The Mississippi Department of Education (MDE) requires that each school district throughout the state employ a licensed administrator serving as the federal programs coordinator, director, or administrator in a full or part-time capacity (Mississippi Department of Education, 2013). The federal program director is responsible for the management and implementation of federal funds in public schools. Federal funds are defined by law and used to improve student achievement, enhance teacher quality, increase equity and access to educational resources, and provide innovative strategies for recruiting teachers and improving graduation rates (No Child Left Behind, 2001). The work of federal program directors involves a number of activities such as promoting student achievement through strategic planning, administering professional development, providing research-based curriculum and instructional materials, and organizing extended school day and school year tutorial or enrichment learning opportunities for students. Federal program directors in Mississippi are required to be properly licensed and endorsed by the Mississippi Department of Education’s Office of Teacher Certification and Licensure (Mississippi Department of Education, 2015). In addition to certification, several other factors are associated with the role of the federal programs director. These areas include working knowledge of federal program requirements, legal issues, personnel evaluation, and effective school reform initiatives. In terms of educational leadership, the federal programs director’s role includes establishing the vision and direction of a school district’s federally funded programs, resolving complex issues and problems, and continually staying abreast of new state and federal regulations (Lunenburg & Ornstein, 2004). Role definition varies from school district to school district. For example, some federal programs directors may also function as assistant superintendents and are integral members of the district leadership team. Conversely, other federal programs directors may be given leadership roles such as technology coordinator, special education coordinator, or curriculum director.

A projective plane tropical curve is a proper immersion of a graph into the real Cartesian plane subject to some conditions such as that the images of all the edges must be lines with rational slopes. Two important combinatorial invariants of a projective plane tropical curve are its degree, d, and genus g. First, we explore Gathmann and Markwig's approach to the study of the moduli spaces of such curves and explain their proof that the number of projective plane tropical curves, counting multiplicity, passing through n = 3d + g -1 points does not depend on the choice of points, provided they are in tropical general position. This number of curves is called a Gromov-Written invariant. Second, we discuss the proof of a theorem of Mikhalkin that allows one to compute the Gromov-Written invariant by a purely combinatorial process of counting certain lattice paths.

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<p> The rapid development of the use of lasers in therapeutic and diagnostic medicine in the past few years has generated interest in measuring the optical properties of tissue. In particular, the development of photodynamic therapy (PDT) has necessitated studies of the optical properties of tissue at wavelengths around 630nm, this being the wavelength at which the photosensitizer commonly used in PDT, namely dihematoporphyrin ether (DHE), is normally activated.</p> <p> The control of the volume of tissue from which information about the interaction coefficients of the tissue is obtained is an important problem in diffuse reflectance spectroscopy and other applications of light, because it is critical to understanding which tissue volumes are sampled by the injected photons that eventually are re-emitted. This report describes a simple model that predicts the parameters that control the volume of tissue interrogated by photons during reflectance spectroscopy.</p> <p> In optical fiber based diffuse reflectance spectroscopy, incident radiation is applied at one point on a tissue surface and collected at another point, a radial distance, r, away. Information about the light multiply scattered by the tissue is used to deduce optical scattering and absorption coefficients of the tissue. In this report both steady state and pulse techniques are studied. In the steady state method, the spatial dependence of the backscattered light is the measured quantity, while the pulse technique uses the temporal broadening of a picosecond (ps) pulse to determine the interaction coefficients.</p> <p> The relative contribution of a volume element of tissue to the observed signal depends on its location, the measurement geometry and the optical properties of the tissue. Knowledge of this dependence would allow some control of the volume interrogated by reflectance spectroscopy, and would provide insight into the influence of inhomogeneities.</p> <p> In the work reported here a simple diffusion model of light propagation in tissue based on the Boltzmann radiative transfer equation has been used to derive mathematical expressions for the relative time spent by photons in a given tissue volume element. Using optical interaction coefficients typical of mammalian soft tissues, results are presented for both steady state and pulse irradiation in both semi-infinite and infinite media.</p> <p> The residency time depth profile calculated by this model for index matched and zero fluence boundary conditions has the same shape as that predicted by Weiss (1989), who used a somewhat different model based on a 3-dimensional random walk theory. These profiles are characterized by a build-up region near the surface and exponential fall far away from the surface in the 'diffusion region'. The influence of the absorption coefficient μa and the fiber separation on the residency time as predicted by this model is in good agreement to that predicted by the random-walk theory (i.e the depth-profile of the residency time tends to sharpen as the absorption coefficient increases. This is attributed to the fact that long trajectories are less likely with large absorption probabilities. As well, the greater the fiber separation, the wider and flatter the depth distribution of the residency time. This is because photons that reach the surface at greater r values have, in general, migrated farther from the immediate vicinity of the source and detector and hence have sampled a larger volume of tissue). All the integrations in this report were performed numerically using the IMSL/LIB on the Microvax computer system in the Hamilton Regional Cancer Center. The adequacy of this numerical integration was tested and was found to be good.</p> <p> This model therefore suggests that during diffuse reflectance spectroscopy, the volume sampled by re-emitted photons can be controlled by changing parameters such as the fiber separation (in both steady state and time-resolved techniques) and the detection time (in the time-resolved method).</p> / Thesis / Master of Science (MSc)

Signaling pathways are widely studied in systems biology. Several databases catalog our knowledge of these pathways, including the proteins and interactions that comprise them. However, high-quality curation of this information is slow and painstaking. As a result, many interactions still lack annotation concerning the pathways they participate in. A natural question that arises is whether or not it is possible to automatically leverage existing annotations to identify new interactions for inclusion in a given pathway. Here, we present RegLinker, an algorithm that achieves this purpose by computing multiple short paths from pathway receptors to transcription factors (TFs) within a background interaction network. The key idea underlying RegLinker is the use of regular-language constraints to control the number of non-pathway edges present in the computed paths. We systematically evaluate RegLinker and alternative approaches against a comprehensive set of 15 signaling pathways and demonstrate that RegLinker exhibits superior recovery of withheld pathway proteins and interactions. These results show the promise of our approach for prioritizing candidates for experimental study and the broader potential of automated analysis to attenuate difficulties of traditional manual inquiry. / Master of Science / Cells in the human body are constantly receiving signals that inform their response to a variety of conditions. These signals serve as cues to a cell, allowing it to make informed decisions that impact cellular processes such as movement, growth, and death. Cells employ proteins and the interactions between them to achieve these capabilities. Signals manifest as molecules that interact with proteins bound to membrane of a cell. When this happens, a cascade of interactions between the proteins inside the cell will be set off. Ultimately, this cascade activate or inhibit the cell’s production of new proteins, constituting a response to the signal received. The proteins and interactions involved in such a cascade together form what is known as a signaling pathway. Experiments have uncovered the interactions that are present in many signaling pathways, and researchers have carefully cataloged this information in publicly available databases. However, high-quality curation is slow and painstaking, and many known interactions have not been annotated as belonging to any pathway. A natural question that arises is whether or not it is possible to leverage existing annotations to automatically determine which new interactions to include in a given pathway. In this thesis, we present an efficient algorithm, RegLinker, for this purpose. We evaluate this method and alternative approaches on a comprehensive set of 15 signaling pathways and demonstrate that RegLinker is better at recovering interactions withheld from these pathways. In particular, we show RegLinker’s superior ability to identify interactions that utilize proteins that were not previously considered part of a pathway. These results underscore the promise of our approach for prioritizing candidates for experimental study and the broader potential of automated analysis to attenuate difficulties of traditional manual inquiry.

The minimum-time for a robot arm has been a longstanding and unsolved problem of considerable interest. We present a general solution to this problem that involves joint-space tesselation, a dynamic time-scaling algorithm, and graph search. The solution incorporates full dynamics of movement and actuator constraints, and can be easily extended for joint limits and work space obstacles, but is subject to the particular tesselation scheme used. The results presented show that, in general the optimal paths are not straight lines, bit rather curves in joint-space that utilize the dynamics of the arm and gravity to help in moving the arm faster to its destination. Implementation difficulties due to the tesselation and to combinatorial proliferation of paths are discussed.

Walden's Paths, created by the Center for the Study of Digital Libraries, provides a mechanism for leveraging student learning with the incredible amount of educational material on the web by organizing selected web pages into a structured learning activity. Applying specialized templates to the creation of Walden's Paths can aid a path author in creating pedagogically sound, Web-based activities, by assisting in the collection of information and organization of the activity. Authoring templates may be based on established educational frameworks, learning theories or specific activity type. This research project investigates how using pedagogically based templates affects the authoring process for paths created using Walden's Paths. A template based on the educational framework Inquiry-Based Learning was created and tested by a group of users to determine what effects the template has on creating paths as compared to creating similar paths using the existing Walden's Paths interface.

The problem of computing K shortest loopless paths, or ranking of the K shortest loopless paths between a pair of given vertices in a network is a well-studied generalization of shortest path problem. The K shortest paths problem determines not only one shortest path but the K best shortest paths from s to t in an increasing order of weight of the paths. Yen’s algorithm is known to be the efficient and widely used algorithm for determining K shortest loopless paths. Here, we introduce a new algorithm by modifying the Yen’s algorithm in the following way: instead of removing the vertices and the edges from the graph, we store them in two different sets. Then we modified the Dijkstra’s algorithm by taking these two sets into consideration. Thus the algorithm applies glass box methodology by using the modified Dijkstra’s algorithm for our dedicated purpose. Thus the efficiency is improved. The computational results conducted over different datasets, shows the proposed algorithm has better performance results.

Induced graphs are used to describe the structure of a graph, one such type of induced graph that has been studied are long paths. In this thesis we show a way to represent such graphs in terms of an array with two colors and a labeled graph. Using this representation and the techniques of Polya counting we will then be able to get upper and lower bounds for graphs containing a long path as an induced subgraph. In particular, if we let P(n,k) be the number of graphs on n+k vertices which contains P_n, a path on n vertices, as an induced subgraph then using our upper and lower bounds for P(n,k) we will show that for any fixed value of k that P(n,k)~2^(nk+k_C_2)/(2k!).

A set of subsets is said to have the Helly property if the condition that each pair of subsets has a non-empty intersection implies that the intersection of all subsets has a non-empty intersection. In 1966, Gallai noticed that the set of all longest paths of a connected graph is pairwise intersecting and asked if the set had the Helly property. While it is not true in general, a number of classes of graphs have been shown to have the property. In this dissertation, we show that K4-minor-free graphs, interval graphs, circular arc graphs, and the intersection graphs of spider graphs are classes that have this property. The accuracy of facial recognition algorithms on images taken in controlled conditions has improved significantly over the last two decades. As the focus is turning to more unconstrained or relaxed conditions and toward videos, there is a need to better understand what factors influence performance. If these factors were better understood, it would be easier to predict how well an algorithm will perform when new conditions are introduced. Previous studies have studied the effect of various factors on the verification rate (VR), but less attention has been paid to the false accept rate (FAR). In this dissertation, we study the effect various factors have on the FAR as well as the correlation between marginal FAR and VR. Using these relationships, we propose two models to predict marginal VR and demonstrate that the models predict better than using the previous global VR.