Evidence of the heterogeneous market hypothesis using wavelet multi -resolution analysis

In finance literature many economic theories and models have been proposed to explain and estimate the relationship between risk and return. Assuming risk averseness and rational behavior on part of the investor, the models are developed which are supposed to help in forming efficient portfolios that either maximize (minimize) the expected rate of return (risk) for a given level of risk (rates of return). One of the most used models to form these efficient portfolios is the Sharpe's Capital Asset Pricing Model (CAPM). In the development of this model it is assumed that the investors have homogeneous expectations about the future probability distribution of the rates of return. That is, every investor assumes the same values of the parameters of the probability distribution. Likewise financial volatility homogeneity is commonly assumed, where volatility is taken as investment risk which is usually measured by the variance of the rates of return. Typically the square root of the variance is used to define financial volatility, furthermore it is also often assumed that the data generating process is made of independent and identically distributed random variables. This again implies that financial volatility is measured from homogeneous time series with stationary parameters. In this dissertation, we investigate the assumptions of homogeneity of market agents and provide evidence for the case of heterogeneity in market participants' information, objectives, and expectations about the parameters of the probability distribution of prices as given by the differences in the empirical distributions corresponding to different time scales, which in this study are associated with different classes of investors, as well as demonstrate that statistical properties of the underlying data generating processes including the volatility in the rates of return are quite heterogeneous. In other words, we provide empirical evidence against the traditional views about homogeneity using non-parametric wavelet analysis on trading data, The results show heterogeneity of financial volatility at different time scales, and time-scale is one of the most important aspects in which trading behavior differs. In fact we conclude that heterogeneity as posited by the Heterogeneous Markets Hypothesis is the norm and not the exception.

3D TerraFly: Quality of service management for online interactive 3D geographic information system

3D geographic information system (GIS) is data and computation intensive in nature. Internet users are usually equipped with low-end personal computers and network connections of limited bandwidth. Data reduction and performance optimization techniques are of critical importance in quality of service (QoS) management for online 3D GIS. In this research, QoS management issues regarding distributed 3D GIS presentation were studied to develop 3D TerraFly, an interactive 3D GIS that supports high quality online terrain visualization and navigation. ^ To tackle the QoS management challenges, multi-resolution rendering model, adaptive level of detail (LOD) control and mesh simplification algorithms were proposed to effectively reduce the terrain model complexity. The rendering model is adaptively decomposed into sub-regions of up-to-three detail levels according to viewing distance and other dynamic quality measurements. The mesh simplification algorithm was designed as a hybrid algorithm that combines edge straightening and quad-tree compression to reduce the mesh complexity by removing geometrically redundant vertices. The main advantage of this mesh simplification algorithm is that grid mesh can be directly processed in parallel without triangulation overhead. Algorithms facilitating remote accessing and distributed processing of volumetric GIS data, such as data replication, directory service, request scheduling, predictive data retrieving and caching were also proposed. ^ A prototype of the proposed 3D TerraFly implemented in this research demonstrates the effectiveness of our proposed QoS management framework in handling interactive online 3D GIS. The system implementation details and future directions of this research are also addressed in this thesis. ^

Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Rigid and Non-rigid Point-based Medical Image Registration

The primary goal of this dissertation is to develop point-based rigid and non-rigid image registration methods that have better accuracy than existing methods. We first present point-based PoIRe, which provides the framework for point-based global rigid registrations. It allows a choice of different search strategies including (a) branch-and-bound, (b) probabilistic hill-climbing, and (c) a novel hybrid method that takes advantage of the best characteristics of the other two methods. We use a robust similarity measure that is insensitive to noise, which is often introduced during feature extraction. We show the robustness of PoIRe using it to register images obtained with an electronic portal imaging device (EPID), which have large amounts of scatter and low contrast. To evaluate PoIRe we used (a) simulated images and (b) images with fiducial markers; PoIRe was extensively tested with 2D EPID images and images generated by 3D Computer Tomography (CT) and Magnetic Resonance (MR) images. PoIRe was also evaluated using benchmark data sets from the blind retrospective evaluation project (RIRE). We show that PoIRe is better than existing methods such as Iterative Closest Point (ICP) and methods based on mutual information. We also present a novel point-based local non-rigid shape registration algorithm. We extend the robust similarity measure used in PoIRe to non-rigid registrations adapting it to a free form deformation (FFD) model and making it robust to local minima, which is a drawback common to existing non-rigid point-based methods. For non-rigid registrations we show that it performs better than existing methods and that is less sensitive to starting conditions. We test our non-rigid registration method using available benchmark data sets for shape registration. Finally, we also explore the extraction of features invariant to changes in perspective and illumination, and explore how they can help improve the accuracy of multi-modal registration. For multimodal registration of EPID-DRR images we present a method based on a local descriptor defined by a vector of complex responses to a circular Gabor filter.

A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as “histogram binning” inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. ^ Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. ^ The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. ^ These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. ^ In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation. ^

Foundational forensic techniques for cellular and ad hoc multi-hop networks

The Internet has become an integral part of our nation’s critical socio-economic infrastructure. With its heightened use and growing complexity however, organizations are at greater risk of cyber crimes. To aid in the investigation of crimes committed on or via the Internet, a network forensics analysis tool pulls together needed digital evidence. It provides a platform for performing deep network analysis by capturing, recording and analyzing network events to find out the source of a security attack or other information security incidents. Existing network forensics work has been mostly focused on the Internet and fixed networks. But the exponential growth and use of wireless technologies, coupled with their unprecedented characteristics, necessitates the development of new network forensic analysis tools. This dissertation fostered the emergence of a new research field in cellular and ad-hoc network forensics. It was one of the first works to identify this problem and offer fundamental techniques and tools that laid the groundwork for future research. In particular, it introduced novel methods to record network incidents and report logged incidents. For recording incidents, location is considered essential to documenting network incidents. However, in network topology spaces, location cannot be measured due to absence of a ‘distance metric’. Therefore, a novel solution was proposed to label locations of nodes within network topology spaces, and then to authenticate the identity of nodes in ad hoc environments. For reporting logged incidents, a novel technique based on Distributed Hash Tables (DHT) was adopted. Although the direct use of DHTs for reporting logged incidents would result in an uncontrollably recursive traffic, a new mechanism was introduced that overcome this recursive process. These logging and reporting techniques aided forensics over cellular and ad-hoc networks, which in turn increased their ability to track and trace attacks to their source. These techniques were a starting point for further research and development that would result in equipping future ad hoc networks with forensic components to complement existing security mechanisms.

Multi-temporal monitoring of wetland water levels in the Florida Everglades using interferometric synthetic aperture radar (InSAR)

Interferometric synthetic aperture radar (InSAR) techniques can successfully detect phase variations related to the water level changes in wetlands and produce spatially detailed high-resolution maps of water level changes. Despite the vast details, the usefulness of the wetland InSAR observations is rather limited, because hydrologists and water resources managers need information on absolute water level values and not on relative water level changes. We present an InSAR technique called Small Temporal Baseline Subset (STBAS) for monitoring absolute water level time series using radar interferograms acquired successively over wetlands. The method uses stage (water level) observation for calibrating the relative InSAR observations and tying them to the stage's vertical datum. We tested the STBAS technique with two-year long Radarsat-1 data acquired during 2006–2008 over the Water Conservation Area 1 (WCA1) in the Everglades wetlands, south Florida (USA). The InSAR-derived water level data were calibrated using 13 stage stations located in the study area to generate 28 successive high spatial resolution maps (50 m pixel resolution) of absolute water levels. We evaluate the quality of the STBAS technique using a root mean square error (RMSE) criterion of the difference between InSAR observations and stage measurements. The average RMSE is 6.6 cm, which provides an uncertainty estimation of the STBAS technique to monitor absolute water levels. About half of the uncertainties are attributed to the accuracy of the InSAR technique to detect relative water levels. The other half reflects uncertainties derived from tying the relative levels to the stage stations' datum.

Foundational Forensic Techniques for Cellular and Ad Hoc Multi-hop Networks

The Internet has become an integral part of our nation's critical socio-economic infrastructure. With its heightened use and growing complexity however, organizations are at greater risk of cyber crimes. To aid in the investigation of crimes committed on or via the Internet, a network forensics analysis tool pulls together needed digital evidence. It provides a platform for performing deep network analysis by capturing, recording and analyzing network events to find out the source of a security attack or other information security incidents. Existing network forensics work has been mostly focused on the Internet and fixed networks. But the exponential growth and use of wireless technologies, coupled with their unprecedented characteristics, necessitates the development of new network forensic analysis tools. This dissertation fostered the emergence of a new research field in cellular and ad-hoc network forensics. It was one of the first works to identify this problem and offer fundamental techniques and tools that laid the groundwork for future research. In particular, it introduced novel methods to record network incidents and report logged incidents. For recording incidents, location is considered essential to documenting network incidents. However, in network topology spaces, location cannot be measured due to absence of a 'distance metric'. Therefore, a novel solution was proposed to label locations of nodes within network topology spaces, and then to authenticate the identity of nodes in ad hoc environments. For reporting logged incidents, a novel technique based on Distributed Hash Tables (DHT) was adopted. Although the direct use of DHTs for reporting logged incidents would result in an uncontrollably recursive traffic, a new mechanism was introduced that overcome this recursive process. These logging and reporting techniques aided forensics over cellular and ad-hoc networks, which in turn increased their ability to track and trace attacks to their source. These techniques were a starting point for further research and development that would result in equipping future ad hoc networks with forensic components to complement existing security mechanisms.

A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as "histogram binning" inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation.