Trust based security mechanisms for wireless sensor networks

Wireless sensor networks are emerging as effective tools in the gathering and dissemination of data. They can be applied in many fields including health, environmental monitoring, home automation and the military. Like all other computing systems it is necessary to include security features, so that security sensitive data traversing the network is protected. However, traditional security techniques cannot be applied to wireless sensor networks. This is due to the constraints of battery power, memory, and the computational capacities of the miniature wireless sensor nodes. Therefore, to address this need, it becomes necessary to develop new lightweight security protocols. This dissertation focuses on designing a suite of lightweight trust-based security mechanisms and a cooperation enforcement protocol for wireless sensor networks. This dissertation presents a trust-based cluster head election mechanism used to elect new cluster heads. This solution prevents a major security breach against the routing protocol, namely, the election of malicious or compromised cluster heads. This dissertation also describes a location-aware, trust-based, compromise node detection, and isolation mechanism. Both of these mechanisms rely on the ability of a node to monitor its neighbors. Using neighbor monitoring techniques, the nodes are able to determine their neighbors’ reputation and trust level through probabilistic modeling. The mechanisms were designed to mitigate internal attacks within wireless sensor networks. The feasibility of the approach is demonstrated through extensive simulations. The dissertation also addresses non-cooperation problems in multi-user wireless sensor networks. A scalable lightweight enforcement algorithm using evolutionary game theory is also designed. The effectiveness of this cooperation enforcement algorithm is validated through mathematical analysis and simulation. This research has advanced the knowledge of wireless sensor network security and cooperation by developing new techniques based on mathematical models. By doing this, we have enabled others to build on our work towards the creation of highly trusted wireless sensor networks. This would facilitate its full utilization in many fields ranging from civilian to military applications.

Trust Based Security Mechanisms for Wireless Sensor Networks

Wireless sensor networks are emerging as effective tools in the gathering and dissemination of data. They can be applied in many fields including health, environmental monitoring, home automation and the military. Like all other computing systems it is necessary to include security features, so that security sensitive data traversing the network is protected. However, traditional security techniques cannot be applied to wireless sensor networks. This is due to the constraints of battery power, memory, and the computational capacities of the miniature wireless sensor nodes. Therefore, to address this need, it becomes necessary to develop new lightweight security protocols. This dissertation focuses on designing a suite of lightweight trust-based security mechanisms and a cooperation enforcement protocol for wireless sensor networks. This dissertation presents a trust-based cluster head election mechanism used to elect new cluster heads. This solution prevents a major security breach against the routing protocol, namely, the election of malicious or compromised cluster heads. This dissertation also describes a location-aware, trust-based, compromise node detection, and isolation mechanism. Both of these mechanisms rely on the ability of a node to monitor its neighbors. Using neighbor monitoring techniques, the nodes are able to determine their neighbors’ reputation and trust level through probabilistic modeling. The mechanisms were designed to mitigate internal attacks within wireless sensor networks. The feasibility of the approach is demonstrated through extensive simulations. The dissertation also addresses non-cooperation problems in multi-user wireless sensor networks. A scalable lightweight enforcement algorithm using evolutionary game theory is also designed. The effectiveness of this cooperation enforcement algorithm is validated through mathematical analysis and simulation. This research has advanced the knowledge of wireless sensor network security and cooperation by developing new techniques based on mathematical models. By doing this, we have enabled others to build on our work towards the creation of highly trusted wireless sensor networks. This would facilitate its full utilization in many fields ranging from civilian to military applications.

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. ^

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. ^

Statistical analysis and optimal classification of blood cell populations using Gaussian distributions

This dissertation develops a new figure of merit to measure the similarity (or dissimilarity) of Gaussian distributions through a novel concept that relates the Fisher distance to the percentage of data overlap. The derivations are expanded to provide a generalized mathematical platform for determining an optimal separating boundary of Gaussian distributions in multiple dimensions. Real-world data used for implementation and in carrying out feasibility studies were provided by Beckman-Coulter. It is noted that although the data used is flow cytometric in nature, the mathematics are general in their derivation to include other types of data as long as their statistical behavior approximate Gaussian distributions. ^ Because this new figure of merit is heavily based on the statistical nature of the data, a new filtering technique is introduced to accommodate for the accumulation process involved with histogram data. When data is accumulated into a frequency histogram, the data is inherently smoothed in a linear fashion, since an averaging effect is taking place as the histogram is generated. This new filtering scheme addresses data that is accumulated in the uneven resolution of the channels of the frequency histogram. ^ The qualitative interpretation of flow cytometric data is currently a time consuming and imprecise method for evaluating histogram data. This method offers a broader spectrum of capabilities in the analysis of histograms, since the figure of merit derived in this dissertation integrates within its mathematics both a measure of similarity and the percentage of overlap between the distributions under analysis. ^

Subdural electroencephalogram analysis for extracting discriminating measures in epileptogenic data

This dissertation introduces an integrated algorithm for a new application dedicated at discriminating between electrodes leading to a seizure onset and those that do not, using interictal subdural EEG data. The significance of this study is in determining among all of these channels, all containing interictal spikes, why some electrodes eventually lead to seizure while others do not. A first finding in the development process of the algorithm is that these interictal spikes had to be asynchronous and should be located in different regions of the brain, before any consequential interpretations of EEG behavioral patterns are possible. A singular merit of the proposed approach is that even when the EEG data is randomly selected (independent of the onset of seizure), we are able to classify those channels that lead to seizure from those that do not. It is also revealed that the region of ictal activity does not necessarily evolve from the tissue located at the channels that present interictal activity, as commonly believed.^ The study is also significant in terms of correlating clinical features of EEG with the patient's source of ictal activity, which is coming from a specific subset of channels that present interictal activity. The contributions of this dissertation emanate from (a) the choice made on the discriminating parameters used in the implementation, (b) the unique feature space that was used to optimize the delineation process of these two type of electrodes, (c) the development of back-propagation neural network that automated the decision making process, and (d) the establishment of mathematical functions that elicited the reasons for this delineation process. ^

An experimental and theoretical analysis of nitric oxide availability in the microcirculation

Nitric Oxide (NO) is produced in the vascular endothelium where it then diffuses to the adjacent smooth muscle cells (SMC) activating agents known to regulate vascular tone. The close proximity of the site of NO production to the red blood cells (RBC) and its known fast consumption by hemoglobin, suggests that the blood will scavenge most of the NO produced. Therefore, it is unclear how NO is able to play its role in accomplishing vasodilation. Investigation of NO production and consumption rates will allow insight into this paradox. DAF-FM is a sensitive NO fluorescence probe widely used for qualitative assessment of cellular NO production. With the aid of a mathematical model of NO/DAF-FM reaction kinetics, experimental studies were conducted to calibrate the fluorescence signal showing that the slope of fluorescent intensity is proportional to [NO]2 and exhibits a saturation dependence on [DAF-FM]. In addition, experimental data exhibited a Km dependence on [NO]. This finding was incorporated into the model elucidating NO 2 as the possible activating agent of DAF-FM. A calibration procedure was formed and applied to agonist stimulated cells, providing an estimated NO release rate of 0.418 ± 0.18 pmol/cm2s. To assess NO consumption by RBCs, measurements of the rate of NO consumption in a gas stream flowing on top of an RBC solution of specified Hematocrit (Hct) was performed. The consumption rate constant (kbl)in porcine RBCs at 25°C and 45% Hct was estimated to be 3500 + 700 s-1. kbl is highly dependent on Hct and can reach up to 9900 + 4000 s-1 for 60% Hct. The nonlinear dependence of kbl on Hct suggests a predominant role for extracellular diffusion in limiting NO uptake. Further simulations showed a linear relationship between varying NO production rates and NO availability in the SMCs utilizing the estimated NO consumption rate. The corresponding SMC [NO] level for the average NO production rate estimated was approximately 15.1 nM. With the aid of experimental and theoretical methods we were able to examine the NO paradox and exhibit that endothelial derived NO is able to escape scavenging by RBCs to diffuse to the SMCs.

Differential effects of single -sex versus coed education on the mathematical reasoning ability, verbal reasoning ability, and self-concept of high school girls

This study explored the differential effects of single-sex versus coed education on the cognitive and affective development of young women in senior year of high school. The basic research question was: What are the differential effects of single-sex versus coed education on the development of mathematical reasoning ability, verbal reasoning ability, or self-concept of high school girls?^ This study was composed of two parts. In the first part, the SAT verbal and mathematical ability scores were recorded for those subjects in the two schools from which the sample populations were drawn. The second part of the study required the application of the Piers-Harris Children's Self-Concept Scale to subjects in each of the two sample populations. The sample schools were deliberately selected to minimize between group differences in the populations. One was an all girls school, the other coeducational.^ The research design employed in this study was the causal-comparative method, used to explore causal relationships between variables that already exist. Based on a comprehensive analysis of the data produced by this research, no significant difference was found to exist between the mean scores of the senior girls in the single-sex school and the coed school on the SAT 1 verbal reasoning section. Nor was any significant difference found to exist between the mean scores of the senior girls in the single-sex school and the coed school on the SAT 1 mathematical reasoning section. Finally, no significant difference between the mean total scores of the senior girls in the single-sex school and the coed school on the Piers-Harris Children's Self-Concept Scale was found to exist.^ Contrary to what many other studies have found in the past about single-sex schools and their advantages for girls, this study found no support for such advantages in the cognitive areas of verbal and mathematical reasoning as measured by the SAT or in the affective area of self-concept as measured by the Piers-Harris Children's Self-Concept Scale. ^

A generalized adaptive mathematical morphological filter for LIDAR data

Airborne Light Detection and Ranging (LIDAR) technology has become the primary method to derive high-resolution Digital Terrain Models (DTMs), which are essential for studying Earth's surface processes, such as flooding and landslides. The critical step in generating a DTM is to separate ground and non-ground measurements in a voluminous point LIDAR dataset, using a filter, because the DTM is created by interpolating ground points. As one of widely used filtering methods, the progressive morphological (PM) filter has the advantages of classifying the LIDAR data at the point level, a linear computational complexity, and preserving the geometric shapes of terrain features. The filter works well in an urban setting with a gentle slope and a mixture of vegetation and buildings. However, the PM filter often removes ground measurements incorrectly at the topographic high area, along with large sizes of non-ground objects, because it uses a constant threshold slope, resulting in "cut-off" errors. A novel cluster analysis method was developed in this study and incorporated into the PM filter to prevent the removal of the ground measurements at topographic highs. Furthermore, to obtain the optimal filtering results for an area with undulating terrain, a trend analysis method was developed to adaptively estimate the slope-related thresholds of the PM filter based on changes of topographic slopes and the characteristics of non-terrain objects. The comparison of the PM and generalized adaptive PM (GAPM) filters for selected study areas indicates that the GAPM filter preserves the most "cut-off" points removed incorrectly by the PM filter. The application of the GAPM filter to seven ISPRS benchmark datasets shows that the GAPM filter reduces the filtering error by 20% on average, compared with the method used by the popular commercial software TerraScan. The combination of the cluster method, adaptive trend analysis, and the PM filter allows users without much experience in processing LIDAR data to effectively and efficiently identify ground measurements for the complex terrains in a large LIDAR data set. The GAPM filter is highly automatic and requires little human input. Therefore, it can significantly reduce the effort of manually processing voluminous LIDAR measurements.

Analysis of Students’ Misconceptions and Error Patterns in Mathematics: The Case of Fractions

This study analyzed three fifth grade students’ misconceptions and error patterns when working with equivalence, addition and subtraction of fractions. The findings revealed that students used both conceptual and procedural knowledge to solve the problems. They used pictures, gave examples, and made connections to other mathematical concepts and to daily life topics. Error patterns found include using addition and subtraction of numerators and denominators, and finding the greatest common factor.

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.

GIS-integrated mathematical modeling of social phenomena at macro- and micro- levels—a multivariate geographically-weighted regression model for identifying locations vulnerable to hosting terrorist safe-houses: France as case study

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to terrorist locations such as safe-houses (rather than their targets or training sites) are rare and possibly nonexistent. At the time of this research, there were no publically available models designed to predict locations where violent extremists are likely to reside. This research uses France as a case study to present a complex systems model that incorporates multiple quantitative, qualitative and geospatial variables that differ in terms of scale, weight, and type. Though many of these variables are recognized by specialists in security studies, there remains controversy with respect to their relative importance, degree of interaction, and interdependence. Additionally, some of the variables proposed in this research are not generally recognized as drivers, yet they warrant examination based on their potential role within a complex system. This research tested multiple regression models and determined that geographically-weighted regression analysis produced the most accurate result to accommodate non-stationary coefficient behavior, demonstrating that geographic variables are critical to understanding and predicting the phenomenon of terrorism. This dissertation presents a flexible prototypical model that can be refined and applied to other regions to inform stakeholders such as policy-makers and law enforcement in their efforts to improve national security and enhance quality-of-life.