scholarly journals Translation-Equivariant Matchings of Coin Flips on ℤd

2010 ◽  
Vol 42 (1) ◽  
pp. 69-82 ◽  
Author(s):  
Terry Soo
Keyword(s):  
Perfect Matching ◽  
Fair Coin ◽  
Matching Rule ◽  
Deterministic Function ◽  
Tail Behaviour ◽  
Matching Rules

Consider independent fair coin flips at each site of the lattice ℤd. A translation-equivariant matching rule is a perfect matching of heads to tails that commutes with translations of ℤd and is given by a deterministic function of the coin flips. Let ZΦ be the distance from the origin to its partner, under the translation-equivariant matching rule Φ. Holroyd and Peres (2005) asked, what is the optimal tail behaviour of ZΦ for translation-equivariant perfect matching rules? We prove that, for every d ≥ 2, there exists a translation-equivariant perfect matching rule Φ such that EZΦ2/3-ε < ∞ for every ε > 0.

scholarly journals Translation-Equivariant Matchings of Coin Flips on ℤd

2010 ◽  
Vol 42 (01) ◽  
pp. 69-82
Author(s):  
Terry Soo
Keyword(s):  
Perfect Matching ◽  
Fair Coin ◽  
Matching Rule ◽  
Deterministic Function ◽  
Tail Behaviour ◽  
Matching Rules

Consider independent fair coin flips at each site of the lattice ℤd. A translation-equivariant matching rule is a perfect matching of heads to tails that commutes with translations of ℤdand is given by a deterministic function of the coin flips. LetZΦbe the distance from the origin to its partner, under the translation-equivariant matching rule Φ. Holroyd and Peres (2005) asked, what is the optimal tail behaviour ofZΦfor translation-equivariant perfect matching rules? We prove that, for everyd≥ 2, there exists a translation-equivariant perfect matching rule Φ such that EZΦ2/3-ε&lt; ∞ for every ε &gt; 0.

PERFECT MATCHING RULES FOR UNDECORATED TRIANGULAR TILINGS WITH 10-, 12-, AND 8-FOLD SYMMETRY

1993 ◽  
Vol 07 (06n07) ◽  
pp. 1455-1473 ◽  
Author(s):  
RICHARD KLITZING ◽  
MARTIN SCHLOTTMANN ◽  
MICHAEL BAAKE
Keyword(s):  
Perfect Matching ◽  
Decomposition Approach ◽  
Matching Rules

Perfect matching rules are derived for quasiperiodic triangular tilings with 10-, 12-, and 8-fold symmetry. We use the composition/decomposition approach via local inflation/deflation symmetry and emphasize the locality of our procedure: The matching rules given here are formulated using certain decorations of the tilings. These decorations turn out to be redundant, i.e., they are locally derivable from the undecorated tilings. Hence, the latter are determined by perfect matching rules as well.

Negative Selection Algorithm Based on Double Matching Rules

2011 ◽  
Vol 204-210 ◽  
pp. 42-45 ◽  
Author(s):  
Yu Hu ◽  
Bin Li
Keyword(s):  
False Alarm ◽  
False Alarm Rate ◽  
Negative Selection ◽  
Hamming Distance ◽  
Network Intrusion Detection ◽  
Selection Algorithm ◽  
Matching Rule ◽  
Negative Selection Algorithm ◽  
Network Intrusion ◽  
Matching Rules

The theory of artificial immune had been widely used in the research of network intrusion detection. Nowadays, the existing detector generating algorithms based on negative selection usually use a certain matching rule, as a result, too many detectors may generate, and the false alarm rate will become more serious. This paper proposes an improved negative selection algorithm using double matching rule: candidate detectors should be selected by the improved Hamming distance matching first, then the remaining detectors go through the segmented r-chunks(rch) matching rule. Experiments show that compared with traditional algorithms, this method brings a small number and more efficient detectors, reduces the false alarm rate and guarantees the efficiency of detectors.

scholarly journals AN APERIODIC TILE WITH EDGE-TO-EDGE ORIENTATIONAL MATCHING RULES

2021 ◽  
pp. 1-29
Author(s):  
James J. Walton ◽  
Michael F. Whittaker
Keyword(s):  
Central Idea ◽  
Dynamical Spectrum ◽  
Matching Rule ◽  
Simple Rules ◽  
New Type ◽  
Aperiodic Tile ◽  
Model Set ◽  
Matching Rules ◽  
Almost All ◽  
Uniquely Ergodic

Abstract We present a single, connected tile which can tile the plane but only nonperiodically. The tile is hexagonal with edge markings, which impose simple rules as to how adjacent tiles are allowed to meet across edges. The first of these rules is a standard matching rule, that certain decorations match across edges. The second condition is a new type of matching rule, which allows tiles to meet only when certain decorations in a particular orientation are given the opposite charge. This forces the tiles to form a hierarchy of triangles, following a central idea of the Socolar–Taylor tilings. However, the new edge-to-edge orientational matching rule forces this structure in a very different way, which allows for a surprisingly simple proof of aperiodicity. We show that the hull of all tilings satisfying our rules is uniquely ergodic and that almost all tilings in the hull belong to a minimal core of tilings generated by substitution. Identifying tilings which are charge-flips of each other, these tilings are shown to have pure point dynamical spectrum and a regular model set structure.

Technological Research on Information Extraction of Part Process Model Based on Machining Feature

2014 ◽  
Vol 696 ◽  
pp. 287-292 ◽  
Author(s):  
Li Gang Qu ◽  
Hai Jun Zhou ◽  
Zhi Liang Dong
Keyword(s):  
Information Extraction ◽  
Process Model ◽  
Feature Recognition ◽  
Feature Matching ◽  
Parameter Extraction ◽  
Extraction Process ◽  
Application Development ◽  
Matching Rule ◽  
Machining Feature ◽  
Matching Rules

The information extraction mode based on machining feature was presented for studying information extraction of part process model in the 3D CAPP system. The classification and its data structure of machining feature were investigated for defining the matching rule about the features. The feature authentication were availably fulfilled by converting the correlations of geometric topological into surface-edge adjacency graph for the part model, and the corresponding parameters extraction of feature were derived from traversing the feature tree of application development CATIA. The whole feature recognition process and parameter extraction process can become more directly and effectively by adopting the method of comparing machining feature with the predefined feature matching rules of the feature database.

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