Properties Of Vertices Research Articles

Secondary vertex reconstruction with MaskFormers

In high-energy particle collisions, the reconstruction of secondary vertices from heavy-flavour hadron decays is crucial for identifying and studying jets initiated by b- or c-quarks. Traditional methods, while effective, require extensive manual optimisation and struggle to perform consistently across wide regions of phase space. Meanwhile, recent advancements in machine learning have improved performance but are unable to fully reconstruct multiple vertices. In this work we propose a novel approach to secondary vertex reconstruction based on recent advancements in object detection and computer vision. Our method directly predicts the presence and properties of an arbitrary number of vertices in a single model. This approach overcomes the limitations of existing techniques. Applied to simulated proton-proton collision events, our approach demonstrates significant improvements in vertex finding efficiency, achieving a 10% improvement over an existing state-of-the-art method. Moreover, it enables vertex fitting, providing accurate estimates of key vertex properties such as transverse momentum, radial flight distance, and angular displacement from the jet axis. When integrated into a flavour tagging pipeline, our method yields a 50% improvement in light-jet rejection and a 15% improvement in c-jet rejection at a b-jet selection efficiency of 70%. These results demonstrate the potential of adapting advanced object detection techniques for particle physics, and pave the way for more powerful and flexible reconstruction tools in high-energy physics experiments.

Fraud risk assessment in car insurance using claims graph features in machine learning

The article proposes a process for claims assessment in car insurance, which makes it possible to calculate the fraud rate on the annual set of claims using a reduced set of attributes and graph vertex properties. This approach improves the security of insurance companies’ assets against fraudulent attacks. A method for constructing a claims graph and extracting additional features from it for evaluation is described. It is shown that in order to build a graph, it is not necessary to have data on the connection of the claim participants. Two tests were carried out on a real opensource datasets with labelling of fraudulent cases. The results of the first one show the increase in classification metrics when using attributes obtained from the graph. The application of the proposed approach resulted in doubling the area under the Precision-Recall curve. The experimental results demonstrated high quality metrics for fraud detection, with a Recall rate of 83.33% and a Specificity rate of 91.05%. The second test confirmed the possibility of determining the insurance fraud level based on decision rule, which includes the condition of claims being connected to each other. The rule is able to detect claim groups with a high concentration of fraud, in which every second participant is a fraudster.

On subgroups product graph of finite groups

This paper explores Subgroup Product Graphs (SPG) in cyclic groups, presenting a Vertex Degrees Formula based on the prime factorization of a positive integer n. The Isolated Vertex Property asserts that for a positive integer n, the SPG γ_sp(G) lacks isolated vertices. The Matrix Degree and Edge Formula provide a matrix representation and calculate the edges in SPG. Additionally, a Subgraph Relation identifies the complete graph Kπ(n) as a subgraph in γ_sp(G). Specific Examples illustrate vertex degrees for different n values. In essence, the study contributes isomorphisms, characterizes properties, and computes degrees and edges for diverse subgroups in Subgroup Product Graphs.

On maximal block topological space

In this paper we create a new topological structure induced by connected simple undirected graphs called maximal block topological space and study some properties of this new type of topology. Also, define some concepts in maximal block topological space like (derived subgraph, closure subgraph and interior subgraph). Some results and properties of vertices and subgraphs in G due to maximal block topological space are proved and discussed. Moreover, showed that a maximal block topological space is T0-space and T1/2-space if and only if G is acyclic graph. Finally, irreducibility and topologically independent of maximal block topological space are introduced.

Colorful path detection in vertex-colored temporal

AbstractFinding paths is a fundamental problem in graph theory and algorithm design due to its many applications. Recently, this problem has been considered on temporal graphs, where edges may change over a discrete time domain. The analysis of graphs has also taken into account the relevance of vertex properties, modeled by assigning to vertices labels or colors. In this work, we deal with a problem that, given a static or temporal graph, whose vertices are colored graph looks for a path such that (1) the vertices of the path have distinct colors and (2) that path includes the maximum number of colors. We analyze the approximation complexity of the problem on static and temporal graphs, and we prove an inapproximability bound. Then, we consider the problem on temporal graphs, and we design a heuristic for it. We present an experimental evaluation of our heuristic, both on synthetic and real-world graphs. The experimental results show that for many instances of the problem, our method is able to return near-optimal solutions.

Chemical Reaction Optimization for Minimum Weight Dominating Set

Dominating set of a graph can be defined as the set of vertices that can cover all other vertices of the graph. The minimum weight dominating set (MWDS) is the minimum number of vertices in the dominating set with minimum total weight. In recent times, the chemical reaction optimization algorithm (CRO) has shown its supremacy in solving these types of problems. Therefore in this paper, a novel approach based on CRO has been proposed to solve the MWDS problem. The proposed method uses a repair-based technique to generate a molecule. To make the solution feasible by covering all vertices and to get better results, three supporting operators are implemented along with the CRO operators. Besides this, two repair operators are introduced. In the first repair operator, the searching procedure works based on the scaling properties of vertices, and the second one is a unique method for eliminating common neighbors of vertices of the dominating set. The performance of the proposed method is better than any other existing related algorithms. The performance is measured from different graphs of the benchmark datasets. It can be mentioned that the proposed method takes minimal running time to obtain the minimum weight compared to other benchmark methods.

Approximating probabilistic group steiner trees in graphs

Consider an edge-weighted graph, and a number of properties of interests (PoIs). Each vertex has a probability of exhibiting each PoI. The joint probability that a set of vertices exhibits a PoI is the probability that this set contains at least one vertex that exhibits this PoI. The probabilistic group Steiner tree problem is to find a tree such that (i) for each PoI, the joint probability that the set of vertices in this tree exhibits this PoI is no smaller than a threshold value, e.g. , 0.97; and (ii) the total weight of edges in this tree is the minimum. Solving this problem is useful for mining various graphs with uncertain vertex properties, but is NP-hard. The existing work focuses on certain cases, and cannot perform this task. To meet this challenge, we propose 3 approximation algorithms for solving the above problem. Let |Γ| be the number of PoIs, and ξ be an upper bound of the number of vertices for satisfying the threshold value of exhibiting each PoI. Algorithms 1 and 2 have tight approximation guarantees proportional to |Γ| and ξ, and exponential time complexities with respect to ξ and |Γ|, respectively. In comparison, Algorithm 3 has a looser approximation guarantee proportional to, and a polynomial time complexity with respect to, both |Γ| and ξ. Experiments on real and large datasets show that the proposed algorithms considerably outperform the state-of-the-art related work for finding probabilistic group Steiner trees in various cases.

Theory and phenomenology of the three-gluon vertex

The three-gluon vertex is a fundamental ingredient of the intricate QCD dynamics, being inextricably connected to key nonperturbative phenomena, such as the emergence of a mass scale in the gauge sector of the theory. In this presentation, we review the main theoretical properties of the three-gluon vertex in the Landau gauge, obtained from the fruitful synergy between functional methods and lattice simulations. We pay particular attention to the manifestation and origin of the infrared suppression of its main form factors and the associated zero crossing. In addition, we discuss certain characteristic phenomenological applications that require this special vertex as input.

Trees with matrix weights: Laplacian matrix and characteristic-like vertices

It is known that there is an alternative characterization of characteristic vertices for trees with positive weights on their edges via Perron values and Perron branches. Moreover, the algebraic connectivity of a tree with positive edge weights can be expressed in terms of Perron value.In this article, we consider trees with matrix weights on their edges. More precisely, we are interested in trees with the following classes of matrix edge weights:1.positive definite matrix weights,2.lower (or upper) triangular matrix weights with positive diagonal entries. For trees with the above classes of matrix edge weights, we define Perron values and Perron branches. Further, we have shown the existence of vertices satisfying properties analogous to the properties of characteristic vertices of trees with positive edge weights in terms of Perron values and Perron branches, and we call such vertices characteristic-like vertices. In this case, the eigenvalues of the Laplacian matrix are nonnegative, and we obtain a lower bound for the first non-zero eigenvalue of the Laplacian matrix in terms of Perron value. Furthermore, we also compute the Moore-Penrose inverse of the Laplacian matrix of a tree with nonsingular matrix weights on its edges.

Tilings in vertex ordered graphs

Over recent years there has been much interest in both Turán and Ramsey properties of vertex ordered graphs. In this paper we initiate the study of embedding spanning structures into vertex ordered graphs. In particular, we introduce a general framework for approaching the problem of determining the minimum degree threshold for forcing a perfect H-tiling in an ordered graph. In the (unordered) graph setting, this problem was resolved by Kühn and Osthus [The minimum degree threshold for perfect graph packings, Combinatorica, 2009]. We use our general framework to resolve the perfect H-tiling problem for all ordered graphs H of interval chromatic number 2. Already in this restricted setting the class of extremal examples is richer than in the unordered graph problem. In the process of proving our results, novel approaches to both the regularity and absorbing methods are developed.

Evaluation of Candida Albicans Adhesion to Two Different Types of Acrylic Resin

Background and Aim: A common infection in complete or partial denture wearers is denture stomatitis. One of the most important factors in the adhesion of Candida albicans is the surface and chemical properties of the denture base materials. The aim of this study was to investigate the surface roughness and adhesion of Candida albicans to two different types of acrylic materials. Materials and Methods: In this experimental study, 16 samples were prepared from each of Vertex and Ivoclar acrylic resin. The surface roughness of the samples was measured by a profilometer. The samples were then placed in a cell suspension of Candida albicans. After incubation and staining with acridine orange, the yeast cells attached to the acrylic samples were counted using a fluorescent microscope. Data were statistically analyzed by T-test. Ethical considerations: This article is approved by the ethics committee of Arak University of Medical Sciences with the ethics code: IR.ARAKMU.REC.1398.301. Findings: There was no statistically significant difference in the mean of surface roughness between the two study groups (P = 0.311). However, Candida albicans colonization in ivoclar acrylic was significantly lower than vertex acrylic. (P = 0.000). Conclusion: Differences in surface topography and physical and chemical properties of Vertex and Ivoclar acrylic resin affect the adhesion of Candida albicans.

Exploring smoking-gun signals of the Schwinger mechanism in QCD

In Quantum Chromodynamics, the Schwinger mechanism endows the gluons with an effective mass through the dynamical formation of massless bound-state poles that are longitudinally coupled. The presence of these poles affects profoundly the infrared properties of the interaction vertices, inducing crucial modifications to their fundamental Ward identities. Within this general framework, we present a detailed derivation of the non-Abelian Ward identity obeyed by the pole-free part of the three-gluon vertex in the soft-gluon limit, and determine the smoking-gun displacement that the onset of the Schwinger mechanism produces to the standard result. Quite importantly, the quantity that describes this distinctive feature coincides formally with the bound-state wave function that controls the massless pole formation. Consequently, this signal may be computed in two independent ways: by solving an approximate version of the pertinent Bethe-Salpeter integral equation, or by appropriately combining the elements that enter in the aforementioned Ward identity. For the implementation of both methods we employ two- and three-point correlation functions obtained from recent lattice simulations, and a partial derivative of the ghost-gluon kernel, which is computed from the corresponding Schwinger-Dyson equation. Our analysis reveals an excellent coincidence between the results obtained through either method, providing a highly nontrivial self-consistency check for the entire approach. When compared to the null hypothesis, where the Schwinger mechanism is assumed to be inactive, the statistical significance of the resulting signal is estimated to be 3 standard deviations.

On joint properties of vertices with a given degree or label in the random recursive tree

In this paper, we study the joint behaviour of the degree, depth, and label of and graph distance between high-degree vertices in the random recursive tree. We generalise the results obtained by Eslava [12] and extend these to include the labels of and graph distance between high-degree vertices. The analysis of both these two properties of high-degree vertices is novel, in particular in relation to the behaviour of the depth of such vertices. In passing, we also obtain results for the joint behaviour of the degree and depth of and graph distance between any fixed number of vertices with a prescribed label. This combines several isolated results on the degree [22], depth [7, 24], and graph distance [9, 15] of vertices with a prescribed label already present in the literature. Furthermore, we extend these results to hold jointly for any number of fixed vertices and improve these results by providing more detailed descriptions of the distributional limits. Our analysis is based on a correspondence between the random recursive tree and a representation of the Kingman n-coalescent.

Measurement of inclusive charged-particle b-jet production in pp and p-Pb collisions at sqrt{s_{mathrm{NN}}} = 5.02 TeV

A measurement of the inclusive b-jet production cross section is presented in pp and p-Pb collisions at sqrt{s_{mathrm{NN}}} = 5.02 TeV, using data collected with the ALICE detector at the LHC. The jets were reconstructed in the central rapidity region |η| < 0.5 from charged particles using the anti-kT algorithm with resolution parameter R = 0.4. Identification of b jets exploits the long lifetime of b hadrons, using the properties of secondary vertices and impact parameter distributions. The pT-differential inclusive production cross section of b jets, as well as the corresponding inclusive b-jet fraction, are reported for pp and p-Pb collisions in the jet transverse momentum range 10 ≤ pT,ch jet≤ 100 GeV/c, together with the nuclear modification factor, {R}_{mathrm{pPb}}^{mathrm{b}-mathrm{jet}} . The analysis thus extends the lower pT limit of b-jet measurements at the LHC. The nuclear modification factor is found to be consistent with unity, indicating that the production of b jets in p-Pb at sqrt{s_{mathrm{NN}}} = 5.02 TeV is not affected by cold nuclear matter effects within the current precision. The measurements are well reproduced by POWHEG NLO pQCD calculations with PYTHIA fragmentation.

Properties of Detour Central and Detour Boundary Vertices in Neutrosophic Graphs

In this paper, the idea of neutrosophic detour boundary vertices and neutrosophic detour center vertices in neutrosophic graph is introduced. Here the concept of neutrosophic detour eccentricity, neutrosophic detour radius, neutrosophic detour diameter, neutrosophic detour neighbourhood vertex are studied. Several interesting properties related to of eccentric nodes, peripheral nodes, and central nodes in neutrosophic graphs are established.

Similar Vertices and Isomorphism Detection for Planar Kinematic Chains Based on Ameliorated Multi-Order Adjacent Vertex Assignment Sequence

Isomorphism detection is fundamental to the synthesis and innovative design of kinematic chains (KCs). The detection can be performed accurately by using the similarity of KCs. However, there are very few works on isomorphism detection based on the properties of similar vertices. In this paper, an ameliorated multi-order adjacent vertex assignment sequence (AMAVS) method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs. First, the specific definition of AMAVS is described. Through the calculation of the AMAVS, the adjacent vertex value sequence reflecting the uniqueness of the topology features is established. Based on the value sequence, all possible similar vertices, corresponding relations, and isomorphism discrimination can be realized. By checking the topological graph of KCs with a different number of links, the effectiveness and efficiency of the proposed method are verified. Finally, the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-DOF(degree of freedom) planar KCs.

Properties of non stationer pseudo vertex with the break of smoothness of the target set boarder curvature in the Dirichlet problem to eikonal type equation

Properties of non stationer pseudo vertex with the break of smoothness of the target set boarder curvature in the Dirichlet problem to eikonal type equation

A new family of maximum scattered linear sets in PG(1, q^6)

We generalize the example of linear set presented by the last two authors in “Vertex properties of maximum scattered linear sets of PG(1, qn)" (2019) to a more general family, proving that such linear sets are maximum scattered when q is odd and, apart from a special case, they are new. This solves an open problem posed in “Vertex properties of maximum scattered linear sets of PG(1, qn)" (2019). As a consequence of Sheekey’s results in “A new family of linear maximum rank distance codes" (2016), this family yields to new MRD-codes with parameters (6, 6, q; 5).

Top-[formula omitted] user-specified preferred answers in massive graph databases

There are numerous applications where users wish to identify subsets of vertices in a social network or graph database that are of interest to them. They may specify sets of patterns and vertex properties, and each of these confers a score to a subgraph. The users want to find the subgraphs with top-k highest scores. Examples in the real world where such subgraphs involve custom scoring methods include: techniques to identify sets of coordinated influence bots on Twitter, methods to identify suspicious subgraphs of nodes involved in nuclear proliferation networks, and sets of sockpuppet accounts seeking to illicitly influence star ratings on e-commerce platforms. All of these types of applications have numerous custom scoring methods. This motivates the concept of Scoring Queries presented in this paper — unlike past work, an important aspect of scoring queries is that the users get to choose the scoring mechanism, not the system. We present the Advanced top-k (ATK) algorithm and show that it intelligently leverages graph indexes from the past but also presents novel pruning opportunities. We present an implementation of ATK showing that it beats out a baseline algorithm that builds on advanced subgraph matching methods with multiple graph database backends including Jena and GraphDB. We show that ATK scales well on real world graph databases from YouTube, Flickr, IMDb, and CiteSeerX.

Graph Signal Processing Approach to QSAR/QSPR Model Learning of Compounds.

Quantitative relationship between the activity/property and the structure of compound is critical in chemical applications. To learn this quantitative relationship, hundreds of molecular descriptors have been designed to describe the structure, mainly based on the properties of vertices and edges of molecular graph. However, many descriptors degenerate to the same values for different compounds with the same molecular graph, resulting in model failure. In this paper, we design a multidimensional signal for each vertex of the molecular graph to derive new descriptors with higher discriminability. We treat the new and traditional descriptors as the signals on the descriptor graph learned from the descriptor data, and enhance descriptor dissimilarity using the Laplacian filter derived from the descriptor graph. Combining these with model learning techniques, we propose a graph signal processing based approach to obtain reliable new models for learning the quantitative relationship and predicting the properties of compounds. We also provide insights from chemistry for the boiling point model. Several experiments are presented to demonstrate the validity, effectiveness and advantages of the proposed approach.