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

Assessing the suitability of ship design for human factors issues associated with evacuation and normal operations

Evaluating ship layout for human factors (HF) issues using simulation software such as maritimeEXODUS can be a long and complex process. The analysis requires the identification of relevant evaluation scenarios; encompassing evacuation and normal operations; the development of appropriate measures which can be used to gauge the performance of crew and vessel and finally; the interpretation of considerable simulation data. In this paper we present a systematic and transparent methodology for assessing the HF performance of ship design which is both discriminating and diagnostic. The methodology is demonstrated using two variants of a hypothetical naval ship

Fast MCMC algorithms, Stability and DeepTune

Drawing samples from a known distribution is a core computational challenge common to many disciplines, with applications in statistics, probability, operations research, and other areas involving stochastic models. In statistics, sampling methods are useful for both estimation and inference, including problems such as estimating expectations of desired quantities, computing probabilities of rare events, gauging volumes of particular sets, exploring posterior distributions and obtaining credible intervals etc.Facing massive high dimensional data, both computational efficiency and good statistical guarantees are more and more important in modern statistical and machine learning applications. In this thesis, centered around sampling algorithms, we consider the fundamental questions on their computational and statistical guarantees: How to design a fast sampling algorithm and how long should it be run? What are the statistical learning guarantee of these algorithms? Are there any trade-offs between computation and learning?To answer these questions, first we start with establishing non-asymptotic convergence guarantees for popular MCMC sampling algorithms in Bayesian literature: Metropolized Random Walk, Metropolis-adjusted Langevin algorithm and Hamiltonian Monte Carlo. To address a number of technical challenges arise enroute, we develop results based on the conductance profile in order to prove quantitative convergence guarantees general continuous state space Markov chains. Second, to confront a large class of constrained sampling problems, we introduce two new algorithms, Vaidya and John walks, to sample from polytope-constrained distributions with convergence guarantees. Third, we prove fundamental trade-off results between statistical learning performance and convergence rate of any iterative learning algorithm, including sample algorithms. The trade-off results allow us to show that a too stable algorithm can not converge too fast, and vice-versa. Finally, to help neuroscientists analyze their massive amount of brain data, we develop DeepTune, a stability-driven visualization and interpretation framework via optimization and sampling for the neural-network-based models of neurons in visual cortex