Determining Critical Points of Handwritten Mathematical Symbols Represented as Parametric Curves

We consider the problem of computing critical points of plane curves represented in a finite orthogonal polynomial basis. This is motivated by an approach to the recognition of hand-written mathematical symbols in which the initial data is in such an orthogonal basis and it is desired to avoid ill-conditioned basis conversions. Our main contribution is to assemble the relevant mathematical tools to perform all the necessary operations in the orthogonal polynomial basis. These include implicitization, differentiation, root finding and resultant computation

Advances in Manipulation and Recognition of Digital Ink

Handwriting is one of the most natural ways for a human to record knowledge. Recently, this type of human-computer interaction has received increasing attention due to the rapid evolution of touch-based hardware and software. While hardware support for digital ink reached its maturity, algorithms for recognition of handwriting in certain domains, including mathematics, are lacking robustness. Simultaneously, users may possess several pen-based devices and sharing of training data in adaptive recognition setting can be challenging. In addition, resolution of pen-based devices keeps improving making the ink cumbersome to process and store. This thesis develops several advances for efficient processing, storage and recognition of handwriting, which are applicable to the classification methods based on functional approximation. In particular, we propose improvements to classification of isolated characters and groups of rotated characters, as well as symbols of substantially different size. We then develop an algorithm for adaptive classification of handwritten mathematical characters of a user. The adaptive algorithm can be especially useful in the cloud-based recognition framework, which is described further in the thesis. We investigate whether the training data available in the cloud can be useful to a new writer during the training phase by extracting styles of individuals with similar handwriting and recommending styles to the writer. We also perform factorial analysis of the algorithm for recognition of n-grams of rotated characters. Finally, we show a fast method for compression of linear pieces of handwritten strokes and compare it with an enhanced version of the algorithm based on functional approximation of strokes. Experimental results demonstrate validity of the theoretical contributions, which form a solid foundation for the next generation handwriting recognition systems

Hitting the right target : noninvasive localization of the subthalamic nucleus motor part for specific deep brain stimulation

Deep brain stimulation of the subthalamic nucleus (STN) has gained momentum as a therapy for advanced Parkinson’s disease. The stimulation effectively alleviates the patients’ typical motor symptoms on a long term, but can give rise to cognitive and psychiatric adverse effects as well. Based on primate studies, the STN has been divided into three functionally different parts, which were distinguished by their afferent and efferent connections. The largest part is the motor area, followed by an associative and a limbic area. The serious adverse effects on cognition and behavior occurring after deep brain stimulation are assumed to be caused by electrical current spread to the associative and limbic areas of the STN. Therefore, selective stimulation of the motor part of the STN seems crucial, both to obtain the best possible therapeutic effect on the motor symptoms and to minimize the debilitating effects on cognition and behavior. However, current medical imaging techniques do not yet facilitate the required accurate identification of the STN itself, let alone its different functional areas. The final target for DBS is still often adjusted using intraoperative electrophysiology. Therefore, in this thesis we aimed to improve imaging for deep brain stimulation using noninvasive MRI protocols, in order to identify the STN and its motor part. We studied the advantages and drawbacks of already available noninvasive methods to target the STN. This review did not lead to a straightforward conclusion; identification of the STN motor part remained an open question. In follow-up on this question, we investigated the possibility to distinguish the different functional STN parts based on their connectivity information. Three types of information were carefully analyzed in this thesis. First, we looked into the clustering of local diffusion information within the STN region. We visually inspected the complex diffusion profiles, derived from postmortem rat brain data with high angular resolution, and augmented this manual segmentation method using k-means and graph cuts clustering. Because the weighing of different orders of diffusion information in the traditionally used L2 norm on the orientation distribution functions (ODFs) remained an open issue, we developed a specialized distance measure, the so-called Sobolev norm. This norm does not only take into account the amplitudes of the diffusion profiles, but also their extrema. We showed it to perform better than the L2 norm on synthetic phantom data and real brain (thalamus) data. The research done on this topic facilitates better classification by clustering of gray matter structures in the (deep) brain. Secondly, we were the first to analyze the STN’s full structural connectivity, based on probabilistic fiber tracking in diffusion MRI data of healthy volunteers. The results correspond well to topical literature on STN projections. Furthermore, we assessed the structural connectivity per voxel of the STN seed region and discovered a gradient in connectivity to the premotor cortex within the STN. While going from the medial to the lateral part of the STN, the connectivity increases, confirming the expected lateral location of the STN motor part. Finally, the connectivity analysis produced evidence for the existence of a "hyperdirect" pathway between the motor cortex and the STN in humans, which is very useful for future research into stimulation targets. The results of these experiments indicate that it is possible to find the motor part of the STN as specific target for deep brain stimulation using structural connectivity information acquired in a noninvasive way. Third and last, we studied functional connectivity using resting state functional MRI data of healthy volunteers. The resulting significant clusters provided us with the first complete description of the STN’s resting state functional connectivity, which corresponds with the expectations based on available literature. Moreover, we performed a reverse regression procedure with the average time series signals in motor and limbic areas as principal regressors. The results were analyzed for each STN voxel separately and also showed mediolateral gradients in functional connectivity within the STN. The lateral STN part exhibited more motor connectivity, while the medial part seemed to be more functionally connected to limbic brain areas, as described in neuronal tracer studies. These results show that functional connectivity analysis also is a viable noninvasive method to find the motor part of the STN. The work on noninvasive MRI methods for identification of the STN and its functional parts, as presented in this thesis, thus contributes to future specific stimulation of the motor part of the STN for deep brain stimulation in patients with Parkinson’s disease. This may help to maximize the motor effects and minimize severe cognitive and psychiatric side effects

Automated recognition of handwritten mathematics

Most software programs that deal with mathematical objects require input expressions to be linearized using somewhat awkward and unfamiliar string-based syntax. It is natural to desire a method for inputting mathematics using the same two-dimensional syntax employed with pen and paper, and the increasing prevalence of pen- and touch-based interfaces causes this topic to be of practical as well as theoretical interest. Accurately recognizing two-dimensional mathematical notation is a difficult problem that requires not only theoretical advancement over the traditional theories of string-based languages, but also careful consideration of runtime efficiency, data organization, and other practical concerns that arise during system construction. This thesis describes the math recognizer used in the MathBrush pen-math system. At a high level, the two-dimensional syntax of mathematical writing is formalized using a relational grammar. Rather than reporting a single recognition result, all recognizable interpretations of the input are simultaneously represented in a data structure called a parse forest. Individual interpretations may be extracted from the forest and reported one by one as the user requests them. These parsing techniques necessitate robust tree scoring functions, which themselves rely on several lower-level recognition processes for stroke grouping, symbol recognition, and spatial relation classification. The thesis covers the recognition, parsing, and scoring aspects of the MathBrush recognizer, as well as the algorithms and assumptions necessary to combine those systems and formalisms together into a useful and efficient software system. The effectiveness of the resulting system is measured through two accuracy evaluations. One evaluation uses a novel metric based on user effort, while the other replicates the evaluation process of an international accuracy competition. The evaluations show that not only is the performance of the MathBrush recognizer improving over time, but it is also significantly more accurate than other academic recognition systems

NASA thesaurus. Volume 2: Access vocabulary

The access vocabulary, which is essentially a permuted index, provides access to any word or number in authorized postable and nonpostable terms. Additional entries include postable and nonpostable terms, other word entries and pseudo-multiword terms that are permutations of words that contain words within words. The access vocabulary contains almost 42,000 entries that give increased access to the hierarchies in Volume 1 - Hierarchical Listing

NASA thesaurus. Volume 1: Hierarchical Listing

There are over 17,000 postable terms and nearly 4,000 nonpostable terms approved for use in the NASA scientific and technical information system in the Hierarchical Listing of the NASA Thesaurus. The generic structure is presented for many terms. The broader term and narrower term relationships are shown in an indented fashion that illustrates the generic structure better than the more widely used BT and NT listings. Related terms are generously applied, thus enhancing the usefulness of the Hierarchical Listing. Greater access to the Hierarchical Listing may be achieved with the collateral use of Volume 2 - Access Vocabulary and Volume 3 - Definitions

Ohio State University Bulletin

Classes available for students to enroll in during the 1997-1998 academic year for The Ohio State University

Ohio State University Bulletin

Classes available for students to enroll in during the 1998-1999 academic year for The Ohio State University

Ohio State University Bulletin

Classes available for students to enroll in during the 1983-1984 academic year for The Ohio State University

Ohio State University Bulletin

Classes available for students to enroll in during the 2004-2005 academic year for The Ohio State University