scholarly journals The total path length of split trees

2012 ◽  
Vol 22 (5) ◽  
pp. 1745-1777 ◽  
Author(s):  
Nicolas Broutin ◽  
Cecilia Holmgren
Keyword(s):  
Path Length ◽  
Total Path Length ◽  
Split Trees

scholarly journals Inversions in Split Trees and Conditional Galton–Watson Trees

2018 ◽  
Vol 28 (3) ◽  
pp. 335-364 ◽  
Author(s):  
XING SHI CAI ◽  
CECILIA HOLMGREN ◽  
SVANTE JANSON ◽  
TONY JOHANSSON ◽  
FIONA SKERMAN
Keyword(s):  
Unique Solution ◽  
Path Length ◽  
Random Variable ◽  
Sufficient Condition ◽  
Explicit Formulas ◽  
Total Path Length ◽  
Split Trees ◽  
Common Ancestors

We studyI(T), the number of inversions in a treeTwith its vertices labelled uniformly at random, which is a generalization of inversions in permutations. We first show that the cumulants ofI(T) have explicit formulas involving thek-total common ancestors ofT(an extension of the total path length). Then we considerXn, the normalized version ofI(Tn), for a sequence of treesTn. For fixedTn's, we prove a sufficient condition forXnto converge in distribution. As an application, we identify the limit ofXnfor completeb-ary trees. ForTnbeing split trees [16], we show thatXnconverges to the unique solution of a distributional equation. Finally, whenTn's are conditional Galton–Watson trees, we show thatXnconverges to a random variable defined in terms of Brownian excursions. By exploiting the connection between inversions and the total path length, we are able to give results that significantly strengthen and broaden previous work by Panholzer and Seitz [46].

scholarly journals Differences between Tempos of Step Error and Postural Sway in the Stipulated Tempo Step Test for Children and Their Relationships

2021 ◽  
Vol 11 (6) ◽  
pp. 31
Author(s):  
Hiroki Aoki ◽  
Shin-ichi Demura ◽  
Kenji Takahashi ◽  
Hiroshi Hirai
Keyword(s):  
Repeated Measures ◽  
Path Length ◽  
Postural Sway ◽  
Dynamic Balance ◽  
Step Test ◽  
Total Path Length ◽  
Fast Tempo ◽  
Balance Ability ◽  
Path Lengths ◽  
Slow Tempo

Recently, to evaluate dynamic balance ability, a stipulated tempo step test has been developed, and a step error between tempo and contact time of feet has been used as an evaluation variable. The step error, postural sway, and their relationships may differ between the slow tempo (40 bpm) and fast tempo (120 bpm). This study aimed to examine the aforementioned problem with 62 participant children (30 boys and 32 girls). The step error and postural sway variables (X-axis path length, Y-axis path length, total path length, peripheral area, and rectangular area) during stepping while matching both tempos were measured. Means of one minute and three intervals (0–20 sec, 20–40 sec, and 40–60 sec) for each variable were calculated in both tempos. The results of the paired t-test showed that means of all variables were larger in the 40 bpm tempo than in the 120 bpm tempo. In the multiple comparison tests after the results of the two-way repeated measures ANOVA, the means of three intervals in all variables were larger in the 40 bpm tempo than in the 120 bpm tempo; the means of the sway variables, excluding that of the X-axis path length, in the 40 bpm tempo were larger in the 0–20 sec interval than in the 20–40 sec interval or the 40–60 sec interval. Correlations between step errors and those between the step error and sway variables of both tempos were insignificant or under moderation. The correlations between the step error and sway variables in both tempos were insignificant or significant but low, and those among sway variables were high, except between the X- and Y-axis path lengths. The relationship between both axis path lengths differed according to the tempo. In conclusion, in the case of the stipulated tempo step test targeting children, the slow tempo has a greater step error and postural sway than the fast tempo, and the sway in the early step stage is greater in the slow tempo. The relationships between step errors and between the step error and sway variables of both tempos are low; hence, the ability related to the test may differ in both tempos. The relationships among sway variables in both tempos are high, except between the X- and Y-axis path lengths.

Control of Stance and Developmental Coordination Disorder: The Role of Visual Information

2004 ◽  
Vol 21 (1) ◽  
pp. 19-33 ◽  
Author(s):  
Eryk P. Przysucha ◽  
M. Jane Taylor
Keyword(s):  
Visual Information ◽  
Path Length ◽  
Developmental Coordination Disorder ◽  
Postural Sway ◽  
Quiet Standing ◽  
Eyes Closed ◽  
Total Path Length ◽  
Eyes Open ◽  
Stability Limits ◽  
Coordination Disorder

The purpose of this study was to compare the postural sway profiles of 20 boys with and without Developmental Coordination Disorder (DCD) on two conditions of a quiet standing task: eyes open and eyes closed. Anterior-posterior (AP) sway, medio-lateral sway (LAT), area of sway, total path length, and Romberg’s quotient were analyzed. When visual information was available, there was no difference between groups in LAT sway or path length. However, boys with DCD demonstrated more AP sway (p < .01) and greater area of sway (p < .03), which resulted in pronounced excursions closer to their stability limits. Analysis of Romberg’s quotient indicated that boys with DCD did not over-rely on visual information.

scholarly journals The Dimensionless Squared Jerk: An Objective Parameter That Improves Assessment of Hand Motion Analysis during Simulated Shoulder Arthroscopy

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Erica Kholinne ◽  
Maulik J. Gandhi ◽  
Arnold Adikrishna ◽  
Hanpyo Hong ◽  
Haewon Kim ◽  
...  
Keyword(s):  
Motion Analysis ◽  
Path Length ◽  
Shoulder Arthroscopy ◽  
Tracking System ◽  
Arthroscopic Surgery ◽  
Optical Tracking ◽  
Hand Movements ◽  
Total Path Length ◽  
Acceleration Threshold ◽  
Objective Parameter

Purpose. Attempts to quantify hand movements of surgeons during arthroscopic surgery faced limited progress beyond motion analysis of hands and/or instruments. Surrogate markers such as procedure time have been used. The dimensionless squared jerk (DSJ) is a measure of deliberate hand movements. This study tests the ability of DSJ to differentiate novice and expert surgeons (construct validity) whilst performing simulated arthroscopic shoulder surgical tasks. Methods. Six residents (novice group) and six consultants (expert group) participated in this study. Participants performed three validated tasks sequentially under the same experimental setup (one performance). Each participant had ten performances assessed. Hand movements were recorded with optical tracking system. The DSJ, time taken, total path length, multiple measures of acceleration, and number of movements were recorded. Results. There were significant differences between novices and experts when assessed using time, number of movements with average and minimal acceleration threshold, and DSJ. No significant differences were observed in maximum acceleration, total path length, and number of movements with 10m/s2 acceleration threshold. Conclusion. DSJ is an objective parameter that can differentiate novice and expert surgeons’ simulated arthroscopic performances. We propose DSJ as an adjunct to more conventional parameters for arthroscopic surgery skills assessment.

Two Models of Additional Adjacencies between the Root and Descendants in a Complete Binary Tree Minimizing Total Path Length

2009 ◽  
Author(s):  
Kiyoshi Sawada ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
Hideki Katagiri ◽  
Osca Castillo ◽  
...  
Keyword(s):  
Binary Tree ◽  
Path Length ◽  
Complete Binary Tree ◽  
Total Path Length

scholarly journals Approximation algorithms for the shortest total path length spanning tree problem

2000 ◽  
Vol 105 (1-3) ◽  
pp. 273-289 ◽  
Author(s):  
Bang Ye Wu ◽  
Kun–Mao Chao ◽  
Chuan Yi Tang
Keyword(s):  
Approximation Algorithms ◽  
Spanning Tree ◽  
Path Length ◽  
Total Path Length

scholarly journals A Bayesian Optimisation Procedure for Estimating Optimal Trajectories in Electromagnetic Compliance Testing

2020 ◽  
Vol 3 (1) ◽  
pp. 8
Author(s):  
Rémi Delanghe ◽  
Tom Van Steenkiste ◽  
Ivo Couckuyt ◽  
Dirk Deschrijver ◽  
Tom Dhaene
Keyword(s):  
Path Length ◽  
Electromagnetic Compatibility ◽  
Near Field ◽  
Optimization Technique ◽  
Sampling Strategy ◽  
Bayesian Optimization ◽  
Limiting Factor ◽  
Total Path Length ◽  
Physical Measurements ◽  
Compliance Testing

The need for accurate physical measurements is omnipresent in both scientific and engineering applications. Such measurements can be used to explore and characterize the behavior of a system over the parameters of interest. These procedures are often very costly and time-consuming, requiring many measurements or samples. Therefore, a suitable data collection strategy can be used to reduce the cost of acquiring the required samples. One important consideration which often surfaces in physical experiments, like near-field measurements for electromagnetic compliance testing, is the total path length between consecutively visited samples by the measurement probe, as the time needed to travel along this path is often a limiting factor. A line-based sampling strategy optimizes the sample locations in order to reduce the overall path length while achieving the intended goal. Previous research on line-based sampling techniques solely focused on exploring the measurement space. None of these techniques considered the actual measurements themselves despite these values hold the potential to identify interesting regions in the parameter space, such as an optimum, quickly during the sampling process. In this paper, we extend Bayesian optimization, a point-based optimization technique into a line-based setting. The proposed algorithm is assessed using an artificial example and an electromagnetic compatibility use-case. The results show that our line-based technique is able to find the optimum using a significantly shorter total path length compared to the point-based approach.

scholarly journals Navigation-assisted anchor insertion in shoulder arthroscopy: a validity study

2020 ◽  
Author(s):  
Kyunghwa Jung ◽  
Hyojune Kim ◽  
Erica Kholinne ◽  
Dongjun Park ◽  
Hyunseok Choi ◽  
...  
Keyword(s):  
Rotator Cuff ◽  
Path Length ◽  
Conventional System ◽  
Surgical Performance ◽  
Insertion Angle ◽  
Phantom Model ◽  
Total Path Length ◽  
Significant Difference ◽  
Duration Of Surgery ◽  
Repeatability And Reproducibility

Abstract Purpose This study aimed to compare conventional and navigation-assisted arthroscopic rotator cuff repair in terms of anchor screw insertion.Methods The surgical performance of five operators were compared while using conventional system and the proposed navigation-assisted system in a phantom surgical model and cadaveric shoulders. The participating operators were divided into two groups: expert (n = 3) and novice (n = 2) groups. In phantom model, the experimental tasks included anchor insertion into the rotator cuff footprint and sutures retrieval. Motion analysis camera system was used to track surgeons’ hand movements. Surgical performance metric included total path length, count of movements, and duration of surgery. In cadaveric experiments, repeatability and reproducibility of anchor insertion angle were compared among three experts and the feasibility of the navigation-assisted anchor insertion was validated.Results There was no significant difference in the total path length, the count of movements and time taken, between the conventional system and the proposed system in phantom model. In cadaveric shoulders, however, the clustering of the anchor insertion angle indicated that the proposed system enabled both novice and expert operators to reproducibly insert anchor with an angle close to the predetermined target angle, resulting in an angle error of less than two degrees (P = 0.0002).Conclusion The proposed navigation-assisted system improved the surgical performance of novice to expert level. All experts achieved a high repeatability and reproducibility for anchor insertion. Navigation-assisted system may help to make surgeons be familiar to insertion of suture anchors in right direction easily, even in-experienced, by providing better guidance for anchor orientation.Level of Evidence A retrospective study (level 2)

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