Spanning Tree Research Articles

Analysis of the Association Between Antimicrobial Resistance Genes and Virulence Factors in ST11 and Non-ST11 CR-KP Bloodstream Infections in the Intensive Care Unit.

This study aims to investigate the association between antimicrobial resistance genes and virulence factors in ST11 and non-ST11 types of CR-KP in bloodstream infections in the intensive care unit, providing a theoretical basis for infection control and clinical diagnosis and treatment. From January 2021 to June 2023, samples of Klebsiella pneumoniae from bloodstream infections were collected at our hospital, focusing on those resistant to carbapenems. The resistance genes, housekeeping genes, and virulence genes were identified through PCR and analyzed using the GrapeTree software to perform MLST-based minimum spanning tree typing. Among the 85 CR-KP cases, 61.18% were of the ST11 type, predominantly of the KL64 capsular type; non-ST11 types were mainly ST15, accounting for 25.88%, predominantly of the KL5 capsular type. The carriage rates of virulence genes such as rmpA2, entB, silS, kpn, iucA, peg-344, and terB were significantly higher in the ST11 group than in the non-ST11 group. The primary carbapenemase identified was class A enzyme bla KPC-2, with a higher carriage rate in the ST11 group. Drug susceptibility tests showed that the resistance rates for cefepime, ertapenem, nitrofurantoin, amikacin, and gentamicin were also higher in the ST11 group, consistent with the resistance genotype findings. The study reveals that ST11 type CR-KP in intensive care unit bloodstream infections exhibits stronger resistance and higher virulence compared to non-ST11 types, posing significant challenges to clinical treatment. Thus, strict control over the use of carbapenem antibiotics is essential to prevent the spread of resistant plasmids.

Comparison of data-driven thresholding methods using directed functional brain networks.

Over the past two centuries, intensive empirical research has been conducted on the human brain. As an electroencephalogram (EEG) records millisecond-to-millisecond changes in the electrical potentials of the brain, it has enormous potential for identifying useful information about neuronal transactions. The EEG data can be modelled as graphs by considering the electrode sites as nodes andthe linear and nonlinear statistical dependencies among them as edges (with weights). The graph theoretical modelling of EEG data results in functional brain networks (FBNs), which are fully connected (complete) weighted undirected/directed networks. Since various brain regions are interconnected via sparse anatomical connections, the weak links can be filtered out from the fullyconnected networks using a process called thresholding. Multiple researchers in the past decades proposed many thresholding methods to gather more insights about the influential neuronal connections of FBNs. This paper reviews various thresholding methods used in the literature for FBN analysis. The analysis showed that data-driven methods are unbiased since no arbitrary user-specified threshold is required. The efficacy of four data-driven thresholding methods, namely minimum spanning tree (MST), minimum connected component (MCC), union of shortest path trees (USPT), and orthogonal minimum spanning tree (OMST), in characterizing cognitive behavior of the normal human brain is analysed using directed FBNs constructed from EEG data of different cognitive load states. The experimental results indicate that both MCC and OMST thresholding methods can detect cognitive load-induced changes in the directed functional brain networks.

Maximizing the Index of Signed Complete Graphs Containing a Spanning Tree with k Pendant Vertices

Maximizing the Index of Signed Complete Graphs Containing a Spanning Tree with k Pendant Vertices

Minimum spanning tree analysis of unimpaired individuals at risk of Alzheimer's disease.

Identifying early and non-invasive biomarkers to detect individuals in the earliest stages of the Alzheimer's disease continuum is crucial. As a result, electrophysiology and plasma biomarkers are emerging as great candidates in this pursuit due to their low invasiveness. This is the first magnetoencephalography study to assess the relationship between minimum spanning tree parameters, an alternative to overcome the comparability and thresholding problem issues characteristic of conventional brain network analyses, and plasma phosphorylated tau231 levels in unimpaired individuals, with different risk levels of Alzheimer's disease. Seventy-six individuals with available magnetoencephalography recordings and phosphorylated tau231 plasma determination were included. The minimum spanning tree for the theta, alpha and beta bands for each subject was obtained, and the leaf fraction, tree hierarchy and diameter were calculated. To study the relationship between these topological parameters and phosphorylated tau231, we performed correlation analyses, for the whole sample and considering the two risk sub-groups separately. Increasing concentrations of phosphorylated tau231 were associated with greater leaf fraction and tree hierarchy values, along with lower diameter values, for the alpha and theta frequency bands. These results emerged for the whole sample and the higher risk group, but not for the lower risk group. Our results indicate that the network topology of cognitively unimpaired individuals with elevated plasma phosphorylated tau231 levels, a marker of Alzheimer's disease pathology and amyloid-β accumulation, is already altered, shifting towards a more integrated network increasing its vulnerability and hub-dependency, mostly in the alpha band. This is indicated by increases in leaf fraction and tree hierarchy, along with reductions in diameter. These results match the initial trajectory proposed by theoretical models of disease progression and network disruption and suggest that changes in brain function and organization begin early on.

Molecular epidemiological analysis of Salmonella Schwarzengrund isolated in Japan by newly developed multi-locus variable-number tandem repeat analysis method

To establish molecular epidemiological analysis method for Salmonella Schwarzengrund and investigate its origin and genetic relationships among isolates in Japan, S. Schwarzengrund strains were examined by the pulsed-field gel electrophoresis (PFGE), the multi-locus sequencing typing (MLST), and the multi-locus variable-number tandem repeat analysis (MLVA) developed in this study. By the PFGE and MLST methods, the strains were typed into two clades (A and B) and two sequence types (STs) (96 and 241), respectively. Minimum spanning tree showed that the strains belonging ST241 genetically close to ST96, suggesting that ST241 originates from ST96. For MLVA, new primers for variable-number tandem repeat (VNTR) loci were designed, and five VNTR loci finally selected. In the MLVA method, the strains were typed into 11 sequence types. The MLVA method was able to differentiate strains belonging to the same clade of PFGE and MLST methods. These results indicate that the MLVA developed in this study shows a higher discriminatory power for S. Schwarzengrund compared to the PFGE and MLST methods and that it appears to be a useful method for the molecular epidemiological investigation of S. Schwarzengrund despite the low genetic diversity of this serotype in Japan.

Correction to “Sharp threshold for embedding balanced spanning trees in random geometric graphs”

Correction to “Sharp threshold for embedding balanced spanning trees in random geometric graphs”

Simulating Spanning Tree Protocols in a Cable-based Tsunameter System with an Arbitrary Number of Ocean Bottom Units

Simulating Spanning Tree Protocols in a Cable-based Tsunameter System with an Arbitrary Number of Ocean Bottom Units

Minimum spanning tree clustering approach for effective feature partitioning in multi-view ensemble learning

Minimum spanning tree clustering approach for effective feature partitioning in multi-view ensemble learning

Approximation algorithms for maximum weighted internal spanning trees in regular graphs and subdivisions of graphs

Abstract Let $G$ be a vertex-weighted connected graph of $n$ vertices and let $T$ be a spanning tree of $G$. We call $T$ a maximum weighted internal spanning tree of $G$ if the sum of the weights of the internal vertices of $T$ is the maximum over all spanning trees of $G$. The maximum weighted internal spanning tree (MaxwIST) problem asks to find such a spanning tree $T$ of $G$. The problem is NP-hard. We give an $O(dn)$ time approximation algorithm for $d$-regular graphs of $n=|V|$ vertices that computes a spanning tree with total weight of the internal vertices is at least $\frac{\beta _{d}}{\beta _{d} +d-2} - \epsilon $ of the total weight of all the vertices of the graph for any $\epsilon>0$, where $\beta _{d} = (d-1)H_{d-1}$, and $H_{d-1} = \sum _{i=1}^{d-1} i^{-1}$ is the $(d-1)$th harmonic number. For every $d \geq 3$ and $n_{0} \geq 1$, we show the construction of a $d$-regular graph of at least $n_{0}$ vertices, such that for any of its spanning trees, $\frac{w(I)}{w(V)}\le \frac{d}{d+1}$ holds. We give an $O(dn)$ time approximation algorithm for subdivisions of $d$-regular graphs, where the ratio of the internal weight of the spanning tree with the total vertex weight of the graph is at least $\frac{d-1}{2d-3} - \epsilon $ for $\epsilon>0$. We extend our study to $x$-subdivisions of Hamiltonian and hypoHamiltonian graphs, where each edge of the original Hamiltonian or hypoHamiltonian graph has been subdivided at least $x$ times. For those two graph classes, we show that there exists a spanning tree with internal vertex weight at least $1-\frac{2}{x-1}$ of the total vertex weight of the graph. Furthermore, we give $O(n)$ time algorithm for $x$-subdivisions of biconnected outerplanar graphs and $4$-connected planar graphs to achieve the above bound.

Clustering with Minimum Spanning Trees: How Good Can It Be?

AbstractMinimum spanning trees (MSTs) provide a convenient representation of datasets in numerous pattern recognition activities. Moreover, they are relatively fast to compute. In this paper, we quantify the extent to which they are meaningful in low-dimensional partitional data clustering tasks. By identifying the upper bounds for the agreement between the best (oracle) algorithm and the expert labels from a large battery of benchmark data, we discover that MST methods can be very competitive. Next, we review, study, extend, and generalise a few existing, state-of-the-art MST-based partitioning schemes. This leads to some new noteworthy approaches. Overall, the Genie and the information-theoretic methods often outperform the non-MST algorithms such as K-means, Gaussian mixtures, spectral clustering, Birch, density-based, and classical hierarchical agglomerative procedures. Nevertheless, we identify that there is still some room for improvement, and thus the development of novel algorithms is encouraged.

Genomic characterization of Klebsiella pneumoniae carbapenemase-producing Klebsiella pneumoniae (KPC-Kp) strains circulating in three university hospitals in Northern Italy over three years

ObjectivesGenomic surveillance of Klebsiella pneumoniae carbapenemase-producing Klebsiella pneumoniae (KPC-Kp) is crucial for virulence, drug-resistance monitoring, and outbreak containment.MethodsGenomic analysis on 87 KPC-Kp strains isolated from 3 Northern Italy hospitals in 2019-2021 was performed by whole genome sequencing (WGS), to characterize resistome, virulome, and mobilome, and to assess potential associations with phenotype resistance and clinical presentation. Maximum Likelihood and Minimum Spanning Trees were used to determine strain correlations and identify potential transmission clusters.ResultsOverall, 15 different STs were found; the predominant ones included ST307 (35, 40.2%), ST512/1519 (15, 17.2%), ST20 (12, 13.8%), and ST101 (7, 8.1%). 33 (37.9%) KPC-Kp strains were noticed to be in five transmission clusters (median number of isolates in each cluster: 5 [3-10]), four of them characterized by intra-hospital transmission. All 87 strains harbored Tn4401a transposon, carrying blaKPC-3 (48, 55.2%), blaKPC-2 (38, 43.7%), and in one case (1.2%) blaKPC-33, the latter gene conferred resistance to ceftazidime/avibactam (CZA). Thirty strains (34.5%) harbored porin mutations; of them, 7 (8.1%) carried multiple Tn4401a copies. These strains were characterized by significantly higher CZA minimum inhibitory concentration compared with strains with no porin mutations or single Tn4401a copy, respectively, even if they did not overcome the resistance breakpoint of 8 ug/mL. Median 2 (IQR:1-2) virulence factors per strain were detected. The lowest number was observed in ST20 compared to the other STs (p<0.001). While ST307 was associated with infection events, a trend associated with colonization events could be observed for ST20.ConclusionsIntegration of genomic, resistance score, and clinical data allowed us to define a relative diversification of KPC-Kp in Northern Italy between 2019 and 2021, characterized by few large transmission chains and rare inter-hospital transmission. Our results also provided initial evidence of correlation between KPC-Kp genomic signatures and higher MIC levels to some antimicrobial agents or colonization/infection status, once again underlining WGS's importance in bacterial surveillance.

A Big Ring on the sky

We present the discovery of `A Big Ring on the Sky' (BR), the second ultra-large large-scale structure (uLSS) found in Mg II-absorber catalogues, following the previously reported Giant Arc (GA). In cosmological terms the BR is close to the GA — at the same redshift z ∼ 0.8 and with a separation on the sky of only ∼ 12°. Two extraordinary uLSSs in such close configuration raises the possibility that together they form an even more extraordinary cosmological system. The BR is a striking circular, annulus-like, structure of diameter ∼ 400 Mpc (proper size, present epoch). The method of discovery is as described in the GA paper, but here using the new Mg II-absorber catalogues restricted to DR16Q quasars. Using the Convex Hull of Member Spheres (CHMS) algorithm, we estimate that the annulus and inner absorbers of the BR have departures from random expectations, at the density of the control field, of up to 5.2σ. We present the discovery of the BR, assess its significance using the CHMS, Minimal Spanning Tree (MST), FilFinder and Cuzick & Edwards (CE) methods, discuss it in the context of the GA+BR system, and suggest some implications for the origins of uLSS and for our understanding of cosmology. For example, it may be that unusual geometric patterns, such as these uLSSs, have an origin in cosmic strings.

Correlations versus noise in the NFT market.

The non-fungible token (NFT) market emerges as a recent trading innovation leveraging blockchain technology, mirroring the dynamics of the cryptocurrency market. The current study is based on the capitalization changes and transaction volumes across a large number of token collections on the Ethereum platform. In order to deepen the understanding of the market dynamics, the inter-collection dependencies are examined by using the multivariate formalism of detrended correlation coefficient and correlation matrix. It appears that correlation strength is lower here than that observed in previously studied markets. Consequently, the eigenvalue spectra of the correlation matrix more closely follow the Marchenko-Pastur distribution, still, some departures indicating the existence of correlations remain. The comparison of results obtained from the correlation matrix built from the Pearson coefficients and, independently, from the detrended cross-correlation coefficients suggests that the global correlations in the NFT market arise from higher frequency fluctuations. Corresponding minimal spanning trees for capitalization variability exhibit a scale-free character while, for the number of transactions, they are somewhat more decentralized.

Piping network optimization for district heating system using an enhanced Genetic Algorithm searching method

Given the substantial construction and operational expenses associated with a district heating system (DHS), achieving an optimal layout for the piping network is paramount for its successful deployment. In this study, the optimization of DHS piping configuration has been explored. Traditional exhaustive search methods for network design are often impractical due to computational constraints, making Genetic Algorithm (GA) a preferred alternative for navigating the vast search space of optimization problems efficiently. However, GA, which relies on probabilistic heuristics, may not always pinpoints the most effective solutions, particularly those in close proximity to the current near-optimal configuration. To address this issue, an enhanced GA-based neighboring search method for identifying optimal or near-optimal piping layout for DHS more effectively has been developed in this study. When a local minimum is detected in the GA optimization process, the method initiates a neighboring search by selecting an elite candidate. The link with the highest piping cost from the elite candidate's configuration is identified. Subsequently, one of the other nodes in the configuration is connected to the nodes of the identified link to explore solutions beyond the local optimum. This new approach was firstly validated against an Optimal Communication Spanning Tree (OCST) benchmark problem, where it demonstrated superior efficacy by achieving higher success rate and quicker first-hit generation compared to conventional GA method. Specifically, this method showed a 60 % success rate with a minimum first-hit generation number of 140, outperforming the traditional GA's 40 % success rate and 263 generations. Further modification to the OCST benchmark to better simulate a real-world DHS application underscored the ability of this neighboring search method to exceed the previously established optimal configuration, uncovering a “better' solution with superior fitness value. This promising methodology was subsequently applied to the hypothetical design of a DHS piping network, illustrating its potential to enhance the planning and implementation of efficient, cost-effective district heating systems.

Finding Optimal Spanning Trees For Damaged Networks

We use a representation for the spanning tree where a parent function maps non-root vertices to vertices. Two spanning trees are defined to be adjacent if their function representations differ at exactly one vertex. Given a graph G , we show that the graph H with all spanning trees of G as vertices and any two vertices being adjacent if and only if their parent functions differ at exactly one vertex is connected.

Review on graph theory-based image segmentation with its methods

In areas of digital image processing and computer vision, image segmentation is defined as a crucial process that divides an image into many segments for more straightforward and accurate object analysis. Making use of graph-based techniques as an effective tool for segmenting images has drawn more consideration recently. Since graph-based techniques are attractive and increasingly prevalent and can designate image properties, in this article, some of the primary graph-based techniques have been presented. This scheme utilizes graph theory to create a graph depiction of an image in which each pixel is represented as a node and the edges show the degree of similarity between two pixels. When items are represented by vertices and an edge connects them, a graph may be used to depict the relationship between them. To divide a graph into sub-graphs that reflect significant items of interest, this study explores some graph theoretical approaches for image segmentation, including minimum spanning tree, pyramid-based, graph cut-based, and interactive image segmentation and their employing in significant image processing fields such as medical image analysis for infection diagnosis, and remote sensing.

Sampling and active learning methods for network reliability estimation using K-terminal spanning tree

Network reliability analysis remains a challenge due to the increasing size and complexity of networks. This paper presents a novel sampling method and an active learning method for efficient and accurate network reliability estimation under node failure and edge failure scenarios. The proposed sampling method adopts Monte Carlo technique to sample component lifetimes and the K-terminal spanning tree algorithm to accelerate structure function computation. Unlike existing methods that compute only one structure function value per sample, our method generates multiple component state vectors and corresponding structure function values from each sample. Network reliability is estimated based on survival signatures derived from these values. A transformation technique extends this method to handle both node failure and edge failure. To enhance efficiency of proposed sampling method and achieve adaptability to network topology changes, we introduce an active learning method utilizing a random forest (RF) classifier. This classifier directly predicts structure function values, integrates network behaviors across diverse topologies, and undergoes iterative refinement to enhance predictive accuracy. Importantly, the trained RF classifier can directly predict reliability for variant networks, a capability beyond the sampling method alone. Through investigating several network examples and two practical applications, the effectiveness of both proposed methods is demonstrated.

Stable set reformulations for the degree preserving spanning tree problem

Let G=(V,E) be a connected undirected graph and assume that a spanning tree is available for it. Any vertex in this tree is called degree preserving if it has the same degree in the graph and in the tree. Building upon this concept, the Degree Preserving Spanning Tree Problem (DPSTP) asks for a spanning tree of G with as many degree preserving vertices as possible. DPSTP is very much intertwined with the most important application for it, so far, i.e., the online monitoring of arc flows in a water distribution network, what serves us as an additional motivation for our investigation. We show that degree preserving vertices correspond to a stable set of a properly defined DPSTP conflict graph. This, in turn, allows us to use valid inequalities for the Stable Set Polytope (SSP) and thus strengthen the DPSTP formulations previously suggested in the literature. In doing so, the Branch-and-cut and Benders Decomposition algorithms suggested for these formulations are greatly enhanced. Additionally, as a further contribution, we also introduce a new and very challenging set of DPSTP test instances, given by graphs that closely resemble water distribution networks. For these instances, the new algorithms very clearly outperform all previous DPSTP algorithms. They not only run faster than their competitors but are also less dependent on good initial DPSTP primal bounds. For previous DPSTP test sets, the new algorithms lag behind the best existing algorithm for them, which is based on Lagrangian relaxation. However, as compared to additional DPSTP previous algorithms that do not benefit from SSP inequalities, the new ones come much closer to the Lagrangian relaxation one.

Rural Electrification of Selected Areas in the Northern Region of Ghana Viewed as a Minimum Spanning Tree Problem

Rural Electrification of Selected Areas in the Northern Region of Ghana Viewed as a Minimum Spanning Tree Problem

Enhancing Network Security: Rogue Switch Detection and Prevention in Local Area Network

Our paper comprehensively examines ways to detect and handle unauthorized switches in Local Area Networks (LANs) within today's intricate and interconnected network landscape. We demonstrate the utilization of PortFast and BPDU guard configurations to reinforce LAN security against unauthorized devices and potential complications arising from the spanning tree protocol. These measures not only enhance network performance but also function as robust protective mechanisms, safeguarding the integrity of the LAN infrastructure. Furthermore, this paper delves into advanced techniques for the proactive identification and prevention of rogue switches, fostering an overall enhanced security posture within LANs. By synergistically integrating PortFast, BPDU guard, and advanced rogue switch detection methods, the paper proposes a robust methodology to strengthen LAN security and maintain uninterrupted network operations. It equips organizations with crucial resources to establish a resilient, secure, and dependable digital infrastructure, addressing the evolving demands of network security.