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<p>A common problem of hearing aids is whistling caused by feedback from the loudspeaker back to the microphone. A method of reducing the negative effects, caused by the feedback, is called feedback cancellation. A variant of feedback cancellation uses a probe signal, which is applied to the speaker of the hearing aid and is used to continuously estimate the feedback. Oticon A/S has suggested a master's thesis with the purpose of designing and evaluating an algorithm generating a probe signal for feedback cancellation systems. The challenge was to find an inaudible probe signal with as much energy as possible. </p><p>Two approaches have been investigated for generating a probe signal. In the first approach the psychoacoustic principle of masking was used to estimate how much noise that could be added to a signal without being heard. Psychoacoustic models, including masking, are used in MPEG (Moving Pictures Expert Group) audio coding and one of these models has been examined in the thesis. In the second approach a standard LPC (Linear Prediction Coding) algorithm was used. In both the MPEG and the LPC approach, warped signal processing has been utilized improving the methods. </p><p>A listening test was performed, evaluating the methods generating the probe signal. The purpose of the test was to determine whether the noise, generated using the MPEG and LPC approach, was inaudible. A hearing aid system with feedback cancellation, using the probe signal, was also simulated. The listening test showed that the noise (probe signal) had to be lowered, much more than expected, to be inaudible. As a consequence, shown in the simulations, the feedback cancellation system, using the probe signal, had trouble identifying the feedback of the hearing aid.</p>

A common problem of hearing aids is whistling caused by feedback from the loudspeaker back to the microphone. A method of reducing the negative effects, caused by the feedback, is called feedback cancellation. A variant of feedback cancellation uses a probe signal, which is applied to the speaker of the hearing aid and is used to continuously estimate the feedback. Oticon A/S has suggested a master's thesis with the purpose of designing and evaluating an algorithm generating a probe signal for feedback cancellation systems. The challenge was to find an inaudible probe signal with as much energy as possible. Two approaches have been investigated for generating a probe signal. In the first approach the psychoacoustic principle of masking was used to estimate how much noise that could be added to a signal without being heard. Psychoacoustic models, including masking, are used in MPEG (Moving Pictures Expert Group) audio coding and one of these models has been examined in the thesis. In the second approach a standard LPC (Linear Prediction Coding) algorithm was used. In both the MPEG and the LPC approach, warped signal processing has been utilized improving the methods. A listening test was performed, evaluating the methods generating the probe signal. The purpose of the test was to determine whether the noise, generated using the MPEG and LPC approach, was inaudible. A hearing aid system with feedback cancellation, using the probe signal, was also simulated. The listening test showed that the noise (probe signal) had to be lowered, much more than expected, to be inaudible. As a consequence, shown in the simulations, the feedback cancellation system, using the probe signal, had trouble identifying the feedback of the hearing aid.

Whilst the underlying mechanisms of atmospheric turbulence are complex, the observed effects on imaging can be described in simpler terms. In this thesis, I address the effects seen as geometric distortions in anisoplanatic imaging and propose new digital restorations techniques that are real-time capable and predictive. The anisoplanatic problem arises in wide-field telescopic imaging and in new ventures of astronomy such as giant telescopes that process wide-field imagery. The methods proposed here, both digital and digital-optical hybrid, remove the position dependent distortions as a precursor to image analysis. Previous existing digital restoration techniques have used a prototype formed by averaging an image time sequence for image registration where valuable high frequencies information is lost due to the low-pass filtering effect of averaging. The proposed techniques are capable of using any arbitrary frame in the sequence as prototype, thus circumventing the low pass filtering effect and also allowing real-time implementation. Furthermore, these techniques are made predictive by the use of Kalman filtering. The predictive capabilities of these techniques open a new path to the combination of digital processing and adaptive optics that can result in hybrid systems. The key to adoption of hybrid systems is to reduce the complexity and expense of the optics and couple this with digital processing prediction. To this end I also propose a new type of inexpensive and fast piezoelectric deformable mirror based on the vibration modes of circular PVDF membranes that exhibit striking similarities to Zernike polynomials. It requires only two electrodes for actuation and a very simple driving signal generator, therefore constituting an inexpensive and viable alternative to existing deformable mirrors. With the emergence of multi-conjugate adaptive optics (MCAO) and multiobject adaptive optics (MOAO) in astronomy, and the more demanding correction required for long range surveillance imaging, this inexpensive deformable mirror and the real-time capable digital algorithms are promising building blocks for a hybrid solution to the anisoplanatic imaging problem.

Durant la passada d`ecada, els models de dimensions extra corbades han estat estudiats com a candidats per a completar el Model Est`andard (ME) de la f´ısica de part´ıcules. En aquesta tesi estudiarem una s`erie d’aspectes dels models amb una dimensi´o extra corbada; en particular, la possibilitat de generalitzar la ben coneguda soluci´o de Randall-Sundrum (RS), la qual es basa en la m`etrica Anti-de Sitter (AdS). Primer, discutim la construcci´o dels models de soft-wall, que s´on una modificaci ´o de RS on la brana infraroja ha sigut substitu¨ıda per una singularitat nua a la m`etrica. Donem receptes per a construir models consistents d’aquests tipus i estudiem com la longitud de la dimensi´o extra pot ser estabilitzada. Tamb´e estudiem l’espectre de les fluctuacions que apareixen en els models de soft-wall, i trobem que podem obtenir des d’un espectre continu a partir d’una certa massa fins a un espectre discret amb un espaiament variable. Discutim les possibles aplicacions dels models de soft-wall, i finalment presentem un model concret on es pot generar una jerarquia ultravioleta/infraroja prou gran sense necessitat de cap ajust fi. Despr´es, retornem a la construcci´o original amb dues branes per tal d’estudiar com la simetria electrod`ebil pot ser trencada en models amb m`etriques generalitzades quan el bos´o de Higgs es propaga a l’engr´os de la dimensi´o extra. Veiem com les cotes sobre l’escala dels modes de Kaluza-Klein (KK), que apareixen a causa dels observables electrod`ebils de precisi´o, poden ser redu¨ıdes quan el Higgs est`a localitzat a prop de la brana infraroja. Apliquem els nostres resultats a una extensi´o m´ınima del ME en 5D, i considerem la geometria AdS i una deformaci´o d’aquesta inspirada pels models de soft-wall. Trobemque la geometria deformada redueix enormement les cotes sobre l’escala de KK, fins al punt en qu`e els estats de KK es poden trobar dins del rang de l’LHC i el problema de la petita jerarquia pot ser eliminat sense requerir la introducci´o de cap simetria custodial. Finalment, estudiem la propagaci´o de tots els fermions del ME al llarg de la dimensi´o extra, la qual cosa fem servir per tractar el problema del sabor en el ME. Trobem expressions generals i expl´ıcites per als observables electrod`ebils oblics i no oblics, aix´ı com per als operadors que violen sabor i la simetria CP. Apliquem aquest resultat al model RS i al model amb geometria deformada, per la qual cosa fem un estudi estad´ıstic a partir d’un conjunt aleatori d’acoblaments de Yukawa en 5D. La comparaci´o de les prediccions amb les dades experimentals actuals mostren una millora de les cotes en el nostre model en comparaci´o amb RS. / Models of warped extra-dimensions have been studied over the last decade as candidates to complete the Standard Model (SM) of particle physics, for they provide a natural mechanism to address its hierarchy problem. In this thesis we study a number of aspects of the five-dimensional warped models, and in particular the possibility of generalizing the well-known Randall-Sundrum (RS) solution, which is based on the Anti-de Sitter metric (AdS). We first discuss on the construction of soft-wall models, which are a modification of RS where the infrared brane is substituted by a naked singularity in the metric. We provide recipes for constructing consistent models of this kind and address the issue of how the length of the extra dimension can be stabilized. We also discuss on the spectrum of fluctuations that arise in soft-wall models, finding that it can range from a continuous spectrum above a mass gap to a discrete spectrum with a variable level spacing. We discuss on the possible applications of soft-wall models, and finally present a concrete model where a large ultraviolet/infrared hierarchy can be generated without any fine-tuning. Next, we return to the original two-brane setup to study how the electroweak symmetry can be broken in warped models with generalized metrics when the Higgs boson propagates in the bulk. We show how the bounds on the Kaluza-Klein (KK) scale that arise from electroweak precision observables can be alleviated when the Higgs is localized towards the infrared brane. We apply our results to a minimal 5D extension of the SM and consider the AdS geometry and a deformation of it inspired by soft-walls. We find that the deformed geometry greatly reduces the bounds on the KK scale, to a point where the KK states can be within the range of the LHC and the little hierarchy problem can be removed without requiring the introduction of any custodial symmetry. Finally, we study the propagation of all SM fermions in the bulk of the extra dimension, which we use to address the flavor puzzle of the SM. We find general explicit expressions for oblique and non-oblique electroweak observables, as well as flavor and CP violating operators. We apply these results to the RS model and the model with deformed geometry, for which we perform a statistical analysis departing from a random set of 5D Yukawa couplings. The comparison of the predictions with the current experimental data exhibits an improvement of the bounds in our model with respect to the RS model.

SILVA, Marcos Raineri da Silva.Variedades quasi-Einstein completas e métricas críticas do funcional volume em variedades compactas com bordo. 2016. 69 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2016. / Submitted by Rocilda Sales (rocilda@ufc.br) on 2016-11-18T13:40:56Z No. of bitstreams: 1 2016_tese_mrsilva.pdf: 676064 bytes, checksum: b3c50c90fe4265ade898b8c259d3882c (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-11-21T13:51:06Z (GMT) No. of bitstreams: 1 2016_tese_mrsilva.pdf: 676064 bytes, checksum: b3c50c90fe4265ade898b8c259d3882c (MD5) / Made available in DSpace on 2016-11-21T13:51:06Z (GMT). No. of bitstreams: 1 2016_tese_mrsilva.pdf: 676064 bytes, checksum: b3c50c90fe4265ade898b8c259d3882c (MD5) Previous issue date: 2016 / The purpose of this work is to study quasi-Einstein manifolds and Miao-Tam critical metrics. In the first part, we will study the structure at infinity of a complete non-compact quasi-Einstein manifold. In particular, we show that if M is the basis of a warped product Ricci-flat then M is connected at infinity. When M is a quasi-Einstein manifold with λ < 0 there are examples showing that such a result is not true. In this case, we show that M is f -non-parabolic and, under a certain hypothesis on the scalar curvature, M has only one f -non-parabolic end. Furthermore, we obtain two estimates for the volume of the geodesic balls of M. Next, we show that a Bach-flat non-compact quasi-Einstein manifold with λ= 0 and positive Ricci curvature must be isometric to a warped product metric g = dt2+ψ2(t)gL, where gL is an Einstein metric. In the second part, we will study the critical metrics of the functional volume restricted to the set of metrics with constant scalar curvature and boundary prescribed metric on a compact manifold. We obtain a sharp upper bound for the area of the boundary of a Miao-Tam critical metric (M3;g) with non-negative scalar curvature. Moreover, we show that the equality holds if and only if (M3;g) is isometric to a geodesic ball in simply connected space form R3 or S3. Finally, we get a type-Bochner formula for a 3-dimensional Miao-Tam critical metric, which allows us to get the same rigid result provided that/ Ric/ ≤R6 . / O objetivo do trabalho é estudar as variedades quasi-Einstein e métricas críticas de Miao-Tam. Na primeira parte, estudamos a estrutura no infinito de uma variedade quasi-Einstein completa e não-compacta. Em particular, mostramos que se M é a base de um produto warped Ricci-flat, então M é conexa no infinito. Quando M é uma variedade quasi-Einstein com λ < 0 existem exemplos que mostram que tal resultado não é verdadeiro. Neste caso, mostramos que M é f -não-parabólica e sobre uma determinada hipótese sobre a curvatura escalar, que M tem apenas um fim f-não-parabólico. Além disso, obtemos duas estimativas para o volume das bolas geodésicas de M. Em seguida, mostramos que variedades quasi-Einstein Bach-flat não-compactas com λ = 0 e curvatura de Ricci positiva são isométricas a uma métrica produto warped g = dt2+ψ2(t)gL, onde gL é uma métrica Einstein. Na segunda parte do trabalho, estudamos as métricas críticas do funcional volume restrito ao conjunto das métricas com curvatura escalar constante e métrica de bordo prescrita em uma variedade compacta. Obtemos uma estimativa superior sharp para a área do bordo de uma métrica crítica de Miao-Tam (M3;g) com curvatura escalar não-negativa. Além disso, vale a igualdade se, e somente se, (M3;g) for isométrica a uma bola geodésica em espaço forma simplesmente conexo R3 ou S3. Por último, obtemos uma fórmula tipo-Bochner para uma métrica crítica de Miao-Tam tridimensional, a qual nos permite obter o mesmo resultado de rigidez desde que / Ric/ ≤R6. .

Indiana University-Purdue University Indianapolis (IUPUI) / In the present work, we consider a class of Finsler metrics using the warped product notion introduced by B. Chen, Z. Shen and L. Zhao (2018), with another “warping”, one that is consistent with the form of metrics modeling static spacetimes and simplified by spherical symmetry over spatial coordinates, which emerged from the Schwarzschild metric in isotropic coordinates. We will give the PDE characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with Lorentz signature. For the latter, the 4-dimensional metrics may also be studied as Finsler spacetimes.

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