scholarly journals Thermal expansions in quartz: A geometrical consideration.

2001 ◽  
Vol 96 (4) ◽  
pp. 159-163 ◽  
Author(s):  
Kuniaki KIHARA
Keyword(s):  
Geometrical Consideration

Nonholonomic Orthogonal Learning Algorithms for Blind Source Separation

2000 ◽  
Vol 12 (6) ◽  
pp. 1463-1484 ◽  
Author(s):  
Shun-ichi Amari ◽  
Tian-Ping Chen ◽  
Andrzej Cichocki
Keyword(s):  
Blind Source Separation ◽  
Learning Algorithm ◽  
Learning Algorithms ◽  
Source Separation ◽  
Rapid Change ◽  
Nonholonomic Constraints ◽  
Mixing Coefficients ◽  
Linear Mixtures ◽  
Source Signals ◽  
Geometrical Consideration

Independent component analysis or blind source separation extracts independent signals from their linear mixtures without assuming prior knowledge of their mixing coefficients. It is known that the independent signals in the observed mixtures can be successfully extracted except for their order and scales. In order to resolve the indeterminacy of scales, most learning algorithms impose some constraints on the magnitudes of the recovered signals. However, when the source signals are nonstationary and their average magnitudes change rapidly, the constraints force a rapid change in the magnitude of the separating matrix. This is the case with most applications (e.g., speech sounds, electroencephalogram signals). It is known that this causes numerical instability in some cases. In order to resolve this difficulty, this article introduces new nonholonomic constraints in the learning algorithm. This is motivated by the geometrical consideration that the directions of change in the separating matrix should be orthogonal to the equivalence class of separating matrices due to the scaling indeterminacy. These constraints are proved to be nonholonomic, so that the proposed algorithm is able to adapt to rapid or intermittent changes in the magnitudes of the source signals. The proposed algorithm works well even when the number of the sources is overestimated, whereas the existent algorithms do not (assuming the sensor noise is negligibly small), because they amplify the null components not included in the sources. Computer simulations confirm this desirable property.

A GEOMETRICAL VIEW OF THE MINUS-SIGN PROBLEM

1992 ◽  
Vol 03 (01) ◽  
pp. 185-193 ◽  
Author(s):  
A. MURAMATSU ◽  
G. ZUMBACH ◽  
X. ZOTOS
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Topological Invariant ◽  
Minus Sign ◽  
Sign Problem ◽  
Trial Wavefunction ◽  
Geometrical Consideration

It is shown that the sign of the fermionic determinant in the projector Monte Carlo method is directly related to a topological invariant. A key ingredient to obtain this result is the identification of the appropriate manifolds to describe the evolution of a fermionic trial wavefunction. They allow for a purely geometrical consideration of the minus-sign problem.

Designing localized waves

1993 ◽  
Vol 440 (1910) ◽  
pp. 541-565 ◽  
Keyword(s):  
Wave Equation ◽  
Fourier Transforms ◽  
Transform Domain ◽  
Localized Solutions ◽  
Homogeneous Wave ◽  
Klein Gordon ◽  
Domain Phase ◽  
Localized Waves ◽  
Homogeneous Wave Equation ◽  
Geometrical Consideration

In this paper we re-interpret a recently introduced method for obtaining non-separable, localized solutions of homogeneous partial differential equations. This reinterpretation is in the form of a geometrical consideration of the algebraic constraint that the Fourier transforms of such solutions must satisfy in the transform domain (phase space). With this approach we link two classes of localized, non-separable solutions of the homogeneous wave equation, and examine the transform domain characteristic that determines the space-time localization properties of these classes. This characterization allows us to design classes of solutions with better localization properties. In particular, we design and discuss the properties of several novel subluminal and superluminal solutions of the homogeneous wave equation. We also design families of non-separable, localized, subluminal and superluminal solutions of the Klein-Gordon equation by using the same technique.

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