scholarly journals Concurrent Binary Trees (with application to longest edge bisection)

2020 ◽  
Vol 3 (2) ◽  
pp. 1-20
Author(s):  
Jonathan Dupuy
Keyword(s):  
Processing Speed ◽  
Binary Tree ◽  
Large Scale ◽  
Binary Search ◽  
Parallel Processors ◽  
Leaf Node ◽  
Binary Trees ◽  
Bitwise Operations

We introduce the concurrent binary tree (CBT), a novel concurrent representation to build and update arbitrary binary trees in parallel. Fundamentally, our representation consists of a binary heap, i.e., a 1D array, that explicitly stores the sum-reduction tree of a bitfield. In this bitfield, each one-valued bit represents a leaf node of the binary tree encoded by the CBT, which we locate algorithmically using a binary-search over the sum-reduction. We show that this construction allows to dispatch down to one thread per leaf node and that, in turn, these threads can safely split and/or remove nodes concurrently via simple bitwise operations over the bitfield. The practical benefit of CBTs lies in their ability to accelerate binary-tree-based algorithms with parallel processors. To support this claim, we leverage our representation to accelerate a longest-edge-bisection-based algorithm that computes and renders adaptive geometry for large-scale terrains entirely on the GPU. For this specific algorithm, the CBT accelerates processing speed linearly with the number of processors.

Age of Acquisition Norms for a Large Set of Object Names and Their Relation to Adult Estimates and Other Variables

1997 ◽  
Vol 50 (3) ◽  
pp. 528-559 ◽  
Author(s):  
Catriona M. Morrison ◽  
Tameron D. Chappell ◽  
Andrew W. Ellis
Keyword(s):  
Word Learning ◽  
Processing Speed ◽  
Large Scale ◽  
Lexical Processing ◽  
Objective Measure ◽  
Age Of Acquisition ◽  
Large Set ◽  
Name Agreement ◽  
Object Familiarity ◽  
The Relationship

Studies of lexical processing have relied heavily on adult ratings of word learning age or age of acquisition, which have been shown to be strongly predictive of processing speed. This study reports a set of objective norms derived in a large-scale study of British children's naming of 297 pictured objects (including 232 from the Snodgrass & Vanderwart, 1980, set). In addition, data were obtained on measures of rated age of acquisition, rated frequency, imageability, object familiarity, picture-name agreement, and name agreement. We discuss the relationship between the objective measure and adult ratings of word learning age. Objective measures should be used when available, but where not, our data suggest that adult ratings provide a reliable and valid measure of real word learning age.

scholarly journals Reducibility and Solvability of Some Classes of Kryuchkov Binary Tree Pairs

10.37236/2028 ◽  
2012 ◽  
Vol 18 (2) ◽  
Author(s):  
Maria Madonia ◽  
Giuseppe Scollo
Keyword(s):  
Induction Hypothesis ◽  
Binary Tree ◽  
Binary Trees ◽  
Equal Size ◽  
Future Research ◽  
Theoretic Approach ◽  
Research Directions ◽  
Open Questions ◽  
Future Research Directions

This paper addresses the problem of characterizing classes of pairs of binary trees of equal size for which a signed reassociation sequence, in the Eliahou-Kryuchkov sense, can be shown to exist, either with a size induction hypothesis (reducible pairs), or without it (solvable pairs). A few concepts proposed by Cooper, Rowland and Zeilberger, in the context of a language-theoretic approach to the problem, are here reformulated in terms of signed reassociation sequences, and some of their results are recasted and proven in this framework. A few strategies, tactics and combinations thereof for signed reassociation are introduced, which prove useful to extend the results obtained by the aforementioned authors to new classes of binary tree pairs. In particular, with reference to path trees, i.e. binary trees that have a leaf at every level, we show the reducibility of pairs where (at least) one of the two path trees has a triplication at the first turn below the top level, and we characterize a class of weakly mutually crooked path tree pairs that are neither reducible nor solvable by any previously known result, but prove solvable by appropriate reassociation strategies. This class also includes a subclass of mutually crooked path tree pairs. A summary evaluation of the achieved results, followed by an outline of open questions and future research directions conclude the paper.

Binary Trees and the n-Cutset Property

1991 ◽  
Vol 34 (1) ◽  
pp. 23-30 ◽  
Author(s):  
Peter Arpin ◽  
John Ginsburg
Keyword(s):  
Positive Integer ◽  
Partially Ordered Set ◽  
Binary Tree ◽  
Ordered Set ◽  
Maximal Chain ◽  
Binary Trees ◽  
Complete Binary Tree ◽  
Maximal Elements ◽  
Extremal Case ◽  
Result Theorem

AbstractA partially ordered set P is said to have the n-cutset property if for every element x of P, there is a subset S of P all of whose elements are noncomparable to x, with |S| ≤ n, and such that every maximal chain in P meets {x} ∪ S. It is known that if P has the n-cutset property then P has at most 2n maximal elements. Here we are concerned with the extremal case. We let Max P denote the set of maximal elements of P. We establish the following result. THEOREM: Let n be a positive integer. Suppose P has the n-cutset property and that |Max P| = 2n. Then P contains a complete binary tree T of height n with Max T = Max P and such that C ∩ T is a maximal chain in T for every maximal chain C of P. Two examples are given to show that this result does not extend to the case when n is infinite. However the following is shown. THEOREM: Suppose that P has the ω-cutset property and that |Max P| = 2ω. If P — Max P is countable then P contains a complete binary tree of height ω

DC simulator of large-scale nonlinear systems for parallel processors

2012 ◽  
Author(s):  
Diego Ernesto Cortés Udave ◽  
Jan Ogrodzki ◽  
Miguel Angel Gutiérrez de Anda
Keyword(s):  
Nonlinear Systems ◽  
Large Scale ◽  
Parallel Processors

A New SVM Multi-Class Classification Algorithm Based on Sample Scale and Distribution Area

2013 ◽  
Vol 712-715 ◽  
pp. 2529-2533
Author(s):  
Yu Ping Qin ◽  
Peng Da Qin ◽  
Shu Xian Lun ◽  
Yi Wang
Keyword(s):  
Binary Tree ◽  
Classification Performance ◽  
Classification Algorithm ◽  
Experimental Results ◽  
Leaf Node ◽  
Distribution Area ◽  
Root Node ◽  
Multi Class Classification

A new SVM multi-class classification algorithm is proposed. Firstly, the optimal binary tree is constructed by the scale and the distribution area of every class sample, and then the sub-classifiers are trained for every non-leaf node in the binary tree. For the sample to be classified, the classification is done from the root node until someone leaf node, and the corresponding class of the leaf node is the class of the sample. The experimental results show that the algorithm improves the classification precision and classification speed, especially in the situation that the sample scale is less but its distribution area is bigger, the algorithm can improve greatly the classification performance.

scholarly journals Connections on Valuated Binary Tree and Their Applications in Factoring Odd Integers

2021 ◽  
pp. 134-153
Author(s):  
Xingbo Wang ◽  
Jinfeng Luo ◽  
Ying Tian ◽  
Li Ma
Keyword(s):  
Binary Tree ◽  
Numerical Experiments ◽  
Mathematical Reasoning ◽  
Binary Trees ◽  
Integer Factorization ◽  
Parallel Connection ◽  
Central Lines ◽  
Factorization Problem ◽  
Integer Factorization Problem

This paper makes an investigation on geometric relationships among nodes of the valuated binary trees, including parallelism, connection and penetration. By defining central lines and distance from a node to a line, some intrinsic connections are discovered to connect nodes between different subtrees. It is proved that a node out of a subtree can penetrate into the subtree along a parallel connection. If the connection starts downward from a node that is a multiple of the subtree’s root, then all the nodes on the connection are multiples of the root. Accordingly composite odd integers on such connections can be easily factorized. The paper proves the new results with detail mathematical reasoning and demonstrates several numerical experiments made with Maple software to factorize rapidly a kind of big odd integers that are of the length from 59 to 99 decimal digits. It is once again shown that the valuated binary tree might be a key to unlock the lock of the integer factorization problem.

scholarly journals State-dependent control of cortical processing speed via gain modulation

2020 ◽  
Author(s):  
David Wyrick ◽  
Luca Mazzucato
Keyword(s):  
Information Processing ◽  
Processing Speed ◽  
Visual Processing ◽  
Large Scale ◽  
Internal State ◽  
Gain Modulation ◽  
Cell Type ◽  
Information Processing Speed ◽  
Afferent Projections ◽  
Cell Type Specific

AbstractTo thrive in dynamic environments, animals can generate flexible behavior and rapidly adapt responses to a changing context and internal state. Examples of behavioral flexibility include faster stimulus responses when attentive and slower responses when distracted. Contextual modulations may occur early in the cortical hierarchy and may be implemented via afferent projections from top-down pathways or neuromodulation onto sensory cortex. However, the computational mechanisms mediating the effects of such projections are not known. Here, we investigate the effects of afferent projections on the information processing speed of cortical circuits. Using a biologically plausible model based on recurrent networks of excitatory and inhibitory neurons arranged in cluster, we classify the effects of cell-type specific perturbations on the circuit’s stimulus-processing capability. We found that perturbations differentially controlled processing speed, leading to counter-intuitive effects such as improved performance with increased input variance. Our theory explains the effects of all perturbations in terms of gain modulation, which controls the timescale of the circuit dynamics. We tested our model using large-scale electrophysiological recordings from the visual hierarchy in freely running mice, where a decrease in single-cell gain during locomotion explained the observed acceleration of visual processing speed. Our results establish a novel theory of cell-type specific perturbations linking connectivity, dynamics, and information processing via gain modulations.

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