Our research mainly consisted by two parts. First, apply p-norm error measure instead of 1-norm measure in a linear programming discrimination, which generates a linear hyperplane to classify two data sets. With this p-norm error measure, the errors generated by the classifier are not treated equally but rather biased. For 1, the bigger one error is, the more weight it obtains in the objective function. Second, investigation is conducted on a psychophysiological data set. Various methods are tested on this multi-dimensional time-series data set, from the linear programming method to the neural network method. With the help of DFT, The data is able to be transferred from the time domain to the frequency domain, in which the data set has interesting patterns

Phase Space Reconstruction is a method that allows to reconstruct the phase space of a system using only an one dimensional time series as input. It can be used for calculating Lyapunov-exponents and detecting chaos. It helps to understand complex dynamics and their behavior. And it can reproduce datasets which were not measured. There are many different methods which produce correct reconstructions such as time-delay, Hilbert-transformation, derivation and integration. The most used one is time-delay but all methods have special properties which are useful in different situations. Hence, every reconstruction method has some situations where it is the best choice. Looking at all these different methods the questions are: Why can all these different looking methods be used for the same purpose? Is there any connection between all these functions? The answer is found in the frequency domain : Performing a Fourier transformation all these methods getting a similar shape: Every presented reconstruction method can be described as a multiplication in the frequency domain with a frequency-depending reconstruction function. This structure is also known as a filter. From this point of view every reconstructed dimension can be seen as a filtered version of the measured time series. It contains the original data but applies just a new focus: Some parts are amplified and other parts are reduced. Furthermore I show, that not every function can be used for reconstruction. In the thesis three characteristics are identified, which are mandatory for the reconstruction function. Under consideration of these restrictions one gets a whole bunch of new reconstruction functions. So it is possible to reduce noise within the reconstruction process itself or to use some advantages of already known reconstructions methods while suppressing unwanted characteristics of it. / Attraktorrekonstruktion („Phase Space Reconstruction“) ist eine Technik, die es ermöglicht, aus einer einzelnen Zeitreihe den vollständigen Phasenraum eines Systems zu rekonstruieren und somit Rückschlüsse auf topologische Eigenschaften dieses dynamischen Systems zu ziehen. Sie findet Verwendung in der Bestimmung von Lyapunov-Exponenten und zur Reproduktion von unbeobachteten Systemgrößen. Es gibt viele verschiedene Methoden zur Attraktorrekonstruktion wie z.B. die Time-Delay-Methode or Rekonstruktion durch Ableitung, Integration oder mithilfe einer Hilbert-Transformation. Zumeist wird der Time-Delay-Ansatz verwendet, es gibt jedoch auch diverse Problemstellungen, in welchen die alternativen Methoden bessere Ergebnisse liefern. Die Kernfragen, die beim Vergleich dieser Methoden entsteht, sind: Wie kommt es, dass alle Ansätze, trotz ihrer teilweise sehr unterschiedlichen Struktur, denselben Zweck erfüllen? Gibt es Übereinstimmungen zwischen all diesen Methoden? Die Antwort lässt sich im Frequenzraum finden: Nach einer Fourier-Transformation besitzen alle genannten Methoden plötzlich eine sehr ähnliche Struktur. Jede Methode transformiert sich im Frequenzraum zu einer einfachen Multiplikation des Eingangssignals mit einer frequenzabhängigen Rekonstruktionsfunktion. Diese Struktur ist in der Datenanalyse auch bekannt als Filter. Aus dieser Perspektive lässt sich jede Rekonstruktionsdimension als gefilterte Zeitreihe der ursprünglichen Zeitreihe interpretieren: Sie enthält den Originaldatensatz, allerdings mit einem verschobenen Fokus: Einige Eigenschaften der Originalzeitreihe werden unterdrückt, während andere Teile verstärkt wiedergegeben werden. Des weiteren zeige ich in der Diplomarbeit, dass nicht jede beliebige Funktion im Frequenzraum zur Rekonstruktion verwendet werden kann. Ich stelle drei Eigenschaften vor, welche jede Rekonstruktionsfunktion erfüllen muss. Unter Beachtung dieser Bedingungen ergeben sich nun diverse Möglichkeiten für neue Rekonstruktionsfunktionen. So ist es z.B. möglich gleichzeitig mit der Rekonstruktion das Ursprungssignal auch zu filtern, oder man kann bereits bestehende Rekonstruktionsfunktionen so abwandeln, dass unerwünschte Nebeneffekte der Rekonstruktion abgemildert oder gar ganz unterdrückt werden.

Theoretical and experimental studies of real-time interrogation of fiber Bragg grating (FBG) sensors based on chirped pulse compression with increased interrogation resolution and signal-to-noise ratio are presented. Two interrogation systems are proposed in this thesis. In the first interrogation system, a linearly chirped FBG (LCFBG) is employed as the sensing element. By incorporating the LCFBG in an optical interferometer as the sensor encoding system, employing wavelength-to-time mapping and chirped pulse compression technique, the correlation of output microwave waveform with a chirped reference waveform would provide an interrogation result with high speed and high resolution. The proposed system can provide an interrogation resolution as high as 0.25 μ at a speed of 48.6 MHz. The second interrogation system is designed to achieve simultaneous measurement of strain and temperature. In this system, a high-birefringence LCFBG (Hi-Bi LCFBG) is employed as a sensing element.

Theoretical and experimental studies of real-time interrogation of fiber Bragg grating (FBG) sensors based on chirped pulse compression with increased interrogation resolution and signal-to-noise ratio are presented. Two interrogation systems are proposed in this thesis. In the first interrogation system, a linearly chirped FBG (LCFBG) is employed as the sensing element. By incorporating the LCFBG in an optical interferometer as the sensor encoding system, employing wavelength-to-time mapping and chirped pulse compression technique, the correlation of output microwave waveform with a chirped reference waveform would provide an interrogation result with high speed and high resolution. The proposed system can provide an interrogation resolution as high as 0.25 μ at a speed of 48.6 MHz. The second interrogation system is designed to achieve simultaneous measurement of strain and temperature. In this system, a high-birefringence LCFBG (Hi-Bi LCFBG) is employed as a sensing element.

Invariant object recognition is maybe the most basic and fundamental property of our visual system. It is the basis of many other cognitive tasks, like motor actions and social interactions. Hence, the theoretical understanding and modeling of invariant object recognition is one of the central problems in computational neuroscience. Indeed, object recognition consists of two different tasks: classification and identification. The focus of this thesis is on object identification under the basic geometrical transformations shift, scaling, and rotation. The visual system can perform shift, size, and rotation invariant object identification. This thesis consists of two parts. In the first part, we present and investigate the VisNet model proposed by Rolls. The generalization problems of VisNet triggered our development of a new neural network model for invariant object identification. Starting point for an improved generalization behavior is the search for an operation that extracts images features that are invariant under shifts, rotations, and scalings. Extracting invariant features guarantees that an object seen once in a specific pose can be identified in any pose. We present and investigate our model in the second part of this thesis.

In this paper we study the error behavior of the well known fast Fourier transform for nonequispaced data (NFFT) with respect to the L2-norm. We compare the arising errors for different window functions and show that the accuracy of the algorithm can be significantly improved by modifying the shape of the window function. Based on the considered error estimates for different window functions we are able to state an easy and efficient method to tune the involved parameters automatically. The numerical examples show that the optimal parameters depend on the given Fourier coefficients, which are assumed not to be of a random structure or roughly of the same magnitude but rather subject to a certain decrease.

Theoretical and experimental studies of real-time interrogation of fiber Bragg grating (FBG) sensors based on chirped pulse compression with increased interrogation resolution and signal-to-noise ratio are presented. Two interrogation systems are proposed in this thesis. In the first interrogation system, a linearly chirped FBG (LCFBG) is employed as the sensing element. By incorporating the LCFBG in an optical interferometer as the sensor encoding system, employing wavelength-to-time mapping and chirped pulse compression technique, the correlation of output microwave waveform with a chirped reference waveform would provide an interrogation result with high speed and high resolution. The proposed system can provide an interrogation resolution as high as 0.25 μ at a speed of 48.6 MHz. The second interrogation system is designed to achieve simultaneous measurement of strain and temperature. In this system, a high-birefringence LCFBG (Hi-Bi LCFBG) is employed as a sensing element.

Zugl.: Siegen, Univ., Diss., 2009

Pyroelectric activity is exhibited by materials which possess a spontaneous temperature-dependent electric polarisation. These materials generate a current as their temperature is changed. Many classes of organic materials exhibit pyroelectric activity but only if processed in such a way that a non-centrosymmetric arrangement of dipole results. When deposited as alternate layers by the Langmuir-Blodgett (LB) technique a macroscopically polar assembly is formed. To date, the best performance has been achieved by alternately depositing two materials, one containing acid groups and the other containing amine groups. Calixarenes are one family of materials which are particularly good vehicles for the acid and amine groups. Alternate layer LB films of acid- and amine-substituted calixarenes have high pyroelectric coefficients and form extremely robust films. Fourier transform infrared (FTIR) spectroscopy is a useful tool in examining the properties of thin film samples. Using the FTIR techniques of attenuated total reflection (ATR) and reflection-absorption infrared spectroscopy (RAIRS) it is possible to study the behaviour of the acid and amine groups within the pyroelectric samples. This thesis describes the pyroelectric properties of a series of calix[8]arenes. The dependence of the pyroelectric coefficient on temperature, film thickness and substituent chain length is analysed. The infrared spectra show that the acid and amine groups interact by proton transfer but also that the remaining acid groups form either facing dimers with the amine or sideways dimers between themselves. The spectra do not change with temperature. This demonstrates that the films are thermally stable. Additionally, this invariance shows that the pyroelectric activity in these films does not arise from a change in the proton transfer as has been previously postulated. Theoretical calculations undertaken predict that the source of the dipole change required for the level of pyroelectric activity seen is likely to be a change in distance between the acid and amine groups. Further observations, quantitatively examined by curve fitting techniques, show that the greater the number of proton-transferred pairs, the lower the pyroelectric coefficient. Thus, only the temperature-dependent separation of the acid and amine pairs which have not undergone proton transfer is responsible for the pyroelectric activity in these systems.

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