Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

Visual results with the use of prismatic lenses in the treatment of congenital nystagmus: a clinical case

Purpose: It is important to establish a differential diagnosis between the different types of nystagmus, in order to give the appropriate clinical approach to every situation and to improve visual acuity. The nystagmus is normally blocked when the eyes are positioned in a particular way. This makes the child adopt a posture of ocular torticollis that reduces the nistagmiformes movements, improving the vision in this position. A way to promote the blocking of the nystagmic movements is by using prismatic lenses with opposite bases, to block or minimize the oscillatory movements. This results in a vision improvement and it reduces the anomalous head position. There is limited research on the visual results in children with nystagmus after using prisms with opposing bases. Our aim is to describe the impact on the visual acuity (VA ) of theprescription prism lenses in a nystagmus patient starting at 3 months of age. Methods: Case report on thirty month old caucasian male infant, with normal growth and development for their age, with an early onset of horizontal nystagmus at 3 months of age. Ophthalmic examination included slit lamp examination, fundus, refractive study, electrophysiological and magnetic resonance tests, measurement of VA over time with the Teller Acuity Cards (TAC ) in the distance agreed for the age. At age ten months, the mother noted a persistent turn to the right of the child’s head, which became increasingly more severe along the months. There’s no oscillopcia. At 24 months, an atropine refraction showed the following refractive error: 0D.: -1,50, OS: -0,50 and prismatic lens adapting OD 8 Δ nasal base and OE 8 Δ temporal base. Results: Thirty month old child, with adequate development for their age, with onset of idiopatic horizontal nystagmus, at 3 months of age. Normal ocular fundus and magnetic ressoance without alterations, sub-normal results in electrophysiological tests and VA with values below normal for age. At 6 months OD 20/300; OE 20/400; OU 20/300. At 9 months OD 20/250; OE 20/300; OU 20/150 (TAC a 38 cm). At 18 months OD 20/200; OE 20/100; OU 20/80 (TAC at 38 cm), when the head is turned to the right and the eyes in levoversão, the nystagmus decreases in a “neutral” area. At 24 month, with the prismatic glasses, OD 20/200 OE 20/100, OU20/80 (TAC at 54 cm, reference value is 20/30 – 20/100 para OU e 20/40 – 20/100 monocular), there was an increase in the visual acuity. The child did visual stimulation with multimedia devices and using glasses. After adaptation of prisms: at 30 months VA (with Cambridge cards) OD e OE = 6/18. The child improved the VA and reduced the anomalous head position. There is also improvement in mobility and fine motricity. Conclusion: Prisms with opposing bases., were used in the treatment of idiopathic nystagmus. Said prisms were adapted to reduce the skewed position of the head, and to improve VA and binocular function. Monitoring of visual acuity and visual stimulation was done using electronic devices. Following the use of prismatic, the patient improved significantly VA and the anomalous head position was reduced.

O desenvolvimento da leitura em crianças com dificuldades graves de aprendizagem

Projeto de Intervenção apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Especial, especialidade em Multideficiência