Velocity Computation from Measures of Spatiotemporal Gradients at Multiple Orientations

Perception ◽  
1996 ◽  
Vol 25 (1_suppl) ◽  
pp. 77-77 ◽  
Author(s):  
A Johnston ◽  
P W McOwan
Keyword(s):  
Natural Extension ◽  
Image Brightness ◽  
Motion Patterns ◽  
One Dimensional ◽  
Aperture Problem ◽  
Motion Models ◽  
Temporal Domain ◽  
Moving Stimulus ◽  
Zero Values ◽  
Derivatives Of

Current models of speed and direction of motion which use measures of spatiotemporal gradients can suffer from ill-conditioning. This problem arises either because local measures of the derivatives of image brightness take zero values or because the motion equations cannot be solved for one-dimensional (1-D) signals in two-dimensional (2-D) images—the aperture problem. One way around this predicament is to select image points or introduce constants to deal with ill-conditioned calculations. Here we describe an analytic method that combines measures of speed in a range of directions to provide a well-conditioned measure of velocity at all points in the moving stimulus. This approach is a natural extension of a one-dimensional model which has been successful in predicting perceived motion in a variety of 1-D spatiotemporal motion patterns (Johnston, McOwan and Buxton 1992 Proceedings of the Royal Society of London, Series B250 297 – 306). Speed is computed with the use of biologically plausible filters that are derivatives of Gaussians in the spatial domain and log Gaussians in the temporal domain. Measures of speed and inverse speed are computed for a range of orientations consistent with the number of direction columns in MT/V5. The pattern of velocities measured over this set of orientations is then used to recover the speed and direction of motion of the stimulus. The model can correctly compute the velocity of moving 1-D patterns, such as gratings, patterns that prove a problem for many current 2-D motion models as they form degenerate cases, as well as the motion of rigid 2-D patterns.

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

The combined effect of lattice’s uniaxial strains and electron–phonon interaction’s screening on TBEC of the intersite bipolarons

2016 ◽  
Vol 30 (26) ◽  
pp. 1650186
Author(s):  
B. Yavidov ◽  
SH. Djumanov ◽  
T. Saparbaev ◽  
O. Ganiyev ◽  
S. Zholdassova ◽  
...  
Keyword(s):  
Ideal Gas ◽  
Einstein Condensation ◽  
Chain Model ◽  
One Dimensional ◽  
Electron Phonon Interaction ◽  
Model Lattice ◽  
Experimental Values ◽  
Bose Einstein ◽  
Derivatives Of ◽  
The Ideal

Having accepted a more generalized form for density-displacement type electron–phonon interaction (EPI) force we studied the simultaneous effect of uniaxial strains and EPI’s screening on the temperature of Bose–Einstein condensation [Formula: see text] of the ideal gas of intersite bipolarons. [Formula: see text] of the ideal gas of intersite bipolarons is calculated as a function of both strain and screening radius for a one-dimensional chain model of cuprates within the framework of Extended Holstein–Hubbard model. It is shown that the chain model lattice comprises the essential features of cuprates regarding of strain and screening effects on transition temperature [Formula: see text] of superconductivity. The obtained values of strain derivatives of [Formula: see text] [Formula: see text] are in qualitative agreement with the experimental values of [Formula: see text] [Formula: see text] of La[Formula: see text]Sr[Formula: see text]CuO4 under moderate screening regimes.

scholarly journals The Perceived Direction of Textured Gratings and Their Motion Aftereffects

Perception ◽  
1995 ◽  
Vol 24 (12) ◽  
pp. 1383-1396 ◽  
Author(s):  
David Alais ◽  
Maarten J van der Smagt ◽  
Frans A J Verstraten ◽  
Wim A van de Grind
Keyword(s):  
Motion Aftereffect ◽  
Sine Wave ◽  
Circular Aperture ◽  
High Luminance ◽  
One Dimensional ◽  
Square Wave ◽  
Aperture Problem ◽  
Motion Energy ◽  
Motion Aftereffects ◽  
Do So

The stimuli in these experiments are square-wave luminance gratings with an array of small random dots covering the high-luminance regions. Owing to the texture, the direction of these gratings, when seen through a circular aperture, is disambiguated because the visual system is provided with an unambiguous motion energy. Thus, the direction of textured gratings can be varied independently of grating orientation. When subjects are required to judge the direction of textured gratings moving obliquely relative to their orientation, they can do so accurately (experiment 1). This is of interest because most studies of one-dimensional motion perception have involved (textureless) luminance-defined sine-wave or square-wave gratings, and the perceived direction of these gratings is constrained by the aperture problem to be orthogonal to their orientation. Thus, direction and orientation have often been confounded. Interestingly, when subjects are required to judge the direction of an obliquely moving textured grating during a period of adaptation and then the direction of the motion aftereffect (MAE) immediately following adaptation (experiments 2 and 3), these directions are not directly opposite each other. MAE directions were always more orthogonal to the orientation of the adapting grating than the corresponding direction judgments during adaptation (by as much as 25°). These results are not readily explained by conventional MAE models and possible accounts are considered.

Modified Unsplitted Perfectly Matched Layer Absorbing Boundary Conditions for Truncating Anisotropic Medium

2014 ◽  
Vol 900 ◽  
pp. 386-389
Author(s):  
Zhi Chao Cai ◽  
Li Xia Yang ◽  
Hao Chuan Deng ◽  
Xiao Wei ◽  
Hong Cheng Yin
Keyword(s):  
Boundary Conditions ◽  
Anisotropic Medium ◽  
Electromagnetic Wave Propagation ◽  
Simulation Analysis ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
One Dimensional ◽  
Derivatives Of ◽  
Difference Time

To simulate Electromagnetic wave propagation in anisotropic media, absorbing boundary conditions are needed to truncate the computation domains. Based on the finite difference time domain method in anisotropic medium, the implementation of the modified nearly perfectly matched layer absorbing boundary conditions for truncating anisotropic medium is presented. By using the partial derivatives of space variables stretched-scheme in the coordinate system, the programming complexity is reduced greatly. According to one dimensional numerical simulation analysis, the modified nearly perfectly matched layer absorbing boundary condition is validated.

scholarly journals A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function

2002 ◽  
Vol 65 (2) ◽  
pp. 253-258 ◽  
Author(s):  
Hitoshi Tanaka
Keyword(s):  
Sobolev Space ◽  
Maximal Function ◽  
60Th Birthday ◽  
One Dimensional ◽  
Partial Derivatives ◽  
First Order ◽  
Littlewood Maximal Function ◽  
The One ◽  
Derivatives Of

Dedicated to Professor Kôzô Yabuta on the occasion of his 60th birthdayJ. Kinnunen proved that of P > 1, d ≤ 1 and f is a function in the Sobolev space W1,P(Rd), then the first order weak partial derivatives of the Hardy-Littlewood maximal function ℳf belong to LP(Rd). We shall show that, when d = 1, Kinnunen's result can be extended to the case where P = 1.

AN UPPER BOUND OF THE DIRECTIONAL ENTROPY WITH RESPECT TO THE MARKOV MEASURES

2012 ◽  
Vol 22 (11) ◽  
pp. 1250263 ◽  
Author(s):  
HASAN AKIN
Keyword(s):  
Upper Bound ◽  
Stochastic Matrix ◽  
Natural Extension ◽  
Short Paper ◽  
Probability Vector ◽  
Compact Metric Space ◽  
One Dimensional ◽  
Markov Measure ◽  
Shift Map ◽  
Markov Measures

In this short paper, without considering the natural extension we study the directional entropy of a Z2-action Φ generated by an invertible one-dimensional linear cellular automaton [Formula: see text] and [Formula: see text], over the ring Zpk(with p a prime number and k ≥ 2), where gcd (p, λr) = 1 and p ∣ λifor all i ≠ r, and the shift map acting on the compact metric space [Formula: see text]. Without loss of generality, we consider k = 2. We prove that the directional entropy hv(Φ)(v = (s, q) ∈ R) of a Z2-action with respect to a Markov measure μπPover space [Formula: see text] defined by a stochastic matrix P = (aij) and a probability vector π = {π0, π1, …, πp2-1} is bounded above by [Formula: see text].

An Analytical Solution of the Generalized Phase-Lagging Equation for Ultra-Fast Heat Transfer in One-Dimensional Semi-Infinite Domain

2012 ◽  
Author(s):  
Vladimir Kulish ◽  
Kirill V. Poletkin
Keyword(s):  
Analytical Solution ◽  
Domain Boundary ◽  
Integral Form ◽  
Solution Procedure ◽  
Generalized Derivatives ◽  
Infinite Domain ◽  
One Dimensional ◽  
Confluent Hypergeometric Functions ◽  
The Laplace Transform ◽  
Derivatives Of

The paper presents an integral solution of the generalized one-dimensional phase-lagging heat equation with the convective term. The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of non-integer orders). Confluent hypergeometric functions, known as Whittaker’s functions, appear in the course of the solution procedure, upon applying the Laplace transform to the original transport equation. The analytical solution of the problem is written in the integral form and provides a relationship between the local values of the temperature and heat flux. The solution is valid everywhere within the domain, including the domain boundary.

scholarly journals Causality and passivity in elastodynamics

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150256 ◽  
Author(s):  
Ankit Srivastava
Keyword(s):  
Fourier Transforms ◽  
Constitutive Relations ◽  
Higher Order ◽  
Causal Effects ◽  
Passive System ◽  
One Dimensional ◽  
The Real ◽  
Analogous Question ◽  
Derivatives Of ◽  
Special Case

What are the constraints placed on the constitutive tensors of elastodynamics by the requirements that the linear elastodynamic system under consideration be both causal (effects succeed causes) and passive (system does not produce energy)? The analogous question has been tackled in other areas but in the case of elastodynamics its treatment is complicated by the higher order tensorial nature of its constitutive relations. In this paper, we clarify the effect of these constraints on highly general forms of the elastodynamic constitutive relations. We show that the satisfaction of passivity (and causality) directly requires that the hermitian parts of the transforms (Fourier and Laplace) of the time derivatives of the constitutive tensors be positive semi-definite. Additionally, the conditions require that the non-hermitian parts of the Fourier transforms of the constitutive tensors be positive semi-definite for positive values of frequency. When major symmetries are assumed these definiteness relations apply simply to the real and imaginary parts of the relevant tensors. For diagonal and one-dimensional problems, these positive semi-definiteness relationships reduce to simple inequality relations over the real and imaginary parts, as they should. Finally, we extend the results to highly general constitutive relations which include the Willis inhomogeneous relations as a special case.

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