@article{22406,
  abstract     = {It is known that for a uniform morphic sequence 𝒖 =⟨𝑢𝑛⟩∞
𝑛=0 and an algebraic number 𝛽 such that |𝛽| >1, the number [[𝒖]]𝛽 :=∑∞
𝑛=0(𝑢𝑛/𝛽𝑛) either lies in ℚ⁡(𝛽) or is transcendental. In this paper, we show a similar rational–transcendental dichotomy for sequences defined by irreducible Pisot morphisms on binary alphabets. Subject to the Pisot conjecture (an irreducible Pisot morphism has pure discrete spectrum), we generalise the latter result to arbitrary finite alphabets. In certain cases, we are able to show transcendence of [[𝒖]]𝛽 outright. In particular, for 𝑘 ≥2, if 𝒖 is the k-Bonacci word, then [[𝒖]]𝛽 is transcendental.},
  author       = {Kebis, Pavol and LUCA, FLORIAN and OUAKNINE, JOEL and SCOONES, ANDREW and WORRELL, JAMES},
  issn         = {1469-4417},
  journal      = {Ergodic Theory and Dynamical Systems},
  keywords     = {balanced-pair algorithm, Cobham’s conjecture, k-Bonacci words, Pisot conjecture, subspace theorem},
  pages        = {1--22},
  publisher    = {Cambridge University Press},
  title        = {{Transcendence for Pisot morphic words over an algebraic base}},
  doi          = {10.1017/etds.2026.10324},
  year         = {2026},
}

@article{21516,
  abstract     = {The notion of elliptic or ellipsoidal conformal equivalent structure is introduced to model rough surface topography by use of convex homogenized shapes. The method is based on classical stereological results dealing with the relation between the number of intersections of an object with a set of parallel straight lines. The approach leads to an algorithm comparing the number of intercepts on both sampled surfaces and homogenized shapes selected for modeling. Some applications using the comparative values of the parameters of the homogenized structures are presented in this paper.},
  author       = {Roques-Carmes, Charles and Bodin, N. and Monteil, G. and Quiniou, J.F.},
  issn         = {1873-2577},
  journal      = {Wear},
  keywords     = {Rough surface topography, Stereology, Algorithm, Equivalent structure concept},
  number       = {1-2},
  pages        = {82--91},
  publisher    = {Elsevier},
  title        = {{Description of rough surfaces using conformal equivalent structure concept: Part 1. Stereological approach}},
  doi          = {10.1016/s0043-1648(00)00562-7},
  volume       = {248},
  year         = {2001},
}

@article{11694,
  abstract     = {We consider exploration problems where a robot has to construct a complete map of an unknown environment. We assume that the environment is modeled by a directed, strongly connected graph. The robot's task is to visit all nodes and edges of the graph using the minimum number R of edge traversals. Deng and Papadimitriou [Proceedings of the 31st Symposium on the Foundations of Computer Science, 1990, pp. 356-361] showed an upper bound for R ofd O(d)m and Koutsoupias (reported by Deng and Papadimitriou) gave a lower bound of Ω≠(d2m), where m is the number of edges in the graph and d is the minimum number of edges that have to be added to make the graph Eulerian.  We give the 1rst subexponential algorithm for this exploration problem, which achieves an upper bound of dO(logd)m.  We also show a matching lower bound of d≠(logd)m for our algorithm. Additionally, we give lower bounds of 2≠(d)m, respectively, d≠(logd)m for various other natural exploration algorithms.},
  author       = {Albers, Susanne and Henzinger, Monika H},
  issn         = {1095-7111},
  journal      = {SIAM Journal on Computing},
  keywords     = {directed graph, exploration algorithm},
  location     = {El Paso, TX, United States},
  number       = {4},
  pages        = {1164--1188},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Exploring unknown environments}},
  doi          = {10.1137/s009753979732428x},
  volume       = {29},
  year         = {2000},
}

@article{11680,
  abstract     = {We present a model for edge updates with restricted randomness in dynamic graph algorithms and a general technique for analyzing the expected running time of an update operation. This model is able to capture the average case in many applications, since (1) it allows restrictions on the set of edges which can be used for insertions and (2) the type (insertion or deletion) of each update operation is arbitrary, i.e., not random. We use our technique to analyze existing and new dynamic algorithms for the following problems: maximum cardinality matching, minimum spanning forest, connectivity, 2-edge connectivity, k -edge connectivity, k -vertex connectivity, and bipartiteness. Given a random graph G with m 0 edges and n vertices and a sequence of l update operations such that the graph contains m i edges after operation i , the expected time for performing the updates for any l is O(llogn+∑li=1n/m−−√i) in the case of minimum spanning forests, connectivity, 2-edge connectivity, and bipartiteness. The expected time per update operation is O(n) in the case of maximum matching. We also give improved bounds for k -edge and k -vertex connectivity. Additionally we give an insertions-only algorithm for maximum cardinality matching with worst-case O(n) amortized time per insertion.},
  author       = {Alberts, D. and Henzinger, Monika H},
  issn         = {1432-0541},
  journal      = {Algorithmica},
  keywords     = {Dynamic graph algorithm, Average-case analysis, Minimum spanning forest, Connectivity, Bipartiteness, Maximum matching.},
  pages        = {31--60},
  publisher    = {Springer Nature},
  title        = {{Average-case analysis of dynamic graph algorithms}},
  doi          = {10.1007/pl00009186},
  volume       = {20},
  year         = {1998},
}