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. ^

Predictors of developmental gains in children enrolled in an early intervention setting

The purpose of this research was to determine whether initial developmental delay, site of intervention, frequency of intervention, age of the child, socio-economic status (SES), gender and ethnicity significantly predict developmental gains in a group of children enrolled in an early intervention setting. The records of 134 children enrolled in an inner-city program in Miami, Florida were reviewed for inclusion in this study. ^ Demographic variables, site placement and treatment frequencies were collected during a retrospective chart review. Level of delay was expressed using the developmental quotient and developmental gain was calculated using the mean gain on age equivalent scores or developmental tests. A multiple regression analysis was performed to determine which of the above variables significantly predicted developmental gains. Multivariate analysis compared developmental gains for all the developmental domains based on intervention site (center versus home-based) while controlling for developmental delay. ^ Children made greater developmental gains if they had higher developmental quotients and if they were younger at the time services were initiated. Frequency of intervention significantly improved developmental outcomes in children attending center-based programs. Children attending center-based programs also made significantly greater gains in gross motor skills compared to children attending home-based programs. ^ These findings emphasize the importance of early screening and referral of children with developmental delay and adjusting intervention for the child's developmental quotient. Children should receive intense treatment to maximize results. Decisions regarding program placement should be individualized according to the child's unique developmental pattern. Policy and program decisions affecting the curriculum of a child in early intervention need to reflect these multivariate considerations. ^

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. ^

Color-based surface reflectance separation for scene illumination estimation and rendering

Given the importance of color processing in computer vision and computer graphics, estimating and rendering illumination spectral reflectance of image scenes is important to advance the capability of a large class of applications such as scene reconstruction, rendering, surface segmentation, object recognition, and reflectance estimation. Consequently, this dissertation proposes effective methods for reflection components separation and rendering in single scene images. Based on the dichromatic reflectance model, a novel decomposition technique, named the Mean-Shift Decomposition (MSD) method, is introduced to separate the specular from diffuse reflectance components. This technique provides a direct access to surface shape information through diffuse shading pixel isolation. More importantly, this process does not require any local color segmentation process, which differs from the traditional methods that operate by aggregating color information along each image plane. ^ Exploiting the merits of the MSD method, a scene illumination rendering technique is designed to estimate the relative contributing specular reflectance attributes of a scene image. The image feature subset targeted provides a direct access to the surface illumination information, while a newly introduced efficient rendering method reshapes the dynamic range distribution of the specular reflectance components over each image color channel. This image enhancement technique renders the scene illumination reflection effectively without altering the scene’s surface diffuse attributes contributing to realistic rendering effects. ^ As an ancillary contribution, an effective color constancy algorithm based on the dichromatic reflectance model was also developed. This algorithm selects image highlights in order to extract the prominent surface reflectance that reproduces the exact illumination chromaticity. This evaluation is presented using a novel voting scheme technique based on histogram analysis. ^ In each of the three main contributions, empirical evaluations were performed on synthetic and real-world image scenes taken from three different color image datasets. The experimental results show over 90% accuracy in illumination estimation contributing to near real world illumination rendering effects. ^

The role of emotional intelligence in college students' success

The purpose of this study was to determine if higher academic performance was positively correlated to higher emotional intelligence among traditional age male and female college students enrolled in an Introduction to Business course at a large multi-campus state college in Florida. The Bar-On 2004 (Emotional Quotient Inventory) EQ-i 133-item inventory was used to assess students’ emotional intelligence. Within the scope of this ex-post facto study, a quasi-experimental design was included to further determine if emotional intelligence could be increased through the inclusion of a curricular component on emotional intelligence. Four groups of students (N=111) participated in the three-phase study over two semesters. The first phase (pre-intervention) was limited to students with an established GPA and an attempted-to-completed credit hour ratio within the institution (N=82). Results showed a slight positive correlation between the two factors and the students’ emotional intelligence pretest assessment scores. The second phase of the study involved establishing a control and an experimental group in each of two semesters to compare the attainment of overall emotional intelligence scores as measured by the EQ-i. The third phase of the study examined four measures of academic success (GPA, the attempted-to-completed credit hour ratio, grade in the business course, and persistence in college) to determine if these factors were positively correlated with the students’ posttest EQ-i scores. The study also included a research question to determine if significant differences in overall EQ-i scores existed between male and female students during the three phases. Findings from the study indicated that (a) there was a slight positive correlation in the pre-intervention stage between emotional intelligence and traditional measures of academic success specifically, GPA and the attempted-to-completed credit hour ratio; (b) curricular intervention made a significant difference at the p <.05 level, with an .5 effect size, in one semester but failed to meet that threshold in the following semester with the second pair of groups; (c) at the post-intervention phase, the four measures of traditional academic success yielded a low positive correlation with the students’ emotional intelligence assessment scores, and (d) female students showed significant gains in their overall EQ-i scores.

Comparison of snail density, standing stock, and body size between Caribbean karst wetlands and other freshwater ecosystems

Synthesizing data from multiple studies generates hypotheses about factors that affect the distribution and abundance of species among ecosystems. Snails are dominant herbivores in many freshwater ecosystems, but there is no comprehensive review of snail density, standing stock, or body size among freshwater ecosystems. We compile data on snail density and standing stock, estimate body size with their quotient, and discuss the major pattern that emerges. We report data from 215 freshwater ecosystems taken from 88 studies that we placed into nine categories. Sixty-five studies reported density, seven reported standing stock, and 16 reported both. Despite the breadth of studies, spatial and temporal sampling scales were limited. Researchers used 25 different sampling devices ranging in area from 0.0015 to 2.5 m2. Most ecosystem categories had similar snail densities, standing stocks, and body sizes suggesting snails shared a similar function among ecosystems. Caribbean karst wetlands were a striking exception with much lower density and standing stock, but large body size. Disparity in body size results from the presence of ampullariids in Caribbean karst wetlands suggesting that biogeography affects the distribution of taxa, and in this case size, among aquatic ecosystems. We propose that resource quality explains the disparity in density and standing stock between Caribbean karst wetlands and other categories. Periphyton in Caribbean karst wetlands has high carbon-to-phosphorous ratios and defensive characteristics that inhibit grazers. Unlike many freshwater ecosystems where snails are key grazers, we hypothesize that a microbial loop captures much of the primary production in Caribbean karst wetlands.

The impact of Round II Urban Empowerment Zones on local communities

In the United States, the federal Empowerment Zone (EZ) program aimed to create and retain business investment in poor communities and to encourage local hiring through the use of special tax credits, relaxed regulations, social service grants, and other incentives. My dissertation explores whether the Round II Urban EZs had a beneficial impact on local communities and what factors influenced the implementation and performance of the EZs, using three modes of inquiry. First, linear regression models investigate whether the federal revitalization program had a statistically significant impact on the creation of new businesses and jobs in Round II Urban EZ communities. Second, location quotient and shift-share analysis are used to reveal the industry clusters in three EZ communities that experienced positive business and job growth. Third, qualitative analysis is employed to explore factors that influenced the implementation and performance of EZs in general, and in particular, Miami-Dade County, Florida. The results show an EZ's presence failed to have a significant influence on local business and job growth. In communities that experienced a beneficial impact from EZs, there has been a pattern of decline in manufacturing companies and increase in service-driven firms. The case study suggests that institutional factors, such as governance structure, leadership, administrative capacity, and community participation have affected the effectiveness of the program's implementation and performance.

Rank and k-nullity of contact manifolds

We prove that the dimension of the 1-nullity distribution N(1) on a closed Sasakian manifold M of rankl is at least equal to 2l−1 provided that M has an isolated closed characteristic. The result is then used to provide some examples of k-contact manifolds which are not Sasakian. On a closed, 2n+1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension of N(1) is less than or equal to n+1 or N(1) is the entire tangent bundle TM. In the latter case, the Sasakian manifold Mis isometric to a quotient of the Euclidean sphere under a finite group of isometries. We also point out some interactions between k-nullity, Weinstein conjecture, and minimal unit vector fields.

Ensemble Stream Model for Data-Cleaning in Sensor Networks

Ensemble Stream Modeling and Data-cleaning are sensor information processing systems have different training and testing methods by which their goals are cross-validated. This research examines a mechanism, which seeks to extract novel patterns by generating ensembles from data. The main goal of label-less stream processing is to process the sensed events to eliminate the noises that are uncorrelated, and choose the most likely model without over fitting thus obtaining higher model confidence. Higher quality streams can be realized by combining many short streams into an ensemble which has the desired quality. The framework for the investigation is an existing data mining tool. First, to accommodate feature extraction such as a bush or natural forest-fire event we make an assumption of the burnt area (BA*), sensed ground truth as our target variable obtained from logs. Even though this is an obvious model choice the results are disappointing. The reasons for this are two: One, the histogram of fire activity is highly skewed. Two, the measured sensor parameters are highly correlated. Since using non descriptive features does not yield good results, we resort to temporal features. By doing so we carefully eliminate the averaging effects; the resulting histogram is more satisfactory and conceptual knowledge is learned from sensor streams. Second is the process of feature induction by cross-validating attributes with single or multi-target variables to minimize training error. We use F-measure score, which combines precision and accuracy to determine the false alarm rate of fire events. The multi-target data-cleaning trees use information purity of the target leaf-nodes to learn higher order features. A sensitive variance measure such as ƒ-test is performed during each node's split to select the best attribute. Ensemble stream model approach proved to improve when using complicated features with a simpler tree classifier. The ensemble framework for data-cleaning and the enhancements to quantify quality of fitness (30% spatial, 10% temporal, and 90% mobility reduction) of sensor led to the formation of streams for sensor-enabled applications. Which further motivates the novelty of stream quality labeling and its importance in solving vast amounts of real-time mobile streams generated today.

Foundations of quantitative information flow: Channels, cascades, and the information order

Secrecy is fundamental to computer security, but real systems often cannot avoid leaking some secret information. For this reason, the past decade has seen growing interest in quantitative theories of information flow that allow us to quantify the information being leaked. Within these theories, the system is modeled as an information-theoretic channel that specifies the probability of each output, given each input. Given a prior distribution on those inputs, entropy-like measures quantify the amount of information leakage caused by the channel. ^ This thesis presents new results in the theory of min-entropy leakage. First, we study the perspective of secrecy as a resource that is gradually consumed by a system. We explore this intuition through various models of min-entropy consumption. Next, we consider several composition operators that allow smaller systems to be combined into larger systems, and explore the extent to which the leakage of a combined system is constrained by the leakage of its constituents. Most significantly, we prove upper bounds on the leakage of a cascade of two channels, where the output of the first channel is used as input to the second. In addition, we show how to decompose a channel into a cascade of channels. ^ We also establish fundamental new results about the recently-proposed g-leakage family of measures. These results further highlight the significance of channel cascading. We prove that whenever channel A is composition refined by channel B, that is, whenever A is the cascade of B and R for some channel R, the leakage of A never exceeds that of B, regardless of the prior distribution or leakage measure (Shannon leakage, guessing entropy leakage, min-entropy leakage, or g-leakage). Moreover, we show that composition refinement is a partial order if we quotient away channel structure that is redundant with respect to leakage alone. These results are strengthened by the proof that composition refinement is the only way for one channel to never leak more than another with respect to g-leakage. Therefore, composition refinement robustly answers the question of when a channel is always at least as secure as another from a leakage point of view.^

The relationships between elementary school principals' emotional intelligence, leadership style and school culture

The role of the principal in school settings and the principal's perceived effect on student achievement have frequently been considered vital factors in school reform. The relationships between emotional intelligence, leadership style and school culture have been widely studied. The literature reveals agreement among scholars regarding the principal's vital role in developing and fostering a positive school culture. The purpose of this study was to explore the relationships between elementary school principals' emotional intelligence, leadership style and school culture. ^ The researcher implemented a non-experimental ex post facto research design to investigate four specific research hypotheses. Utilizing the Qualtrics Survey Software, 57 elementary school principals within a large urban school district in southeast Florida completed the Emotional Quotient Inventory (EQ-i), and 850 of their faculty members completed the Multifactor Leadership Questionnaire (MLQ Form 5X). Faculty responses to the school district's School Climate Survey retrieved from the district's web site were used as the measure of school culture. ^ Linear regression analyses revealed significant positive associations between emotional intelligence and the following leadership measures: Idealized Influence-Attributes (β = .23, p = < .05), Idealized Influence-Behaviors (β = .34, p = < .01), Inspirational Motivation (β = .39, p = < .01) and Contingent Reward (β = .33, p = < .01). Hierarchical regression analyses revealed positive associations between school culture and both transformational and transactional leadership measures, and negative associations between school culture and passive-avoidant leadership measures. Significant positive associations were found between school culture and the principals' emotional intelligence over and above leadership style. Hierarchical linear regressions to test the statistical hypothesis developed to account for alternative explanations revealed significant associations between leadership style and school culture over and above school grade. ^ These results suggest that emotional intelligence merits consideration in the development of leadership theory. Practical implications include suggestions that principals employ both transformational and transactional leadership strategies, and focus on developing their level of emotional intelligence. The associations between emotional intelligence, transformational leadership, Contingent Reward and school culture found in this study validate the role of the principal as the leader of school reform.^

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.

The Relationships between Elementary School Principals' Emotional Intelligence, Leadership Style and School Culture

The role of the principal in school settings and the principal’s perceived effect on student achievement have frequently been considered vital factors in school reform. The relationships between emotional intelligence, leadership style and school culture have been widely studied. The literature reveals agreement among scholars regarding the principal’s vital role in developing and fostering a positive school culture. The purpose of this study was to explore the relationships between elementary school principals’ emotional intelligence, leadership style and school culture. The researcher implemented a non-experimental ex post facto research design to investigate four specific research hypotheses. Utilizing the Qualtrics Survey Software, 57 elementary school principals within a large urban school district in southeast Florida completed the Emotional Quotient Inventory (EQ-i), and 850 of their faculty members completed the Multifactor Leadership Questionnaire (MLQ Form 5X). Faculty responses to the school district’s School Climate Survey retrieved from the district’s web site were used as the measure of school culture. Linear regression analyses revealed significant positive associations between emotional intelligence and the following leadership measures: Idealized Influence-Attributes (β = .23, p = < .05), Idealized Influence-Behaviors (β = .34, p = < .01), Inspirational Motivation (β = .39, p = < .01) and Contingent Reward (β = .33, p = < .01). Hierarchical regression analyses revealed positive associations between school culture and both transformational and transactional leadership measures, and negative associations between school culture and passive-avoidant leadership measures. Significant positive associations were found between school culture and the principals’ emotional intelligence over and above leadership style. Hierarchical linear regressions to test the statistical hypothesis developed to account for alternative explanations revealed significant associations between leadership style and school culture over and above school grade. These results suggest that emotional intelligence merits consideration in the development of leadership theory. Practical implications include suggestions that principals employ both transformational and transactional leadership strategies, and focus on developing their level of emotional intelligence. The associations between emotional intelligence, transformational leadership, Contingent Reward and school culture found in this study validate the role of the principal as the leader of school reform.

Ensemble Stream Model for Data-Cleaning in Sensor Networks

Ensemble Stream Modeling and Data-cleaning are sensor information processing systems have different training and testing methods by which their goals are cross-validated. This research examines a mechanism, which seeks to extract novel patterns by generating ensembles from data. The main goal of label-less stream processing is to process the sensed events to eliminate the noises that are uncorrelated, and choose the most likely model without over fitting thus obtaining higher model confidence. Higher quality streams can be realized by combining many short streams into an ensemble which has the desired quality. The framework for the investigation is an existing data mining tool. First, to accommodate feature extraction such as a bush or natural forest-fire event we make an assumption of the burnt area (BA*), sensed ground truth as our target variable obtained from logs. Even though this is an obvious model choice the results are disappointing. The reasons for this are two: One, the histogram of fire activity is highly skewed. Two, the measured sensor parameters are highly correlated. Since using non descriptive features does not yield good results, we resort to temporal features. By doing so we carefully eliminate the averaging effects; the resulting histogram is more satisfactory and conceptual knowledge is learned from sensor streams. Second is the process of feature induction by cross-validating attributes with single or multi-target variables to minimize training error. We use F-measure score, which combines precision and accuracy to determine the false alarm rate of fire events. The multi-target data-cleaning trees use information purity of the target leaf-nodes to learn higher order features. A sensitive variance measure such as f-test is performed during each node’s split to select the best attribute. Ensemble stream model approach proved to improve when using complicated features with a simpler tree classifier. The ensemble framework for data-cleaning and the enhancements to quantify quality of fitness (30% spatial, 10% temporal, and 90% mobility reduction) of sensor led to the formation of streams for sensor-enabled applications. Which further motivates the novelty of stream quality labeling and its importance in solving vast amounts of real-time mobile streams generated today.