Nearest neighbor lattice statistics on semi‐infinite two‐dimensional rectangular lattices of various widths

1989 ◽  
Vol 30 (6) ◽  
pp. 1380-1384 ◽  
Author(s):  
J. M. Maeder ◽  
R. B. McQuistan
Keyword(s):  
Nearest Neighbor ◽  
Lattice Statistics ◽  
Two Dimensional ◽  
Rectangular Lattices

scholarly journals Semantics of Voids within Data: Ignorance-Aware Machine Learning

2021 ◽  
Vol 10 (4) ◽  
pp. 246
Author(s):  
Vagan Terziyan ◽  
Anton Nikulin
Keyword(s):  
Spatial Data ◽  
Information Science ◽  
Nearest Neighbor ◽  
Geographical Information ◽  
Two Dimensional ◽  
Prototype Selection ◽  
Data Space ◽  
Important Concern ◽  
Traditional Classification ◽  
Nearest Neighbor Classifiers

Operating with ignorance is an important concern of geographical information science when the objective is to discover knowledge from the imperfect spatial data. Data mining (driven by knowledge discovery tools) is about processing available (observed, known, and understood) samples of data aiming to build a model (e.g., a classifier) to handle data samples that are not yet observed, known, or understood. These tools traditionally take semantically labeled samples of the available data (known facts) as an input for learning. We want to challenge the indispensability of this approach, and we suggest considering the things the other way around. What if the task would be as follows: how to build a model based on the semantics of our ignorance, i.e., by processing the shape of “voids” within the available data space? Can we improve traditional classification by also modeling the ignorance? In this paper, we provide some algorithms for the discovery and visualization of the ignorance zones in two-dimensional data spaces and design two ignorance-aware smart prototype selection techniques (incremental and adversarial) to improve the performance of the nearest neighbor classifiers. We present experiments with artificial and real datasets to test the concept of the usefulness of ignorance semantics discovery.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

THE EXACT SOLUTION OF SOME LATTICE STATISTICS MODELS WITH FOUR STATES PER SITE

1964 ◽  
Vol 42 (8) ◽  
pp. 1564-1572 ◽  
Author(s):  
D. D. Betts
Keyword(s):  
Partition Function ◽  
Nearest Neighbor ◽  
Quaternary Alloy ◽  
Interesting Property ◽  
Two Dimensions ◽  
Lattice Statistics ◽  
Critical Temperatures ◽  
Different Types ◽  
Interacting Systems ◽  
Statistical Mechanical

Statistical mechanical ensembles of interacting systems localized at the sites of a regular lattice and each having four possible states are considered. A set of lattice functions is introduced which permits a considerable simplification of the partition function for general nearest-neighbor interactions. The particular case of the Potts four-state ferromagnet model is solved exactly in two dimensions. The order–disorder problem for a certain quaternary alloy model is also solved exactly on a square net. The quaternary alloy model has the interesting property that it has two critical temperatures and exhibits two different types of long-range order. The partition function for the spin-3/2 Ising model on a square net is expressed in terms of graphs without odd vertices, but has not been solved exactly.

scholarly journals Patch-Based Principal Component Analysis for Face Recognition

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Tai-Xiang Jiang ◽  
Ting-Zhu Huang ◽  
Xi-Le Zhao ◽  
Tian-Hui Ma
Keyword(s):  
Principal Component Analysis ◽  
Face Recognition ◽  
Nearest Neighbor ◽  
Spatial Information ◽  
Principal Component ◽  
Component Analysis ◽  
Two Dimensional ◽  
Face Images ◽  
Pca Method ◽  
Local Spatial Information

We have proposed a patch-based principal component analysis (PCA) method to deal with face recognition. Many PCA-based methods for face recognition utilize the correlation between pixels, columns, or rows. But the local spatial information is not utilized or not fully utilized in these methods. We believe that patches are more meaningful basic units for face recognition than pixels, columns, or rows, since faces are discerned by patches containing eyes and noses. To calculate the correlation between patches, face images are divided into patches and then these patches are converted to column vectors which would be combined into a new “image matrix.” By replacing the images with the new “image matrix” in the two-dimensional PCA framework, we directly calculate the correlation of the divided patches by computing the total scatter. By optimizing the total scatter of the projected samples, we obtain the projection matrix for feature extraction. Finally, we use the nearest neighbor classifier. Extensive experiments on the ORL and FERET face database are reported to illustrate the performance of the patch-based PCA. Our method promotes the accuracy compared to one-dimensional PCA, two-dimensional PCA, and two-directional two-dimensional PCA.

scholarly journals Selection of Pairings Reaching Evenly Across the Data (SPREAD): A simple algorithm to design maximally informative fully crossed mating experiments

2014 ◽  
Author(s):  
Kolea Zimmerman ◽  
Daniel Levitis ◽  
Ethan Addicott ◽  
Anne Pringle
Keyword(s):  
Nearest Neighbor ◽  
Simple Algorithm ◽  
Two Dimensional ◽  
Neighbor Distance ◽  
Crossing Experiments ◽  
The Mean ◽  
Parameter Values ◽  
Selection Of ◽  
Novel Algorithm ◽  
Trait Space

We present a novel algorithm for the design of crossing experiments. The algorithm identifies a set of individuals (a ?crossing-set?) from a larger pool of potential crossing-sets by maximizing the diversity of traits of interest, for example, maximizing the range of genetic and geographic distances between individuals included in the crossing-set. To calculate diversity, we use the mean nearest neighbor distance of crosses plotted in trait space. We implement our algorithm on a real dataset ofNeurospora crassastrains, using the genetic and geographic distances between potential crosses as a two-dimensional trait space. In simulated mating experiments, crossing-sets selected by our algorithm provide better estimates of underlying parameter values than randomly chosen crossing-sets.

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