Homotopy Equivalence and Groups of Measure-Preserving Homeomorphisms

2006 ◽  
Vol 49 (3) ◽  
pp. 337-346
Author(s):  
R. Berlanga
Keyword(s):  
Direct Limit ◽  
Homotopy Equivalence ◽  
General Group ◽  
Compactly Supported

AbstractIt is shown that the group of compactly supported, measure-preserving homeomorphisms of a connected, second countable manifold is locally contractible in the direct limit topology. Furthermore, this group is weakly homotopically equivalent to the more general group of compactly supported homeomorphisms.

Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

2013 ◽  
Author(s):  
Friedhelm Waldhausen ◽  
Bjørn Jahren ◽  
John Rognes
Keyword(s):  
Main Tool ◽  
Homotopy Equivalence ◽  
Classifying Space ◽  
Deformation Retract ◽  
Simplicial Sets ◽  
Full Proof

Since its introduction by the author in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing the author's program from more than thirty years ago. The main result is a stable parametrized h-cobordism theorem, derived from a homotopy equivalence between a space of PL h-cobordisms on a space X and the classifying space of a category of simple maps of spaces having X as deformation retract. The smooth and topological results then follow by smoothing and triangulation theory. The proof has two main parts. The essence of the first part is a “desingularization,” improving arbitrary finite simplicial sets to polyhedra. The second part compares polyhedra with PL manifolds by a thickening procedure. Many of the techniques and results developed should be useful in other connections.

Efficacy evaluation of the CEUS-LI-RADS-v2017 system in differential diagnosis of liver tumors

2019 ◽  
pp. 57-67
Author(s):  
A. N. Katrich ◽  
V. A. Porkhanov ◽  
N. S. Ryabin
Keyword(s):  
Risk Factors ◽  
Differential Diagnosis ◽  
Liver Tumors ◽  
Morphological Data ◽  
Malignant Neoplasms ◽  
Diagnostic Efficiency ◽  
Efficacy Evaluation ◽  
General Group ◽  
Group 2 ◽  
Group 1

Objective: efficacy evaluation of the CEUS LI RADS v2017® system for differential diagnosis of liver tumors in patients with and without cirrhosis.Materials and methods. Retrospective analysis of diagnostic results of the 165 patients with liver tumors (177 nodules) was done. All patients underwent CEUS with results interpretation in accordance to the CEUS LIRADSv2017 ® criteria. Patients were divided into 2 groups based on clinical and morphological data. Group 1 included 62 patients with cirrhosis and/or CVH. Group 2 included 110 patients without risk factors for HCC.Results. Diagnostic efficiency of CEUS LI RADS v2017® for HCC identification was: group 1 – Se – 100%, Sp – 88%, Ac – 95.5%; group 2 – Se – 100%, Sp – 68.8%, Ac – 72.7%; general group Se – 100%, Sp – 72.2%, Ac – 81.4%. In the 2nd group, 21 out of 22 neoplasms, confirmed morphologically as FNH, we classified as LR 4. By applying benign character and specific contrasting patterns of FNG, they were transferred from LR 4 to LR 3. This allowed to increase sensitivity and specificity of differential diagnosis in group 2 (Se – 100%, Sp – 90.6%, Ac – 91.8%) and in general group (Se – 100%, Sp – 90.1%, Ac – 93.2%). Diagnostic efficiency of the criteria for non hepatocellular malignant neoplasms (LR M) was: group 1 – Se – 77.8%, Sp – 100%, Ac – 97%; group 2 – Se – 90%, Sp – 96.7%, Ac – 93.6%; general group- Se – 88.1%, Sp – 98.3%, Ac – 94.9%.Conclusion. Our study confirmed high accuracy of the CEUS LI RADS v2017® system in the differential diagnosis of focal liver tumors. Modification of the system (in particular, transfer of typical FNG forms from the LR 4 category) will make it possible to increase the accuracy of diagnostics by 20%. It will allow to use the LI RADS v2017® system for interpretation CEUS not only among patients with liver cirrhosis, but also in a general group without risk factors of GCC.

Extrascleral Filling Using Endoillumination the First Experiencethe

2020 ◽  
pp. 43-49
Author(s):  
V.Y. Markevich ◽  
◽  
T.A. Imshenetskaya ◽  
O.A. Yarmak ◽  
◽  
...  
Keyword(s):  
Surgical Treatment ◽  
Retinal Detachment ◽  
Rhegmatogenous Retinal Detachment ◽  
Silicone Oil ◽  
Subretinal Fluid ◽  
Crystalline Lens ◽  
Vitreous Cavity ◽  
Macular Area ◽  
General Group ◽  
Anatomical Outcome

Purpose. To study the effectiveness of extrascleral filling (ESF) using endoillumination in the surgical treatment of patients with primary rhegmatogenous retinal detachment (RRD). Material and methods. The material for the study was the data of a comprehensive clinical examination and surgical treatment by ESF method using endoillumination in 17 patients (17 eyes) with RRD. In 7 cases (41%), the macular area was involved in the detachment process. In 5 cases (29.4%), local scleral filling was performed. In the remaining 12 cases (70.6%), the local ESF was supplemented with a circling silicone element. Surgical intervention was supplemented by transscleral drainage of subretinal fluid (SRF) in 10 cases (59%) and pneumatic retinopexy with SF6 gas 50% in 8 cases (48%). Results. In the general group of patients, best corrected visual acuity (BCVA) increased from 0.35 to 0.46. In the subgroup of patients with a detached macular area, the positive dynamics is more pronounced, BCVA increased from 0.1 to 0.28. The progression of proliferative vitreoretinopathy caused the recurrence of retinal detachment in two patients (11.8%). Recurrences were diagnosed after 3 and 5 months, respectively. In both cases, a vitrectomy with tamponade of the vitreous cavity with silicone oil 5000 Cst was performed. The percentage of successful anatomical outcome after the first operation in our study was 82%. The percentage of successful achievement of the final anatomical result was 94%. In two cases, additional injection of SF6 gas into the vitreous cavity was required. Conclusion. This type of surgical treatment is an effective method of surgical treatment of patients with RRD. In our study, the successful anatomical outcome after the first operation was recorded in 82% of patients, which correlates with the data of the authors who also used this method (83–92%). Surgeons who performed surgical treatment using this technique in our study note improved workplace ergonomics when visualizing the fundus using an operating microscope and endoillumination compared with indirect ophthalmoscopy. Other teams of authors came to this conclusion as well. In our study, there were no complications associated with the introduction of a light pipe into the vitreous cavity (iatrogenic crystalline lens injury, endophthalmitis), which indicates the safety of this type of surgical treatment.

Constructing symplectic manifolds

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Final Section ◽  
Symplectic Manifolds ◽  
Homotopy Equivalence ◽  
Codimension Two ◽  
Open Manifolds ◽  
Connected Sums ◽  
Symplectic Forms ◽  
Ambient Manifold ◽  
Blowing Up ◽  
Four Manifolds

This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.

scholarly journals THE SYMMETRIC SIGNATURE OF A WITT SPACE

2013 ◽  
Vol 05 (02) ◽  
pp. 121-159 ◽  
Author(s):  
GREG FRIEDMAN ◽  
JAMES McCLURE
Keyword(s):  
Intersection Homology ◽  
Homotopy Equivalence ◽  
New Construction

Witt spaces are pseudomanifolds for which the middle-perversity intersection homology with rational coefficients is self-dual. We give a new construction of the symmetric signature for Witt spaces which is similar in spirit to the construction given by Miščenko for manifolds. Our construction has all of the expected properties, including invariance under stratified homotopy equivalence.

scholarly journals Discussion on Competition for Spatial Statistics for Large Datasets

2021 ◽  
Author(s):  
Roman Flury ◽  
Reinhard Furrer
Keyword(s):  
Spatial Statistics ◽  
Covariance Function ◽  
Likelihood Function ◽  
Large Datasets ◽  
Missing Observations ◽  
Covariance Model ◽  
Compactly Supported ◽  
Covariance Tapering ◽  
Simple Kriging ◽  
Estimated Parameters

AbstractWe discuss the experiences and results of the AppStatUZH team’s participation in the comprehensive and unbiased comparison of different spatial approximations conducted in the Competition for Spatial Statistics for Large Datasets. In each of the different sub-competitions, we estimated parameters of the covariance model based on a likelihood function and predicted missing observations with simple kriging. We approximated the covariance model either with covariance tapering or a compactly supported Wendland covariance function.

Erdélyi–Kober fractional integrals and radon transforms for mutually orthogonal affine planes

2020 ◽  
Vol 23 (4) ◽  
pp. 967-979
Author(s):  
Boris Rubin ◽  
Yingzhan Wang
Keyword(s):  
Fractional Integrals ◽  
Radon Transforms ◽  
Affine Planes ◽  
Inversion Formulas ◽  
Radial Functions ◽  
Compactly Supported ◽  
Radial Case ◽  
Compactly Supported Functions

AbstractWe apply Erdélyi–Kober fractional integrals to the study of Radon type transforms that take functions on the Grassmannian of j-dimensional affine planes in ℝn to functions on a similar manifold of k-dimensional planes by integration over the set of all j-planes that meet a given k-plane at a right angle. We obtain explicit inversion formulas for these transforms in the class of radial functions under minimal assumptions for all admissible dimensions. The general (not necessarily radial) case, but for j + k = n − 1, n odd, was studied by S. Helgason [8] and F. Gonzalez [4, 5] on smooth compactly supported functions.

scholarly journals The Comparison of Physical Activity, Sedentary Behavior, and Mental Health between Early Menopausal Women and Age-Matched General Middle-Aged Women

2021 ◽  
Vol 18 (14) ◽  
pp. 7256
Author(s):  
Ji-Su Kim ◽  
Ju-Pil Choe ◽  
Jeong-Hui Park ◽  
Eunhye Yoo ◽  
Jung-Min Lee
Keyword(s):  
Mental Health ◽  
Physical Activity ◽  
Sedentary Behavior ◽  
Healthy Lifestyle ◽  
Multinomial Logistic Regression ◽  
Middle Aged ◽  
General Group ◽  
Menopausal Women ◽  
Global Physical Activity Questionnaire ◽  
Causes Of Mortality

The current study is to examine the differences in physical activity (PA), sedentary behavior (SB), and mental health (i.e., stress, depression, and suicidal behaviors) between early menopausal women and age-matched general middle-aged women. Among 1348 participants in South Korea, 674 participants who experienced menopause before the age of 45 were defined as the early menopausal group, and 674 women who experienced menopause from 45 years to 55 years were classified as the general group by matching age based on early menopausal women. PA, SB, and mental health were evaluated by using the Global Physical Activity Questionnaire (GPAQ). An independent t-test was used to compare the associations of PA, SB, and mental health between the two groups. To demonstrate the predictors of early menopause, variables in the study were analyzed by multinomial logistic regression. The main findings were that moderate-to-vigorous PA (MVPA) and light PA (LPA) had significant differences between the two groups, but SB had no significant differences. In mental health, only perceived stress had significant differences in this study. The moderate level of stress in the early menopausal group was twice as high as that of the general group, and the severe level of stress was even 2.6 times higher than the general group. PA plays an essential role in mitigating the causes of mortality and the risk of various chronic diseases and improving quality of life; thus, the main findings of this study could be important to provide insights on the corresponding impact between early menopausal women and PA to encourage their healthy lifestyle. Further longitudinal studies are needed to examine the mechanisms underlying the effects of PA, SB, and mental health on early menopausal women.

Sign in / Sign up

Export Citation Format

Share Document