Towards a perceptually optimal spectral amplitude estimator for audio signal enhancement

We present a statistical model-based approach to signal enhancement in the case of additive broadband noise. Because broadband noise is localised in neither time nor frequency, its removal is one of the most pervasive and difficult signal enhancement tasks. In order to improve perceived signal quality, we take advantage of human perception and define a best estimate of the original signal in terms of a cost function incorporating perceptual optimality criteria. We derive the resultant signal estimator and implement it in a short-time spectral attenuation framework. Audio examples, references, and further information may be found at http://www-sigproc.eng.cam.ac.uk/~pjw47.

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.

A novel brain partition highlights the modular skeleton shared by structure and function

Elucidating the intricate relationship between brain structure and function, both in healthy and pathological conditions, is a key challenge for modern neuroscience. Recent progress in neuroimaging has helped advance our understanding of this important issue, with diffusion images providing information about structural connectivity (SC) and functional magnetic resonance imaging shedding light on resting state functional connectivity (rsFC). Here, we adopt a systems approach, relying on modular hierarchical clustering, to study together SC and rsFC datasets gathered independently from healthy human subjects. Our novel approach allows us to find a common skeleton shared by structure and function from which a new, optimal, brain partition can be extracted. We describe the emerging common structure-function modules (SFMs) in detail and compare them with commonly employed anatomical or functional parcellations. Our results underline the strong correspondence between brain structure and resting-state dynamics as well as the emerging coherent organization of the human brain.

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.

A unified approach to known and unknown cases of Berge's conjecture

Berge's elegant dipath partition conjecture from 1982 states that in a dipath partition P of the vertex set of a digraph minimizing , there exists a collection Ck of k disjoint independent sets, where each dipath P?P meets exactly min{|P|, k} of the independent sets in C. This conjecture extends Linial's conjecture, the GreeneKleitman Theorem and Dilworth's Theorem for all digraphs. The conjecture is known to be true for acyclic digraphs. For general digraphs, it is known for k=1 by the GallaiMilgram Theorem, for k?? (where ?is the number of vertices in the longest dipath in the graph), by the GallaiRoy Theorem, and when the optimal path partition P contains only dipaths P with |P|?k. Recently, it was proved (Eur J Combin (2007)) for k=2. There was no proof that covers all the known cases of Berge's conjecture. In this article, we give an algorithmic proof of a stronger version of the conjecture for acyclic digraphs, using network flows, which covers all the known cases, except the case k=2, and the new, unknown case, of k=?-1 for all digraphs. So far, there has been no proof that unified all these cases. This proof gives hope for finding a proof for all k.

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.

On optimal message vector length for block single parallel partition algorithm in a three-dimensional ADI solver

It has long been recognized that many direct parallel tridiagonal solvers are only efficient for solving a single tridiagonal equation of large sizes, and they become inefficient when naively used in a three-dimensional ADI solver. In order to improve the parallel efficiency of an ADI solver using a direct parallel solver, we implement the single parallel partition (SPP) algorithm in conjunction with message vectorization, which aggregates several communication messages into one to reduce the communication costs. The measured performances show that the longest allowable message vector length (MVL) is not necessarily the best choice. To understand this observation and optimize the performance, we propose an improved model that takes the cache effect into consideration. The optimal MVL for achieving the best performance is shown to depend on number of processors and grid sizes. Similar dependence of the optimal MVL is also found for the popular block pipelined method.

The effect of sub-optimal control and the spectral wave climate on the performance of wave energy converter arrays

A linear hydrodynamic model is used to assess the sensitivity of the performance of a wave energy converter (WEC) array to control parameters. It is found that WEC arrays have a much smaller tolerance to imprecision of the control parameters than isolated WECs and that the increase in power capture of WEC arrays is only achieved with larger amplitudes of motion of the individual WECs. The WEC array radiation pattern is found to provide useful insight into the array hydrodynamics. The linear hydrodynamic model is used, together with the wave climate at the European Marine Energy Centre (EMEC), to assess the maximum annual average power capture of a WEC array. It is found that the maximum annual average power capture is significantly reduced compared to the maximum power capture for regular waves and that the optimum array configuration is also significantly modified. It is concluded that the optimum configuration of a WEC array will be as much influenced by factors such as mooring layout, device access and power smoothing as it is by the theoretical optimum hydrodynamic configuration. © 2009 Elsevier Ltd.

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.