scholarly journals Products of Euclidean Metrics, Applied to Proximity Problems among Curves

2020 ◽  
Vol 6 (4) ◽  
pp. 1-20
Author(s):  
Ioannis Z. Emiris ◽  
Ioannis Psarros
Keyword(s):  
Euclidean Metrics

NFL Draftnikology: Euclidean Metrics and Other Approaches to Scoring Ranking Predictions

2013 ◽  
Vol 43 (2) ◽  
pp. 237-248
Author(s):  
Steven B. Caudill ◽  
Franklin G. Mixon ◽  
C. Paul Mixon
Keyword(s):  
Euclidean Metrics

Smooth Gradation of Anisotropic Meshes Using Log–Euclidean Metrics

AIAA Journal ◽  
2021 ◽  
pp. 1-18
Author(s):  
Zhoufang Xiao ◽  
Carl Ollivier-Gooch
Keyword(s):  
Anisotropic Meshes ◽  
Euclidean Metrics

Neuroclusterization method of stabilometric data

2021 ◽  
Author(s):  
I.V. Stepanyan ◽  
S.S. Grokhovsky ◽  
O.V. Kubryak
Keyword(s):  
Center Of Pressure ◽  
Modern Method ◽  
Individual Characteristics ◽  
Automatic Mode ◽  
Support Reaction ◽  
Subsequent Determination ◽  
Euclidean Metrics ◽  
Postural Regulation ◽  
The Individual ◽  
Neural Maps

Stabilometry is a modern method for assessing the functional state of a person by the ability to maintain a stable balance of an upright posture. Technically, the implementation of the stabilometry method consists in measuring, with the help of specialized devices, the values that make up the support reaction, with the subsequent determination, according to these measurements, of the coordinates of the center of body pressure on the support. The nature of the migrations of the center of pressure during the stabilometric study is a source of information about the features of the processes of postural regulation. At the same time, up to the present time, there is a problem of the correct interpretation of the results of stabilometry. The adequacy of the conclusions is largely determined by the human factor, i.e. qualification of a specialist analyzing stabilometry data. Thus, in our opinion, the task of objectifying the assessment of stabilometry results is urgent. The aim of this work is to study the possibility of applying the neurocluster method using self-organizing neural networks to objectify the analysis of stabilometry data. The authors proposed a technique for analyzing the structure of individual and group stabilometric data by clustering them using selforganizing Kohonen neural maps with Euclidean metrics. Neuroclusterization of stabilometric data allows in automatic mode (without human intervention) to identify the type of group of subjects corresponding to the norm or pathology, various types of pathologies, as well as individual biometric characteristics of the subjects. The subsequent analysis of the individual characteristics of the data of the subjects, grouped in this way, makes it possible to detect deviations indicating the presence of abnormalities or the formation of various pathological conditions, which can be useful for the early diagnosis of diseases.

scholarly journals Multiple covering of a closed set on a plane with non-Euclidean metrics

2018 ◽  
Vol 51 (32) ◽  
pp. 850-854 ◽  
Author(s):  
Lempert Anna ◽  
Le Quang Mung
Keyword(s):  
Closed Set ◽  
Multiple Covering ◽  
Euclidean Metrics

scholarly journals Geometric Dynamics on Riemannian Manifolds

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 79 ◽  
Author(s):  
Constantin Udriste ◽  
Ionel Tevy
Keyword(s):  
Differential Equations ◽  
Riemannian Manifolds ◽  
Riemannian Metrics ◽  
Second Order ◽  
Time Dynamics ◽  
Outer Planets ◽  
Time Motion ◽  
Euclidean Metrics ◽  
Economical System ◽  
Geometric Dynamics

The purpose of this paper is threefold: (i) to highlight the second order ordinary differential equations (ODEs) as generated by flows and Riemannian metrics (decomposable single-time dynamics); (ii) to analyze the second order partial differential equations (PDEs) as generated by multi-time flows and pairs of Riemannian metrics (decomposable multi-time dynamics); (iii) to emphasise second order PDEs as generated by m-distributions and pairs of Riemannian metrics (decomposable multi-time dynamics). We detail five significant decomposed dynamics: (i) the motion of the four outer planets relative to the sun fixed by a Hamiltonian, (ii) the motion in a closed Newmann economical system fixed by a Hamiltonian, (iii) electromagnetic geometric dynamics, (iv) Bessel motion generated by a flow together with an Euclidean metric (created motion), (v) sinh-Gordon bi-time motion generated by a bi-flow and two Euclidean metrics (created motion). Our analysis is based on some least squares Lagrangians and shows that there are dynamics that can be split into flows and motions transversal to the flows.

Non-euclidean Metrics and Chordal Space Structures

2006 ◽  
pp. 30-39
Author(s):  
José Andrés Díaz Severiano ◽  
César Otero Gonzalez ◽  
Reinaldo Togores Fernandez ◽  
Cristina Manchado del Val
Keyword(s):  
Space Structures ◽  
Euclidean Metrics

scholarly journals MÖBIUS TRANSFORMATIONS OF POLYGONS AND PARTITIONS OF 3-SPACE

2008 ◽  
Vol 17 (11) ◽  
pp. 1401-1413 ◽  
Author(s):  
RICHARD RANDELL ◽  
JONATHAN SIMON ◽  
JOSHUA TOKLE
Keyword(s):  
Simple Closed Curve ◽  
Exact Formula ◽  
Mirror Image ◽  
Line Segments ◽  
Large N ◽  
Möbius Group ◽  
Euclidean Metrics ◽  
Straight Lines ◽  
Figure Eight Knot ◽  
Polygonal Knots

The image of a polygonal knot K under a spherical inversion of ℝ3 ∪ ∞ is a simple closed curve made of arcs of circles, perhaps some line segments, having the same knot type as the mirror image of K. But suppose we reconnect the vertices of the inverted polygon with straight lines, making a new polygon [Formula: see text]. This may be a different knot type. For example, a certain 7-segment figure-eight knot can be transformed to a figure-eight knot, a trefoil, or an unknot, by selecting different inverting spheres. Which knot types can be obtained from a given original polygon K under this process? We show that for large n, most n-segment knot types cannot be reached from one initial n-segment polygon, using a single inversion or even the whole Möbius group. The number of knot types is bounded by the number of complementary domains of a certain system of round 2-spheres in ℝ3. We show the number of domains is at most polynomial in the number of spheres, and the number of spheres is itself a polynomial function of the number of edges of the original polygon. In the analysis, we obtain an exact formula for the number of complementary domains of any collection of round 2-spheres in ℝ3. On the other hand, the number of knot types that can be represented by n-segment polygons is exponential in n. Our construction can be interpreted as a particular instance of building polygonal knots in non-Euclidean metrics. In particular, start with a list of n vertices in ℝ3 and connect them with arcs of circles instead of line segments: Which knots can be obtained? Our polygonal inversion construction is equivalent to picking one fixed point p ∈ ℝ3 and replacing each edge of K by an arc of the circle determined by p and the endpoints of the edge.

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