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<p>A metric relation by definition is symmetric. Since many data sets are non-symmetric, in this paper we develop a systematic theory of non-symmetric cost functions. Betweenness relations play an important role. We also introduce the notion of a Dress group in the non-symmetric setting and indicate a notion of curvature.</p>

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Geometry and Dress Groups with Non-symmetric Cost Functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月5日

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  • Lukas Silvester Barth,
  • Parvaneh Joharinad,
  • Jürgen Jost,
  • Walter Wenzel

摘要

A metric relation by definition is symmetric. Since many data sets are non-symmetric, in this paper we develop a systematic theory of non-symmetric cost functions. Betweenness relations play an important role. We also introduce the notion of a Dress group in the non-symmetric setting and indicate a notion of curvature.