Neural network based off-line handwritten text recognition system

This dissertation introduces a new system for handwritten text recognition based on an improved neural network design. Most of the existing neural networks treat mean square error function as the standard error function. The system as proposed in this dissertation utilizes the mean quartic error function, where the third and fourth derivatives are non-zero. Consequently, many improvements on the training methods were achieved. The training results are carefully assessed before and after the update. To evaluate the performance of a training system, there are three essential factors to be considered, and they are from high to low importance priority: (1) error rate on testing set, (2) processing time needed to recognize a segmented character and (3) the total training time and subsequently the total testing time. It is observed that bounded training methods accelerate the training process, while semi-third order training methods, next-minimal training methods, and preprocessing operations reduce the error rate on the testing set. Empirical observations suggest that two combinations of training methods are needed for different case character recognition. Since character segmentation is required for word and sentence recognition, this dissertation provides also an effective rule-based segmentation method, which is different from the conventional adaptive segmentation methods. Dictionary-based correction is utilized to correct mistakes resulting from the recognition and segmentation phases. The integration of the segmentation methods with the handwritten character recognition algorithm yielded an accuracy of 92% for lower case characters and 97% for upper case characters. In the testing phase, the database consists of 20,000 handwritten characters, with 10,000 for each case. The testing phase on the recognition 10,000 handwritten characters required 8.5 seconds in processing time.

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 comparison of academic achievement of Montessori and non -Montessori students in a public school setting

Relationships between academic achievement and type of curriculum delivery system, Montessori or traditional, in a diverse group of learners from a public school district were examined in this study. In a repeated measures, within subjects design, students from an elementary Montessori program were paired with agemates from a traditional group on the basis of similar Stanford Achievement Test Scores in reading or math during the baseline year. Two subsequent administrations of the Stanford were observed for each subject to elucidate possible differences which might emerge based on program affiliation over the three year duration of the study. ^ Mathematics scores for both groups were not observed to be significantly different, although following the initial observation, the Montessori group continued to produce higher mean scores than did the traditional students. Marginal significance between the groups suggests that the data analysis should continue in an effort to elucidate a possible trend toward significance at the .05 level. ^ Reading scores for the groups demonstrated marginally significant differences by one analytical method, and significant differences when analyzed with a second method. In the second and third years of the study, Montessori students produced means which consistently outperformed the traditional group. ^ Recommendations included tracking subsequent administrations of the Stanford Achievement Test for all pairs of subjects in order to evaluate emerging trends in both subject areas. ^