scholarly journals Total Positivity of the Cubic Trigonometric Bézier Basis

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xuli Han ◽  
Yuanpeng Zhu
Keyword(s):  
General Framework ◽  
Total Positivity ◽  
Point Of View ◽  
Shape Parameters ◽  
Positive Basis ◽  
Corner Cutting ◽  
Curve Design ◽  
Totally Positive ◽  
Chebyshev Space ◽  
Cutting Algorithm

Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parametersλandμgiven in Han et al. (2009) forms an optimal normalized totally positive basis forλ,μ∈(-2,1]. Moreover, we show that forλ=-2orμ=-2the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric Bézier curves stably and efficiently, we also develop a new corner cutting algorithm.

scholarly journals A Class of Trigonometric Bernstein-Type Basis Functions with Four Shape Parameters

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Yuanpeng Zhu ◽  
Zhuo Liu
Keyword(s):  
Total Positivity ◽  
Basis Functions ◽  
Tension Control ◽  
Control Points ◽  
Shape Parameters ◽  
Bernstein Type ◽  
Bézier Curves ◽  
Type Curves ◽  
Corner Cutting ◽  
Cutting Algorithm

In this work, a family of four new trigonometric Bernstein-type basis functions with four shape parameters is constructed, which form a normalized basis with optimal total positivity. Based on the new basis functions, a kind of trigonometric Bézier-type curves with four shape parameters, analogous to the cubic Bézier curves, is constructed. With appropriate choices of control points and shape parameters, the resulting trigonometric Bézier-type curves can represent exactly any arc of an ellipse or parabola. The four shape parameters have tension control roles on adjusting the shape of resulting curves. Moreover, a new corner cutting algorithm is also proposed for calculating the trigonometric Bézier-type curves stably and efficiently.

scholarly journals Quasi Cubic Trigonometric Curve and Surface

2019 ◽  
Author(s):  
Guicang Zhang ◽  
Kai Wang
Keyword(s):  
Partition Of Unity ◽  
Shape Features ◽  
Bernstein Basis ◽  
Order Continuity ◽  
B Spline ◽  
Spline Curve ◽  
Totally Positive ◽  
Chebyshev Space ◽  
Spline Basis ◽  
Cutting Algorithm

Firstly, a new set of Quasi-Cubic Trigonometric Bernstein basis with two tension shape parameters is constructed, and we prove that it is an optimal normalized totally basis in the framework of Quasi Extended Chebyshev space. And the Quasi-Cubic Trigonometric Bézier curve is generated by the basis function and the cutting algorithm of the curve are given, the shape features (cusp, inflection point, loop and convexity) of the Quasi-Cubic Trigonometric Bézier curve are analyzed by using envelope theory and topological mapping; Next we construct the non-uniform Quasi-Cubic Trigonometric B-spline basis by assuming the linear combination of the optimal normalized totally positive basis have partition of unity and continuity, and its expression is obtained. And the non-uniform B-spline basis is proved to have totally positive and high-order continuity. Finally, the non-uniform Quasi Cubic Trigonometric B-spline curve and surface are defined, the shape features of the non-uniform Quasi-Cubic Trigonometric B-spline curve are discussed, and the curve and surface are proved to be continuous.

scholarly journals New Trigonometric Basis Possessing Denominator Shape Parameters

2018 ◽  
Vol 2018 ◽  
pp. 1-25 ◽  
Author(s):  
Kai Wang ◽  
Guicang Zhang
Keyword(s):  
Basis Function ◽  
Shape Parameters ◽  
B Spline ◽  
Triangular Domain ◽  
New Class ◽  
Totally Positive ◽  
Product Method ◽  
Special Value ◽  
Cutting Algorithm ◽  
Parameter Values

Four new trigonometric Bernstein-like bases with two denominator shape parameters (DTB-like basis) are constructed, based on which a kind of trigonometric Bézier-like curve with two denominator shape parameters (DTB-like curves) that are analogous to the cubic Bézier curves is proposed. The corner cutting algorithm for computing the DTB-like curves is given. Any arc of an ellipse or a parabola can be exactly represented by using the DTB-like curves. A new class of trigonometric B-spline-like basis function with two local denominator shape parameters (DT B-spline-like basis) is constructed according to the proposed DTB-like basis. The totally positive property of the DT B-spline-like basis is supported. For different shape parameter values, the associated trigonometric B-spline-like curves with two denominator shape parameters (DT B-spline-like curves) can be C2 continuous for a non-uniform knot vector. For a special value, the generated curves can be C(2n-1)  (n=1,2,3,…) continuous for a uniform knot vector. A kind of trigonometric B-spline-like surfaces with four denominator shape parameters (DT B-spline-like surface) is shown by using the tensor product method, and the associated DT B-spline-like surfaces can be C2 continuous for a nonuniform knot vector. When given a special value, the related surfaces can be C(2n-1)  (n=1,2,3,…) continuous for a uniform knot vector. A new class of trigonometric Bernstein–Bézier-like basis function with three denominator shape parameters (DT BB-like basis) over a triangular domain is also constructed. A de Casteljau-type algorithm is developed for computing the associated trigonometric Bernstein–Bézier-like patch with three denominator shape parameters (DT BB-like patch). The condition for G1 continuous jointing two DT BB-like patches over the triangular domain is deduced.

scholarly journals Theoretical perspectives upon the return to work of cancer patients: The difficult path of integration in the organization

2015 ◽  
Vol 13 (2) ◽  
pp. 113-135 ◽  
Author(s):  
Radu-Ioan Popa
Keyword(s):  
Return To Work ◽  
Cancer Patients ◽  
General Framework ◽  
Well Being ◽  
Point Of View ◽  
Organizational Life ◽  
Theoretical Perspectives ◽  
Depth Analysis ◽  
Returning To Work

Abstract The present article follows an in-depth analysis of several relevant articles and major findings concerning the return to work of cancer patients, in various situations, from a manager and patient point of view, putting into discussion the effects and consequences of different factors that may influence the well-being of the patient at work and impact the organizational life. The concepts of returning to work and integration are scarcely analysed throughout the scholarly literature in the case of employees diagnosed with cancer, due to several reasons presented in the paper: from the complex topic of investigation that many studies fail to approach in terms of confidentiality, technical, ethical and moral grounds to the specific and difficult apparatus for research in the case of an even more complex, multiple instances and personalized manifestation long-term illness. In conclusion, the general framework solicits for a more integrated model of research and future multi-facet schemes for interventions, considering that there is a general consensus focusing on the need for connecting the health services with the employee and employer level, alongside stakeholders’ active participation.

scholarly journals Covariance Matrix Estimation under Total Positivity for Portfolio Selection*

2020 ◽  
Author(s):  
Raj Agrawal ◽  
Uma Roy ◽  
Caroline Uhler
Keyword(s):  
Covariance Matrix ◽  
Total Positivity ◽  
General Purpose ◽  
Shrinkage Estimators ◽  
Positive Dependence ◽  
Matrix Estimation ◽  
Sample Covariance ◽  
Totally Positive ◽  
Markowitz Portfolio ◽  
Previous State

Abstract Selecting the optimal Markowitz portfolio depends on estimating the covariance matrix of the returns of N assets from T periods of historical data. Problematically, N is typically of the same order as T, which makes the sample covariance matrix estimator perform poorly, both empirically and theoretically. While various other general-purpose covariance matrix estimators have been introduced in the financial economics and statistics literature for dealing with the high dimensionality of this problem, we here propose an estimator that exploits the fact that assets are typically positively dependent. This is achieved by imposing that the joint distribution of returns be multivariate totally positive of order 2 (MTP2). This constraint on the covariance matrix not only enforces positive dependence among the assets but also regularizes the covariance matrix, leading to desirable statistical properties such as sparsity. Based on stock market data spanning 30 years, we show that estimating the covariance matrix under MTP2 outperforms previous state-of-the-art methods including shrinkage estimators and factor models.

scholarly journals Advantages and Restrictions of Tort Law to Deal with Environmental Damages

2014 ◽  
Vol 38 (1) ◽  
pp. 111-130
Author(s):  
Pamela Carina Tolosa
Keyword(s):  
General Framework ◽  
Law And Economics ◽  
Environmental Law ◽  
Environmental Issues ◽  
Tort Law ◽  
Environmental Risks ◽  
Point Of View ◽  
Environmental Harm ◽  
Environmental Damages ◽  
Ex Ante

The idea prevailing in mainstream environmental law literature is that ex ante safety regulation is preferable to tort law remedies to deal with environmental issues. The main reason usually invoked to prefer ex ante regulation is that generally, tort law takes its part only after the harm has already been done; and that is considered not compatible with the objective of avoiding environmental harm. On the contrary, from the law and economics point of view, I will argue that tort law systems have some important properties that make it compatible with the goal of reducing environmental risks, and that it can be superior to ex ante regulation in avoiding environmental harm. Consequently, the purpose of this paper is drawing up a general framework to describe the relative advantages of tort law and their related conditions to deal with environmental harm.

Optimal couplings are totally positive and more

2004 ◽  
Vol 41 (A) ◽  
pp. 321-332 ◽  
Author(s):  
Paul Glasserman ◽  
David D. Yao
Keyword(s):  
Transportation Problem ◽  
Random Variables ◽  
Total Positivity ◽  
Bivariate Distribution ◽  
Discrete Distributions ◽  
Optimal Solutions ◽  
Totally Positive ◽  
Maximal Correlation ◽  
Optimal Coupling

An optimal coupling is a bivariate distribution with specified marginals achieving maximal correlation. We show that optimal couplings are totally positive and, in fact, satisfy a strictly stronger condition we call the nonintersection property. For discrete distributions we illustrate the equivalence between optimal coupling and a certain transportation problem. Specifically, the optimal solutions of greedily-solvable transportation problems are totally positive, and even nonintersecting, through a rearrangement of matrix entries that results in a Monge sequence. In coupling continuous random variables or random vectors, we exploit a characterization of optimal couplings in terms of subgradients of a closed convex function to establish a generalization of the nonintersection property. We argue that nonintersection is not only stronger than total positivity, it is the more natural concept for the singular distributions that arise in coupling continuous random variables.

The diversity of inflectional periphrasis in Persian

2014 ◽  
Vol 51 (2) ◽  
pp. 327-382 ◽  
Author(s):  
OLIVIER BONAMI ◽  
POLLET SAMVELIAN
Keyword(s):  
General Framework ◽  
Point Of View ◽  
The Other ◽  
Inflectional Morphology ◽  
Formal Grammar ◽  
Conjugation System ◽  
Testing Ground ◽  
Other Hand ◽  
Different Types ◽  
A Cell

Modern Persian conjugation makes use of five periphrastic constructions with typologically divergent properties. This makes the Persian conjugation system an ideal testing ground for theories of inflectional periphrasis, since different types of periphrasis can be compared within the frame of a single grammatical system. We present contrasting analyses of the five constructions within the general framework of a lexicalist constraint-based grammatical architecture (Pollard & Sag 1994) embedding an inferential and realizational view of inflectional morphology (Stump 2001). We argue that the perfect periphrase can only be accounted for by assuming that the periphrase literally fills a cell in the inflectional paradigm, and provide a formal account drawing on using valence for exponence. On the other hand, other periphrastic constructions are best handled by using standard tools of either morphology or syntax. The overall conclusion is that not all constructions that qualify as periphrastic inflection from the point of view of typology should receive the same type of analysis in an explicit formal grammar.

Optimal couplings are totally positive and more

2004 ◽  
Vol 41 (A) ◽  
pp. 321-332
Author(s):  
Paul Glasserman ◽  
David D. Yao
Keyword(s):  
Transportation Problem ◽  
Random Variables ◽  
Total Positivity ◽  
Bivariate Distribution ◽  
Discrete Distributions ◽  
Optimal Solutions ◽  
Totally Positive ◽  
Maximal Correlation ◽  
Optimal Coupling

An optimal coupling is a bivariate distribution with specified marginals achieving maximal correlation. We show that optimal couplings are totally positive and, in fact, satisfy a strictly stronger condition we call the nonintersection property. For discrete distributions we illustrate the equivalence between optimal coupling and a certain transportation problem. Specifically, the optimal solutions of greedily-solvable transportation problems are totally positive, and even nonintersecting, through a rearrangement of matrix entries that results in a Monge sequence. In coupling continuous random variables or random vectors, we exploit a characterization of optimal couplings in terms of subgradients of a closed convex function to establish a generalization of the nonintersection property. We argue that nonintersection is not only stronger than total positivity, it is the more natural concept for the singular distributions that arise in coupling continuous random variables.

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