Alternating maps on Hatcher–Thurston graphs

2017 ◽  
Vol 26 (11) ◽  
pp. 1750064 ◽  
Author(s):  
Jesús Hernández Hernández
Keyword(s):  
Edge Preserving ◽  
Genus Formula ◽  
Orientable Surfaces

Let [Formula: see text] and [Formula: see text] be connected orientable surfaces of genus [Formula: see text], [Formula: see text] punctures, and empty boundary. Let also [Formula: see text] be an edge-preserving alternating map between their Hatcher–Thurston graphs. We prove that [Formula: see text] and that there is also a multicurve of cardinality [Formula: see text] contained in every element of the image. We also prove that if [Formula: see text] and [Formula: see text], then the map [Formula: see text] obtained by filling the punctures of [Formula: see text], is induced by a homeomorphism of [Formula: see text].

scholarly journals Edge-preserving maps of the nonseparating curve graphs, curve graphs and rectangle preserving maps of the Hatcher–Thurston graphs

2020 ◽  
Vol 29 (11) ◽  
pp. 2050078
Author(s):  
Elmas Irmak
Keyword(s):  
Orientable Surface ◽  
Edge Preserving ◽  
Curve Graph ◽  
Genus Formula

Let [Formula: see text] be a compact, connected, orientable surface of genus [Formula: see text] with [Formula: see text] boundary components with [Formula: see text], [Formula: see text]. Let [Formula: see text] be the nonseparating curve graph, [Formula: see text] be the curve graph and [Formula: see text] be the Hatcher–Thurston graph of [Formula: see text]. We prove that if [Formula: see text] is an edge-preserving map, then [Formula: see text] is induced by a homeomorphism of [Formula: see text]. We prove that if [Formula: see text] is an edge-preserving map, then [Formula: see text] is induced by a homeomorphism of [Formula: see text]. We prove that if [Formula: see text] is closed and [Formula: see text] is a rectangle preserving map, then [Formula: see text] is induced by a homeomorphism of [Formula: see text]. We also prove that these homeomorphisms are unique up to isotopy when [Formula: see text].

scholarly journals On model-theoretic connected components in some group extensions

2015 ◽  
Vol 15 (02) ◽  
pp. 1550009 ◽  
Author(s):  
Jakub Gismatullin ◽  
Krzysztof Krupiński
Keyword(s):  
Free Groups ◽  
Invariant Subgroup ◽  
Universal Cover ◽  
Connected Components ◽  
Fundamental Groups ◽  
Bounded Cohomology ◽  
Central Extensions ◽  
Finite Image ◽  
Genus Formula ◽  
Orientable Surfaces

We analyze model-theoretic connected components in extensions of a given group by abelian groups which are defined by means of 2-cocycles with finite image. We characterize, in terms of these 2-cocycles, when the smallest type-definable subgroup of the corresponding extension differs from the smallest invariant subgroup. In some situations, we also describe the quotient of these two connected components. Using our general results about extensions of groups together with Matsumoto–Moore theory or various quasi-characters considered in bounded cohomology, we obtain new classes of examples of groups whose smallest type-definable subgroup of bounded index differs from the smallest invariant subgroup of bounded index. This includes the first known example of a group with this property found by Conversano and Pillay, namely the universal cover of [Formula: see text] (interpreted in a monster model), as well as various examples of different nature, e.g. some central extensions of free groups or of fundamental groups of closed orientable surfaces. As a corollary, we get that both non-abelian free groups and fundamental groups of closed orientable surfaces of genus [Formula: see text], expanded by predicates for all subsets, have this property, too. We also obtain a variant of the example of Conversano and Pillay for [Formula: see text] instead of [Formula: see text], which (as most of our examples) was not accessible by the previously known methods.

scholarly journals Roots of Dehn twists on nonorientable surfaces

2019 ◽  
Vol 28 (12) ◽  
pp. 1950077
Author(s):  
Anna Parlak ◽  
Michał Stukow
Keyword(s):  
Mapping Class Group ◽  
Class Group ◽  
Mapping Class ◽  
Maximal Degree ◽  
Simple Arithmetic ◽  
Nonorientable Surface ◽  
Dehn Twists ◽  
Nonorientable Surfaces ◽  
Genus Formula ◽  
Orientable Surfaces

Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist [Formula: see text] about a nonseparating circle [Formula: see text] in the mapping class group [Formula: see text] of a nonorientable surface [Formula: see text] of genus [Formula: see text]. We explore the existence of roots and, following the work of McCullough, Rajeevsarathy and Monden, give a simple arithmetic description of their conjugacy classes. We also study roots of maximal degree and prove that if we fix an odd integer [Formula: see text], then for each sufficiently large [Formula: see text], [Formula: see text] has a root of degree [Formula: see text] in [Formula: see text]. Moreover, for any possible degree [Formula: see text], we provide explicit expressions for a particular type of roots of Dehn twists about nonseparating circles in [Formula: see text].

Edge-Preserving Error Diffusion for Multi-Toning Based on Dual Quantization

2017 ◽  
Vol 2017 (18) ◽  
pp. 123-129
Author(s):  
Takuma Kiyotomo ◽  
Keisuke Hoshino ◽  
Yuki Tsukano ◽  
Hiroki Kibushi ◽  
Takahiko Horiuchi
Keyword(s):  
Error Diffusion ◽  
Edge Preserving

Material Identification in Presence of Metal for Baggage Screening

2020 ◽  
Vol 2020 (14) ◽  
pp. 294-1-294-8
Author(s):  
Sandamali Devadithya ◽  
David Castañón
Keyword(s):  
Atomic Number ◽  
Effective Atomic Number ◽  
Simulated Data ◽  
Dual Energy ◽  
Basis Functions ◽  
Total Variation Regularization ◽  
Ct Scanner ◽  
Edge Preserving ◽  
Baggage Screening ◽  
Dual Energy Imaging

Dual-energy imaging has emerged as a superior way to recognize materials in X-ray computed tomography. To estimate material properties such as effective atomic number and density, one often generates images in terms of basis functions. This requires decomposition of the dual-energy sinograms into basis sinograms, and subsequently reconstructing the basis images. However, the presence of metal can distort the reconstructed images. In this paper we investigate how photoelectric and Compton basis functions, and synthesized monochromatic basis (SMB) functions behave in the presence of metal and its effect on estimation of effective atomic number and density. Our results indicate that SMB functions, along with edge-preserving total variation regularization, show promise for improved material estimation in the presence of metal. The results are demonstrated using both simulated data as well as data collected from a dualenergy medical CT scanner.

Pre-Processing of Hyperspectral Images Using Nonlinear Filters

2013 ◽  
Vol 11 (1) ◽  
pp. 8-13
Author(s):  
V. Behar ◽  
V. Bogdanova
Keyword(s):  
Signal To Noise Ratio ◽  
Correlation Coefficients ◽  
Hyperspectral Images ◽  
Spectral Correlation ◽  
Edge Preserving ◽  
Improvement Factor ◽  
Filter Output ◽  
Average Improvement ◽  
Processing Procedure

Abstract In this paper the use of a set of nonlinear edge-preserving filters is proposed as a pre-processing stage with the purpose to improve the quality of hyperspectral images before object detection. The capability of each nonlinear filter to improve images, corrupted by spatially and spectrally correlated Gaussian noise, is evaluated in terms of the average Improvement factor in the Peak Signal to Noise Ratio (IPSNR), estimated at the filter output. The simulation results demonstrate that this pre-processing procedure is efficient only in case the spatial and spectral correlation coefficients of noise do not exceed the value of 0.6

New edge preserving enlargement algorithm for images

2013 ◽  
Vol 32 (11) ◽  
pp. 3182-3184
Author(s):  
Ye YUAN ◽  
Zhong-xu TIAN
Keyword(s):  
Edge Preserving
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