exhibit a disconjugacy in the appropriate direction: disconjugacy is convergent for leftward saccades (Figs. 3A and 3C) and divergent for rightward saccades (Figs. 3B and 3D). Its amplitude corresponds quite well to the requirement ...

Author: J.M. Findlay

Publisher: Elsevier

ISBN: 0080531547

Category: Psychology

Page: 561

View: 407

This volume contains selected and edited papers from the 7th European Conference on Eye Movements (ECEM 7) held in Durham, UK on August 31-September 3 1993. The volume is organized as follows:- Invited Lectures, Pursuit and Co-Ordination, Saccade and Fixation Control, Oculomotor Physiology, Clinical and Medical Aspects of Eye Movements, Eye Movements and Cognition, Eye Movements and Language and finally, Displays and Applications.

The analysis of disconjugacy was continued in the works [9,10] of Johnson et al. The use of the methods of the modern theory of nonautonomous differential systems allows the authors to study the dynamical and ergodic properties of the ...

Author: Ferenc Hartung

Publisher: Springer

ISBN: 9783319082516

Category: Mathematics

Page: 263

View: 981

Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic and oscillatory properties of the solutions; stability theory; numerical approximations; and applications to real world phenomena using deterministic and stochastic discrete and continuous dynamical systems.

But in fact the interest of weak disconjugacy goes beyond this first analysis. As shown in Johnson et al. [78], under different additional conditions (still often providing a scenario less restrictive than the disconjugate one), ...

Author: Russell Johnson

Publisher: Springer

ISBN: 9783319290256

Category: Mathematics

Page: 497

View: 524

This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense. The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory.

For each saccade in the reading task, the disconjugacy of the saccade is shown in degrees (x-axis) and the disconjugacy of the postsaccadic ... Positive values indicate convergent disconjugacy, negative values divergent disconjugacy.

Author: John Stein

Publisher: OUP Oxford

ISBN: 9780191636332

Category: Psychology

Page: 216

View: 774

Dyslexia affects about 10% of all children and is a potent cause of loss of self-confidence, personal and family misery, and waste of potential. Although the dominant view is that it is caused by specifically linguistic/phonological weakness, recent research within the field of neuroscience has shown that it is associated wtih visual processing problems as well. These discoveries have led to a resurgence in visual methods of treatment, which have shown promising results. 'Visual aspects of dyslexia' brings together cutting edge research from a range of disciplines - including neurology, neuroscience, and the vision sciences, to present the first comprehensive review of this recent research. It includes chapters from leading specialists which, in addition to reporting on the latest research, show how this knowledge is being successfully applied in the development of effective visual treatments for this common problem. Sections within the book cover the role of eye movements in reading, visual attention and reading, the neural bases of reading, and the relationship between visual stress and dyslexia. Making a valuable contribution in helping us develop a deeper understanding of dyslexia, this is an important book for those in the fields of psychology, neuroscience, and education.

We say that an interval I c [a, ce) is a (+)-disconjugacy interval for the differential equation (l) if every ultimately positive solution of (l) has at most one zero on I. (In our investigations the function y (t) = 0 , held on some ...

(B) Comparison of segmented saccade amplitude and corresponding disconjugacy. Each data-point depicts one segmented saccade. orientation. We found that the number of “catch-up” saccades per gaze shift ranged between 1 and 5; ...

Author: Aasef G. Shaikh

Publisher: Frontiers Media SA

ISBN: 9782889455638

Category:

Page: 247

View: 180

Eye movements provide rich source of information about brain functioning for neurologists and neuroscientists. They provide diagnostic clues, define, and localize motor and cognitive disorders. Objective eye movement assessments associated with clinical observation and genetic testing in neurodegenerative, neurometabolic, and neurogenetic diseases provide insight into their pathophysiology and disease mechanism. Finally the eye movements may be used for testing and following the response to therapies. The concrete value of studying eye movement stems from a number of advantages compared to the study of movements of axial or limb muscles. The eye movements are accessible to clinical inspection, they can be measured precisely, their interpretation is clear and therefore ocular motility examination has high localization value. There are several standardized tasks to study of each subclass of eye movements that are recognized for motor or cognitive behavior. Indeed the studies of eye movement had allowed test of motor and cognitive functions of the brain in a vast range of neurological disease. Both cortical and subcortical dysfunctions may be detected with the analysis of subclasses of eye movements and interpreted in association with other clinical, laboratory and neuroimaging features. The goal of this topic-focused volume of Frontiers in Neurology is to gather seminal studies, from well-known scientists and laboratories from across the world, delineating the features of eye movements and vestibular system in neurogenetic, neurometabolic, and neurodegenerative disorders. Such collection of articles, to our knowledge, is unique and never done in the past. The topics and the compilation will be of interest to broad groups of neuroscientists and neurologists for the reasons as follows: 1) Neurodegenerative diseases represent a large portion of neurological diseases encountered in neurological clinical practice. Eye movement changes may occur early in their course and may be specific, thus orienting the diagnosis. 2) Neurometabolic and neurogenetic conditions, although rare, show specific and characteristic eye movements that represent the hallmark of the disease. Such disorders often represent a pathologic model that helps to understand the normal functioning of specific brain regions and networks.

Now we are in the possession of several values of k by each of which it is possible to deduce “(k, n-k)disconjugacy implies (l, m-l)-disconjugacy”. To get the most from Theorem 7.11, let us take either k = [n/2] or k = [n/2]+ 1, ...

Author: Uri Elias

Publisher: Springer Science & Business Media

ISBN: 9789401725170

Category: Mathematics

Page: 226

View: 415

Oscillation theory was born with Sturm's work in 1836. It has been flourishing for the past fifty years. Nowadays it is a full, self-contained discipline, turning more towards nonlinear and functional differential equations. Oscillation theory flows along two main streams. The first aims to study prop erties which are common to all linear differential equations. The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc. Our work belongs to the second type and considers two term linear equations modeled after y(n) + p(x)y = O. More generally, we investigate LnY + p(x)y = 0, where Ln is a disconjugate operator and p(x) has a fixed sign. These equations enjoy a very rich structure and are the natural generalization of the Sturm-Liouville operator. Results about such equations are distributed over hundreds of research papers, many of them are reinvented again and again and the same phenomenon is frequently discussed from various points of view and different definitions of the authors. Our aim is to introduce an order into this plenty and arrange it in a unified and self contained way. The results are readapted and presented in a unified approach. In many cases completely new proofs are given and in no case is the original proof copied verbatim. Many new results are included.

FIGURE 7 | Disconjugacy during the saccades in the reading (A) and visual search tasks (B) for both group of subjects. ... We found no effect of age on the disconjugacy during the saccades (see Figure 7), neither in the reading task (R2 ...

Author: Olivier A. Coubard

Publisher:

ISBN: 9782889196555

Category:

Page:

View: 625

Binocular vision is achieved by five neurovisual systems originating in the retina but varying in their destination within the brain. Two systems have been widely studied: the retino-tectal or retino-collicular route, which subserves an expedient and raw estimate of the visual scene through the magnocellular pathway, and the retino-occipital or retino-cortical route, which allows slower but refined analysis of the visual scene through the parvocellular pathway. But there also exist further neurovisual systems: the retino-hypothalamic, retino-pretectal, and accessory optic systems, which play a crucial role in vision though they are less understood. The retino-pretectal pathway projecting onto the pretectum is critical for the pupillary or photomotor reflex. The retino-hypothalamic pathway projecting onto the suprachiasmatic nucleus regulates numerous behavioral and biological functions as well as circadian rhythms. The accessory optic system targeting terminal lateral, medial and dorsal nuclei through the paraoptic fasciculus plays a role in head and gaze orientation as well as slow movements. Taken together, these neurovisual systems involve 60% of brain activity, thus highlighting the importance of vision in the functioning and regulation of the central nervous system. But vision is first and foremost action, which makes perception impossible without movement. Binocular coordination is a prerequisite for binocular fusion of the object of interest on the two foveas, thus ensuring visual perception. The retino-collicular pathway is sufficient to elicit reflexive eye movements with short latencies. Thanks to its motor neurons, the superior colliculus activates premotor neurons, which themselves activate motor neurons of the oculomotor, trochlear and abducens nuclei. At a higher level, a cascade of neural mechanisms participates in the control of decisional eye movements. The superior colliculus is controlled by the substancia nigra pars reticulata, which is itself gated by subcortical structures such as the dorsal striatum. The superior colliculus is also inhibited by the dorsolateral prefrontal cortex through a direct prefrontotectal tract. Cortical areas are crucial for the triggering of eye movements: the frontal eye field, supplementary eye field, and parietal eye field. Finally the cerebellum maintains accuracy. The focus of the present research topic, entitled Neural bases of binocular vision and coordination and their implications in visual training programs, is to review the most recent findings in brain imaging and neurophysiology of binocular vision and coordination in humans and animals with frontally-placed eyes. The emphasis is put on studies that enable transfer of knowledge toward visual training programs targeting visual field defects (e.g., hemianopia) and binocular functional disorders (e.g., amblyopia).

Disconjugacy is closely related to solvability of the de la Vallée-Poussin multiple-point problem Ly = g, y")(xj) = aii, i = 0,..., ri-1, XX" r = n. The Green's function of a disconjugate operator L and the related homogeneous boundary ...

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

ISBN: 9789401512886

Category: Mathematics

Page: 588

View: 574

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.

In Section 2, we state a theorem that establishes the equivalence of disconjugacy and two-point disconjugacy for linear equations. This will then provide the framework on which we apply in Section 3 the Pontryagin Maximum Principle, ...

Author: R P Agarwal

Publisher: World Scientific

ISBN: 9789814505628

Category: Mathematics

Page: 600

View: 185

This series aims at reporting new developments of a high mathematical standard and of current interest. Each volume in the series shall be devoted to mathematical analysis that has been applied, or potentially applicable to the solutions of scientific, engineering, and social problems. The first volume of WSSIAA contains 42 research articles on differential equations by leading mathematicians from all over the world. This volume has been dedicated to V Lakshmikantham on his 65th birthday for his significant contributions in the field of differential equations. Contents:Semilinear and Quasilinear Stochastic Differential Equations in Banach Spaces (N U Ahmed)Asymptotic Behaviour of the Nonoscillating Solutions of First Order Linear Nonautonomous Neutral Equations (D Bainov & V Petrov)Boundary and Angular Layer Behavior in Singularly Perturbed Quasilinear Systems (K W Chang & G X Liu)Singular Perturbation for a System of Differential-Difference Equations (S-N Chow & W Huang)Bounds for Solutions Sets of Multivalued ODES (K Deimling)Comparison of Eigenvalues for a Class of Multipoint Boundary Value Problems (P W Eloe & J Henderson)A Solution to the General Bessel Moment Problem (W D Evans et al.)Boundedness in Linear Functional Differential Equations with Infinite Delay (J Kato)Foundation of Invariant Manifold Theory for Ordinary Differential Equations (H W Knobloch)and other papers Readership: Mathematicians and engineers. keywords:Differential Equations