scholarly journals Local and Global Gestalt Laws: A Neurally Based Spectral Approach

2017 ◽  
Vol 29 (2) ◽  
pp. 394-422 ◽  
Author(s):  
Marta Favali ◽  
Giovanna Citti ◽  
Alessandro Sarti
Keyword(s):  
Mathematical Model ◽  
Spectral Analysis ◽  
Group Theory ◽  
Visual Cortex ◽  
Connectivity Matrix ◽  
Spectral Approach ◽  
Good Continuation ◽  
Functional Architecture ◽  
Lie Group Theory ◽  
Gestalt Laws

This letter presents a mathematical model of figure-ground articulation that takes into account both local and global gestalt laws and is compatible with the functional architecture of the primary visual cortex (V1). The local gestalt law of good continuation is described by means of suitable connectivity kernels that are derived from Lie group theory and quantitatively compared with long-range connectivity in V1. Global gestalt constraints are then introduced in terms of spectral analysis of a connectivity matrix derived from these kernels. This analysis performs grouping of local features and individuates perceptual units with the highest salience. Numerical simulations are performed, and results are obtained by applying the technique to a number of stimuli.

scholarly journals Lie-Group Modeling and Numerical Simulation of a Helicopter

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2682
Author(s):  
Alessandro Tarsi ◽  
Simone Fiori
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Group Theory ◽  
Lie Group ◽  
Technical Literature ◽  
Lie Group Theory ◽  
Pontryagin Principle ◽  
Group Modeling ◽  
The Many ◽  
The Mathematical Model

Helicopters are extraordinarily complex mechanisms. Such complexity makes it difficult to model, simulate and pilot a helicopter. The present paper proposes a mathematical model of a fantail helicopter type based on Lie-group theory. The present paper first recalls the Lagrange–d’Alembert–Pontryagin principle to describe the dynamics of a multi-part object, and subsequently applies such principle to describe the motion of a helicopter in space. A good part of the paper is devoted to the numerical simulation of the motion of a helicopter, which was obtained through a dedicated numerical method. Numerical simulation was based on a series of values for the many parameters involved in the mathematical model carefully inferred from the available technical literature.

Model calculations in reconstructions of measured fields

Open Physics ◽  
2003 ◽  
Vol 1 (1) ◽  
Author(s):  
Mihály Makai ◽  
Yuri Orechwa
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Group Theory ◽  
Point Group ◽  
Iterative Solution ◽  
The Finite Element Method ◽  
Technological Systems ◽  
Convergence Problem ◽  
Model Calculations

AbstractThe state of technological systems, such as reactions in a confined volume, are usually monitored with sensors within as well as outside the volume. To achieve the level of precision required by regulators, these data often need to be supplemented with the solution to a mathematical model of the process. The present work addresses an observed, and until now unexplained, convergence problem in the iterative solution in the application of the finite element method to boundary value problems. We use point group theory to clarify the cause of the non-convergence, and give rule problems. We use the appropriate and consistent orders of approximation on the boundary and within the volume so as to avoid non-convergence.

scholarly journals FORMATION CONTROL OF MULTIPLE UNICYCLE-TYPE ROBOTS USING LIE GROUP

2016 ◽  
Vol 56 (1) ◽  
pp. 1
Author(s):  
Youwei Dong ◽  
Ahmed Rahmani
Keyword(s):  
Group Theory ◽  
Numerical Simulations ◽  
Lie Group ◽  
Formation Control ◽  
Directed Acyclic Graph ◽  
Control Law ◽  
Lie Group Theory ◽  
Acyclic Graph ◽  
Communication Topology

In this paper the formation control of a multi-robots system is investigated. The proposed control law, based on Lie group theory, is applied to control the formation of a group of unicycle-type robots. The communication topology is supposed to be a rooted directed acyclic graph and fixed. Some numerical simulations using Matlab are made to validate our results.

Chebyshev Spectra Resistance to Trend of Random Noise

2018 ◽  
Vol 17 (03) ◽  
pp. 1850028 ◽  
Author(s):  
Boris M. Grafov ◽  
Alexey L. Kluev ◽  
Tatyana B. Kabanova ◽  
Alexey D. Davydov
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Fourier Analysis ◽  
Random Process ◽  
Chebyshev Polynomials ◽  
Random Noise ◽  
Spectral Lines ◽  
Spectral Approach ◽  
Experimental Conditions ◽  
Strong Trend

Spectral analysis of random noise in the space of discrete Chebyshev polynomials is an alternative to spectral Fourier analysis. The importance of Chebyshev spectral approach is associated with the fact that the discrete Chebyshev transformation of the [Formula: see text]-th order eliminates automatically the polynomial trend of the ([Formula: see text]−1) order. Using the method of artificial trend, it was found that, under the real experimental conditions, the intensity of Chebyshev spectral lines with numbers higher than 1 is resistant to a strong trend of random process. This effect is observed when we use both the arithmetic averaging and the median. The Chebyshev spectral approach is a powerful tool for spectral analysis of random time series with a strong trend.

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