Sinc-Galerkin estimation of diffusivity in parabolic problems

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise

Numerical recovery of material parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness parameter in fourth-order time-dependence problems with fixed and cantilever boundary conditions is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains. This yields an approximation solution which converges exponentially and is valid on the infinite time interval. When the forward methods are applied to parameter recovery problems, the resulting inverse problems are ill-posed. Tikhonov regularization is applied and the resulting minimization problems are solved via a quasi-Newton/trust region algorithm. The L-curve method is used to determine an appropriate value of the regularization parameter. Numerical results which highlight the method are given for problems with both fixed and cantilever boundary conditions

Orthotic management of cerebral palsy : recommendations from a consensus conference

An international multidisciplinary group of healthcare professionals and researchers participated in a consensus conference on the management of cerebral palsy, convened by the International Society for Prosthetics and Orthotics. Participants reviewed the evidence and considered contemporary thinking on a range of treatment options including physical and occupational therapy, and medical, surgical and orthotic interventions. The quality of many of the reviewed papers was compromised by inadequate reporting and lack of transparency, in particular regarding the types of patients and the design of the interventions being evaluated. Substantial evidence suggests that ankle-foot orthoses (AFOs) that control the foot and ankle in stance and swing phases can improve gait efficiency in ambulant children (GMFCS levels I-III). By contrast, little high quality evidence exists to support the use of orthoses for the hip, spine or upper limb. Where the evidence for orthosis use was not compelling consensus was reached on recommendations for orthotic intervention. Subsequent group discussions identified recommendations for future research. The evidence to support using orthoses is generally limited by the brevity of follow-up periods in research studies; hence the extent to which orthoses may prevent deformities developing over time remains unclear. The full report of the conference can be accessed free of charge at www.ispoint.org

Skeleton Structures and Origami Design

In this dissertation we study problems related to polygonal skeleton structures that have applications to computational origami. The two main structures studied are the straight skeleton of a simple polygon (and its generalizations to planar straight line graphs) and the universal molecule of a Lang polygon. This work builds on results completed jointly with my advisor Ileana Streinu. Skeleton structures are used in many computational geometry algorithms. Examples include the medial axis, which has applications including shape analysis, optical character recognition, and surface reconstruction; and the Voronoi diagram, which has a wide array of applications including geographic information systems (GIS), point location data structures, motion planning, etc. The straight skeleton, studied in this work, has applications in origami design, polygon interpolation, biomedical imaging, and terrain modeling, to name just a few. Though the straight skeleton has been well studied in the computational geometry literature for over 20 years, there still exists a significant gap between the fastest algorithms for constructing it and the known lower bounds. One contribution of this thesis is an efficient algorithm for computing the straight skeleton of a polygon, polygon with holes, or a planar straight-line graph given a secondary structure called the induced motorcycle graph. The universal molecule is a generalization of the straight skeleton to certain convex polygons that have a particular relationship to a metric tree. It is used in Robert Lang\u27s seminal TreeMaker method for origami design. Informally, the universal molecule is a subdivision of a polygon (or polygonal sheet of paper) that allows the polygon to be ``folded\u27\u27 into a particular 3D shape with certain tree-like properties. One open problem is whether the universal molecule can be rigidly folded: given the initial flat state and a particular desired final ``folded\u27\u27 state, is there a continuous motion between the two states that maintains the faces of the subdivision as rigid panels? A partial characterization is known: for a certain measure zero class of universal molecules there always exists such a folding motion. Another open problem is to remove the restriction of the universal molecule to convex polygons. This is of practical importance since the TreeMaker method sometimes fails to produce an output on valid input due the convexity restriction and extending the universal molecule to non-convex polygons would allow TreeMaker to work on all valid inputs. One further interesting problem is the development of faster algorithms for computing the universal molecule. In this thesis we make the following contributions to the study of the universal molecule. We first characterize the tree-like family of surfaces that are foldable from universal molecules. In order to do this we define a new family of surfaces we call Lang surfaces and prove that a restricted class of these surfaces are equivalent to the universal molecules. Next, we develop and compare efficient implementations for computing the universal molecule. Then, by investigating properties of broader classes of Lang surfaces, we arrive at a generalization of the universal molecule from convex polygons in the plane to non-convex polygons in arbitrary flat surfaces. This is of both practical and theoretical interest. The practical interest is that this work removes the case from Lang\u27s TreeMaker method that causes TreeMaker to fail to produce output in the presence of non-convex polygons. The theoretical interest comes from the fact that our generalization encompasses more than just those surfaces that can be cut out of a sheet of paper, and pertains to polygons that cannot be lied flat in the plane without self-intersections. Finally, we identify a large class of universal molecules that are not foldable by rigid folding motions. This makes progress towards a complete characterization of the foldability of the universal molecule

The Role of Dopamine in Decision Making Processes in Drosophila Melanogaster

Understanding the neural processes that mediate decision making is a relatively new field of investigation in the scientific community. With the ultimate goal of understanding how humans decide between one path and another, simpler models such as Drosophila Melanogaster, the common fruit fly, are often utilized as a way of determining the neural circuits involved in these decision-making processes. One of the most important decisions flies make is the decision of where to lay their eggs (oviposit). Choosing the proper substrate upon which to lay eggs is a crucial decision that can ultimately impact their fecundity. This paper investigates the field of decision-making neuroscience research previously conducted in order to provide background information and point out the void that my research is attempting to fill. In conducting research, I first began by collecting data on the number of eggs laid by wildtype flies on each substrate type (sucrose, yeast, combination, or plain) within the 20 chamber two-choice preference assay. Following this, the same procedure was conducted using dopamine knockout flies created by crossing KIR2.1 genetically encoded flies with specific dopamine output neurons which inhibited their function. Our lab found that wildtype flies prefer yeast and avoid sucrose. They also tend to choose a plain substrate in Plain vs. Sucrose-Yeast. Though the genetically altered flies also prefer plain, a significant decrease in preference was observed in four of the mushroom body output neuron lines (057B, 027C, 542B, 543B) indicating that these lines may play a more significant role in determining this preference for Plain over Sucrose-yeast. These neurons that mediate crucial decisions for fruit flies can hopefully one day be correlated to the dopamine neurons in the human brain that help us make simple, everyday decisions and even life-changing decisions such as where to settle down someday and lay our own eggs

Numerical Investigation of Statistical Turbulence Effects on Beam Propagation through 2-D Shear Mixing Layer

A methodology is developed for determining the validity of making a statistical turbulent approach using Kolmogorov theory to an aero-optical turbulent ow. Kolmogorov theory provides a stochastic method that has a greatly simplified and robust method for calculating atmospheric turbulence effects on optical beam propagation, which could simplify similar approaches to chaotic aero-optical flows. A 2-D laminar Navier-Stokes CFD Solver (AVUS) is run over a splitter plate type geometry to create an aero-optical like shear mixing layer turbulence field. A Matlab algorithm is developed to import the flow data and calculates the structure functions, structure constant, and Fried Parameter (ro) and compares them to expected Kolmogorov distributions assuming an r2/3 power law. The range of C2n\u27s developed from the structure functions are not constant with separation distance, and ranged between 10-12-10-10. There is a consistent range of data overlap within the C2n\u27s derived from various methods for separation distances within the range 0.01m-0.02m. Within this range ro is found to be approximately 0.05m which is a reasonable value. This particular 2-D shear mixing layer was found to be non-Kolmogorov, but further grid refinement and data sampling may provide a more Kolmogorov like distribution