On the distribution of points of maximal deviation in complex Čebyšev approximation

1981 ◽  
Vol 7 (4) ◽  
pp. 257-263 ◽  
Author(s):  
A. Kroó
Keyword(s):  
Distribution Of Points ◽  
Maximal Deviation

scholarly journals Distribution of points on Abelian covers over finite fields

2018 ◽  
Vol 14 (05) ◽  
pp. 1375-1401 ◽  
Author(s):  
Patrick Meisner
Keyword(s):  
Finite Fields ◽  
Galois Extension ◽  
Random Variables ◽  
Families Of Curves ◽  
Abelian Covers ◽  
Distribution Of Points ◽  
Genus Formula

We determine in this paper the distribution of the number of points on the covers of [Formula: see text] such that [Formula: see text] is a Galois extension and [Formula: see text] is abelian when [Formula: see text] is fixed and the genus, [Formula: see text], tends to infinity. This generalizes the work of Kurlberg and Rudnick and Bucur, David, Feigon and Lalin who considered different families of curves over [Formula: see text]. In all cases, the distribution is given by a sum of [Formula: see text] random variables.

Acute activation and inactivation of macaque frontal eye field with GABA-related drugs

1995 ◽  
Vol 74 (6) ◽  
pp. 2744-2748 ◽  
Author(s):  
E. C. Dias ◽  
M. Kiesau ◽  
M. A. Segraves
Keyword(s):  
Injection Site ◽  
Rhesus Monkeys ◽  
Frontal Eye Field ◽  
Surgical Removal ◽  
Gamma Aminobutyric Acid ◽  
Eye Field ◽  
Distribution Of Points ◽  
Direction Opposite ◽  
Voluntary Saccades

1. This project tests the behavioral effects of reversible activation and inactivation of sites within the frontal eye field of rhesus monkeys with microinjections of the gamma-aminobutyric acid (GABA)-related drugs bicuculline and muscimol. 2. Muscimol injections impaired the monkeys' ability to make both visually and memory-guided saccades to targets at the center of the area represented by the injection site. The latencies of saccades to targets in regions flanking the injection were increased. For memory-guided saccades, saccades in the direction opposite to that represented by the injection site, were made with shorter latency than controls and often occurred before the movement cue. 3. Bicuculline injections produced irrepressible saccades equivalent to the saccade vector represented by the injection site, often in a staircase of several closely spaced movements. 4. Both substances decreased the accuracy of fixation of a central light. The distribution of points of fixation on different trials was diffuse, and the angle of gaze tended to deviate towards the side of the injection. 5. The results of these acute injections are similiar to those observed in the superior colliculus and are much more substantial than the effects observed in the long term after surgical removal of the frontal eye field. The results of this study promote a central role for the frontal eye field in the generation of all voluntary saccades and in the control of fixation.

scholarly journals Why knees move like they do: A simulation of the effect of varying distal femoral and proximal tibial anatomy on coronal kinematic curve morphology

2017 ◽  
Vol 5 (5_suppl5) ◽  
pp. 2325967117S0016
Author(s):  
Peter McEwen
Keyword(s):  
Total Knee Arthroplasty ◽  
Knee Arthroplasty ◽  
Proximal Tibia ◽  
Coronal Plane ◽  
Curve Shape ◽  
Femoral Rotation ◽  
Full Extension ◽  
Reciprocal Effect ◽  
Maximal Deviation ◽  
Total Knee

Objective: Computer assisted total knee arthroplasty (CA TKA) platforms can provide detailed kinematic data that is presented in various forms including a coronal plane graphic that maps the flexion arc from full extension to deep flexion. Graphics obtained from normal tibiofemoral articulations reveal varied and complex kinematic patterns that have yet to be explained. An understanding of what drives curve variation would allow prediction of how a preoperative curve would be altered by total knee arthroplasty. Implant position could then be tailored to maintain a desirable curve or avoid an undesirable one. Methods: An articulated lower limb saw bone with a stable hip pivot was obtained. Adjustable osteotomies were created so that femoral torsion, femoral varus-valgus and tibial varus-valgus could be altered independently. The saw bone limb was registered with a CA TKA navigation system using the posterior condyles as a rotational axis. Axial and coronal plane morphology of the distal femur and coronal plane morphology of the proximal tibia were systematically altered and a kinematic curve obtained for each morphologic combination. Femoral rotational position was varied from 100 of internal torsion to 100 of external torsion in 20 increments. Similarly, femoral coronal position was varied from 20 of varus to 60 of valgus and tibial coronal position was varied from 5.50 of varus to 10 of valgus. Curves were obtained by manually flexing the joint through a full range of motion with the femoral condyles in contact with proximal tibia at all times. Results: Varying femoral rotation has no effect in full extension but drives the curve away from neutral as the knee flexes. Maximal deviation is seen at around 900 of flexion. Internal torsion drives the curve into valgus as the knee flexes and external torsion has a reciprocal effect. Varying femoral varus-valgus causes maximal deviation from neutral in full extension. Femoral varus drives the curve from varus in extension towards valgus as the knee flexes with the effect peaking in maximal flexion. Femoral valgus has a reciprocal effect. Varying tibial varus-valgus has no effect on curve shape but does move the curve either side of neutral. Complex (parabolic) curves are caused by large rotations or the opposing effects of femoral varus-valgus and femoral rotation. The modal human anatomy of slight femoral internal rotation, slight femoral valgus and slight tibial varus produces a straight neutral curve. Conclusion: Kinematic curve shape is driven by distal femoral anatomy. The typical changes made to distal femoral articular anatomy in TKA by externally rotating a neutrally orientated femoral component will bring many native curves towards neutral. Externally rotating when the preoperative curve begins neutral and drives into varus as the knee flexes will drive the curve harder into varus. Conversely, kinematic femoral placement will reconstitute the premorbid curve morphology. Which outcome is preferable has yet to be determined.

scholarly journals Melting–Refreezing at the Glacier Sole and the Isotopic Composition of the Ice

1982 ◽  
Vol 28 (98) ◽  
pp. 35-42 ◽  
Author(s):  
J. Jouzel ◽  
R. A. Souchez
Keyword(s):  
Isotopic Composition ◽  
Water System ◽  
Alpine Glacier ◽  
Basal Ice ◽  
Distribution Of Points ◽  
Rock Interface ◽  
Ice Water

AbstractA model for the isotopic composition in δD and δ18O of ice formed by refreezing at the glacier sole is developed. This model predicts relatively well the distribution of points representing samples from basal layers of an Arctic and an Alpine glacier on a δD–δ18O diagram. The frozen fraction which is the part of the liquid that refreezes can be determined for each basal ice layer. This may have implications on the study of the ice–water system at the ice–rock interface.

scholarly journals T-ReX: a graph-based filament detection method

2020 ◽  
Vol 637 ◽  
pp. A18 ◽  
Author(s):  
Tony Bonnaire ◽  
Nabila Aghanim ◽  
Aurélien Decelle ◽  
Marian Douspis
Keyword(s):  
Numerical Simulations ◽  
Large Scale ◽  
Spanning Trees ◽  
Filamentary Structure ◽  
Underlying Distribution ◽  
Galaxy Surveys ◽  
Automatic Retrieval ◽  
Diffuse Part ◽  
Distribution Of Points ◽  
The Impact

Numerical simulations and observations show that galaxies are not uniformly distributed in the universe but, rather, they are spread across a filamentary structure. In this large-scale pattern, highly dense regions are linked together by bridges and walls, all of them surrounded by vast, nearly-empty areas. While nodes of the network are widely studied in the literature, simulations indicate that half of the mass budget comes from a more diffuse part of the network, which is made up of filaments. In the context of recent and upcoming large galaxy surveys, it becomes essential that we identify and classify features of the Cosmic Web in an automatic way in order to study their physical properties and the impact of the cosmic environment on galaxies and their evolution. In this work, we propose a new approach for the automatic retrieval of the underlying filamentary structure from a 2D or 3D galaxy distribution using graph theory and the assumption that paths that link galaxies together with the minimum total length highlight the underlying distribution. To obtain a smoothed version of this topological prior, we embedded it in a Gaussian mixtures framework. In addition to a geometrical description of the pattern, a bootstrap-like estimate of these regularised minimum spanning trees allowed us to obtain a map characterising the frequency at which an area of the domain is crossed. Using the distribution of halos derived from numerical simulations, we show that the proposed method is able to recover the filamentary pattern in a 2D or 3D distribution of points with noise and outliers robustness with a few comprehensible parameters.

Distribution of Points in n-Space

1943 ◽  
Vol 50 (3) ◽  
pp. 181-185 ◽  
Author(s):  
L. M. Blumenthal ◽  
B. E. Gillam
Keyword(s):  
Distribution Of Points

Uniform Distribution in Model Sets

2002 ◽  
Vol 45 (1) ◽  
pp. 123-130 ◽  
Author(s):  
Robert V. Moody
Keyword(s):  
Uniform Distribution ◽  
Physical Space ◽  
Pure Point ◽  
Internal Space ◽  
Compact Closure ◽  
Related Model ◽  
Model Sets ◽  
Distribution Property ◽  
Distribution Of Points ◽  
Model Set

AbstractWe give a new measure-theoretical proof of the uniform distribution property of points in model sets (cut and project sets). Each model set comes as a member of a family of related model sets, obtained by joint translation in its ambient (the ‘physical’) space and its internal space. We prove, assuming only that the window defining themodel set ismeasurable with compact closure, that almost surely the distribution of points in any model set from such a family is uniform in the sense of Weyl, and almost surely the model set is pure point diffractive.

Distribution of Points in n-Space

1943 ◽  
Vol 50 (3) ◽  
pp. 181 ◽  
Author(s):  
L. M. Blumenthal ◽  
B. E. Gillam
Keyword(s):  
Distribution Of Points
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