Piercing problems arise often in facility location, which is a well-studied area of computational geometry. The general form of the piercing problem discussed in this dissertation asks for the minimum number of facilities for a set of given rectangular demand regions such that each region has at least one facility located within it. It has been shown that even if all regions are uniform sized squares, the problem is NP-hard. Therefore we concentrate on approximation algorithms for the problem. As the known approximation ratio for arbitrarily sized rectangles is poor, we restrict our effort to designing approximation algorithms for unit-height rectangles. Our e-approximation scheme requires <I>n</I>^{<I>O</I>(1/&epsilon;²)} time. We also consider the problem with restrictions like bounding the depth of a point and the width of the rectangles. The approximation schemes for these two cases take <I>n</I>^{<I>O</I>(1/&epsilon;)} time. We also show how to maintain a factor 2 approximation of the piercing set in <I>O</I>(log <I>n</I>) amortized time in an insertion-only scenario.

Currently, citation indexes used by digital libraries are very limited. They only provide raw citation counts and link scientific articles through their citations. There are more than one type of citations, but citation indexes treat all citations equally. One way to improve citation indexes is to determine the types of citations in scientific articles (background, support, perfunctory reference, etc.) This will enable researchers to query citation indexes more efficiently by locating articles grouped by citation types. For example, it can enable a researcher to locate all background material needed to understand a specific article by locating all "background" citations. Many classification schemes currently exist. However, manual annotation of all existing digital documents is infeasible because of the sheer magnitude of the digital content, which brings about the need for automating the annotating process, but not much research has been done in the area. One of the reasons preventing researchers from researching automated citation classification is the lack on annotated corpora that they can use. This thesis explores automated citation classification. We make several contributions to the field of citation classification. We present a new citation scheme that is easier to work with than most. Also, we present a document acquisition and citation annotation tool that helps with the development of annotated citation corpora. And finally, we present some experiments with automating citation classification.

In this work we formalize a new natural objective (or cost) function for bi-clustering - Monochromatic bi-clustering. Our objective function is suitable for detecting meaningful homogenous clusters based on categorical valued input matrices. Such problems have arisen recently in systems biology where researchers have inferred functional classifications of biological agents based on their pairwise interactions. We analyze the computational complexity of the resulting optimization problems. We show that finding optimal solutions is NP-hard and complement this result by introducing a polynomial time approximation algorithm for this bi-clustering task. This is the first positive approximation guarantee for bi-clustering algorithms. We also show that bi-clustering with our objective function can be viewed as a generalization of correlation clustering.

Time-resolved fluorescence was applied to linear and branched pyrene-labelled macromolecules to study their internal dynamics. The linear macromolecules consisted of two series of pyrene-labelled poly(N-isopropylacrylamide)s where the polymer was either end-labelled (Py2-PNIPAM-Y where Y represents the molecular weight of the polymer and equals 6, 8, 14, 25, and 45 kDa) or randomly labelled (Py-PNIPAM-X% where X represents the pyrene content and is equal to 0.1, 2, 3, 4, 5, and 6 mol%) with pyrene. Four dendrimer generations based on a bis(hydroxymethyl)propionic acid backbone represented the branched macromolecules where the terminal sites were labelled with pyrene (PyX-GY-COOH where X represents the number of pyrene units incorporated into the Y`th generation dendrimer). A polystyrene-dendrimer hybrid was also synthesized (PyX-GY-PS). The fluorescence decays of the Py2-PNIPAM-Y and Py-PNIPAM-X% samples were acquired in solvents of varying viscosity and were analyzed with the Birks Scheme and the Fluorescence Blob Model (FBM) to yield the excimer formation rate constants and , respectively. The two parameters showed the same trends with varying viscosity, implying that the same information concerning chain dynamics is obtained from the randomly and end-labelled PNIPAM samples. The fluorescence decays of the Py2-PNIPAM-Y samples were acquired in ethanol and in water to determine how pyrene solubility affects the behavior of the polymers in solution, as probed by time-resolved fluorescence. It was found that the decreased pyrene solubility in water led to large amounts of intra- and intermolecular pyrene aggregation. Finally, the pyrene-labelled dendrimers were studied in tetrahydrofuran (THF) to probe the mobility of the chain ends as a function of generation number. The average rate of excimer formation, , obtained from the Model-Free analysis of the fluorescence decays in THF, increased linearly with generation number. This finding, combined with molecular mechanics optimizations, led to the conclusion that excimer formation was greatly enhanced due to the branched nature of the dendrimer molecule. Together, these studies illustrate three different applications of the use of time-resolved fluorescence to characterize the internal dynamics of pyrene-labelled macromolecules.

A series of pyrene end-labeled monodisperse poly(ethylene oxide)s (PEO(X)-Py2 where X represents the number average molecular weight (Mn) of the PEOs and equals 2, 5, 10 and 16.5 K) and one pyrene mono-labeled PEO (PEO(2K)-Py1) were synthesized and characterized in solution using fluorescence. First, the end-to-end cyclization (EEC) of PEO(X)-Py2 was investigated in seven organic solvents with viscosities (η) ranging from 0.32 to 1.92 mPa•s. The classical Birks scheme was used to globally fit the pyrene monomer and excimer fluorescence decays. The fraction of pyrenes that did not form excimer (ffree) was found to increase with increasing η and Mn. This result was contrary to the assumptions made by Birks’ scheme. To account for this, ffree was assumed to represent the fraction of PEO chains other than the monolabeled polymer impurities that cannot accomplish EEC. A fluorescence blob model (FBM) was applied to handle this assumption in the process of excimer formation for the PEO(X)-Py2 samples in solution. The radius of a blob, Rblob, in organic solvents was determined according to the results retrieved from the FBM. To quantitatively account for the existence of pyrene impurity in pyrene-labeled macromolecules, known amounts of PEO(2K)-Py1 were added into a PEO(2K)-Py2 solution and the fluorescence decays were fitted globally according to the Birks scheme and “model free” (MF) analysis to verify the validation of the MF analysis. The MF analysis was then applied to determine the amounts of 1-pyrenebutyric acid (PyBA) that had been added to a solution of pyrene end-labeled fourth generation dendritic hybrid (Py16-G4-PS). The results demonstrated that the contribution from unwanted fluorescent species could be isolated and quantitatively accounted for by fitting the fluorescence decays of the pyrene monomer and excimer globally with the MF analysis. Since the PEO(X)-Py2 samples form hydrophobic pyrene aggregates in aqueous solution, a sequential model (SM) was proposed to characterize the pyrene excimer formation of PEO(X)-Py2 in water at different polymer concentration (CP). The capture distance over which the pyrenyl end-groups experience hydrophobic forces in water was determined by assuming that the end-to-end distances of the PEO(X)-Py2 samples adopt a Gaussian distribution and that the fraction of pyrenes that are aggregated (fE0) determined by the sequential model corresponds to the fraction of PEO(X)-Py2 chains whose end-to-end distance is smaller than the hydrophobic capture distance. Since a surfactant can interact with a hydrophobically modified water-soluble polymer in aqueous solution, the interactions taking place between PEO(X)-Py2 and sodium dodecyl sulfate (SDS) were investigated at a low PEO(X)-Py2 concentration. The pyrene monomer and excimer fluorescence decays of the PEO(X)-Py2 and SDS solutions were acquired at various SDS concentrations and globally fitted according to the MF analysis to retrieve the parameters that described the kinetics of pyrene excimer formation. At high SDS concentrations above the critical micelle concentration (CMC), the pyrene end-groups of the short-chain samples (PEO(2K)-Py2 and PEO(5K)-Py2) were incorporated inside the same micelle and excimer was formed intramolecularly, while most pyrene groups of the long-chain samples (PEO(10K)-Py2 and PEO(16.5K)-Py2) were isolated into different micelles. Lastly, both the rheological properties and fluorescence behavior of a pyrene-labeled hydrophobically-modified alkali-swellable emulsion (Py-HASE) polymer in basic aqueous solution with SDS were studied. Furthermore, a joint experimental setup that combined a rheometer and a steady-state fluorometer was applied to investigate at the molecular level the effect that a shearing force had on the polymeric network. However, despite the dramatic decrease in solution viscosity with increasing shear rate, no change in the fluorescence spectra was detected, suggesting that changes in the polymeric network that affected the balance of intra- versus intermolecular pyrene associations did not impact the process of excimer formation. Together the experiments described in this thesis represent the broadest set of examples found in the scientific literature where information on the dynamics and level of association of pyrene-labeled polymers has been retrieved through the quantitative analysis of the fluorescence decays acquired with pyrene-labeled polymers in solution.

Global climate models (GCM) have been used for nearly two decades now as a tool to investigate and analyze past, present, and future weather and climate. Even though the first several generations of climate models were very simple, today's models are very sophisticated. They use complex parameterization schemes to approximate many nonlinear physical fields. In these models, the resolution and time steps can be set to be as small or as large as desired. In either case, the model generates over 100 atmospheric variables and 20 land surface variables that can be reported daily or monthly. The Community Atmospheric Model Version Two global climate model spends over sixty percent of the time computing shortwave and longwave parameterization schemes. Our goal is to replace its shortwave scheme with empirical methods and show that accuracy of the tropospheric variables is not compromised when using these empirical methods. We found that an autoregressive moving average (ARMA) model can be used to simulate the solar radiation at the top of the model atmosphere. However, the calculated insolation value is only valid for one particular grid point. To simulate the radiation over the entire globe, many ARMA models need to be determined. We also found that large 4-10-10-1 neural networks can be used to simulate the solar radiation to within 2 W m-2. However, much smaller and manageable neural networks can be used to simulate the complete solar insolation term if the neural network only simulates the residual after the annual and diurnal cycles and removed from the field (referred to as the - method). By using the neural network in the - method and by setting the eccentricity term to a constant, we were able to cut the models processing of the solar insolation by at least a factor of four.

The mobile technology is being developed very fast and it is a general situation where people can fetch or edit files via the Internet by mobile devices such as notebooks, smart phones, and so on. Due to possible possession of various devices of a user, it may be inconvenient for him to synchronize a file such that he cannot edit the same file via his devices easily. Recently, the cloud technology is becoming more and more popular and there are some new business models launched. One of them is a storage platform Dropbox which can synchronize users' files in their own devices and also allow users to share their files to others. However, Dropbox was indicated that the privacy of the files has not been protected well. Many encryption schemes have been proposed in the literature, but most of them do not support the property of secret file sharing when deploying them in cloud environment. Even though some schemes support the property, they can only provide a file owner to share all of his files with others. In some situations, the file owner may want to ensure that the receiver cannot decrypt the ciphertext until a specified time arrives. The existing encryption schemes cannot achieve these goals simultaneously. Hence, in order to cope with these problems, we propose a timed-release proxy conditional re-encryption scheme for cloud computing. Not only are users¡¦ files stored safely but also each user can freely share a desired file with another user. Furthermore, the receiver cannot obtain any information of the file until the chosen time arrives. Finally, we also demonstrate the security of our proposed scheme via formal proofs.

Wireless sensor networks (WSNs) have been widely used in many areas, such as early earthquake monitoring, building structure monitoring, and military surveillance. In this thesis, we focus on the wireless sensor network deployed in the battlefield, using random key predistribution scheme. Firstly we presented an analysis of the security impacts by node capture attack. Also, based on the node cloning attack, we proposed a new attack scheme, called compromised key redistribution attack, and discussed related attack scenarios. Besides, we have found out and conjectured that, when the overlapping factor of compromised key set is larger than 0.05, it is very possible (almost 90%) that the number of distinct compromised keys is 10.5% of the original key pool. This conjecture helps the adversary estimate the approximated size of original key pool by calculating the overlapping factor, thus calculate the probability that malicious nodes successfully establish connections with legitimate nodes.

In recent years, the requirement of application such as wireless sensor networks and short-range wireless controllers caused the growing of ZigBee technology. ZigBee is a communication technology developed specifically for short-range, low rate, low-cost wireless transmission.There are some characteristic such as short-range, low rate, low cost, and low power. The ZigBee Aliance group developed the specifications of software, and IEEE 802.15.4 group developed the specifications of hardware. IEEE 802.15.4a impulse radio UWB physical layer is one of the ZigBee physical layers. In our study, we designed a baseband signal processing algorithm meeting the specifications of IEEE 802.15.4a. The data processing flow in transmitter followed the specifications. In receiver, we designed baseband algorithms based-on the non-coherent energy detection scheme. Our algorithm including packet detection, synchronization and demodulation, and considering the implementation of algorithm, reducing the complexity of hardware as possible and improving the efficiency. Finally, the system performance is 3.9dB better than the receiver sensitivity.

This dissertation investigated several aspects of middle graders’ mathematical understanding based on representational models. Twenty (11 male, 9 female) sixth grade students were interviewed about their solution strategies and answer justifications when solving difficult mathematics problems. The interview participants represented a stratified demographic sampling of the student body of a culturally diverse middle school in a suburban school district in the southwestern United States. Data from the interviews were analyzed qualitatively. This involved “chunking” cognitive interview transcripts into sections. Major themes were identified and manuscripts were developed around those themes. One theme examined the interviewers’ ethic of care behaviors. Carol Gilligan noted differences in male and female ethic of care behaviors, but it was Nel Noddings who discussed the importance of such behaviors in the educational community. So what impact could the gender of the interviewer have on cognitive interviews? After considering ethic of care behaviors explicated by Hayes, Ryan and Zseller’s (1994) study with middle grades students, the interview transcripts were examined for specific positive and negative ethic of care behaviors. The theme of students’ justifications of mathematical solutions was also selected. The major undertaking involved developing a justification scheme applicable across mathematical strands and grade levels. The justification scheme that emerged was based on the work of Guershon Harel and Larry Sowder. The first-level schemes of Language, Mechanistic, Authoritarian, and Visual were used to classify and define the justifications. Several second-level schemes were also defined. The justification scheme framework was applied to students’ cognitive interview responses on four difficult mathematics problems. The third theme investigated the symbiosis of justification schemes with mathematical representations. This study examined possible links between representational formats and justification scheme categories. The premise of this study was that representations “trigger” students’ choices of justification schemes. Student responses were analyzed as to which aspect of the mathematical representation received the students’ initial attention. The students’ understanding of the representation was pivotal to their solution, as well as the students’ reasoning, or justification, of the answer. Students focused on key aspects of the problem and developed solutions based on that information.