scholarly journals On Counting and Embedding a Subclass of Height-Balanced Trees

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Indhumathi Raman
Keyword(s):  
Binary Tree ◽  
Left And Right ◽  
The Difference ◽  
Balanced Tree ◽  
Balance Factor ◽  
Rooted Binary Tree

A height-balanced tree is a rooted binary tree in which, for every vertexv, the difference in the heights of the subtrees rooted at the left and right child ofv(called the balance factor ofv) is at most one. In this paper, we consider height-balanced trees in which the balance factor of every vertex beyond a level is0. We prove that there are22t-1such trees and embed them into ageneralized join of hypercubes.

scholarly journals Left and right length of paths in binary trees or on a question of Knuth

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Alois Panholzer
Keyword(s):  
Binary Tree ◽  
Limiting Distribution ◽  
Binary Trees ◽  
Tree Model ◽  
Random Size ◽  
International Audience ◽  
Left And Right ◽  
The Common ◽  
The Difference ◽  
The Right

International audience We consider extended binary trees and study the common right and left depth of leaf $j$, where the leaves are labelled from left to right by $0, 1, \ldots, n$, and the common right and left external pathlength of binary trees of size $n$. Under the random tree model, i.e., the Catalan model, we characterize the common limiting distribution of the suitably scaled left depth and the difference between the right and the left depth of leaf $j$ in a random size-$n$ binary tree when $j \sim \rho n$ with $0< \rho < 1$, as well as the common limiting distribution of the suitably scaled left external pathlength and the difference between the right and the left external pathlength of a random size-$n$ binary tree.

scholarly journals perfectphyloR: An R package for reconstructing perfect phylogenies

2019 ◽  
Vol 20 (1) ◽  
Author(s):  
Charith B. Karunarathna ◽  
Jinko Graham
Keyword(s):  
Binary Tree ◽  
Sequence Data ◽  
R Package ◽  
Binary Sequences ◽  
Ancestral Haplotype ◽  
Perfect Phylogeny ◽  
Nested Partitions ◽  
Genetic Sequence ◽  
Insight Into ◽  
Rooted Binary Tree

Abstract Background A perfect phylogeny is a rooted binary tree that recursively partitions sequences. The nested partitions of a perfect phylogeny provide insight into the pattern of ancestry of genetic sequence data. For example, sequences may cluster together in a partition indicating that they arise from a common ancestral haplotype. Results We present an R package to reconstruct the local perfect phylogenies underlying a sample of binary sequences. The package enables users to associate the reconstructed partitions with a user-defined partition. We describe and demonstrate the major functionality of the package. Conclusion The package should be of use to researchers seeking insight into the ancestral structure of their sequence data. The reconstructed partitions have many applications, including the mapping of trait-influencing variants.

Study of the Characteristics of the Pulmonary Vein and Superior Vena Cava of Rabbits

2021 ◽  
Vol 11 (1) ◽  
pp. 112-122
Author(s):  
Pan Wang ◽  
Xin-Chun Yang ◽  
Xiu-Lan Liu ◽  
Rong-Feng Bao ◽  
Huai-Yu Ding ◽  
...  
Keyword(s):  
Action Potential ◽  
Pulmonary Vein ◽  
Refractory Period ◽  
Potassium Current ◽  
Superior Vena ◽  
Vena Cava ◽  
Current Intensity ◽  
Left And Right ◽  
The Difference ◽  
Right Atria

Background: This study aims to (1) investigate the characteristics of the action potential and triggering activity of cardiomyocytes in the pulmonary vein (PV) and superior vena cava (SVC) of rabbits and (2) study the features of cation currents in cardiomyocytes in rabbit PV and SVC-inward rectifier potassium current (IK1), transient outward potassium current (Ito), and non-selective cation currents (INSCC). Methods: The standard glass microelectrode and whole-cell patch-clamp techniques were used to record the action potential and various currents in the above cells. Results: (1) Cardiomyocytes in either PV or SVC had longer action potential durations than in the adjacent atrium, and spontaneous early after depolarization (EAD) could occur in both PV and SVC under normal physiological conditions. (2) The action potential in PV cardiomyocytes had a relative refractory period but did not have an absolute refractory period, and this characteristic enabled a premature beat that triggered a second plateau response, which led to EAD. (3) INSCC was found for the first time in the PV, SVC, and atria. (4) The current intensity of IK1, Ito, and INSCC was significantly lower in the PV and SVC than in the left and right atria, and the difference in the current intensity in INSCC could influence the action potential. Conclusions: PV and SVC can both initiate and maintain AF, but PV is the primary ectopic foci in initiating AF. The present study found that the second plateau response was easily induced in cardiomyocytes in PA shortly after depolarization. This was a specific characteristic of the action potential of PV. In addition, we preliminarily analyzed the differences in the main outward currents and noted a voltage-dependent INSCC in both PV and SVC rabbits’ cardiomyocytes. Furthermore, the current intensities of IK1, Ito, and INSCC were significantly lower in the PV and SVC than in the left and right atria, and the difference in the current intensity of INSCC influenced the action potential. The different permeability of INSCC for cations at different phases may play a role in inducing EAD.

Errors in Estimating the Orientation of Dot Patterns

Perception ◽  
1989 ◽  
Vol 18 (2) ◽  
pp. 237-242 ◽  
Author(s):  
P Lánský ◽  
Naum Yakimoff ◽  
T Radil ◽  
L Mitrani
Keyword(s):  
Pattern Analysis ◽  
Frontoparallel Plane ◽  
The Subject ◽  
Left And Right ◽  
The Mean ◽  
The Difference

The error in estimating the orientation of a dot pattern was measured as the difference between the orientation of the least-squared-distances line (LS-line) of the pattern and the orientation of a line adjusted by the subject to match the perceived orientation of the pattern. Analysis of the mean errors (averaged over ten subjects) obtained for one hundred patterns confirmed that the orientation of the LS-line represents the orientation of elongated dot-patterns. It is shown that estimated orientation was systematically biased towards the nearest 45° oblique meridian. This bias points to the importance of the ±45° directions as natural norms for left- and right-side tilt in the frontoparallel plane.

Magnetic Structure of Multilayers from Soft-X-Ray Magnetic Circular Dichroism

1994 ◽  
Vol 375 ◽  
Author(s):  
C. T. Chen ◽  
Y. U. Idzerda ◽  
C.-C. Kao ◽  
L. H. Tjeng ◽  
H.-J. Lin ◽  
...  
Keyword(s):  
Thin Films ◽  
Circular Dichroism ◽  
Magnetic Circular Dichroism ◽  
Magnetic Thin Films ◽  
X Rays ◽  
X Ray ◽  
Specific Manner ◽  
Left And Right ◽  
The Difference ◽  
Circular Dichroïsm

AbstractSoft-x-ray magnetic circular dichroism (MCD) is the difference between the absorptivity or reflectivity of left and right circularly polarized soft-x-rays at the magnetically interesting L2,3- edges of 3d transition metals or the M4,5-edges of the 4f rare earth elements. Thanks to its large absorption cross-section and strong MCD effect, this technique has become a powerful new means for probing, in an element- and site-specific manner, the magnetic properties of ultra-thin films and multilayers. Soft-x-ray MCD experiments, recently conducted at the Dragon beamline, are utilized to demonstrate the recent progress in this technique and its applications in the research of magnetic thin films.

Evaluation and Analysis of Different Types of Prosthetic Knee Joint Used by above Knee Amputee

2020 ◽  
Vol 398 ◽  
pp. 34-40 ◽  
Author(s):  
Fahad Mohanad Kadhim ◽  
Jumaa Salman Chiad ◽  
Maryam Abdul Salam Enad
Keyword(s):  
Gait Cycle ◽  
Reaction Force ◽  
Maximum Velocity ◽  
Knee Joints ◽  
Von Mises Stress ◽  
Prosthetic Knee ◽  
Prosthetic Limb ◽  
Left And Right ◽  
The Difference ◽  
Von Mises

Four prosthetic knee joints (polycentric knee weight activating-4bar and friction, extension assist controlled),(single axis knee weight activating and friction, internal extension assist controlled), (single axis knee weight activating-4bar and hydraulically, controlled) and (polycentric knee geometric locking-6bar, hydraulically controlled) for a trans-femoral patient were tested. The tests were conducted to find the maximum velocity as well as discussing the most comfortable prosthetic forthe patient and walking stability for these prosthetic knees by examining the gait cycle and measuring the ground reaction force (GRF), using force a plate device. Also, the interface pressure was measured between socket and stump muscles by using F-socket device to get the stress distribution during walking with a prosthetic knee. Results manifested that the polycentric knee geometric locking - 6bar, hydraulically controlled is the best because of the good homogenous distribution of GRF between the healthy and prosthetic limb, during which the difference between both the healthy and prosthetic limb is with the least value (4%).And, K4 gives the minimum value of differences in contact pressure between the left and right limb with a value of (24%), it alsoimparts the maximum symmetry between the left and right limb according to the gait cycle parameters.The best results of the interface pressures and kinovea velocity are achieved whenK4 is used with (132.4KPa, 0.71m/s), respectively. Finally, the polycentric knee geometric locking - 6bar, hydraulically controlled is the best according to the ANSYS results during which it yields the minimum values of Von-Mises stress with 14.24MPa and a maximum factor of safety of 3.11.

Propagator Method for Numerical Solution of Convective Fisher Equation

2011 ◽  
Vol 222 ◽  
pp. 387-390
Author(s):  
Daiga Zaime ◽  
Janis S. Rimshans ◽  
Sharif E. Guseynov
Keyword(s):  
Difference Scheme ◽  
Iteration Process ◽  
Fisher Equation ◽  
Implicit Difference Scheme ◽  
Nonlinear Convection ◽  
First Order ◽  
Truncation Errors ◽  
Propagator Method ◽  
Left And Right ◽  
The Difference

Propagator numerical method was developed as an effective tool for modeling of linear advective dispersive reactive (ADR) processes [1]. In this work implicit propagator difference scheme for Fisher equation with nonlinear convection (convective Fisher equation) is elaborated. Our difference scheme has truncation errors of the second order in space and of the first order in time. Iteration process for implicit difference scheme is proposed by introducing forcing terms in the left and right sides of the difference equation. Convergence and stability criterions for the elaborated implicit propagator difference scheme are obtained.

Sign in / Sign up

Export Citation Format

Share Document