Results 41 to 50 of about 5,579,561 (370)
Discrete Applied Mathematics, 2019 Let $T$ be a random tree taken uniformly at random from the family of labelled trees on $n$ vertices. In this note, we provide bounds for $c(n)$, the number of sub-trees of $T$ that hold asymptotically almost surely. With computer support we show that $1.41805386^n \le c(n) \le 1.41959881^n$. Moreover, there is a strong indication that, in fact, $c(n) \
Bogumił Kamiński, Paweł Prałat
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Journal of Statistical Mechanics: Theory and Experiment, 2010 We investigate a network growth model in which the genealogy controls the evolution. In this model, a new node selects a random target node and links either to this target node, or to its parent, or to its grandparent, etc; all nodes from the target node to its most ancient ancestor are equiprobable destinations.
Paul L. Krapivsky, Eli Ben-Naim
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Advanced Materials Interfaces, EarlyView., 2023 This review discusses the use of Surface‐Enhanced Raman Spectroscopy (SERS) combined with Artificial Intelligence (AI) for detecting antimicrobial resistance (AMR). Various SERS studies used with AI techniques, including machine learning and deep learning, are analyzed for their advantages and limitations.
Zakarya Al‐Shaebi +4 more
wiley +1 more source
Trees with product-form random weights [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 We consider growing random recursive trees in random environment, in which at each step a new vertex is attached according to a probability distribution that assigns the tree vertices masses proportional to their random weights.The main aim of the paper ...
Konstantin Borovkov, Vladimir Vatutin
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Broadcasting induced colourings of random recursive trees and preferential attachment trees [PDF]
Random Structures & Algorithms, 2023, 2021 In this work we consider random two-colourings of random linear preferential attachment trees, which includes random recursive trees, random plane-oriented recursive trees, random binary search trees, and a class of random $d$-ary trees. The random colouring is defined by assigning the root of the tree the colour red or blue with equal probability, and
arxiv +1 more source
Perturbative Quantum Field Theory on Random Trees [PDF]
Communications in Mathematical Physics, 2019 In this paper we start a systematic study of quantum field theory on random trees. Using precise probability estimates on their Galton–Watson branches and a multiscale analysis, we establish the general power counting of averaged Feynman amplitudes and ...
N. Delporte, V. Rivasseau
semanticscholar +1 more source
ESAIM: Proceedings, 2011 These notes provide an elementary and self-contained introduction to branching ran- dom walks. Section 1 gives a brief overview of Galton-Watson trees, whereas Section 2 presents the classical law of large numbers for branching random walks. These two short sections are not exactly in- dispensable, but they introduce the idea of using size-biased trees,
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Pattern distribution in various types of random trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $\mathcal{T}_n$ denote the set of unrooted unlabeled trees of size $n$ and let $\mathcal{M}$ be a particular (finite) tree. Assuming that every tree of $\mathcal{T}_n$ is equally likely, it is shown that the number of occurrences $X_n$ of $\mathcal{M}
Gerard Kok
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30th Annual Symposium on Foundations of Computer Science, 1989 A randomized strategy for maintaining balance in dynamically changing search trees that has optimal expected behavior is presented. In particular, in the expected case an update takes logarithmic time and requires fewer than two rotations. Moreover, the update time remains logarithmic, even if the cost of a rotation is taken to be proportional to the ...
Cecilia Aragon +2 more
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Concentration Properties of Extremal Parameters in Random Discrete Structures [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 The purpose of this survey is to present recent results concerning concentration properties of extremal parameters of random discrete structures. A main emphasis is placed on the height and maximum degree of several kinds of random trees. We also provide
Michael Drmota
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