Skip to main content Accessibility help
×
  1. Home
  2. Browse subjects
  3. Mathematics
  4. Discrete Mathematics, Information Theory and Coding
  5. Content listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

9084 results in Discrete Mathematics, Information Theory and Coding

Page 15 of 455

  • 1 - The idea behind tangles

  • from Part I - Tangles
  • Reinhard Diestel, Universität Hamburg
  • Book:
    Tangles
    Published online:
    16 May 2024
    Print publication:
    23 May 2024, pp 3-14
    • Chapter
      • You have access
    • PDF
    • Export citation

Tangles
  • A Structural Approach to Artificial Intelligence in the Empirical Sciences
  • Reinhard Diestel
  • Published online:
    16 May 2024
    Print publication:
    23 May 2024
  • Tangles offer a precise way to identify structure in imprecise data. By grouping qualities that often occur together, they not only reveal clusters of things but also types of their qualities: types of political views, of texts, of health conditions, or of proteins. Tangles offer a new, structural, approach to artificial intelligence that can help us understand, classify, and predict complex phenomena.This has become possible by the recent axiomatization of the mathematical theory of tangles, which has made it applicable far beyond its origin in graph theory: from clustering in data science and machine learning to predicting customer behaviour in economics; from DNA sequencing and drug development to text and image analysis. Such applications are explored here for the first time. Assuming only basic undergraduate mathematics, the theory of tangles and its potential implications are made accessible to scientists, computer scientists, and social scientists.

  • Rainbow Hamiltonicity in uniformly coloured perturbed digraphs

  • Part of
  • Kyriakos Katsamaktsis, Shoham Letzter, Amedeo Sgueglia
  • Journal:
    Combinatorics, Probability and Computing / Volume 33 / Issue 5 / September 2024
    Published online by Cambridge University Press:
    13 May 2024, pp. 624-642
    • Article
      • You have access
      • Open access
    • PDF
    • HTML
    • Export citation

  • We investigate the existence of a rainbow Hamilton cycle in a uniformly edge-coloured randomly perturbed digraph. We show that for every $\delta \in (0,1)$ there exists $C = C(\delta ) \gt 0$ such that the following holds. Let $D_0$ be an $n$-vertex digraph with minimum semidegree at least $\delta n$ and suppose that each edge of the union of $D_0$ with a copy of the random digraph $\mathbf{D}(n,C/n)$ on the same vertex set gets a colour in $[n]$ independently and uniformly at random. Then, with high probability, $D_0 \cup \mathbf{D}(n,C/n)$ has a rainbow directed Hamilton cycle.

    This improves a result of Aigner-Horev and Hefetz ((2021) SIAM J. Discrete Math. 35(3) 1569–1577), who proved the same in the undirected setting when the edges are coloured uniformly in a set of $(1 + \varepsilon )n$ colours.

Page 15 of 455