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Metric structures associated to Finsler metrics [article]

Sorin V. Sabau, Kazuhiro Shibuya, Hideo Shimada
2014 arXiv   pre-print
We investigate the relation between weighted quasi-metric Spaces and Finsler Spaces. We show that the induced metric of a Randers space with reversible geodesics is a weighted quasi-metric space.  ...  The authors are extremely grateful to the referee for several useful suggestions that have considerable improved the paper.  ...  Then the graph manifold G f inherits a natural structure of weighted quasi-metric space (G f , Q, W ) that coincides with the weighted quasimetric space (M, d F , 2f ) induced by F , up to an isomorphism  ... 
arXiv:1305.5880v2 fatcat:jrnpa4b6azbdneh7ndgi6dotmm

Page 184 of Mathematical Reviews Vol. 47, Issue 1 [page]

1974 Mathematical Reviews  
The author considers the problem of generalizing the concept of a metric structure to an -metric structure (a set with a function defined for (n + 1)-tuples of points) and the influence it will have on  ...  The local weight of a space is not an invariant in the above sense. The author shows that the property oLW(<t) provides the essential invariant (Theorem 1).  ... 

A Characterization of Uniquely Representable Graphs [article]

Péter G. N. Szabó
2020 arXiv   pre-print
The betweenness structure of a finite metric space M = (X, d) is a pair B(M) = (X,β_M) where β_M is the so-called betweenness relation of M that consists of point triplets (x, y, z) such that d(x, z) =  ...  The underlying graph of a betweenness structure B = (X,β) is the simple graph G(B) = (X, E) where the edges are pairs of distinct points with no third point between them.  ...  Acknowledgment The author is grateful to Pierre Aboulker for sharing his thoughts on the results presented here, as well as on other, related results.  ... 
arXiv:1708.01272v4 fatcat:mgaox6lufjeahblyhoc3kqjrxa

Non-metric similarity search problems in very large collections

Benjamin Bustos, Tomas Skopal
2011 2011 IEEE 27th International Conference on Data Engineering  
postulates alone are not a guarantee of efficient indexing The structure of distance distribution indicates the indexability of the database Intrinsic dimensionality ρ ρ ρ ρ(S,δ δ δ δ) (idim) -an indexability  ...  zero + nonzero weight = nonzero (all lists must be visited) d i sorted wrt the weights (desc.)  ... 
doi:10.1109/icde.2011.5767955 dblp:conf/icde/BustosS11 fatcat:rllzyyp6hfgcrjho3slo76tewm

Applying Inner Metric Analysis to 20th Century Compositions [chapter]

Anja Volk
2009 Communications in Computer and Information Science  
Inner Metric Analysis assigns to each note of a piece a metric weight. The analysis is based on the detection of regular pulses created by the onsets of notes.  ...  Hence these pieces are characterized as being metric coherent since the notes generate a metrical structure that is in sink with the abstract grid of the bar lines (see (2) ).  ...  The excerpts of the metric weights of the entire piece in figure 2 make this difference in the metric structures of the right and left hand more explicit.  ... 
doi:10.1007/978-3-642-04579-0_19 fatcat:euqczdq3a5hlrgam5emhzk3zb4

Angle-based Search Space Shrinking for Neural Architecture Search [article]

Yiming Hu, Yuding Liang, Zichao Guo, Ruosi Wan, Xiangyu Zhang, Yichen Wei, Qingyi Gu, Jian Sun
2020 arXiv   pre-print
We provide comprehensive evidences showing that, in weight-sharing supernet, the proposed metric is more stable and accurate than accuracy-based and magnitude-based metrics to predict the capability of  ...  We also show that the angle-based metric can converge fast while training supernet, enabling us to get promising shrunk search spaces efficiently. ABS can easily apply to most of NAS approaches (e.g.  ...  We evaluate five different NAS algorithms [24,10,11,15,29] on eight search spaces Fig. 3 . 3 Examples of the weight vector determined by structure and weights.  ... 
arXiv:2004.13431v3 fatcat:mgsw5qgnmzco3hcxre2flyyowm

New Einstein metrics on 8#(S2×S3)

Charles P. Boyer, Krzysztof Galicki
2003 Differential geometry and its applications  
These are the first known non-regular Sasakian-Einstein metrics on this 5-manifold.  ...  We show that #8(S 2 × S 3 ) admits two 8-dimensional complex families of inequivalent non-regular Sasakian-Einstein structures.  ...  Acknowledgements During the preparation of this work the authors were partially supported by NSF grants DMS-9970904 and DMS-0203219  ... 
doi:10.1016/s0926-2245(03)00033-0 fatcat:l2abuaw7pfbw7a56crzgvt22cu

Macromolecular refinement of X-ray and cryo-electron microscopy structures with Phenix / OPLS3e for improved structure and ligand quality [article]

Gydo van Zundert, Kenneth Borrelli, Nigel W. Moriarty, Oleg V Sobolev
2020 biorxiv/medrxiv   pre-print
For real space refinement of cryo-EM based structures, we find comparable quality structures, goodness-of-fit and reduced ligand strain.  ...  In addition, we explicitly show how structure quality is related with the map-model cross correlation as a function of data weight, and how it can be an insightful tool for detecting both over- and underfitting  ...  This work was supported by the US National Institutes of Health (NIH) (grant P01GM063210) and the Phenix Industrial Consortium.  ... 
doi:10.1101/2020.07.10.198093 fatcat:23oe5sgahfam3giqyvcwcpc2ne

On the reversible geodesics of a Finsler space with special (α,β )-metric

Mohammad Rafee, Avdhesh Kumar, G. C. Chaubey
2018 Journal of Mathematics and Computer Science  
We study some geometrical properties of F with reversible geodesics and prove that the Finsler metric F induces a weighted quasi-metric d F on M.  ...  This paper deals with the existence of reversible geodesics on a Finsler space with some (α, β)-metrics. The conditions for a Finsler space (M, F) to be with reversible geodesics are obtained.  ...  Finsler metrics associated with weighted quasi-metrics It is well known fact that the Riemannian space are expressible as metric spaces.  ... 
doi:10.22436/jmcs.018.03.12 fatcat:3oxcon47frh2tjwycxqiz3khj4

Weighted E-Spaces and Epistemic Information Operators

Mark Burgin
2014 Information  
In this paper, both types of information are studied as operators in epistemic spaces based on the general theory of information.  ...  Infological systems are modeled by epistemic spaces, while operators in these spaces are mathematical models of information.  ...  Acknowledgment The author is grateful to unknown reviewers for their useful comments. Conflicts of Interest The author declares no conflict of interest.  ... 
doi:10.3390/info5020357 fatcat:p3zsexpsu5gffi4vlur2aioyjy

Dynamic similarity search in multi-metric spaces

Benjamin Bustos, Tomáý Skopal
2006 Proceedings of the 8th ACM international workshop on Multimedia information retrieval - MIR '06  
A recent approach, that has been shown to improve the effectiveness of similarity search in multimedia databases, resorts to the usage of combinations of metrics where the desirable contribution (weight  ...  This paper presents the Multi-Metric M-tree (M 3 -tree), a metric access method that supports similarity queries with dynamic combinations of metric functions.  ...  The first author is on leave from the Department of Computer Science, University of Chile.  ... 
doi:10.1145/1178677.1178698 dblp:conf/mir/BustosS06 fatcat:wxxf6qulhze3bhaewp5fhz2prm

Tight spans, Isbell completions and semi-tropical modules [article]

Simon Willerton
2013 arXiv   pre-print
In this paper we consider the categorical Isbell completion construction for generalized metric spaces in the sense of Lawvere.  ...  We show that this is an analogue of the tight span construction of classical metric spaces, and that the Isbell completion coincides with the directed tight span of Hirai and Koichi.  ...  Acknowledgements This paper was inspired by a short conversation at the n-Category Café [1] ; I would like to thank Bruce Bartlett, Tom Leinster and Andrew Stacey for their contributions.  ... 
arXiv:1302.4370v1 fatcat:5sclskurhfee5lzakvekf7dk6e

Intrinsic approach spaces on domains

E. Colebunders, S. De Wachter, B. Lowen
2011 Topology and its Applications  
quasi metric Approach space Scott topology Quantification Kernel condition The paper is a contribution to quantifiability of domains.  ...  gauge of quasi metrics, inducing the Scott topology.  ...  The collection of all (quasi) metrics on a set X is denoted by (q)Met(X). Quasi metric structures do not behave well with respect to the formation of initial structures, in particular products.  ... 
doi:10.1016/j.topol.2011.01.025 fatcat:vcmuvlyrozhylpuqcb2lnmysrm

The fundamental weighted category of a weighted space (From directed to weighted algebraic topology) [article]

Marco Grandis
2006 arXiv   pre-print
In the fundamental weighted category of a generalised metric space, introduced here, each homotopy class of paths has a weight (or seminorm), which is subadditive with respect to composition.  ...  Its algebraic counterpart will be 'weighted algebraic structures', equipped with a sort of directed seminorm.  ...  Generalised metric spaces We begin with recalling the structure of Lawvere's generalised metric spaces [Lw] , which will be used as a first setting for weighted algebraic topology.  ... 
arXiv:math/0604506v1 fatcat:xmnertzjlzatxmpon6gw6tw5v4

A Variety Metric Accounting for Unbalanced Idea Space Distributions

Paul-Armand Verhaegen, Dennis Vandevenne, Jef Peeters, Joost R. Duflou
2015 Procedia Engineering  
This paper gives an overview of the existing metrics, and demonstrates a number of shortcomings in the variety metric, such as not accounting for the fairness of the distribution of ideas over nodes on  ...  This necessitates the development of a set of widely accepted metrics covering the different aspects on which idea generation methods can be characterized.  ...  This metric is applied to an encoded tree-like structure of the idea space, and gives higher weights to differentiation occurring in higher abstraction levels.  ... 
doi:10.1016/j.proeng.2015.12.368 fatcat:7jnd63hsxzczvdt4wkzyf3feqy
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