scholarly journals Tropical limit of log-inflection points for planar curves

2018 ◽  
Vol 209 (9) ◽  
pp. 1273-1286
Author(s):  
G. B. Mikhalkin ◽  
A. Renaudineau
Keyword(s):  
Planar Curves ◽  
Inflection Points ◽  
Tropical Limit

Support function at inflection points of planar curves

2018 ◽  
Vol 63 ◽  
pp. 109-121
Author(s):  
Eva Blažková ◽  
Zbyněk Šír
Keyword(s):  
Support Function ◽  
Planar Curves ◽  
Inflection Points

Identifying Market Inflection Points

CFA Digest ◽  
2010 ◽  
Vol 40 (1) ◽  
Author(s):  
Russell Napier
Keyword(s):  
Inflection Points

scholarly journals Affine Subspaces of Curvature Functions from Closed Planar Curves

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Leonardo Alese
Keyword(s):  
Arc Length ◽  
Planar Curves ◽  
Affine Subspaces ◽  
Planar Curve ◽  
Real Functions ◽  
Discrete Counterpart ◽  
Equivalent Conditions

AbstractGiven a pair of real functions (k, f), we study the conditions they must satisfy for $$k+\lambda f$$ k + λ f to be the curvature in the arc-length of a closed planar curve for all real $$\lambda $$ λ . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied.

scholarly journals Clothoid fitting and geometric Hermite subdivision

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Ulrich Reif ◽  
Andreas Weinmann
Keyword(s):  
Building Block ◽  
Numerical Results ◽  
Normal Vector ◽  
Subdivision Schemes ◽  
Planar Curves ◽  
Nonlinear Subdivision ◽  
New Strategy ◽  
Vector Information ◽  
Hermite Subdivision

AbstractWe consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive a new strategy to approximate Hermite interpolating clothoids. We employ the proposed approach to define the geometric Hermite analogues of the well-known Lane-Riesenfeld and four-point schemes. We present numerical results produced by the proposed schemes and discuss their features.

A Novel Thyroid Ultrasound Proficiency Metric Designed Through a Multidisciplinary Delphi Approach

2021 ◽  
pp. 000313482110111
Author(s):  
Yinin Hu ◽  
Alex D. Michaels ◽  
Rachita Khot ◽  
Worthington G. Schenk ◽  
John B. Hanks ◽  
...  
Keyword(s):  
Learning Curves ◽  
Delphi Panel ◽  
Thyroid Ultrasound ◽  
Point Scale ◽  
Image Capture ◽  
Delphi Approach ◽  
Inflection Points ◽  
Operative Planning ◽  
Positioning Technique ◽  
Formally Trained

Background Thyroid ultrasounds extend surgeons’ outpatient capabilities and are essential for operative planning. However, most residents are not formally trained in thyroid ultrasound. The purpose of this study was to create a novel thyroid ultrasound proficiency metric through a collaborative Delphi approach. Methods Clinical faculty experienced in thyroid ultrasound participated on a Delphi panel to design the thyroid Ultrasound Proficiency Scale (UPS-Thyroid). Participants proposed items under the categories of Positioning, Technique, Image Capture, Measurement, and Interpretation. In subsequent rounds, participants voted to retain, revise, or exclude each item. The process continued until all items had greater than 70% consensus for retention. The UPS-Thyroid was pilot tested across 5 surgery residents with moderate ultrasound experience. Learning curves were assessed with cumulative sum. Results Three surgeons and 4 radiologists participated on the Delphi panel. Following 3 iterative Delphi rounds, the panel arrived at >70% consensus to retain 14 items without further revisions or additions. The metric included the following items on a 3-point scale for a maximum of 42 points: Positioning (1 item), Technique (4 items), Image Capture (2 items), Measurement (2 items), and Interpretation (5 items). A pilot group of 5 residents was scored against a proficiency threshold of 36 points. Learning curve inflection points were noted at between 4 to 7 repetitions. Conclusions A multidisciplinary Delphi approach generated consensus for a thyroid ultrasound proficiency metric (UPS-Thyroid). Among surgery residents with moderate ultrasound experience, basic proficiency at thyroid ultrasound is feasible within 10 repetitions.

scholarly journals How Many Inflections are There in the Lyapunov Spectrum?

2021 ◽  
Author(s):  
O. Jenkinson ◽  
M. Pollicott ◽  
P. Vytnova
Keyword(s):  
Piecewise Linear ◽  
Lyapunov Spectrum ◽  
Stat Phys ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Expanding Map ◽  
Lyapunov Spectra ◽  
Linear Maps ◽  
Inflection Points ◽  
Piecewise Linear Maps

AbstractIommi and Kiwi (J Stat Phys 135:535–546, 2009) showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture in Iommi and Kiwi (2009) by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.

Collaborative Study of a Titrimetric Method for the Assay of Amitrole Formulations

1967 ◽  
Vol 50 (3) ◽  
pp. 568-572
Author(s):  
J Russell Bishop
Keyword(s):  
Collaborative Study ◽  
Statistical Analyses ◽  
Standard Samples ◽  
Titrimetric Method ◽  
Inflection Points ◽  
Good Agreement

Abstract titrimetric method for the assay of dry and liquid amitrole formulations was studied by 10 collaborators. In the method, acid is added to the prepared amitrole sample, the solution is titrated potentiometrically with standard alkali, and the amitrole content is measured as the amount of alkali consumed between the first and second inflection points. Collaborative results on standard samples of a dry 90% formulation, a dry 50% formulation, and a liquid 2 lb/gallon formulation showed good agreement between samples and laboratories. Statistical analyses of the results were satisfactory, and the method for the assay of amitrole formulations is recommended for adoption as official, first action

scholarly journals Analysis of a Method to Parameterize Planar Curves Immersed In Triangulations

2013 ◽  
Vol 51 (3) ◽  
pp. 1392-1420 ◽  
Author(s):  
Ramsharan Rangarajan ◽  
Adrian J. Lew
Keyword(s):  
Planar Curves
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