scholarly journals Existence of a Non-Averaging Regime for the Self-Avoiding Walk on a High-Dimensional Infinite Percolation Cluster

2014 ◽  
Vol 154 (6) ◽  
pp. 1461-1482 ◽  
Author(s):  
Hubert Lacoin
Keyword(s):  
Percolation Cluster ◽  
The Self ◽  
High Dimensional ◽  
Self Avoiding Walk

PSS Business Case Map: Supporting Idea Generation in PSS Design

2012 ◽  
Author(s):  
Fumiya Akasaka ◽  
Kazuki Fujita ◽  
Yoshiki Shimomura
Keyword(s):  
Idea Generation ◽  
Business Case ◽  
Literature Survey ◽  
The Self ◽  
High Dimensional ◽  
Self Organizing Map ◽  
Two Dimensional ◽  
Service Type ◽  
Business Cases ◽  
Low Dimensional

This paper proposes the PSS Business Case Map as a tool to support designers’ idea generation in PSS design. The map visualizes the similarities among PSS business cases in a two-dimensional diagram. To make the map, PSS business cases are first collected by conducting, for example, a literature survey. The collected business cases are then classified from multiple aspects that characterize each case such as its product type, service type, target customer, and so on. Based on the results of this classification, the similarities among the cases are calculated and visualized by using the Self-Organizing Map (SOM) technique. A SOM is a type of artificial neural network that is trained using unsupervised learning to produce a low-dimensional (typically two-dimensional) view from high-dimensional data. The visualization result is offered to designers in a form of a two-dimensional map, which is called the PSS Business Case Map. By using the map, designers can figure out the position of their current business and can acquire ideas for the servitization of their business.

scholarly journals The XY-model and the self-avoiding walk approximation

1976 ◽  
Vol 84 (1) ◽  
pp. 197-204
Author(s):  
R. Dekeyser ◽  
M. Reynaert
Keyword(s):  
The Self ◽  
Xy Model ◽  
Self Avoiding Walk

scholarly journals Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 153
Author(s):  
Damien Foster ◽  
Ralph Kenna ◽  
Claire Pinettes
Keyword(s):  
Phase Transitions ◽  
Partition Function ◽  
Critical Behavior ◽  
Finite Size ◽  
The Self ◽  
Partition Function Zeros ◽  
Adsorption Transition ◽  
Function Zeros ◽  
Complex Zeros ◽  
Self Avoiding Walk

The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, ϕ and ϕ S , are estimated from the scaling behavior of the leading partition function zeros.

Renormalization of the self-avoiding walk on a lattice

1976 ◽  
Vol 56 (3) ◽  
pp. 153-154 ◽  
Author(s):  
H.J. Hilhorst
Keyword(s):  
The Self ◽  
Self Avoiding Walk

SPHERICAL SELF-ORGANIZING FEATURE MAP: AN INTRODUCTORY REVIEW

2006 ◽  
Vol 16 (11) ◽  
pp. 3195-3206 ◽  
Author(s):  
ARCHANA P. SANGOLE ◽  
ALEXANDROS LEONTITSIS
Keyword(s):  
Fractal Dimension ◽  
Chaotic Maps ◽  
High Dimensional Data ◽  
The Self ◽  
High Dimensional ◽  
Feature Map ◽  
Engineering Sciences ◽  
Physical Measures ◽  
Introductory Review ◽  
Self Organizing

The self-organizing feature map (SOFM) has received great attention from researchers in a variety of areas such as engineering sciences, medicine, biology and economics. The topology of these maps is usually based on 1, 2, or 3 dimensions, forming a lattice. This article discusses various aspects of the spherical SOFMs along with examples illustrating its implementation on high-dimensional data. The main advantage of the spherical SOFM is the ability to visualize complex high-dimensional data by encapsulating physical measures of the data within the 3D attributes of its spherical lattice. The article presents the potential of the spherical SOFM to visualize nonlinear data using examples of two chaotic maps, Hénon and Ikeda, with a fractal dimension of 1.2 and 1.7 respectively embedded in 2–5 dimensions.

scholarly journals Subspace Clustering with Sparsity and Grouping Effect

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Binbin Zhang ◽  
Weiwei Wang ◽  
Xiangchu Feng
Keyword(s):  
State Of The Art ◽  
Subspace Clustering ◽  
The Self ◽  
Dimensional Structure ◽  
High Dimensional ◽  
Affinity Matrix ◽  
Grouping Effect ◽  
Art Methods ◽  
Data Points ◽  
Low Dimensional

Subspace clustering aims to group a set of data from a union of subspaces into the subspace from which it was drawn. It has become a popular method for recovering the low-dimensional structure underlying high-dimensional dataset. The state-of-the-art methods construct an affinity matrix based on the self-representation of the dataset and then use a spectral clustering method to obtain the final clustering result. These methods show that sparsity and grouping effect of the affinity matrix are important in recovering the low-dimensional structure. In this work, we propose a weighted sparse penalty and a weighted grouping effect penalty in modeling the self-representation of data points. The experimental results on Extended Yale B, USPS, and Berkeley 500 image segmentation datasets show that the proposed model is more effective than state-of-the-art methods in revealing the subspace structure underlying high-dimensional dataset.

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