The Experts below are selected from a list of 195 Experts worldwide ranked by ideXlab platform
Joakim Ekström - One of the best experts on this subject based on the ideXlab platform.
-
The Phi-coefficient, the Tetrachoric Correlation Coefficient, and the Pearson-Yule Debate
2011Co-Authors: Joakim EkströmAbstract:Author(s): Ekstrom, Joakim | Abstract: Two measures of association for dichotomous variables, the phi-coefficient and the tetrachoric correlation coefficient, are reviewed and differences between the two are discussed in the context of the famous so-called Pearson-Yule debate, that took place in the early 20th century. The two measures of association are given mathematically rigorous definitions, their underlying assumptions are formalized, and some key properties are derived. Furthermore, existence of a Continuous Bijection between the phi-coefficient and the tetrachoric correlation coefficient under given marginal probabilities is shown. As a consequence, the tetrachoric correlation coefficient can be computed using the assumptions of the phi-coefficient construction, and the phi-coefficient can be computed using the assumptions of the tetrachoric correlation construction. The efforts lead to an attempt to reconcile the Pearson-Yule debate, showing that the two measures of association are in fact more similar than different and that between the two, the choice of measure of association does not carry a substantial impact on the conclusions of the association analysis.
-
The Phi-coefficient, the Tetrachoric Correlation Coefficient, and the Pearson-Yule Debate - eScholarship
2011Co-Authors: Joakim EkströmAbstract:Two measures of association for dichotomous variables, the phi-coefficient and the tetrachoric correlation coefficient, are reviewed and differences between the two are discussed in the context of the famous so-called Pearson-Yule debate, that took place in the early 20th century. The two measures of association are given mathematically rigorous definitions, their underlying assumptions are formalized, and some key properties are derived. Furthermore, existence of a Continuous Bijection between the phi-coefficient and the tetrachoric correlation coefficient under given marginal probabilities is shown. As a consequence, the tetrachoric correlation coefficient can be computed using the assumptions of the phi-coefficient construction, and the phi-coefficient can be computed using the assumptions of the tetrachoric correlation construction. The efforts lead to an attempt to reconcile the Pearson-Yule debate, showing that the two measures of association are in fact more similar than different and that between the two, the choice of measure of association does not carry a substantial impact on the conclusions of the association analysis.
-
On the relation between the phi-coefficient and the tetrachoric correlation coefficient
2009Co-Authors: Joakim EkströmAbstract:We show existence of a Continuous Bijection between the tetrachoric correlation coefficient and the phi-coefficient under given marginal probabilities. Implications are that the tetrachoric correla ...
Yaron Lipman - One of the best experts on this subject based on the ideXlab platform.
-
Lifted Bijections for Low Distortion Surface Mappings
2015Co-Authors: Noam Aigerman, Roi Poranne, Yaron LipmanAbstract:Figure 1: The algorithm presented in this paper generates low-distortion bijective mappings between surfaces from a sparse set of landmarks (visualized as colored spheres here). The maps are visualized by transferring the texture of the visible part in the left mesh of each pair to the right mesh, using the computed mappings. For example, the right pair shows a mapping of a horse to a giraffe; note how the map stretches gracefully at the neck area. This paper introduces an algorithm for computing low-distortion, bijective mappings between surface meshes. The algorithm re-ceives as input a coarse set of corresponding pairs of points on the two surfaces, and follows three steps: (i) cutting the two meshes to disks in a consistent manner; (ii) jointly flattening the two disks via a novel formulation for minimizing isometric distortion while guar-anteeing local injectivity (the flattenings can overlap, however); and (iii) computing a unique Continuous Bijection that is consistent with the flattenings. The construction of the algorithm stems from two novel observa-tions: first, Bijections between disk-type surfaces can be uniquely and efficiently represented via consistent locally injective flatten-ings that are allowed to be globally overlapping. This observation reduces the problem of computing bijective surface mappings to the task of computing locally injective flattenings, which is shown to be easier. Second, locally injective flattenings that minimize isometric distortion can be efficiently characterized and optimized in a con-vex framework. Experiments that map a wide baseline of pairs of surface meshes us-ing the algorithm are provided. They demonstrate the ability of the algorithm to produce high-quality Continuous bijective mappings between pairs of surfaces of varying isometric distortion levels
-
Lifted Bijections for low distortion surface mappings
ACM Transactions on Graphics, 2014Co-Authors: Noam Aigerman, Roi Poranne, Yaron LipmanAbstract:This paper introduces an algorithm for computing low-distortion, bijective mappings between surface meshes. The algorithm recieves as input a coarse set of corresponding pairs of points on the two surfaces, and follows three steps: (i) cutting the two meshes to disks in a consistent manner; (ii) jointly flattening the two disks via a novel formulation for minimizing isometric distortion while guaranteeing local injectivity (the flattenings can overlap, however); and (iii) computing a unique Continuous Bijection that is consistent with the flattenings. The construction of the algorithm stems from two novel observations: first, Bijections between disk-type surfaces can be uniquely and efficiently represented via consistent locally injective flattenings that are allowed to be globally overlapping. This observation reduces the problem of computing bijective surface mappings to the task of computing locally injective flattenings, which is shown to be easier. Second, locally injective flattenings that minimize isometric distortion can be efficiently characterized and optimized in a convex framework. Experiments that map a wide baseline of pairs of surface meshes using the algorithm are provided. They demonstrate the ability of the algorithm to produce high-quality Continuous bijective mappings between pairs of surfaces of varying isometric distortion levels.
Noam Aigerman - One of the best experts on this subject based on the ideXlab platform.
-
Lifted Bijections for Low Distortion Surface Mappings
2015Co-Authors: Noam Aigerman, Roi Poranne, Yaron LipmanAbstract:Figure 1: The algorithm presented in this paper generates low-distortion bijective mappings between surfaces from a sparse set of landmarks (visualized as colored spheres here). The maps are visualized by transferring the texture of the visible part in the left mesh of each pair to the right mesh, using the computed mappings. For example, the right pair shows a mapping of a horse to a giraffe; note how the map stretches gracefully at the neck area. This paper introduces an algorithm for computing low-distortion, bijective mappings between surface meshes. The algorithm re-ceives as input a coarse set of corresponding pairs of points on the two surfaces, and follows three steps: (i) cutting the two meshes to disks in a consistent manner; (ii) jointly flattening the two disks via a novel formulation for minimizing isometric distortion while guar-anteeing local injectivity (the flattenings can overlap, however); and (iii) computing a unique Continuous Bijection that is consistent with the flattenings. The construction of the algorithm stems from two novel observa-tions: first, Bijections between disk-type surfaces can be uniquely and efficiently represented via consistent locally injective flatten-ings that are allowed to be globally overlapping. This observation reduces the problem of computing bijective surface mappings to the task of computing locally injective flattenings, which is shown to be easier. Second, locally injective flattenings that minimize isometric distortion can be efficiently characterized and optimized in a con-vex framework. Experiments that map a wide baseline of pairs of surface meshes us-ing the algorithm are provided. They demonstrate the ability of the algorithm to produce high-quality Continuous bijective mappings between pairs of surfaces of varying isometric distortion levels
-
Lifted Bijections for low distortion surface mappings
ACM Transactions on Graphics, 2014Co-Authors: Noam Aigerman, Roi Poranne, Yaron LipmanAbstract:This paper introduces an algorithm for computing low-distortion, bijective mappings between surface meshes. The algorithm recieves as input a coarse set of corresponding pairs of points on the two surfaces, and follows three steps: (i) cutting the two meshes to disks in a consistent manner; (ii) jointly flattening the two disks via a novel formulation for minimizing isometric distortion while guaranteeing local injectivity (the flattenings can overlap, however); and (iii) computing a unique Continuous Bijection that is consistent with the flattenings. The construction of the algorithm stems from two novel observations: first, Bijections between disk-type surfaces can be uniquely and efficiently represented via consistent locally injective flattenings that are allowed to be globally overlapping. This observation reduces the problem of computing bijective surface mappings to the task of computing locally injective flattenings, which is shown to be easier. Second, locally injective flattenings that minimize isometric distortion can be efficiently characterized and optimized in a convex framework. Experiments that map a wide baseline of pairs of surface meshes using the algorithm are provided. They demonstrate the ability of the algorithm to produce high-quality Continuous bijective mappings between pairs of surfaces of varying isometric distortion levels.
Jan Hamhalter - One of the best experts on this subject based on the ideXlab platform.
-
Piecewise ⁎-homomorphisms and Jordan maps on C⁎-algebras and factor von Neumann algebras
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Jan HamhalterAbstract:Abstract We investigate maps between C ⁎ -algebras that are well behaved with respect to mutually commuting elements. We contribute to the Mackey–Gleason problem by showing that any Continuous Bijection between self-adjoint parts of C ⁎ -algebras that preserves triple product ( a , b ) → a b a , and is linear on commutative subspaces, is already linear. This allows us to describe such maps as direct differences of linear Jordan isomorphisms. We shall show that any weak⁎-Continuous Bijection between positive invertible elements of von Neumann factors (of dimension at least 9) that preserves products of commuting elements in both directions is of the form a → e ψ ( log a ) θ ( a c ) , where θ is a linear Jordan ⁎-isomorphism, c nonzero real number and ψ is a hermitian Continuous functional. In a similar way we describe the same type of biContinuous maps between unitary groups of von Neumann factors. General form of the above mentioned maps on C ⁎ -algebras is also presented.
-
Nonlinear maps on von Neumann algebras preserving the star order
Linear and Multilinear Algebra, 2013Co-Authors: Martin Bohata, Jan HamhalterAbstract:Star order is defined on a C*-algebra in the following way: a ⪯ b if a*a = a*b and aa* = ba*. Let 𝒜 be a von Neumann algebra without Type I2 direct summand. Let 𝒜 n be the set of all normal elements of 𝒜. Suppose that ϕ: 𝒜 n → 𝒜 n is a Continuous Bijection that preserves the star order on 𝒜 n in both directions. Further, let there is a function f : ℂ → ℂ and an invertible central element c in 𝒜 such that ϕ(λ1) = f(λ)c for all λ ∈ ℂ. We show that there is a unique Jordan *-isomorphism ψ: 𝒜 → 𝒜 such that Ramifications of this result as well as optimality of the assumptions are discussed.
Johannes Hahn - One of the best experts on this subject based on the ideXlab platform.
-
An interesting proof of the nonexistence Continuous Bijection between $\mathbb{R}^n$ and $\mathbb{R}^2$ for $n\neq 2$}
arXiv: General Topology, 2010Co-Authors: Freshteh Malek, Hamed Daneshpajouh, Johannes HahnAbstract:In this article it is shown that there is no Continuous Bijection from $\mathbb{R}^n$ onto $\mathbb{R}^2$ for $n\neq 2$ by an elementary method. This proof is based on showing that for any cardinal number $\beta\leq 2^{\aleph_0}$, there is a partition of $R^n$ ($n\geq 3$) into $\beta$ arcwise connected dense subsets.
-
an interesting proof of the nonexistence Continuous Bijection between mathbb r n and mathbb r 2 for n neq 2
arXiv: General Topology, 2010Co-Authors: Freshteh Malek, Hamed Daneshpajouh, Johannes HahnAbstract:In this article it is shown that there is no Continuous Bijection from $\mathbb{R}^n$ onto $\mathbb{R}^2$ for $n\neq 2$ by an elementary method. This proof is based on showing that for any cardinal number $\beta\leq 2^{\aleph_0}$, there is a partition of $R^n$ ($n\geq 3$) into $\beta$ arcwise connected dense subsets.