scholarly journals On deformation spaces of nonuniform hyperbolic lattices

2016 ◽  
Vol 161 (2) ◽  
pp. 283-303 ◽  
Author(s):  
SUNGWOON KIM ◽  
INKANG KIM
Keyword(s):  
Hyperbolic Manifolds ◽  
Rigidity Theorem ◽  
Connected Components ◽  
Connected Component ◽  
Deformation Spaces ◽  
Representation Variety ◽  
The Real ◽  
Local Rigidity ◽  
Semialgebraic Subset ◽  
Hyperbolic Lattices

AbstractLet Γ be a nonuniform lattice acting on the real hyperbolic n-space. We show that in dimension greater than or equal to 4, the volume of a representation is constant on each connected component of the representation variety of Γ in SO(n, 1). Furthermore, in dimensions 2 and 3, there is a semialgebraic subset of the representation variety such that the volume of a representation is constant on connected components of the semialgebraic subset. Combining our approach with the main result of [2] gives a new proof of the local rigidity theorem for nonuniform hyperbolic lattices and the analogue of Soma's theorem, which shows that the number of orientable hyperbolic manifolds dominated by a closed, connected, orientable 3-manifold is finite, for noncompact 3-manifolds.

scholarly journals Local quaternionic rigidity for complex hyperbolic lattices

2010 ◽  
Vol 11 (1) ◽  
pp. 133-159 ◽  
Author(s):  
Inkang Kim ◽  
Bruno Klingler ◽  
P. Pansu
Keyword(s):  
Lie Group ◽  
The Other ◽  
Natural Sequence ◽  
The Real ◽  
Local Rigidity ◽  
Other Hand ◽  
Hyperbolic Lattices

AbstractLet $\smash{\sGa\stackrel{i}{\hookrightarrow}L}$ be a lattice in the real simple Lie group L. If L is of rank at least 2 (respectively locally isomorphic to Sp(n, 1)) any unbounded morphism ρ : Γ → G into a simple real Lie group G essentially extends to a Lie morphism ρL : L → G (Margulis's superrigidity theorem, respectively Corlette's theorem). In particular any such morphism is infinitesimally, thus locally, rigid. On the other hand, for L = SU(n, 1) even morphisms of the form $\smash{\rho:\sGa\stackrel{i}{\hookrightarrow}L \rightarrow G}$ are not infinitesimally rigid in general. Almost nothing is known about their local rigidity. In this paper we prove that any cocompact lattice Γ in SU(n, 1) is essentially locally rigid (while in general not infinitesimally rigid) in the quaternionic groups Sp(n, 1), SU(2n, 2) or SO(4n, 4) (for the natural sequence of embeddings SU(n, 1) ⊂ Sp(n, 1) ⊂ SU(2n, 2) ⊂ SO(4n, 4)).

scholarly journals The number of connected components of certain real algebraic curves

2001 ◽  
Vol 25 (11) ◽  
pp. 693-701
Author(s):  
Seon-Hong Kim
Keyword(s):  
Algebraic Curve ◽  
Algebraic Curves ◽  
Connected Components ◽  
Connected Component ◽  
The Real ◽  
Real Algebraic Curves ◽  
Real Algebraic Curve

For an integern≥2, letp(z)=∏k=1n(z−αk)andq(z)=∏k=1n(z−βk), whereαk,βkare real. We find the number of connected components of the real algebraic curve{(x,y)∈ℝ2:|p(x+iy)|−|q(x+iy)|=0}for someαkandβk. Moreover, in these cases, we show that each connected component contains zeros ofp(z)+q(z), and we investigate the locus of zeros ofp(z)+q(z).

scholarly journals Schreir graphs: Transitivity and coverings

2016 ◽  
Vol 26 (01) ◽  
pp. 69-93 ◽  
Author(s):  
Paul-Henry Leemann
Keyword(s):  
Hyperbolic Manifolds ◽  
Rigidity Theorem ◽  
Partial Answer ◽  
Schreier Graphs

We give a characterization of isomorphisms between Schreier graphs in terms of the groups, subgroups and generating systems. This characterization may be thought as a graph analog of Mostow’s rigidity theorem for hyperbolic manifolds. This allows us to give a transitivity criterion for Schreier graphs. Finally, we show that Tarski monsters satisfy a strong simplicity criterion. This gives a partial answer to a question of Benjamini and Duminil-Copin.

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 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.

The Selberg–Weil–Kobayashi rigidity theorem: The rank one solvable case

2016 ◽  
Vol 27 (10) ◽  
pp. 1650085
Author(s):  
A. Baklouti ◽  
N. Elaloui ◽  
I. Kedim
Keyword(s):  
Homogeneous Space ◽  
Symmetric Spaces ◽  
Homogeneous Spaces ◽  
Rigidity Theorem ◽  
General Context ◽  
Affine Transformations ◽  
Discontinuous Group ◽  
Solvable Case ◽  
Local Rigidity ◽  
Discontinuous Groups

A local rigidity theorem was proved by Selberg and Weil for Riemannian symmetric spaces and generalized by Kobayashi for a non-Riemannian homogeneous space [Formula: see text], determining explicitly which homogeneous spaces [Formula: see text] allow nontrivial continuous deformations of co-compact discontinuous groups. When [Formula: see text] is assumed to be exponential solvable and [Formula: see text] is a maximal subgroup, an analog of such a theorem states that the local rigidity holds if and only if [Formula: see text] is isomorphic to the group Aff([Formula: see text]) of affine transformations of the real line (cf. [L. Abdelmoula, A. Baklouti and I. Kédim, The Selberg–Weil–Kobayashi rigidity theorem for exponential Lie groups, Int. Math. Res. Not. 17 (2012) 4062–4084.]). The present paper deals with the more general context, when [Formula: see text] is a connected solvable Lie group and [Formula: see text] a maximal nonnormal subgroup of [Formula: see text]. We prove that any discontinuous group [Formula: see text] for a homogeneous space [Formula: see text] is abelian and at most of rank 2. Then we discuss an analog of the Selberg–Weil–Kobayashi local rigidity theorem in this solvable setting. In contrast to the semi-simple setting, the [Formula: see text]-action on [Formula: see text] is not always effective, and thus the space of group theoretic deformations (formal deformations) [Formula: see text] could be larger than geometric deformation spaces. We determine [Formula: see text] and also its quotient modulo uneffective parts when the rank [Formula: see text]. Unlike the context of exponential solvable case, we prove the existence of formal colored discontinuous groups. That is, the parameter space admits a mixture of locally rigid and formally nonrigid deformations.

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.

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