scholarly journals On the variance of the internal path length of generalized digital trees – The Mellin convolution approach

2000 ◽  
Vol 242 (1-2) ◽  
pp. 143-168 ◽  
Author(s):  
Friedrich Hubalek
Keyword(s):  
Path Length ◽  
Digital Trees ◽  
Convolution Approach ◽  
Mellin Convolution

scholarly journals Dependence between path-length and size in random digital trees

2017 ◽  
Vol 54 (4) ◽  
pp. 1125-1143
Author(s):  
Michael Fuchs ◽  
Hsien-Kuei Hwang
Keyword(s):  
Path Length ◽  
Normal Limit ◽  
Limit Laws ◽  
Normal Distributions ◽  
Digital Trees ◽  
Bivariate Normal ◽  
Asymmetric Case ◽  
Periodic Fluctuations ◽  
Type Of Behavior ◽  
Small Periodic

AbstractWe study the size and the external path length of random tries and show that they are asymptotically independent in the asymmetric case but strongly dependent with small periodic fluctuations in the symmetric case. Such an unexpected behavior is in sharp contrast to the previously known results on random tries, that the size is totally positively correlated to the internal path length and that both tend to the same normal limit law. These two dependence examples provide concrete instances of bivariate normal distributions (as limit laws) whose components have correlation either zero or one or periodically oscillating. Moreover, the same type of behavior is also clarified for other classes of digital trees such as bucket digital trees and Patricia tries.

scholarly journals One-sided Variations on Tries: Path Imbalance, Climbing, and Key Sampling

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Costas A. Christophi ◽  
Hosam M. Mahmoud
Keyword(s):  
Probability Distribution ◽  
Generating Function ◽  
Path Length ◽  
Mellin Transform ◽  
Moment Generating Function ◽  
Exact Probability ◽  
Digital Trees ◽  
Exact Probability Distribution ◽  
International Audience ◽  
The Mean

International audience One-sided variations on path length in a trie (a sort of digital trees) are investigated: They include imbalance factors, climbing under different strategies, and key sampling. For the imbalance factor accurate asymptotics for the mean are derived for a randomly chosen key in the trie via poissonization and the Mellin transform, and the inverse of the two operations. It is also shown from an analysis of the moving poles of the Mellin transform of the poissonized moment generating function that the imbalance factor (under appropriate centering and scaling) follows a Gaussian limit law. The method extends to several variations of sampling keys from a trie and we sketch results of climbing under different strategies. The exact probability distribution is computed in one case, to demonstrate that such calculations can be done, at least in principle.

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 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.

scholarly journals Speeds of Sound in Methanol at Temperatures from 233.33 to 353.21 K at Pressures up to 20 MPa

2021 ◽  
Vol 42 (5) ◽  
Author(s):  
Christian W. Scholz ◽  
Roland Span
Keyword(s):  
Equation Of State ◽  
Path Length ◽  
Speeds Of Sound ◽  
Pulse Timing ◽  
Combined Uncertainty ◽  
Pulse Echo

AbstractWe report experimental speeds of sound in methanol. Measurements were conducted at temperatures from 233 to 353 K with pressures up to 20 MPa using the double-path length pulse-echo technique. The relative expanded combined uncertainty (k = 2) in measurement was estimated to vary from 0.012 to 0.014%, considering contributions from temperature, pressure, path length calibration, pulse timing, and purity of the sample. Experimental speeds of sound gained in the scope of this work were compared with the equation of state by de Reuck and Craven, as well as with further data from literature.

scholarly journals Research on path planning of three-neighbor search A* algorithm combined with artificial potential field

2021 ◽  
Vol 18 (3) ◽  
pp. 172988142110264
Author(s):  
Jiqing Chen ◽  
Chenzhi Tan ◽  
Rongxian Mo ◽  
Hongdu Zhang ◽  
Ganwei Cai ◽  
...  
Keyword(s):  
Path Planning ◽  
Mobile Robot ◽  
Obstacle Avoidance ◽  
Potential Field ◽  
Path Length ◽  
Search Time ◽  
Experimental Results ◽  
Artificial Potential Field ◽  
A Algorithm ◽  
Neighbor Search

Among the shortcomings of the A* algorithm, for example, there are many search nodes in path planning, and the calculation time is long. This article proposes a three-neighbor search A* algorithm combined with artificial potential fields to optimize the path planning problem of mobile robots. The algorithm integrates and improves the partial artificial potential field and the A* algorithm to address irregular obstacles in the forward direction. The artificial potential field guides the mobile robot to move forward quickly. The A* algorithm of the three-neighbor search method performs accurate obstacle avoidance. The current pose vector of the mobile robot is constructed during obstacle avoidance, the search range is narrowed to less than three neighbors, and repeated searches are avoided. In the matrix laboratory environment, grid maps with different obstacle ratios are compared with the A* algorithm. The experimental results show that the proposed improved algorithm avoids concave obstacle traps and shortens the path length, thus reducing the search time and the number of search nodes. The average path length is shortened by 5.58%, the path search time is shortened by 77.05%, and the number of path nodes is reduced by 88.85%. The experimental results fully show that the improved A* algorithm is effective and feasible and can provide optimal results.

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