Makine Mühendisliği Bölümü Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.11779/1944

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Department: search.filters.department.Mühendislik Fakültesi, Makine Mühendisliği BölümüInstitution Author: search.filters.institutionAuthor.Arslan, İlker

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  • Article
    A Distance-Dependent Random Graph Model and Its Analysis
    (Taylor & Francis Inc, 2026) Arslan, İlker; Işlak, Ümit; 02.03. Department of Mechanical Engineering; 02. Faculty of Engineering; 01. MEF University
    Let W-1,..., Wn be non-negative random variables. We consider an undirected random graph model on the node set {1,. ..,n}, where two nodes i < j are adjacent if W-i < W-j. In our setting, the Wi's are independent but not necessarily identically distributed, resulting in a model that generalizes the classical random permutation graphs. The model exhibits a certain dependence among the edges. Moreover, when nodes have physical interpretations- such as points on the real line R with node i located at position x = i-the model gains spatial structure and becomes, in particular, distance-dependent. We derive theoretical results on degree distributions, the number of isolated vertices, and the number of close neighbors. Simulation-based observations are also provided for the average clustering and the global efficiency.
  • Article
    Increasing and Other Subsequence Problems for Random Interval Sequences
    (Elsevier, 2026) Arslan, İlker; Islak, Umit; 01. MEF University; 02.03. Department of Mechanical Engineering; 02. Faculty of Engineering
    Various relations for comparison of intervals of real numbers are introduced, and the expected length of the corresponding longest increasing subsequence is analyzed. When intervals are randomly generated by taking the minimum and maximum of two independent uniform random variables, we prove that the expected length of the longest increasing subsequence grows on root the order of 3 n. We also investigate the asymptotic behavior of the expected length under alternative comparison relations and random interval models. Discussions on other subsequence problems for interval sequences are included.