Partitions spectrales optimales pour les problèmes aux valeurs propres de Dirichlet et de Neumann

Les façons d'aborder l'étude du spectre du laplacien sont multiples. Ce mémoire se concentre sur les partitions spectrales optimales de domaines planaires. Plus précisément, lorsque nous imposons des conditions aux limites de Dirichlet, nous cherchons à trouver la ou les partitions qui réalisent l'infimum (sur l'ensemble des partitions à un certain nombre de composantes) du maximum de la première valeur propre du laplacien sur tous ses sous-domaines. Dans les dernières années, cette question a été activement étudiée par B. Helffer, T. Hoffmann-Ostenhof, S. Terracini et leurs collaborateurs, qui ont obtenu plusieurs résultats analytiques et numériques importants. Dans ce mémoire, nous proposons un problème analogue, mais pour des conditions aux limites de Neumann cette fois. Dans ce contexte, nous nous intéressons aux partitions spectrales maximales plutôt que minimales. Nous cherchons alors à vérifier le maximum sur toutes les $k$-partitions possibles du minimum de la première valeur propre non nulle de chacune des composantes. Cette question s'avère plus difficile que sa semblable dans la mesure où plusieurs propriétés des valeurs propres de Dirichlet, telles que la monotonicité par rapport au domaine, ne tiennent plus. Néanmoins, quelques résultats sont obtenus pour des 2-partitions de domaines symétriques et des partitions spécifiques sont trouvées analytiquement pour des domaines rectangulaires. En outre, des propriétés générales des partitions spectrales optimales et des problèmes ouverts sont abordés.

Susceptibility to pattern glare and the effect of spectral filters on rate of reading and visual search in stroke patients

The present thesis investigates pattern glare susceptibility following stroke and the immediate and prolonged impact of prescribing optimal spectral filters on reading speed, accuracy and visual search performance. Principal observations: A case report has shown that visual stress can occur following stroke. The use of spectral filters and precision tinted lenses proved to be a successful intervention in this case, although the parameters required modification following a further stroke episode. Stroke subjects demonstrate elevated levels of pattern glare compared to normative data values and a control group. Initial use of an optimal spectral filter in a stroke cohort increased reading speed by ~6% and almost halved error scores, findings not replicated in a control group. With the removal of migraine subjects reading speed increased by ~8% with an optimal filter and error scores almost halved. Prolonged use of an optimal spectral filter for stroke subjects, increased reading speed by >9% and error scores more than halved. When the same subjects switched to prolonged use of a grey filter, reading speed reduced by ~4% and error scores increased marginally. When a second group of stroke subjects used a grey filter first, reading speed decreased by ~3% but increased by ~3% with prolonged use of an optimal filter, with error scores almost halving; these findings persisted with migraine subjects excluded. Initial use of an optimal spectral filter improved visual search response time but not error scores in a stroke cohort with migraine subjects excluded. Neither prolonged use of an optimal nor grey filter improved response time or reduced error scores in a stroke group; these findings persisted with the exclusion of migraine subjects.

The effect of spectral filters on visual search in stroke patients

Visual search impairment can occur following stroke. The utility of optimal spectral filters on visual search in stroke patients has not been considered to date. The present study measured the effect of optimal spectral filters on visual search response time and accuracy, using a task requiring serial processing. A stroke and control cohort undertook the task three times: (i) using an optimally selected spectral filter; (ii) the subjects were randomly assigned to two groups with group 1 using an optimal filter for two weeks, whereas group 2 used a grey filter for two weeks; (iii) the groups were crossed over with group 1 using a grey filter for a further two weeks and group 2 given an optimal filter, before undertaking the task for the final time. Initial use of an optimal spectral filter improved visual search response time but not error scores in the stroke cohort. Prolonged use of neither an optimal nor a grey filter improved response time or reduced error scores. In fact, response times increased with the filter, regardless of its type, for stroke and control subjects; this outcome may be due to contrast reduction or a reflection of task design, given that significant practice effects were noted. © 2013 a Pion publication.

The effect of spectral filters on reading speed and accuracy following stroke

Purpose - The aim of the study was to determine the effect of optimal spectral filters on reading performance following stroke. Methods - Seventeen stroke subjects, aged 43-85, were considered with an age-matched Control Group (n = 17). Subjects undertook the Wilkins Rate of Reading Test on three occasions: (i) using an optimally selected spectral filter; (ii) subjects were randomly assigned to two groups: Group 1 used an optimal filter, whereas Group 2 used a grey filter, for two-weeks. The grey filter had similar photopic reflectance to the optimal filters, intended as a surrogate for a placebo; (iii) the groups were crossed over with Group 1 using a grey filter and Group 2 given an optimal filter, for two weeks, before undertaking the task once more. An increase in reading speed of >5% was considered clinically relevant. Results - Initial use of a spectral filter in the stroke cohort, increased reading speed by ~8%, almost halving error scores, findings not replicated in controls. Prolonged use of an optimal spectral filter increased reading speed by >9% for stroke subjects; errors more than halved. When the same subjects switched to using a grey filter, reading speed reduced by ~4%. A second group of stroke subjects used a grey filter first; reading speed decreased by ~3% but increased by ~4% with an optimal filter, with error scores almost halving. Conclusions - The present study has shown that spectral filters can immediately improve reading speed and accuracy following stroke, whereas prolonged use does not increase these benefits significantly. © 2013 Spanish General Council of Optometry.

Beurling zeta functions, generalised primes, and fractal membranes

We study generalised prime systems P (1 < p(1) <= p(2) <= ..., with p(j) is an element of R tending to infinity) and the associated Beurling zeta function zeta p(s) = Pi(infinity)(j=1)(1 - p(j)(-s))(-1). Under appropriate assumptions, we establish various analytic properties of zeta p(s), including its analytic continuation, and we characterise the existence of a suitable generalised functional equation. In particular, we examine the relationship between a counterpart of the Prime Number Theorem (with error term) and the properties of the analytic continuation of zeta p(s). Further we study 'well-behaved' g-prime systems, namely, systems for which both the prime and integer counting function are asymptotically well-behaved. Finally, we show that there exists a natural correspondence between generalised prime systems and suitable orders on N-2. Some of the above results are relevant to the second author's theory of 'fractal membranes', whose spectral partition functions are given by Beurling-type zeta functions, as well as to joint work of that author and R. Nest on zeta functions attached to quasicrystals.

Infrared filters for space-flight focal plane array applications

Infrared filters and coatings have been employed on many sensing radiometer instruments to measure the thermal emission profiles and concentrations of certian chemical constituents found in planetary atmospheres. The High Resolution Dynamics Limb Sounder ( HIRDLS) is an example of the most recent developments in limb-viewing radiometry by employing a cooled focal plane detector array to provide simultaneous multi-channel monitoring of emission from gas and aerosols over an altitude range between 8 - 70 km. The use of spectrally selective cooled detectors in focal plane arrays has simplified the optical layout of radiometers, greatly reducing the number of components in the optical train. this has inevitably led to increased demands for the enviromnetal durability of the focal plane filters because of the need to cut sub-millimeter sizes, whilst maintaining an optimal spectral performance. Additionally the remaining refractive optical elements require antireflection coatings which must cover the entire spectral range of the focal plane array channels, in this case 6 to 18µm, with a minimum of reflection and absorption. This paper describes the optical layout and spectral design requirements for filteriong in the HIRDLS instrument, and reports progress on the manufacturing and testing of the sub-millimetre sized cooled filters. We also report on the spectral and environmental performance of prototype wideband antireflection coatings which satisfy the requirements above.

QUADRUPOLE CENTRAL TRANSITION NMR SPECTROSCOPY OF QUADRUPOLAR NUCLEI IN SOLUTION

This thesis reports on 17O (I = 5/2) and 59Co (I = 7/2) quadrupole central transition (QCT) NMR studies of three classes of biologically important molecules: glucose, nicotinamide and Vitamin B12 derivatives. Extensive QCT NMR experiments were performed over a wide range of molecular motion by changing solvent viscosity and temperature. 17O-labels were introduced at the 5- and 6-positions respectively: D-[5-17O]-glucose and D-[6-17O]-glucose following the literature method. QCT NMR greatly increased the molecular size limit obtained by ordinary solution NMR. It requires much lower temperatures to get the optimal spectral resolution, which are preferable for biological molecules. In addition, quadrupolar product parameter (PQ) and shielding anisotropy product parameter (PSA) were obtained for hydroxide group and amide group for the first time. For conventional NMR studies of quadrupolar nuclei, only PQ is accessible while QCT NMR obtained both PQ and PSA simultaneously. Our experiments also suggest the resolution of QCT NMR can be even better than that obtained by conventional NMR. We observed for the first time that the second-order quadrupolar interaction becomes a dominant relaxation mechanism under ultraslow motion. All these observations suggest that QCT NMR can become a standard technique for studying quadrupolar nuclei in solution.

Endogenous population subgroups: the best population partition and optimal number of groups

The aim of this paper is to suggest a method to find endogenously the points that group the individuals of a given distribution in k clusters, where k is endogenously determined. These points are the cut-points. Thus, we need to determine a partition of the N individuals into a number k of groups, in such way that individuals in the same group are as alike as possible, but as distinct as possible from individuals in other groups. This method can be applied to endogenously identify k groups in income distributions: possible applications can be poverty

Optimal Code Set Selection and Security Issues in Spectral Phase-Encoded Time Spreading (SPECTS) OCDMA Systems

In this paper, we perform a thorough analysis of a spectral phase-encoded time spreading optical code division multiple access (SPECTS-OCDMA) system based on Walsh-Hadamard (W-H) codes aiming not only at finding optimal code-set selections but also at assessing its loss of security due to crosstalk. We prove that an inadequate choice of codes can make the crosstalk between active users to become large enough so as to cause the data from the user of interest to be detected by other user. The proposed algorithm for code optimization targets code sets that produce minimum bit error rate (BER) among all codes for a specific number of simultaneous users. This methodology allows us to find optimal code sets for any OCDMA system, regardless the code family used and the number of active users. This procedure is crucial for circumventing the unexpected lack of security due to crosstalk. We also show that a SPECTS-OCDMA system based on W-H 32(64) fundamentally limits the number of simultaneous users to 4(8) with no security violation due to crosstalk. More importantly, we prove that only a small fraction of the available code sets is actually immune to crosstalk with acceptable BER (<10(-9)) i.e., approximately 0.5% for W-H 32 with four simultaneous users, and about 1 x 10(-4)% for W-H 64 with eight simultaneous users.

Correlations between optimal temporal width and spectral characteristics of an optical signal in a wavelength-paired CS-RZ transmission with high spectral efficiency

We examine the correlations between the parameters of ultra-narrow off-centred filtering and pulse width on the performance of a wavelength paired Nx40Gbit/s DWDM transmission, consisting of carrier suppressed return-to-zero signal with 0.64 bit/s/Hz (without polarization-division multiplexing) spectral efficiency.

Correlations between optimal temporal width and spectral characteristics of an optical signal in a wavelength-paired CS-RZ transmission with high spectral efficiency

We examine the correlations between the parameters of ultra-narrow off-centred filtering and pulse width on the performance of a wavelength paired Nx40Gbit/s DWDM transmission, consisting of carrier suppressed return-to-zero signal with 0.64 bit/s/Hz (without polarization-division multiplexing) spectral efficiency. © 2004 Optical Society of America.

Segmentation of striatal brain structures from high resolution pet images

Dissertation presented at the Faculty of Science and Technology of the New University of Lisbon in fulfillment of the requirements for the Masters degree in Electrical Engineering and Computers

Optimal discrimination and classification of THz spectra in the wavelet domain

In rapid scan Fourier transform spectrometry, we show that the noise in the wavelet coefficients resulting from the filter bank decomposition of the complex insertion loss function is linearly related to the noise power in the sample interferogram by a noise amplification factor. By maximizing an objective function composed of the power of the wavelet coefficients divided by the noise amplification factor, optimal feature extraction in the wavelet domain is performed. The performance of a classifier based on the output of a filter bank is shown to be considerably better than that of an Euclidean distance classifier in the original spectral domain. An optimization procedure results in a further improvement of the wavelet classifier. The procedure is suitable for enhancing the contrast or classifying spectra acquired by either continuous wave or THz transient spectrometers as well as for increasing the dynamic range of THz imaging systems. (C) 2003 Optical Society of America.

Spectral design and verification of HIRDLS filters and antireflection coatings using an integrated system performance approach

The HIRDLS instrument contains 21 spectral channels spanning a wavelength range from 6 to 18mm. For each of these channels the spectral bandwidth and position are isolated by an interference bandpass filter at 301K placed at an intermediate focal plane of the instrument. A second filter cooled to 65K positioned at the same wavelength but designed with a wider bandwidth is placed directly in front of each cooled detector element to reduce stray radiation from internally reflected in-band signals, and to improve the out-of-band blocking. This paper describes the process of determining the spectral requirements for the two bandpass filters and the antireflection coatings used on the lenses and dewar window of the instrument. This process uses a system throughput performance approach taking the instrument spectral specification as a target. It takes into account the spectral characteristics of the transmissive optical materials, the relative spectral response of the detectors, thermal emission from the instrument, and the predicted atmospheric signal to determine the radiance profile for each channel. Using this design approach an optimal design for the filters can be achieved, minimising the number of layers to improve the in-band transmission and to aid manufacture. The use of this design method also permits the instrument spectral performance to be verified using the measured response from manufactured components. The spectral calculations for an example channel are discussed, together with the spreadsheet calculation method. All the contributions made by the spectrally active components to the resulting instrument channel throughput are identified and presented.

Optimal piecewise locally linear modeling

Associative memory networks such as Radial Basis Functions, Neurofuzzy and Fuzzy Logic used for modelling nonlinear processes suffer from the curse of dimensionality (COD), in that as the input dimension increases the parameterization, computation cost, training data requirements, etc. increase exponentially. Here a new algorithm is introduced for the construction of a Delaunay input space partitioned optimal piecewise locally linear models to overcome the COD as well as generate locally linear models directly amenable to linear control and estimation algorithms. The training of the model is configured as a new mixture of experts network with a new fast decision rule derived using convex set theory. A very fast simulated reannealing (VFSR) algorithm is utilized to search a global optimal solution of the Delaunay input space partition. A benchmark non-linear time series is used to demonstrate the new approach.