scholarly journals On martingale tail sums for the path length in random trees

2016 ◽  
Vol 50 (3) ◽  
pp. 493-508
Author(s):  
Henning Sulzbach
Keyword(s):  
Path Length ◽  
Random Trees ◽  
Tail Sums

scholarly journals Limit Theorems for Depths and Distances in Weighted Random B-Ary Recursive Trees

2011 ◽  
Vol 48 (4) ◽  
pp. 1060-1080 ◽  
Author(s):  
Götz Olaf Munsonius ◽  
Ludger Rüschendorf
Keyword(s):  
Path Length ◽  
Limit Theorems ◽  
Wiener Index ◽  
Random Trees ◽  
Random Node ◽  
Recursive Trees

Limit theorems are established for some functionals of the distances between two nodes in weighted random b-ary recursive trees. We consider the depth of the nth node and of a random node, the distance between two random nodes, the internal path length, and the Wiener index. As an application, these limit results imply, by an imbedding argument, corresponding limit theorems for further classes of random trees: plane-oriented recursive trees and random linear recursive trees.

scholarly journals BUILDING RANDOM TREES FROM BLOCKS

2013 ◽  
Vol 28 (1) ◽  
pp. 67-81 ◽  
Author(s):  
M. Gopaladesikan ◽  
H. Mahmoud ◽  
M.D. Ward
Keyword(s):  
Path Length ◽  
Building Blocks ◽  
Random Trees ◽  
Rooted Trees ◽  
Total Path Length ◽  
Number Of Leaves

Many modern networks grow from blocks. We study the probabilistic behavior of parameters of a blocks tree, which models several kinds of networks. It grows from building blocks that are themselves rooted trees. We investigate the number of leaves, depth of nodes, total path length, and height of such trees. We use methods from the theory of Pólya urns and martingales.

scholarly journals Limit Theorems for Depths and Distances in Weighted Random B-Ary Recursive Trees

2011 ◽  
Vol 48 (04) ◽  
pp. 1060-1080 ◽  
Author(s):  
Götz Olaf Munsonius ◽  
Ludger Rüschendorf
Keyword(s):  
Path Length ◽  
Limit Theorems ◽  
Wiener Index ◽  
Random Trees ◽  
Random Node ◽  
Recursive Trees

Limit theorems are established for some functionals of the distances between two nodes in weighted randomb-ary recursive trees. We consider the depth of thenth node and of a random node, the distance between two random nodes, the internal path length, and the Wiener index. As an application, these limit results imply, by an imbedding argument, corresponding limit theorems for further classes of random trees: plane-oriented recursive trees and random linear recursive trees.

scholarly journals The Wiener Index of Random Trees

2002 ◽  
Vol 11 (6) ◽  
pp. 587-597 ◽  
Author(s):  
RALPH NEININGER
Keyword(s):  
Path Length ◽  
Probabilistic Models ◽  
Wiener Index ◽  
Binary Search ◽  
Random Trees ◽  
Binary Search Trees ◽  
Search Trees ◽  
Limit Laws ◽  
Recursive Trees ◽  
Asymptotic Correlations

The Wiener index is analysed for random recursive trees and random binary search trees in uniform probabilistic models. We obtain expectations, asymptotics for the variances, and limit laws for this parameter. The limit distributions are characterized as the projections of bivariate measures that satisfy certain fixed point equations. Covariances, asymptotic correlations, and bivariate limit laws for the Wiener index and the internal path length are given.

The Effect of Path Length and Display Size on Memory for Spatial Information

2012 ◽  
Vol 59 (3) ◽  
pp. 147-152 ◽  
Author(s):  
Katherine Guérard ◽  
Sébastien Tremblay
Keyword(s):  
Path Length ◽  
Potential Role ◽  
Spatial Information ◽  
Recall Performance ◽  
Minor Role ◽  
Length Effect ◽  
Serial Memory ◽  
Fixed Reference ◽  
A Minor

In serial memory for spatial information, some studies showed that recall performance suffers when the distance between successive locations increases relatively to the size of the display in which they are presented (the path length effect; e.g., Parmentier et al., 2005) but not when distance is increased by enlarging the size of the display (e.g., Smyth & Scholey, 1994). In the present study, we examined the effect of varying the absolute and relative distance between to-be-remembered items on memory for spatial information. We manipulated path length using small (15″) and large (64″) screens within the same design. In two experiments, we showed that distance was disruptive mainly when it is varied relatively to a fixed reference frame, though increasing the size of the display also had a small deleterious effect on recall. The insertion of a retention interval did not influence these effects, suggesting that rehearsal plays a minor role in mediating the effects of distance on serial spatial memory. We discuss the potential role of perceptual organization in light of the pattern of results.

Investigation of particulate systems using optical pathlength spectroscopy

2000 ◽  
Vol 627 ◽  
Author(s):  
Gabriel Popescu ◽  
Aristide Dogariu
Keyword(s):  
Path Length ◽  
Random Media ◽  
Michelson Interferometer ◽  
Industrial Process ◽  
Optical Path Length ◽  
Industrial Applications ◽  
Optical Path ◽  
Interference Signal ◽  
Optical Length ◽  
Reference Mirror

ABSTRACTIn many industrial applications involving granular media, knowledge about the structural transformations suffered during the industrial process is desirable. Optical techniques are noninvasive, fast, and versatile tools for monitoring such transformations. We have recently introduced optical path-length spectroscopy as a new technique for random media investigation. The principle of the method is to use a partially coherent source in a Michelson interferometer, where the fields from a reference mirror and the sample are combined to obtain an interference signal. When the system under investigation is a multiple-scattering medium, by tuning the optical length of the reference arm, the optical path-length probability density of light backscattered from the sample is obtained. This distribution carries information about the structural details of the medium. In the present paper, we apply the technique of optical path-length spectroscopy to investigate inhomogeneous distributions of particulate dielectrics such as ceramics and powders. The experiments are performed on suspensions of systems with different solid loads, as well as on powders and suspensions of particles with different sizes. We show that the methodology is highly sensitive to changes in volume concentration and particle size and, therefore, it can be successfully used for real-time monitoring. In addition, the technique is fiber optic-based and has all the advantages associated with the inherent versatility.

ANALISIS PERINGKAT TOP BRAND OJEK ONLINE MENGGUNAKAN JEJARING SOSIAL PERCAKAPAN TWITTER

2019 ◽  
Vol 24 (2) ◽  
pp. 88-104
Author(s):  
Ilham Aminudin ◽  
Dyah Anggraini
Keyword(s):  
Social Media ◽  
Social Network ◽  
Social Network Analysis ◽  
Network Analysis ◽  
Path Length ◽  
Average Path Length ◽  
Average Degree ◽  
Clustering Coefficient ◽  
R Programming

Banyak bisnis mulai muncul dengan melibatkan pengembangan teknologi internet. Salah satunya adalah bisnis di aplikasi berbasis penyedia layanan di bidang moda transportasi berbasis online yang ternyata dapat memberikan solusi dan menjawab berbagai kekhawatiran publik tentang layanan transportasi umum. Kemacetan lalu lintas di kota-kota besar dan ketegangan publik dengan keamanan transportasi umum diselesaikan dengan adanya aplikasi transportasi online seperti Grab dan Gojek yang memberikan kemudahan dan kenyamanan bagi penggunanya Penelitian ini dilakukan untuk menganalisa keaktifan percakapan brand jasa transportasi online di jejaring sosial Twitter berdasarkan properti jaringan. Penelitian dilakukan dengan dengan mengambil data dari percakapan pengguna di social media Twitter dengan cara crawling menggunakan Bahasa pemrograman R programming dan software R Studio dan pembuatan model jaringan dengan software Gephy. Setelah itu data dianalisis menggunakan metode social network analysis yang terdiri berdasarkan properti jaringan yaitu size, density, modularity, diameter, average degree, average path length, dan clustering coefficient dan nantinya hasil analisis akan dibandingkan dari setiap properti jaringan kedua brand jasa transportasi Online dan ditentukan strategi dalam meningkatkan dan mempertahankan keaktifan serta tingkat kehadiran brand jasa transportasi online, Grab dan Gojek.

scholarly journals A Comparison of Local Path Planning Techniques of Autonomous Surface Vehicles for Monitoring Applications: The Ypacarai Lake Case-study

Sensors ◽  
2020 ◽  
Vol 20 (5) ◽  
pp. 1488
Author(s):  
Federico Peralta ◽  
Mario Arzamendia ◽  
Derlis Gregor ◽  
Daniel G. Reina ◽  
Sergio Toral
Keyword(s):  
Path Planning ◽  
Random Trees ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Planning Techniques ◽  
Advantages And Disadvantages ◽  
Autonomous Surface Vehicle ◽  
Local Path Planning ◽  
Custom Made ◽  
Local Path

Local path planning is important in the development of autonomous vehicles since it allows a vehicle to adapt their movements to dynamic environments, for instance, when obstacles are detected. This work presents an evaluation of the performance of different local path planning techniques for an Autonomous Surface Vehicle, using a custom-made simulator based on the open-source Robotarium framework. The conducted simulations allow to verify, compare and visualize the solutions of the different techniques. The selected techniques for evaluation include A*, Potential Fields (PF), Rapidly-Exploring Random Trees* (RRT*) and variations of the Fast Marching Method (FMM), along with a proposed new method called Updating the Fast Marching Square method (uFMS). The evaluation proposed in this work includes ways to summarize time and safety measures for local path planning techniques. The results in a Lake environment present the advantages and disadvantages of using each technique. The proposed uFMS and A* have been shown to achieve interesting performance in terms of processing time, distance travelled and security levels. Furthermore, the proposed uFMS algorithm is capable of generating smoother routes.

scholarly journals Topological measures for identifying and predicting the spread of complex contagions

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Douglas Guilbeault ◽  
Damon Centola
Keyword(s):  
Social Networks ◽  
Shortest Path ◽  
Empirical Data ◽  
Path Length ◽  
Centrality Measures ◽  
Social Phenomena ◽  
Node Centrality ◽  
Network Connectedness ◽  
Topological Measures ◽  
Definition Of

AbstractThe standard measure of distance in social networks – average shortest path length – assumes a model of “simple” contagion, in which people only need exposure to influence from one peer to adopt the contagion. However, many social phenomena are “complex” contagions, for which people need exposure to multiple peers before they adopt. Here, we show that the classical measure of path length fails to define network connectedness and node centrality for complex contagions. Centrality measures and seeding strategies based on the classical definition of path length frequently misidentify the network features that are most effective for spreading complex contagions. To address these issues, we derive measures of complex path length and complex centrality, which significantly improve the capacity to identify the network structures and central individuals best suited for spreading complex contagions. We validate our theory using empirical data on the spread of a microfinance program in 43 rural Indian villages.

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