scholarly journals Asymptotic Properties of Random Unlabelled Block-Weighted Graphs

10.37236/9923 ◽  
2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Benedikt Stufler
Keyword(s):  
Asymptotic Properties ◽  
Scaling Limit ◽  
Connected Components ◽  
Weighted Graphs ◽  
Connected Component ◽  
Outerplanar Graphs ◽  
Asymptotic Shape ◽  
Limit Graph ◽  
Special Case ◽  
Random Limit

We study the asymptotic shape of random unlabelled graphs subject to certain subcriticality conditions. The graphs are sampled with probability proportional to a product of Boltzmann weights assigned to their $2$-connected components. As their number of vertices tends to infinity, we show that they admit the Brownian tree as Gromov–Hausdorff–Prokhorov scaling limit, and converge in a strengthened Benjamini–Schramm sense toward an infinite random graph. We also consider models of random graphs that are allowed to be disconnected. Here a giant connected component emerges and the small fragments converge without any rescaling towards a finite random limit graph. Our main application of these general results treats subcritical classes of unlabelled graphs. We study the special case of unlabelled outerplanar graphs in depth and calculate its scaling constant.

The size of the connected components of excursion sets of χ2, t and F fields

1999 ◽  
Vol 31 (03) ◽  
pp. 579-595 ◽  
Author(s):  
J. Cao
Keyword(s):  
Positron Emission Tomography ◽  
Two Dimensions ◽  
Emission Tomography ◽  
Connected Components ◽  
Gaussian Fields ◽  
Connected Component ◽  
Test Statistic ◽  
Excursion Sets ◽  
Positron Emission ◽  
Excursion Set

The distribution of the size of one connected component and the largest connected component of the excursion set is derived for stationary χ2, t and F fields, in the limit of high or low thresholds. This extends previous results for stationary Gaussian fields (Nosko 1969, Adler 1981) and for χ2 fields in one and two dimensions (Aronowich and Adler 1986, 1988). An application of this is to detect regional changes in positron emission tomography (PET) images of blood flow in human brain, using the size of the largest connected component of the excursion set as a test statistic.

scholarly journals AUTOMORPHISMS OF PARTIALLY COMMUTATIVE GROUPS II: COMBINATORIAL SUBGROUPS

2012 ◽  
Vol 22 (07) ◽  
pp. 1250074 ◽  
Author(s):  
ANDREW J. DUNCAN ◽  
VLADIMIR N. REMESLENNIKOV
Keyword(s):  
Automorphism Group ◽  
Decomposition Theorem ◽  
Direct Decomposition ◽  
Connected Components ◽  
Artin Group ◽  
Special Case

We define several "standard" subgroups of the automorphism group Aut (G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut (G). If C is the commutation graph of G, we show how Aut (G) decomposes in terms of the connected components of C: obtaining a particularly clear decomposition theorem in the special case where C has no isolated vertices. If C has no vertices of a type we call dominated then we give a semi-direct decomposition of Aut (G) into a subgroup of locally conjugating automorphisms by the subgroup stabilizing a certain lattice of "admissible subsets" of the vertices of C. We then characterize those graphs for which Aut (G) is a product (not necessarily semi-direct) of two such subgroups.

scholarly journals Dental Images’ Segmentation Using Threshold Connected Component Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Vincent Majanga ◽  
Serestina Viriri
Keyword(s):  
Deep Learning ◽  
Region Of Interest ◽  
Component Analysis ◽  
Connected Components ◽  
Connected Component ◽  
Low Contrast ◽  
Connected Component Analysis ◽  
Feature Representations ◽  
Learning Techniques ◽  
Performance Results

Recent advances in medical imaging analysis, especially the use of deep learning, are helping to identify, detect, classify, and quantify patterns in radiographs. At the center of these advances is the ability to explore hierarchical feature representations learned from data. Deep learning is invaluably becoming the most sought out technique, leading to enhanced performance in analysis of medical applications and systems. Deep learning techniques have achieved great performance results in dental image segmentation. Segmentation of dental radiographs is a crucial step that helps the dentist to diagnose dental caries. The performance of these deep networks is however restrained by various challenging features of dental carious lesions. Segmentation of dental images becomes difficult due to a vast variety in topologies, intricacies of medical structures, and poor image qualities caused by conditions such as low contrast, noise, irregular, and fuzzy edges borders, which result in unsuccessful segmentation. The dental segmentation method used is based on thresholding and connected component analysis. Images are preprocessed using the Gaussian blur filter to remove noise and corrupted pixels. Images are then enhanced using erosion and dilation morphology operations. Finally, segmentation is done through thresholding, and connected components are identified to extract the Region of Interest (ROI) of the teeth. The method was evaluated on an augmented dataset of 11,114 dental images. It was trained with 10 090 training set images and tested on 1024 testing set images. The proposed method gave results of 93 % for both precision and recall values, respectively.

Feature based Text Extraction System using Connected Component Method

2016 ◽  
Vol 7 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Nitigya Sambyal ◽  
Pawanesh Abrol
Keyword(s):  
Character Segmentation ◽  
Connected Components ◽  
Test Cases ◽  
Connected Component ◽  
Font Size ◽  
Text Extraction ◽  
Component Technique ◽  
Edge Detectors ◽  
Feature Based

Text detection and segmentation system serves as important method for document analysis as it helps in many content based image analysis tasks. This research paper proposes a connected component technique for text extraction and character segmentation using maximally stable extremal regions (MSERs) for text line formation followed by connected components to determined separate characters. The system uses a cluster size of five which is selected by experimental evaluation for identifying characters. Sobel edge detector is used as it reduces the execution time but at the same time maintains quality of the results. The algorithm is tested along a set of JPEG, PNG and BMP images over varying features like font size, style, colour, background colour and text variation. Further the CPU time in execution of the algorithm with three different edge detectors namely prewitt, sobel and canny is observed. Text identification using MSER gave very good results whereas character segmentation gave on average 94.572% accuracy for the various test cases considered for this study.

scholarly journals SELF-STABILIZING COMPUTATION OF 3-EDGE-CONNECTED COMPONENTS

2011 ◽  
Vol 22 (05) ◽  
pp. 1161-1185
Author(s):  
ABUSAYEED SAIFULLAH ◽  
YUNG H. TSIN
Keyword(s):  
Time Complexity ◽  
Computer Network ◽  
Connected Components ◽  
Connected Component ◽  
External Agent ◽  
Tree Construction ◽  
Legitimate State ◽  
Time And Space Complexity ◽  
Better Than ◽  
Made In

A self-stabilizing algorithm is a distributed algorithm that can start from any initial (legitimate or illegitimate) state and eventually converge to a legitimate state in finite time without being assisted by any external agent. In this paper, we propose a self-stabilizing algorithm for finding the 3-edge-connected components of an asynchronous distributed computer network. The algorithm stabilizes in O(dnΔ) rounds and every processor requires O(n log Δ) bits, where Δ(≤ n) is an upper bound on the degree of a node, d(≤ n) is the diameter of the network, and n is the total number of nodes in the network. These time and space complexity are at least a factor of n better than those of the previously best-known self-stabilizing algorithm for 3-edge-connectivity. The result of the computation is kept in a distributed fashion by assigning, upon stabilization of the algorithm, a component identifier to each processor which uniquely identifies the 3-edge-connected component to which the processor belongs. Furthermore, the algorithm is designed in such a way that its time complexity is dominated by that of the self-stabilizing depth-first search spanning tree construction in the sense that any improvement made in the latter automatically implies improvement in the time complexity of the algorithm.

Asymptotic solutions of the Orr—Sommerfeld equation

1975 ◽  
Vol 280 (1295) ◽  
pp. 271-316
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansions ◽  
Asymptotic Properties ◽  
Matched Asymptotic Expansions ◽  
Asymptotic Solutions ◽  
Asymptotic Approximations ◽  
General Kind ◽  
Work Done ◽  
Sommerfeld Equation ◽  
Special Case

A rigorous justification is given of work done by Eagles (1969), in which he applied the method of matched asymptotic expansions to the Orr-Sommerfeld equation to obtain formal uniform asymptotic approximations to a certain pair of solutions. (Somewhat more polished formal expansions of the same general kind were subsequently obtained by Reid (1972).) First, a study is made of the asymptotic properties of solutions of a certain differential equation which admits the Orr—Sommerfeld equation as a special case. Previous work on this differential equation by Lin & Rabenstein ( i960, 1969) is extended to develop a theory suited to our main purpose: to prove the validity of Eagles’s approximations. It is then shown how this theory can be used to prove the existence of actual solutions of the Orr—Sommerfeld equation approximated by these formal expansions. In addition, it is verified that these solutions have the properties assumed by Eagles (1969).

WEIGHTED-EDGE-COLORING OF k-DEGENERATE GRAPHS AND BIN-PACKING

2011 ◽  
Vol 12 (01n02) ◽  
pp. 109-124
Author(s):  
FLORIAN HUC
Keyword(s):  
Bin Packing ◽  
Edge Coloring ◽  
Weighted Graph ◽  
Packing Problem ◽  
Bipartite Graphs ◽  
Specific Class ◽  
Weighted Graphs ◽  
Outerplanar Graphs ◽  
Underlying Graph ◽  
Multiple Edges

The weighted-edge-coloring problem of an edge-weighted graph whose weights are between 0 and 1, consists in finding a coloring using as few colors as possible and satisfying the following constraints: the sum of weights of edges with the same color and incident to the same vertex must be at most 1. In 1991, Chung and Ross conjectured that if G is bipartite, then [Formula: see text] colors are always sufficient to weighted-edge-color (G,w), where [Formula: see text] is the maximum of the sums of the weights of the edges incident to a vertex. We prove this is true for edge-weighted graphs with multiple edges whose underlying graph is a tree. We further generalise this conjecture to non-bipartite graphs and prove the generalised conjecture for simple edge-weighted outerplanar graphs. Finally, we introduce a list version of this coloring together with the list-bin-packing problem, which allows us to obtain new results concerning the original coloring for a specific class of graphs, namely the k-weight-degenerate weighted graph.

scholarly journals Using Distance Measure based Classification in Automatic Extraction of Lungs Cancer Nodules for Computer Aided Diagnosis

2021 ◽  
Vol 12 (3) ◽  
pp. 25-43
Author(s):  
Maan Ammar ◽  
Muhammad Shamdeen ◽  
Mazen Kasedeh ◽  
Kinan Mansour ◽  
Waad Ammar
Keyword(s):  
Euclidean Distance ◽  
Distance Measure ◽  
Ct Images ◽  
Chest Ct ◽  
Connected Components ◽  
Automatic Extraction ◽  
Morphological Operations ◽  
Connected Component ◽  
Overall Performance ◽  
Aided Diagnosis

We introduce in this paper a reliable method for automatic extraction of lungs nodules from CT chest images and shed the light on the details of using the Weighted Euclidean Distance (WED) for classifying lungs connected components into nodule and not-nodule. We explain also using Connected Component Labeling (CCL) in an effective and flexible method for extraction of lungs area from chest CT images with a wide variety of shapes and sizes. This lungs extraction method makes use of, as well as CCL, some morphological operations. Our tests have shown that the performance of the introduce method is high. Finally, in order to check whether the method works correctly or not for healthy and patient CT images, we tested the method by some images of healthy persons and demonstrated that the overall performance of the method is satisfactory.

scholarly journals Enumeration and Asymptotic Properties of Unlabeled Outerplanar Graphs

10.37236/984 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Manuel Bodirsky ◽  
Éric Fusy ◽  
Mihyun Kang ◽  
Stefan Vigerske
Keyword(s):  
Chromatic Number ◽  
Polynomial Time ◽  
Asymptotic Properties ◽  
Statistical Properties ◽  
Cycle Index ◽  
Outerplanar Graphs ◽  
Analytic Combinatorics ◽  
Exact Number ◽  
Asymptotic Number

We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number $g_{n}$ of unlabeled outerplanar graphs on $n$ vertices can be computed in polynomial time, and $g_{n}$ is asymptotically $g\, n^{-5/2}\rho^{-n}$, where $g\approx0.00909941$ and $\rho^{-1}\approx7.50360$ can be approximated. Using our enumerative results we investigate several statistical properties of random unlabeled outerplanar graphs on $n$ vertices, for instance concerning connectedness, the chromatic number, and the number of edges. To obtain the results we combine classical cycle index enumeration with recent results from analytic combinatorics.

scholarly journals Factorial analyses of treatment effects under independent right-censoring

2019 ◽  
Vol 29 (2) ◽  
pp. 325-343
Author(s):  
Dennis Dobler ◽  
Markus Pauly
Keyword(s):  
Asymptotic Properties ◽  
Small Sample ◽  
Right Censoring ◽  
Event Data ◽  
Time To Event ◽  
Sample Design ◽  
Time To Event Data ◽  
Practical Usefulness ◽  
Simulation Results ◽  
Special Case

This paper introduces new effect parameters for factorial survival designs with possibly right-censored time-to-event data. In the special case of a two-sample design, it coincides with the concordance or Wilcoxon parameter in survival analysis. More generally, the new parameters describe treatment or interaction effects and we develop estimates and tests to infer their presence. We rigorously study their asymptotic properties and additionally suggest wild bootstrapping for a consistent and distribution-free application of the inference procedures. The small sample performance is discussed based on simulation results. The practical usefulness of the developed methodology is exemplified on a data example about patients with colon cancer by conducting one- and two-factorial analyses.

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