scholarly journals Spectrum of partial automorphisms of regular rooted tree

2021 ◽  
Author(s):  
Eugenia Kochubinska
Keyword(s):  
Rooted Tree

scholarly journals HTPC: heterogeneous traffic-aware partition coding for random packet spraying in data center networks

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Jiawei Huang ◽  
Shiqi Wang ◽  
Shuping Li ◽  
Shaojun Zou ◽  
Jinbin Hu ◽  
...  
Keyword(s):  
Data Center ◽  
Large Scale ◽  
Network Performance ◽  
Rooted Tree ◽  
Heterogeneous Traffic ◽  
Data Center Networks ◽  
Packet Reordering ◽  
Traffic Characteristics ◽  
Network Utilization ◽  
The Impact

AbstractModern data center networks typically adopt multi-rooted tree topologies such leaf-spine and fat-tree to provide high bisection bandwidth. Load balancing is critical to achieve low latency and high throughput. Although the per-packet schemes such as Random Packet Spraying (RPS) can achieve high network utilization and near-optimal tail latency in symmetric topologies, they are prone to cause significant packet reordering and degrade the network performance. Moreover, some coding-based schemes are proposed to alleviate the problem of packet reordering and loss. Unfortunately, these schemes ignore the traffic characteristics of data center network and cannot achieve good network performance. In this paper, we propose a Heterogeneous Traffic-aware Partition Coding named HTPC to eliminate the impact of packet reordering and improve the performance of short and long flows. HTPC smoothly adjusts the number of redundant packets based on the multi-path congestion information and the traffic characteristics so that the tailing probability of short flows and the timeout probability of long flows can be reduced. Through a series of large-scale NS2 simulations, we demonstrate that HTPC reduces average flow completion time by up to 60% compared with the state-of-the-art mechanisms.

scholarly journals Hierarchical Analysis of Nucleotide Diversity in Geographically Structured Populations

Genetics ◽  
1996 ◽  
Vol 142 (2) ◽  
pp. 629-639 ◽  
Author(s):  
Kent E Holsinger ◽  
Roberta J Mason-Gamer
Keyword(s):  
Nucleotide Diversity ◽  
Restriction Site ◽  
Rooted Tree ◽  
Structured Populations ◽  
Hierarchical Analysis ◽  
Restriction Site Variation ◽  
Hierarchical Levels ◽  
Site Variation ◽  
The Mean ◽  
Mean Time

Abstract Existing methods for analyzing nucleotide diversity require investigators to identify relevant hierarchical levels before beginning the analysis. We describe a method that partitions diversity into hierarchical components while allowing any structure present in the data to emerge naturally. We present an unbiased version of Nei's nucleotide diversity statistics and show that our modification has the same properties as Wright's  F  ST. We compare its statistical properties with several other F  ST estimators, and we describe how to use these statistics to produce a rooted tree of relationships among the sampled populations in which the mean time to coalescence of haplotypes drawn from populations belonging to the same node is smaller than the mean time to coalescence of haplotypes drawn from populations belonging to different nodes. We illustrate the method by applying it to data from a recent survey of restriction site variation in the chloroplast genome of Coreopsis grandiflora.

Optimal Flow Control and Single Split Architecture Exploration for Fluid-Based Thermal Management

2018 ◽  
Author(s):  
Satya R. T. Peddada ◽  
Daniel R. Herber ◽  
Herschel C. Pangborn ◽  
Andrew G. Alleyne ◽  
James T. Allison
Keyword(s):  
Flow Control ◽  
Thermal Management ◽  
High Performance ◽  
Dynamic Models ◽  
Cooling System ◽  
Rooted Tree ◽  
Modeling Framework ◽  
System Architectures ◽  
Tree Graphs ◽  
Heat Loads

High-performance cooling is often necessary for thermal management of high power density systems. Both human intuition and vast experience may not be adequate to identify optimal thermal management designs as systems increase in size and complexity. This paper presents a design framework supporting comprehensive exploration of a class of single phase fluid-based cooling architectures. The candidate cooling system architectures are represented using labeled rooted tree graphs. Dynamic models are automatically generated from these trees using a graph-based thermal modeling framework. Optimal performance is determined by solving an appropriate fluid flow control problem, handling temperature constraints in the presence of exogenous heat loads. Rigorous case studies are performed in simulation, with components having variable sets of heat loads and temperature constraints. Results include optimization of thermal endurance for an enumerated set of 4,051 architectures. In addition, cooling system architectures capable of steady-state operation under a given loading are identified.

scholarly journals Spectral property of certain class of graphs associated with generalized Bethe trees and transitive graphs

2008 ◽  
Vol 2 (2) ◽  
pp. 260-275 ◽  
Author(s):  
Yi-Zheng Fan ◽  
Li Shuang-Dong ◽  
Dong Liang
Keyword(s):  
Spectral Property ◽  
Adjacency Matrix ◽  
Rooted Tree ◽  
Laplacian Matrix ◽  
Transitive Graph ◽  
Tridiagonal Matrices ◽  
Equal Degree ◽  
Transitive Graphs ◽  
Structure Properties

A generalized Bethe tree is a rooted tree for which the vertices in each level having equal degree. Let Bk be a generalized Bethe tree of k level, and let T r be a connected transitive graph on r vertices. Then we obtain a graph Bk?T r from r copies of Bk and T r by appending r roots to the vertices of T r respectively. In this paper, we give a simple way to characterize the eigenvalues of the adjacency matrix A(Bk ? T r) and the Laplacian matrix L(Bk?T r) of Bk?T r by means of symmetric tridiagonal matrices of order k. We also present some structure properties of the Perron vectors of A(Bk?T r) and the Fiedler vectors of L(Bk ? T r). In addition, we obtain some results on transitive graphs.

Axiomatic analysis of liability problems with rooted-tree networks in tort law

2022 ◽  
Author(s):  
Takayuki Oishi ◽  
Gerard van der Laan ◽  
René van den Brink
Keyword(s):  
Rooted Tree ◽  
Tort Law ◽  
Tree Networks ◽  
Axiomatic Analysis

Deleuze, Gilles (1925–95)

2018 ◽  
Author(s):  
Dorothea E. Olkowski
Keyword(s):  
Object Relations ◽  
Lived Experience ◽  
Common Sense ◽  
Rooted Tree ◽  
History Of Philosophy ◽  
Start Up ◽  
Body Without Organs ◽  
History Of ◽  
Fixed Order ◽  
Philosophical Project

Although grounded in the history of philosophy, Gilles Deleuze’s work does not begin with first principles but grasps the philosophical terrain in the middle. This method overthrows subject–object relations in order to initiate a philosophy of difference and chance that is not derived from static conceptions of being. It is a philosophy of the event, a state where sense arises independently of lived experience or scientific fact. The event is a sign without a signifier-signified relationship; a form of content that consists of a complex of forces that are not separable from their form of expression; an assemblage or body without organs, not the organized ego; time, intensity and duration instead of space; in short, a world in constant motion consisting of becomings and encounters that common sense concepts do not grasp. This radical philosophical project is rendered most clearly in Deleuze (and his collaborator Guattari’s concept of the ‘rhizome’). The rhizome is a multiplicity of connections without the unity that could pinpoint or identify a subject or an object. Any point of the rhizome can and must be connected to any other, though in no fixed order and without homogeneity. It can break or rupture at any point, yet old connections will start up again or new connections will be made; the rhizome’s connections thus have the character of a map, not a structural or generative formation. The rhizome, then, is not a model, but consists of lines of escape from from rooted, tree-like structures that open up the route for encounters and makes philosophy into cartography, that is, the mapping of concepts.

A Note on Homogeneous Dendrites

1968 ◽  
Vol 11 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Z. A. Melzak
Keyword(s):  
Branch Point ◽  
Rooted Tree ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Graph Theoretic ◽  
Order Branch

In graph - theoretic terms a homogeneous p-dendrite, p ≥ 2, is defined as a finite singly-rooted tree in which the root has valency 1 while every other vertex has valency 1 or p. More descriptively, a homogeneous p-dendrite may be imagined to start from its root as the main, or 0th order, branch which proceeds to the first - order branch point where it gives rise top first - order branches. Each of these either terminates at its other end (which is a second-order branch point) or it splits there again into p branches (which are of third order), and so on. The order of the dendrite is the highest order of a branch present in it. For completeness, a 0-th order dendrite is also allowed, this consists of the 0-th order branch alone.

scholarly journals Phylosymmetric Algebras: Mathematical Properties of a New Tool in Phylogenetics

2020 ◽  
Vol 82 (12) ◽  
Author(s):  
Michael Hendriksen ◽  
Julia A. Shore
Keyword(s):  
Rooted Tree ◽  
Matrix Multiplication ◽  
Computation Time ◽  
Rate Of Change ◽  
Recent Common Ancestor ◽  
Transition Matrices ◽  
Rate Matrix ◽  
Most Recent Common Ancestor ◽  
Mathematical Properties ◽  
Matrix Exponentials

AbstractIn phylogenetics, it is of interest for rate matrix sets to satisfy closure under matrix multiplication as this makes finding the set of corresponding transition matrices possible without having to compute matrix exponentials. It is also advantageous to have a small number of free parameters as this, in applications, will result in a reduction in computation time. We explore a method of building a rate matrix set from a rooted tree structure by assigning rates to internal tree nodes and states to the leaves, then defining the rate of change between two states as the rate assigned to the most recent common ancestor of those two states. We investigate the properties of these matrix sets from both a linear algebra and a graph theory perspective and show that any rate matrix set generated this way is closed under matrix multiplication. The consequences of setting two rates assigned to internal tree nodes to be equal are then considered. This methodology could be used to develop parameterised models of amino acid substitution which have a small number of parameters but convey biological meaning.

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