Fibonacci Series, Golden Proportions, and the Human Biology

Pythagoras, Plato and Euclid’s paved the way for Classical Geometry. The idea of shapes that can be mathematically defined by equations led to the creation of great structures of modern and ancient civilizations, and milestones in mathematics and science. However, classical geometry fails to explain the complexity of non-linear shapes replete in nature such as the curvature of a flower or the wings of a Butterfly. Such non-linearity can be explained by fractal geometry which creates shapes that emulate those found in nature with remarkable accuracy. Such phenomenon begs the question of architectural origin for biological existence within the universe. While the concept of a unifying equation of life has yet to be discovered, the Fibonacci sequence may establish an origin for such a development. The observation of the Fibonacci sequence is existent in almost all aspects of life ranging from the leaves of a fern tree, architecture, and even paintings, makes it highly unlikely to be a stochastic phenomenon. Despite its wide-spread occurrence and existence, the Fibonacci series and the Rule of Golden Proportions has not been widely documented in the human body. This paper serves to review the observed documentation of the Fibonacci sequence in the human body.

A non-linear discrete stochastic optimization model for Advanced Access patient appointment scheduling

Access to healthcare is a major problem in which patients are deprived of receiving timely admission to healthcare. Poor access has resulted in significant but avoidable healthcare cost, poor quality of healthcare, and deterioration in the general public health. Advanced Access is a simple and direct approach to appointment scheduling in which the majority of a clinic's appointments slots are kept open in order to provide access for immediate or same day healthcare needs and therefore, alleviate the problem of poor access the healthcare. This research formulates a non-linear discrete stochastic mathematical model of the Advanced Access appointment scheduling policy. The model objective is to maximize the expected profit of the clinic subject to constraints on minimum access to healthcare provided. Patient behavior is characterized with probabilities for no-show, balking, and related patient choices. Structural properties of the model are analyzed to determine whether Advanced Access patient scheduling is feasible. To solve the complex combinatorial optimization problem, a heuristic that combines greedy construction algorithm and neighborhood improvement search was developed. The model and the heuristic were used to evaluate the Advanced Access patient appointment policy compared to existing policies. Trade-off between profit and access to healthcare are established, and parameter analysis of input parameters was performed. The trade-off curve is a characteristic curve and was observed to be concave. This implies that there exists an access level at which at which the clinic can be operated at optimal profit that can be realized. The results also show that, in many scenarios by switching from existing scheduling policy to Advanced Access policy clinics can improve access without any decrease in profit. Further, the success of Advanced Access policy in providing improved access and/or profit depends on the expected value of demand, variation in demand, and the ratio of demand for same day and advanced appointments. The contributions of the dissertation are a model of Advanced Access patient scheduling, a heuristic to solve the model, and the use of the model to understand the scheduling policy trade-offs which healthcare clinic managers must make. ^

The non-linear acousto-mechanical and thermodynamic response of spherical absorbers to laser pulses of various temporal profiles

This study is to theoretically investigate shockwave and microbubble formation due to laser absorption by microparticles and nanoparticles. The initial motivation for this research was to understand the underlying physical mechanisms responsible for laser damage to the retina, as well as the predict threshold levels for damage for laser pulses with of progressively shorter durations. The strongest absorbers in the retina are micron size melanosomes, and their absorption of laser light causes them to accrue very high energy density. I theoretically investigate how this absorbed energy is transferred to the surrounding medium. For a wide range of conditions I calculate shockwave generation and bubble growth as a function of the three parameters; fluence, pulse duration and pulse shape. In order to develop a rigorous physical treatment, the governing equations for the behavior of an absorber and for the surrounding medium are derived. Shockwave theory is investigated and the conclusion is that a shock pressure explanation is likely to be the underlying physical cause of retinal damage at threshold fluences for sub-nanosecond pulses. The same effects are also expected for non-biological micro and nano absorbers. ^

Correlates of Vitamin D Status in Healthy Older Adults Living in Miami-Dade and its Association with Non-Skeletal Outcomes: A Cross-Sectional Study

Examining factors that affect vitamin D status in the fast-growing elderly population of Miami-Dade, Florida, is needed. Vitamin D deficiency in older adults has been linked to correlates of disability, including falls and fractures, and cardiovascular disease. The purpose of this study was to determine the proportion of vitamin D insufficient individuals and their relationship with vitamin D insufficiency in older adults (n=97) living in Miami-Dade. We evaluated the association between vitamin D status and 1) dual task physical performance to understand the link between vitamin D and cognition in the context of mobility; and 2) cardiometabolic risk, measured by galvanic skin response, pulse oximetry, and blood pressure to create a composite score based on autonomic nervous system and endothelial function. Participants completed baseline assessments that included serum levels of vitamin D, anthropometrics, body composition, dual task physical performance and cardiometabolic risk. Surveys to evaluate vitamin D intake, sun exposure, physical activity, and depressive symptoms were completed. Spearman’s correlations, independent t-tests, paired t-tests, repeated measures ANOVAs, and multiple logistic and linear regressions were used to examine the relationship of vitamin D insufficiency (25(OH)D /ml) and sufficiency (25(OH)D ≥30 ng/ml) with determinants of vitamin D status, dual task physical performance variables and cardiometabolic risk scores. Although the proportion of vitamin D insufficient individuals was lower when compared to the prevalance of the general United States elderly population, it was still common in healthy community-dwelling older adults living in Miami-Dade County, especially among Hispanics. Factors that affected skin synthesis (ethnicity, and sun exposure), and bioavailability/metabolism (obesity) were significant predictors of vitamin D status. Vitamin D insufficiency was not significantly correlated with worse dual task physical performance; however, cognitive performance was worse in the vitamin D insufficient group. Our results suggest a relationship of vitamin D insufficiency with executive dysfunction, and support an association with cardiometabolic risk using an innovative electro-sensor complex, possibly by modulating autonomic nervous system activity and vascular function, thus affecting cardiac performance.

Algorithms for scheduling parallel batch processing machines with non-identical job ready times

This research is motivated by a practical application observed at a printed circuit board (PCB) manufacturing facility. After assembly, the PCBs (or jobs) are tested in environmental stress screening (ESS) chambers (or batch processing machines) to detect early failures. Several PCBs can be simultaneously tested as long as the total size of all the PCBs in the batch does not violate the chamber capacity. PCBs from different production lines arrive dynamically to a queue in front of a set of identical ESS chambers, where they are grouped into batches for testing. Each line delivers PCBs that vary in size and require different testing (or processing) times. Once a batch is formed, its processing time is the longest processing time among the PCBs in the batch, and its ready time is given by the PCB arriving last to the batch. ESS chambers are expensive and a bottleneck. Consequently, its makespan has to be minimized. ^ A mixed-integer formulation is proposed for the problem under study and compared to a formulation recently published. The proposed formulation is better in terms of the number of decision variables, linear constraints and run time. A procedure to compute the lower bound is proposed. For sparse problems (i.e. when job ready times are dispersed widely), the lower bounds are close to optimum. ^ The problem under study is NP-hard. Consequently, five heuristics, two metaheuristics (i.e. simulated annealing (SA) and greedy randomized adaptive search procedure (GRASP)), and a decomposition approach (i.e. column generation) are proposed—especially to solve problem instances which require prohibitively long run times when a commercial solver is used. Extensive experimental study was conducted to evaluate the different solution approaches based on the solution quality and run time. ^ The decomposition approach improved the lower bounds (or linear relaxation solution) of the mixed-integer formulation. At least one of the proposed heuristic outperforms the Modified Delay heuristic from the literature. For sparse problems, almost all the heuristics report a solution close to optimum. GRASP outperforms SA at a higher computational cost. The proposed approaches are viable to implement as the run time is very short. ^

Graduate program culture and intention to persist: Working adults in cohort and non-cohort programs

Cohort programs have been instituted at many universities to accommodate the growing number of mature adult graduate students who pursue degrees while maintaining multiple commitments such as work and family. While it is estimated that as many as 40–60% of students who begin graduate study fail to complete degrees, it is thought that attrition may be even higher for this population of students. Yet, little is known about the impact of cohorts on the learning environment and whether cohort programs affect graduate student retention. Retention theory stresses the importance of the academic department, quality of faculty-student relationships and student involvement in the life of the academic community as critical determinants in students' decisions to persist to degree completion. However, students who are employed full-time typically spend little time on campus engaged in the learning environment. Using academic and social integration theory, this study examined the experiences of working adult graduate students enrolled in cohort (CEP) and non-cohort (non-CEP) programs and the influence of these experiences on intention to persist. The Graduate Program Context Questionnaire was administered to graduate students (N = 310) to examine measures of academic and social integration and intention to persist. Sample t tests and ANOVAs were conducted to determine whether differences in perceptions could be identified between cohort and non-cohort students. Multiple linear regression was used to identify variables that predict students' intention to persist. While there were many similarities, significant differences were found between CEP and non-CEP student groups on two measures. CEP students rated peer-student relationships higher and scored higher on the intention to persist measure than non-CEP students. The psychological integration measure, however, was the strongest predictor of intention to persist for both the CEP and non-CEP groups. This study supports the research literature which suggests that CEP programs encourage the development of peer-student relationships and promote students' commitment to persistence.

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.

Medical advice and diabetes self-management reported by Mexican-American, Black- and White-non-Hispanic adults across the United States

Background Diabetes has reached epidemic proportions in the United States, particularly among minorities, and if improperly managed can lead to medical complications and death. Healthcare providers play vital roles in communicating standards of care, which include guidance on diabetes self-management. The background of the client may play a role in the patient-provider communication process. The aim of this study was to determine the association between medical advice and diabetes self care management behaviors for a nationally representative sample of adults with diabetes. Moreover, we sought to establish whether or not race/ethnicity was a modifier for reported medical advice received and diabetes self-management behaviors. Methods We analyzed data from 654 adults aged 21 years and over with diagnosed diabetes [130 Mexican-Americans; 224 Black non-Hispanics; and, 300 White non-Hispanics] and an additional 161 with 'undiagnosed diabetes' [N = 815(171 MA, 281 BNH and 364 WNH)] who participated in the National Health and Nutrition Examination Survey (NHANES) 2007-2008. Logistic regression models were used to evaluate whether medical advice to engage in particular self-management behaviors (reduce fat or calories, increase physical activity or exercise, and control or lose weight) predicted actually engaging in the particular behavior and whether the impact of medical advice on engaging in the behavior differed by race/ethnicity. Additional analyses examined whether these relationships were maintained when other factors potentially related to engaging in diabetes self management such as participants' diabetes education, sociodemographics and physical characteristics were controlled. Sample weights were used to account for the complex sample design. Results Although medical advice to the patient is considered a standard of care for diabetes, approximately one-third of the sample reported not receiving dietary, weight management, or physical activity self-management advice. Participants who reported being given medical advice for each specific diabetes self-management behaviors were 4-8 times more likely to report performing the corresponding behaviors, independent of race. These results supported the ecological model with certain caveats. Conclusions Providing standard medical advice appears to lead to diabetes self-management behaviors as reported by adults across the United States. Moreover, it does not appear that race/ethnicity influenced reporting performance of the standard diabetes self-management behavior. Longitudinal studies evaluating patient-provider communication, medical advice and diabetes self-management behaviors are needed to clarify our findings.

Medical Advice and Diabetes Self-Management Reported by Mexican-American, Black- and White-Non-Hispanic Adults Across the United States

Background: Diabetes has reached epidemic proportions in the United States, particularly among minorities, and if improperly managed can lead to medical complications and death. Healthcare providers play vital roles in communicating standards of care, which include guidance on diabetes self-management. The background of the client may play a role in the patient-provider communication process. The aim of this study was to determine the association between medical advice and diabetes self care management behaviors for a nationally representative sample of adults with diabetes. Moreover, we sought to establish whether or not race/ethnicity was a modifier for reported medical advice received and diabetes self-management behaviors. Methods: We analyzed data from 654 adults aged 21 years and over with diagnosed diabetes [130 MexicanAmericans; 224 Black non-Hispanics; and, 300 White non-Hispanics] and an additional 161 with ‘undiagnosed diabetes’ [N = 815(171 MA, 281 BNH and 364 WNH)] who participated in the National Health and Nutrition Examination Survey (NHANES) 2007-2008. Logistic regression models were used to evaluate whether medical advice to engage in particular self-management behaviors (reduce fat or calories, increase physical activity or exercise, and control or lose weight) predicted actually engaging in the particular behavior and whether the impact of medical advice on engaging in the behavior differed by race/ethnicity. Additional analyses examined whether these relationships were maintained when other factors potentially related to engaging in diabetes self management such as participants’ diabetes education, sociodemographics and physical characteristics were controlled. Sample weights were used to account for the complex sample design. Results: Although medical advice to the patient is considered a standard of care for diabetes, approximately onethird of the sample reported not receiving dietary, weight management, or physical activity self-management advice. Participants who reported being given medical advice for each specific diabetes self-management behaviors were 4-8 times more likely to report performing the corresponding behaviors, independent of race. These results supported the ecological model with certain caveats. Conclusions: Providing standard medical advice appears to lead to diabetes self-management behaviors as reported by adults across the United States. Moreover, it does not appear that race/ethnicity influenced reporting performance of the standard diabetes self-management behavior. Longitudinal studies evaluating patient-provider communication, medical advice and diabetes self-management behaviors are needed to clarify our findings.

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.

Tamed and Compatible Symplectic Forms on Four-Dimensional Almost Complex Lie Algebras

We are able to give a complete description of four-dimensional Lie algebras g which satisfy the tame-compatible question of Donaldson for all almost complex structures J on g are completely described. As a consequence, examples are given of (non-unimodular) four-dimensional Lie algebras with almost complex structures which are tamed but not compatible with symplectic forms.? Note that Donaldson asked his question for compact four-manifolds. In that context, the problem is still open, but it is believed that any tamed almost complex structure is in fact compatible with a symplectic form. In this presentation, I will define the basic objects involved and will give some insights on the proof. The key for the proof is translating the problem into a Linear Algebra setting. This is a joint work with Dr. Draghici.