Pattern Recognition in Kittens: Performance on Lie Patterns

Perception ◽  
1983 ◽  
Vol 12 (4) ◽  
pp. 393-410 ◽  
Author(s):  
Peter C Dodwell ◽  
Frances E Wilkinson ◽  
Michael W von Grünau
Keyword(s):  
Experimental Study ◽  
Pattern Recognition ◽  
Pattern Analysis ◽  
Transformation Group ◽  
Transformation Groups ◽  
Continuous Transformation ◽  
Anatomy And Physiology ◽  
Visual Behaviour ◽  
Lie Transformation ◽  
Pattern Information

Despite a vast accumulation of knowledge about the anatomy and physiology of the cat's visual system in recent years, and about its early development, there has been very little experimental study of the development of visual behaviour in this species. This is especially true of the kitten's ability to recognize patterns. Two experiments are reported that aim to remedy some part of this deficiency, and that also serves to examine a particular hypothesis about the basis of pattern analysis in the young organism. This is Hoffman's hypothesis that the orbits of elementary Lie transformation groups (a species of continuous transformation group) represent the basis for coding pattern information.

scholarly journals Transformation Groups with (n-1)-Dimensional Orbits on Non-Compact Manifolds

1959 ◽  
Vol 14 ◽  
pp. 25-38 ◽  
Author(s):  
Tadashi Nagano
Keyword(s):  
Lie Group ◽  
Compact Manifold ◽  
Isometry Group ◽  
Transformation Group ◽  
Differentiable Manifold ◽  
Riemannian Metric ◽  
Compact Manifolds ◽  
Transformation Groups ◽  
Lie Transformation

When a Lie group G operates on a differentiable manifold M as a Lie transformation group, the orbit of a point p in M under G, or the G-orbit of p, is by definition the submanifold G(p) = {G(p); g∈G}. The purpose of this paper is to characterize the structure of a non-compact manifold M such that there exists a compact orbit of dimension (n — 1), n — dim M, under a connected Lie transformation group G, which is assumed to be compact or an isometry group of a Riemannian metric on M.

scholarly journals New Applications of a Kind of Infinitesimal-Operator Lie Algebra

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Honwah Tam ◽  
Yufeng Zhang ◽  
Xiangzhi Zhang
Keyword(s):  
Differential Equation ◽  
Lie Algebras ◽  
Transformation Group ◽  
Order Differential Equation ◽  
Lie Symmetry ◽  
Discrete Equation ◽  
Infinitesimal Operator ◽  
Lie Transformation ◽  
Symmetry Operators ◽  
New Applications

Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism. A corresponding discrete equation approximating it is given as well. Finally, we make use of the Lie algebras to generate some new integrable systems including (1+1) and (2+1) dimensions.

IMBEDDING OF TRANSFORMATION GROUPS IN AFFINE ONES AND RENORMALIZATION OF TWO-DIMENSIONAL HOMOGENEOUS σ-MODELS

1993 ◽  
Vol 08 (31) ◽  
pp. 2937-2942
Author(s):  
A. V. BRATCHIKOV
Keyword(s):  
Homogeneous Space ◽  
Transformation Group ◽  
Affine Group ◽  
Coupling Constants ◽  
Transformation Groups ◽  
Two Dimensional

The BLZ method for the analysis of renormalizability of the O(N)/O(N − 1) model is extended to the σ-model built on an arbitrary homogeneous space G/H and in arbitrary coordinates. For deriving Ward-Takahashi (WT) identities an imbedding of the transformation group G in an affine group is used. The structure of the renormalized action is found. All the infinities can be absorbed in a coupling constants renormalization and in a renormalization of auxiliary constants which are related to the imbedding.

Used Products Return Pattern Analysis Using Agent-Based Modelling and Simulation

2013 ◽  
pp. 38-58
Keyword(s):  
Experimental Study ◽  
Service Quality ◽  
Pattern Analysis ◽  
End Users ◽  
Modelling And Simulation ◽  
Future Trends ◽  
Problem Statement ◽  
Research Directions ◽  
Agent Based ◽  
Agent Based Modelling

This chapter examines the used products return service quality perceived by the end users and their corresponding willingness-to-return with respect to the used products in their possession. The chapter starts with an introduction about the issue of return quantity encountered at the used product collection stage. Then, related studies dealing with returns quantity are discussed in the background section. Next, the focal problem of this chapter is stated in the problem statement section. A detailed description about the approach (i.e., agent-based modelling and simulation) can be found in the proposed methodology section. Right after this, three simulations, with each one linked to a specific used products return scenario, are conducted in the experimental study section. The potential research directions regarding the main problem considered in this chapter are highlighted in the future trends section. Finally, the conclusion drawn in the last section closes this chapter.

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