How to Smooth Curves and Surfaces with Splines and Cross-Validation

1979 ◽  
Author(s):  
Grace Wahba
Keyword(s):  
Cross Validation ◽  
Smooth Curves ◽  
Curves And Surfaces

scholarly journals A Family of Integer-Point Ternary Parametric Subdivision Schemes

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ghulam Mustafa ◽  
Muhammad Asghar ◽  
Shafqat Ali ◽  
Ayesha Afzal ◽  
Jia-Bao Liu
Keyword(s):  
General Formula ◽  
Integer Point ◽  
Laurent Polynomial ◽  
Polynomial Method ◽  
Subdivision Schemes ◽  
Smooth Curves ◽  
Curves And Surfaces

New subdivision schemes are always required for the generation of smooth curves and surfaces. The purpose of this paper is to present a general formula for family of parametric ternary subdivision schemes based on the Laurent polynomial method. The different complexity subdivision schemes are obtained by substituting the different values of the parameter. The important properties of the proposed family of subdivision schemes are also presented. The continuity of the proposed family is C 2 m . Comparison shows that the proposed family of subdivision schemes has higher degree of polynomial generation, degree of polynomial reproduction, and continuity compared with the exiting subdivision schemes. Maple software is used for mathematical calculations and plotting of graphs.

scholarly journals FUZZY/PROBABILITY ~ FRACTAL/SMOOTH

1999 ◽  
Vol 07 (04) ◽  
pp. 363-370 ◽  
Author(s):  
HUNG T. NGUYEN ◽  
VLADIK KREINOVICH ◽  
BERLIN WU
Keyword(s):  
Probability Theory ◽  
Fuzzy Logic ◽  
Relative Frequency ◽  
Real Life ◽  
Single Parameter ◽  
Fuzzy Probability ◽  
Smooth Curves ◽  
Curves And Surfaces ◽  
Natural Description

Many applications of probability theory are based on the assumption that, as the number of cases increase, the relative frequency of cases with a certain property tends to a number – probability that this property is true. L. Zadeh has shown that in many real-life situations, the frequency oscillates and does not converge at all. It is very difficult to describe such situations by using methods from traditional probability theory. Fuzzy logic is not based on any convergence assumptions and therefore, provides a natural description of such situations. However, a natural next question arises: how can we describe this oscillating behavior? Since we cannot describe it by using a single parameter (such as probability), we need to use a multi-D formalism. In this paper, we describe an optimal formalism for describing such oscillations, and show that it complements traditional probability techniques in the same way as fractals complement smooth curves and surfaces.

scholarly journals Elliptic GW invariants of blowups along curves and surfaces

2005 ◽  
Vol 2005 (1) ◽  
pp. 81-90 ◽  
Author(s):  
Jianxun Hu ◽  
Hou-Yang Zhang
Keyword(s):  
Symplectic Manifold ◽  
Smooth Curves ◽  
Curves And Surfaces

We established a relation between elliptic Gromov-Witten invariants of a symplectic manifoldMand its blowups along smooth curves and surfaces.

Item Bias Analysis of the Young Schema-Questionnaire for Psychopathology, Gender, and Educational Level

2011 ◽  
Vol 27 (1) ◽  
pp. 65-70 ◽  
Author(s):  
Marleen M. Rijkeboer ◽  
Huub van den Bergh ◽  
Jan van den Bout
Keyword(s):  
Educational Level ◽  
Cross Validation ◽  
Item Bias ◽  
Response Patterns ◽  
Dutch Population ◽  
Bias Analysis ◽  
Young Schema Questionnaire ◽  
Item Functioning ◽  
Item Level ◽  
Schema Questionnaire

This study examines the construct validity of the Young Schema-Questionnaire at the item level in a Dutch population. Possible bias of items in relation to the presence or absence of psychopathology, gender, and educational level was analyzed, using a cross-validation design. None of the items of the YSQ exhibited differential item functioning (DIF) for gender, and only one item showed DIF for educational level. Furthermore, item bias analysis did not identify DIF for the presence or absence of psychopathology in as much as 195 of the 205 items comprising the YSQ. Ten items, however, spread over the questionnaire, were found to yield relatively inconsistent response patterns for patients and nonclinical participants.

CROSS-VALIDATION IS NEEDED

1972 ◽  
Vol 17 (2) ◽  
pp. 85-86
Author(s):  
RICHARD F. Q. JOHNSON
Keyword(s):  
Cross Validation
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