dorsal attention network (β==0.101, pcorrected==0.018). Additionally, subcortical structures (e.g., amygdala, caudate, and hippocampus) act as less of a central hub in the global flow of information in inmates higher in psychopathy (β==-0.104, pcorrected==0.048). There were no significant effects of psychopathy on neural network organization in the default or salience networks. Together, these shifts in neural organization suggest that the brains of inmates higher in psychopathy are organized in a fundamentally different way than other individuals.

EEG Resting State Functional Connectivity in Adult Dyslexics Using Phase Lag Index and Graph Analysis.

Developmental dyslexia may involve deficits in functional connectivity across widespread brain networks that enable fluent reading. We investigated the large-scale organization of electroencephalography (EEG) functional networks at rest in 28 dyslexics and 36 typically reading adults. For each frequency band (delta, theta alpha and beta), we assessed functional connectivity strength with the phase lag index (PLI). Network topology was examined using minimum spanning tree (MST) graphs derived from the functional connectivity matrices. We found significant group differences in the alpha band (8–13 Hz). The graph analysis indicated more interconnected nodes, in dyslexics compared to typical readers. The graph metrics were significantly correlated with age in dyslexics but not in typical readers, which may indicate more heterogeneity in maturation of brain networks in dyslexics. The present findings support the involvement of alpha oscillations in higher cognition and the sensitivity of graph metrics to characterize functional networks in adult dyslexia. Finally, the current results extend our previous findings on children.

A Combinatorial Proof of a Formula of Biane and Chapuy

Let $G$ be a simple strongly connected weighted directed graph. Let $\mathcal{G}$ denote the spanning tree graph of $G$. That is, the vertices of $\mathcal{G}$ consist of the directed rooted spanning trees on $G$, and the edges of $\mathcal{G}$ consist of pairs of trees $(t_i, t_j)$ such that $t_j$ can be obtained from $t_i$ by adding the edge from the root of $t_i$ to the root of $t_j$ and deleting the outgoing edge from $t_j$. A formula for the ratio of the sum of the weights of the directed rooted spanning trees on $\mathcal{G}$ to the sum of the weights of the directed rooted spanning trees on $G$ was recently given by Biane and Chapuy. Our main contribution is an alternative proof of this formula, which is both simple and combinatorial.

Large-scale network organization of EEG functional connectivity in newborn infants.

The organization of functional brain networks changes across human lifespan. The present study analyzed functional brain networks in healthy full-term infants (N = 139) within 1-6 days from birth by measuring neural synchrony in EEG recordings during quiet sleep. Large-scale phase synchronization was measured in six frequency bands with the Phase Lag Index. Macroscopic network organization characteristics were quantified by constructing unweighted minimum spanning tree graphs. The cortical networks in early infancy were found to be significantly more hierarchical and had a more cost-efficient organization compared with MST of random control networks, more so in the theta and alpha than in other frequency bands. Frontal and parietal sites acted as the main hubs of these networks, the topological characteristics of which were associated with gestation age (GA). This suggests that individual differences in network topology are related to cortical maturation during the prenatal period, when functional networks shift from strictly centralized toward segregated configurations. Hum Brain Mapp 38:4019-4033, 2017. © 2017 Wiley Periodicals, Inc.

How Different Are Alternative Beta Strategies?

In this article, the authors use a quantitative approach to compare different alternative beta strategies, based on statistical relationships among their returns. Using correlations, principal component analysis, regression factor models, and minimum spanning tree graphs, they identify and quantify statistical closeness of these portfolios. The results show that when measured by return comovements and common systematic risk exposures, different alternative beta portfolios are, on average, quite close to each other. Surprisingly, in some cases, returns of portfolios with different strategic approaches can be more similar than those of two portfolios representing different variations of the same approach. Using a formal clustering technique, the authors show how to identify distinct clusters within a set of alternative beta portfolios. Given potential redundancy of alternative beta, their clusters can give a better diversified set of building blocks for multi-strategy allocations than individual strategies themselves. The authors build several portfolio allocations using clusters of alternative beta strategies as building blocks and compare individual strategy-based and cluster-based allocations, within both static and dynamic allocation frameworks. They find that the cluster-based allocations have a better risk–return profile with respect to the portfolios based on individual strategies. <b>TOPICS:</b>Mutual funds/passive investing/indexing, analysis of individual factors/risk premia, portfolio construction, statistical methods

Life-Span Development of Brain Network Integration Assessed with Phase Lag Index Connectivity and Minimum Spanning Tree Graphs.

Graph analysis of electroencephalography (EEG) has previously revealed developmental increases in connectivity between distant brain areas and a decrease in randomness and increased integration in the brain network with concurrent increased modularity. Comparisons of graph parameters across age groups, however, may be confounded with network degree distributions. In this study, we analyzed graph parameters from minimum spanning tree (MST) graphs and compared their developmental trajectories to those of graph parameters based on full graphs published previously. MST graphs are constructed by selecting only the strongest available connections avoiding loops, resulting in a backbone graph that is thought to reflect the major qualitative properties of the network, while allowing a better comparison across age groups by avoiding the degree of distribution confound. EEG was recorded in a large (n = 1500) population-based sample aged 5-71 years. Connectivity was assessed using phase lag index to reduce effects of volume conduction. Connectivity in the MST graph increased significantly from childhood to adolescence, continuing to grow nonsignificantly into adulthood, and decreasing significantly about 57 years of age. Leaf number, degree, degree correlation, and maximum centrality from the MST graph indicated a pattern of increased integration and decreased randomness from childhood into early adulthood. The observed development in network topology suggested that maturation at the neuronal level is aimed to increase connectivity as well as increase integration of the brain network. We confirm that brain network connectivity shows quantitative changes across the life span and additionally demonstrate parallel qualitative changes in the connectivity pattern.

New MYC IHC Classifier Integrating Quantitative Architecture Parameters to Predict MYC Gene Translocation in Diffuse Large B-Cell Lymphoma.

A new automated MYC IHC classifier based on bivariate logistic regression is presented. The predictor relies on image analysis developed with the open-source ImageJ platform. From a histologic section immunostained for MYC protein, 2 dimensionless quantitative variables are extracted: (a) relative distance between nuclei positive for MYC IHC based on euclidean minimum spanning tree graph and (b) coefficient of variation of the MYC IHC stain intensity among MYC IHC-positive nuclei. Distance between positive nuclei is suggested to inversely correlate MYC gene rearrangement status, whereas coefficient of variation is suggested to inversely correlate physiological regulation of MYC protein expression. The bivariate classifier was compared with 2 other MYC IHC classifiers (based on percentage of MYC IHC positive nuclei), all tested on 113 lymphomas including mostly diffuse large B-cell lymphomas with known MYC fluorescent in situ hybridization (FISH) status. The bivariate classifier strongly outperformed the “percentage of MYC IHC-positive nuclei” methods to predict MYC+ FISH status with 100% sensitivity (95% confidence interval, 94-100) associated with 80% specificity. The test is rapidly performed and might at a minimum provide primary IHC screening for MYC gene rearrangement status in diffuse large B-cell lymphomas. Furthermore, as this bivariate classifier actually predicts “permanent overexpressed MYC protein status,” it might identify nontranslocation-related chromosomal anomalies missed by FISH.

Looking for phase-space structures in star-forming regions: an MST-based methodology

We present a method for analysing the phase space of star-forming regions. In particular we are searching for clumpy structures in the 3D subspace formed by two position coordinates and radial velocity. The aim of the method is the detection of kinematic segregated radial velocity groups, that is, radial velocity intervals whose associated stars are spatially concentrated. To this end we define a kinematic segregation index, $\tilde{\Lambda}$(RV), based on the Minimum Spanning Tree (MST) graph algorithm, which is estimated for a set of radial velocity intervals in the region. When $\tilde{\Lambda}$(RV) is significantly greater than 1 we consider that this bin represents a grouping in the phase space. We split a star-forming region into radial velocity bins and calculate the kinematic segregation index for each bin, and then we obtain the spectrum of kinematic groupings, which enables a quick visualization of the kinematic behaviour of the region under study. We carried out numerical models of different configurations in the subspace of the phase space formed by the coordinates and the radial velocity that various case studies illustrate. The analysis of the test cases demonstrates the potential of the new methodology for detecting different kind of groupings in phase space.

Multi-field-of-view strategy for image-based outcome prediction of multi-parametric estrogen receptor-positive breast cancer histopathology: Comparison to Oncotype DX

In this paper, we attempt to quantify the prognostic information embedded in multi-parametric histologic biopsy images to predict disease aggressiveness in estrogen receptor-positive (ER+) breast cancers (BCa). The novel methodological contribution is in the use of a multi-field-of-view (multi-FOV) framework for integrating image-based information from differently stained histopathology slides. The multi-FOV approach involves a fixed image resolution while simultaneously integrating image descriptors from many FOVs corresponding to different sizes. For each study, the corresponding risk score (high scores reflecting aggressive disease and vice versa), predicted by a molecular assay (Oncotype DX), is available and serves as the surrogate ground truth for long-term patient outcome. Using the risk scores, a trained classifier is used to identify disease aggressiveness for each FOV size. The predictions for each FOV are then combined to yield the final prediction of disease aggressiveness (good, intermediate, or poor outcome). Independent multi-FOV classifiers are constructed for (1) 50 image features describing the spatial arrangement of cancer nuclei (via Voronoi diagram, Delaunay triangulation, and minimum spanning tree graphs) in H and E stained histopathology and (2) one image feature describing the vascular density in CD34 IHC stained histopathology. In a cohort of 29 patients, the multi-FOV classifiers obtained by combining information from the H and E and CD34 IHC stained channels were able to distinguish low- and high-risk patients with an accuracy of 0.91 ± 0.02 and a positive predictive value of 0.94 ± 0.10, suggesting that a purely image-based assay could potentially replace more expensive molecular assays for making disease prognostic predictions.