The Geodesic Problem in Quasimetric Spaces

Xia, Qinglan

doi:10.1007/s12220-008-9065-4

Cited by 55 publications

(36 citation statements)

References 13 publications

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“…In addition, MFSP has the symmetric property as the miRNA-miRNA path matrix P is a symmetric matrix, which makes it useful in many applications50.…”

Section: Methodsmentioning

confidence: 99%

A path-based measurement for human miRNA functional similarities using miRNA-disease associations

Ding

Luo

Xiao

et al. 2016

Sci Rep

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Compared with the sequence and expression similarity, miRNA functional similarity is so important for biology researches and many applications such as miRNA clustering, miRNA function prediction, miRNA synergism identification and disease miRNA prioritization. However, the existing methods always utilized the predicted miRNA target which has high false positive and false negative to calculate the miRNA functional similarity. Meanwhile, it is difficult to achieve high reliability of miRNA functional similarity with miRNA-disease associations. Therefore, it is increasingly needed to improve the measurement of miRNA functional similarity. In this study, we develop a novel path-based calculation method of miRNA functional similarity based on miRNA-disease associations, called MFSP. Compared with other methods, our method obtains higher average functional similarity of intra-family and intra-cluster selected groups. Meanwhile, the lower average functional similarity of inter-family and inter-cluster miRNA pair is obtained. In addition, the smaller p-value is achieved, while applying Wilcoxon rank-sum test and Kruskal-Wallis test to different miRNA groups. The relationship between miRNA functional similarity and other information sources is exhibited. Furthermore, the constructed miRNA functional network based on MFSP is a scale-free and small-world network. Moreover, the higher AUC for miRNA-disease prediction indicates the ability of MFSP uncovering miRNA functional similarity.

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“…In addition, MFSP has the symmetric property as the miRNA-miRNA path matrix P is a symmetric matrix, which makes it useful in many applications50.…”

Section: Methodsmentioning

confidence: 99%

A path-based measurement for human miRNA functional similarities using miRNA-disease associations

Ding

Luo

Xiao

et al. 2016

Sci Rep

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“…These follow directly from Theorem 18. 18 For definitions in metric space see [30,43,48,49,60]; in near metric space see [36,41,46,47,62,69,119]. 19 The maximum τ(∞, σ; x, y, z; d) corresponds to the inframetric space.…”

Section: Corollarymentioning

confidence: 99%

Properties of distance spaces with power triangle inequalities

Greenhoe

2016

Carpathian Math. Publ.

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Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle inequality does not hold but in which we may still like to perform analysis. This paper investigates what happens if the triangle inequality is removed all together, leaving what is called a distance space, and also what happens if the triangle inequality is replaced with a much more general two parameter relation, which is herein called the "power triangle inequality". The power triangle inequality represents an uncountably large class of inequalities, and includes the triangle inequality, relaxed triangle inequality, and inframetric inequality as special cases. The power triangle inequality is defined in terms of a function that is herein called the power triangle function. The power triangle function is itself a power mean, and as such is continuous and monotone with respect to its exponential parameter, and also includes the operations of maximum, minimum, mean square, arithmetic mean, geometric mean, and harmonic mean as special cases.

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“…where the function g is defined as in (10). Suppose the maximum of {g ij } is achieved at 1 ≤ i * < j * ≤ N .…”

Section: B the Construction Of An Initial Transport Pathmentioning

confidence: 99%

Numerical simulation of optimal transport paths

Xia

2010

2010 Second International Conference on Computer Modeling and Simulation

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Abstract-Transport networks with branching structures are observable not only in nature as in trees, blood vessels, etc. but also in efficiently designed transport systems such as used in railway configurations and postage delivery networks. Mathematically, such a branching transport network is modeled by an optimal transport path between two probability measures (representing the source and the target). An essential feature of such a transport path is to favor group transportation in a large amount. This article provides numerical simulation of optimal transport paths. We first construct an initial transport path, and then modify the path as much as possible by using both local and global minimization algorithms.

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The Geodesic Problem in Quasimetric Spaces

Cited by 55 publications

References 13 publications

A path-based measurement for human miRNA functional similarities using miRNA-disease associations

A path-based measurement for human miRNA functional similarities using miRNA-disease associations

Properties of distance spaces with power triangle inequalities

Numerical simulation of optimal transport paths

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