Any 2-Sphere in E3 with Uniform Interior Tangent Balls is Flat

1981 ◽  
Vol 33 (1) ◽  
pp. 150-167 ◽  
Author(s):  
R. J. Daverman ◽  
L. D. Loveland
Keyword(s):  
Center Point ◽  
Fixed Positive Number ◽  
Set Of Points

This paper addresses some flatness properties of an (n – 1)-sphere Σ in Euclidean n-space En resulting from the presence of round balls in En tangent to Σ. The notion of tangency used here is geometric rather than differentiable, for a round n-cell Bp (that is, the set of points whose distance, in the standard metric, from some center point is less than or equal to a fixed positive number) is said to be tangent to the (n – 1)-sphere Σ in En at a point p ∈ Σ if p ∈ Bp and Int Bp ⊂ Σ = ∅. The ball Bp is called an interior tangent ball at p if Int Bp ⊂ Int Σ; otherwise, it is called an exterior tangent ball at p.

Video Graphics and High-Voltage Electron Microscopy For Analysis of Microtubule Distributions In Fixed Cells

1990 ◽  
Vol 48 (1) ◽  
pp. 524-525
Author(s):  
Richard Mcintosh ◽  
David Mastronarde ◽  
Kent McDonald ◽  
Rubai Ding
Keyword(s):  
Electron Microscopy ◽  
Cross Sections ◽  
Cell Shape ◽  
Video Camera ◽  
Computer Memory ◽  
High Voltage Electron Microscopy ◽  
Thin Sections ◽  
Voltage Electron ◽  
Morphogenetic Event ◽  
Set Of Points

Microtubules (MTs) are cytoplasmic polymers whose dynamics have an influence on cell shape and motility. MTs influence cell behavior both through their growth and disassembly and through the binding of enzymes to their surfaces. In either case, the positions of the MTs change over time as cells grow and develop. We are working on methods to determine where MTs are at different times during either the cell cycle or a morphogenetic event, using thin and thick sections for electron microscopy and computer graphics to model MT distributions.One approach is to track MTs through serial thin sections cut transverse to the MT axis. This work uses a video camera to digitize electron micrographs of cross sections through a MT system and create image files in computer memory. These are aligned and corrected for relative distortions by using the positions of 8 - 10 MTs on adjacent sections to define a general linear transformation that will align and warp adjacent images to an optimum fit. Two hundred MT images are then used to calculate an “average MT”, and this is cross-correlated with each micrograph in the serial set to locate points likely to correspond to MT centers. This set of points is refined through a discriminate analysis that explores each cross correlogram in the neighborhood of every point with a high correlation score.

scholarly journals A New Multi-Person Pose Estimation Method Using the Partitioned CenterPose Network

2021 ◽  
Vol 11 (9) ◽  
pp. 4241
Author(s):  
Jiahua Wu ◽  
Hyo Jong Lee
Keyword(s):  
Pose Estimation ◽  
Human Body ◽  
State Of The Art ◽  
Estimation Method ◽  
Bottom Up ◽  
Center Point ◽  
Novel Approach ◽  
Body Joints

In bottom-up multi-person pose estimation, grouping joint candidates into the appropriately structured corresponding instance of a person is challenging. In this paper, a new bottom-up method, the Partitioned CenterPose (PCP) Network, is proposed to better cluster the detected joints. To achieve this goal, we propose a novel approach called Partition Pose Representation (PPR) which integrates the instance of a person and its body joints based on joint offset. PPR leverages information about the center of the human body and the offsets between that center point and the positions of the body’s joints to encode human poses accurately. To enhance the relationships between body joints, we divide the human body into five parts, and then, we generate a sub-PPR for each part. Based on this PPR, the PCP Network can detect people and their body joints simultaneously, then group all body joints according to joint offset. Moreover, an improved l1 loss is designed to more accurately measure joint offset. Using the COCO keypoints and CrowdPose datasets for testing, it was found that the performance of the proposed method is on par with that of existing state-of-the-art bottom-up methods in terms of accuracy and speed.

scholarly journals A plane quartic curve with twelve undulations

1945 ◽  
Vol 35 ◽  
pp. 10-13 ◽  
Author(s):  
W. L. Edge
Keyword(s):  
Homogeneous Coordinates ◽  
Quartic Curve ◽  
Base Points ◽  
Octahedral Group ◽  
Quartic Form ◽  
Image Position ◽  
Quartic Curves ◽  
Set Of Points

The pencil of quartic curveswhere x, y, z are homogeneous coordinates in a plane, was encountered by Ciani [Palermo Rendiconli, Vol. 13, 1899] in his search for plane quartic curves that were invariant under harmonic inversions. If x, y, z undergo any permutation the ternary quartic form on the left of (1) is not altered; nor is it altered if any, or all, of x, y, z be multiplied by −1. There thus arises an octahedral group G of ternary collineations for which every curve of the pencil is invariant.Since (1) may also be writtenthe four linesare, as Ciani pointed out, bitangents, at their intersections with the conic C whose equation is x2 + y2 + z2 = 0, to every quartic of the pencil. The 16 base points of the pencil are thus all accounted for—they consist of these eight contacts counted twice—and this set of points must of course be invariant under G. Indeed the 4! collineations of G are precisely those which give rise to the different permutations of the four lines (2), a collineation in a plane being determined when any four non-concurrent lines and the four lines which are to correspond to them are given. The quadrilateral formed by the lines (2) will be called q.

scholarly journals The set of points with Markovian symbolic dynamics for non-uniformly hyperbolic diffeomorphisms

2020 ◽  
pp. 1-26
Author(s):  
SNIR BEN OVADIA
Keyword(s):  
Symbolic Dynamics ◽  
Full Measure ◽  
Probability Measures ◽  
Positive Entropy ◽  
Surface Diffeomorphisms ◽  
Srb Measures ◽  
Hyperbolic Diffeomorphisms ◽  
Set Of Points ◽  
Math Phys ◽  
Homoclinic Classes

Abstract The papers [O. M. Sarig. Symbolic dynamics for surface diffeomorphisms with positive entropy. J. Amer. Math. Soc.26(2) (2013), 341–426] and [S. Ben Ovadia. Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds. J. Mod. Dyn.13 (2018), 43–113] constructed symbolic dynamics for the restriction of $C^r$ diffeomorphisms to a set $M'$ with full measure for all sufficiently hyperbolic ergodic invariant probability measures, but the set $M'$ was not identified there. We improve the construction in a way that enables $M'$ to be identified explicitly. One application is the coding of infinite conservative measures on the homoclinic classes of Rodriguez-Hertz et al. [Uniqueness of SRB measures for transitive diffeomorphisms on surfaces. Comm. Math. Phys.306(1) (2011), 35–49].

scholarly journals A Model-Driven-to-Sample-Driven Method for Rural Road Extraction

2021 ◽  
Vol 13 (8) ◽  
pp. 1417
Author(s):  
Jiguang Dai ◽  
Rongchen Ma ◽  
Litao Gong ◽  
Zimo Shen ◽  
Jialin Wu
Keyword(s):  
Rural Areas ◽  
Template Matching ◽  
Color Space ◽  
Recall Rate ◽  
Road Extraction ◽  
Rural Roads ◽  
Model Driven ◽  
The Road ◽  
Center Point ◽  
Manual Input

Road extraction in rural areas is one of the most fundamental tasks in the practical application of remote sensing. In recent years, sample-driven methods have achieved state-of-the-art performance in road extraction tasks. However, sample-driven methods are prohibitively expensive and laborious, especially when dealing with rural roads with irregular curvature changes, narrow widths, and diverse materials. The template matching method can overcome these difficulties to some extent and achieve impressive road extraction results. This method also has the advantage of the vectorization of road extraction results, but the automation is limited. Straight line sequences can be substituted for curves, and the use of the color space can increase the recognition of roads and nonroads. A model-driven-to-sample-driven road extraction method for rural areas with a much higher degree of automation than existing template matching methods is proposed in this study. Without prior samples, on the basis of the geometric characteristics of narrow and long roads and using the advantages of straight lines instead of curved lines, the road center point extraction model is established through length constraints and gray mean contrast constraints of line sequences, and the extraction of some rural roads is completed through topological connection analysis. In addition, we take the extracted road center point and manual input data as local samples, use the improved line segment histogram to determine the local road direction, and use the panchromatic and hue, saturation, value (HSV) space interactive matching model as the matching measure to complete the road tracking extraction. Experimental results show that, for different types of data and scenarios on the premise, the accuracy and recall rate of the evaluation indicators reach more than 98%, and, compared with other methods, the automation of this algorithm has increased by more than 40%.

scholarly journals Multidimensional Multiplicative Combinatorial Properties of Dynamical Syndetic Sets

2021 ◽  
Author(s):  
Jiahao Qiu ◽  
Jianjie Zhao
Keyword(s):  
Normal Subgroup ◽  
Finite Index ◽  
Minimal System ◽  
Combinatorial Properties ◽  
Return Times ◽  
Residual Set ◽  
Closed Sets ◽  
Open Set ◽  
Geometric Progressions ◽  
Set Of Points

AbstractIn this paper, it is shown that for a minimal system (X, G), if H is a normal subgroup of G with finite index n, then X can be decomposed into n components of closed sets such that each component is minimal under H-action. Meanwhile, we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms, the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension, extending a previous result by Glasscock, Koutsogiannis and Richter.

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