Algebraic Properties of Parikh Matrices of Words under an Extension of Thue Morphism

The Parikh matrix of a word $w$ over an alphabet $\{a_1, \cdots , a_k \}$ with an ordering $a_1 < a_2 < \cdots a_k,$ gives the number of occurrences of each factor of the word $a_1 \cdots a_k$ as a (scattered) subword of the word $w.$ Two words $u,v$ are said to be $M-$equivalent, if the Parikh matrices of $u$ and $v$ are the same. On the other hand properties of image words under different morphisms have been studied in the context of subwords and Parikh matrices. Here an extension to three letters, introduced by S$\acute{e}\acute{e}$bold (2003), of the well-known Thue morphism on two letters, is considered and properties of Parikh matrices of morphic images of words are investigated. The significance of the contribution is that various classes of binary words are obtained whose images are $M-$equivalent under this extended morphism

Two-Dimensional Digitized Picture Arrays and Parikh Matrices

Parikh matrix mapping or Parikh matrix of a word has been introduced in the literature to count the scattered subwords in the word. Several properties of a Parikh matrix have been extensively investigated. A picture array is a two-dimensional connected digitized rectangular array consisting of a finite number of pixels with each pixel in a cell having a label from a finite alphabet. Here we extend the notion of Parikh matrix of a word to a picture array and associate with it two kinds of Parikh matrices, called row Parikh matrix and column Parikh matrix. Two picture arrays A and B are defined to be M-equivalent if their row Parikh matrices are the same and their column Parikh matrices are the same. This enables to extend the notion of M-ambiguity to a picture array. In the binary and ternary cases, conditions that ensure M-ambiguity are then obtained

Algebraic Properties of Parikh Matrices of Binary Picture Arrays

A word is a finite sequence of symbols. Parikh matrix of a word is an upper triangular matrix with ones in the main diagonal and non-negative integers above the main diagonal which are counts of certain scattered subwords in the word. On the other hand a picture array, which is a rectangular arrangement of symbols, is an extension of the notion of word to two dimensions. Parikh matrices associated with a picture array have been introduced and their properties have been studied. Here we obtain certain algebraic properties of Parikh matrices of binary picture arrays based on the notions of power, fairness and a restricted shuffle operator extending the corresponding notions studied in the case of words. We also obtain properties of Parikh matrices of arrays formed by certain geometric operations

Certain Distance-Based Topological Indices of Parikh Word Representable Graphs

Relating graph structures with words which are finite sequences of symbols, Parikh word representable graphs ($PWRGs$) were introduced. On the other hand in chemical graph theory, graphs have been associated with molecular structures. Also several topological indices have been defined in terms of graph parameters and studied for different classes of graphs. In this paper, we derive expressions for computing certain topological indices of $PWRGs$ of binary core words, thereby enriching the study of $PWRGs.

Automated Semantic Understanding of Human Emotions in Writing and Speech

Affective Human Computer Interaction (A-HCI) will be critical for the success of new technologies that will prevalent in the 21st century. If cell phones and the internet are any indication, there will be continued rapid development of automated assistive systems that help humans to live better, more productive lives. These will not be just passive systems such as cell phones, but active assistive systems like robot aides in use in hospitals, homes, entertainment room, office, and other work environments. Such systems will need to be able to properly deduce human emotional state before they determine how to best interact with people. This dissertation explores and extends the body of knowledge related to Affective HCI. New semantic methodologies are developed and studied for reliable and accurate detection of human emotional states and magnitudes in written and spoken speech; and for mapping emotional states and magnitudes to 3-D facial expression outputs. The automatic detection of affect in language is based on natural language processing and machine learning approaches. Two affect corpora were developed to perform this analysis. Emotion classification is performed at the sentence level using a step-wise approach which incorporates sentiment flow and sentiment composition features. For emotion magnitude estimation, a regression model was developed to predict evolving emotional magnitude of actors. Emotional magnitudes at any point during a story or conversation are determined by 1) previous emotional state magnitude; 2) new text and speech inputs that might act upon that state; and 3) information about the context the actors are in. Acoustic features are also used to capture additional information from the speech signal. Evaluation of the automatic understanding of affect is performed by testing the model on a testing subset of the newly extended corpus. To visualize actor emotions as perceived by the system, a methodology was also developed to map predicted emotion class magnitudes to 3-D facial parameters using vertex-level mesh morphing. The developed sentence level emotion state detection approach achieved classification accuracies as high as 71% for the neutral vs. emotion classification task in a test corpus of children’s stories. After class re-sampling, the results of the step-wise classification methodology on a test sub-set of a medical drama corpus achieved accuracies in the 56% to 84% range for each emotion class and polarity. For emotion magnitude prediction, the developed recurrent (prior-state feedback) regression model using both text-based and acoustic based features achieved correlation coefficients in the range of 0.69 to 0.80. This prediction function was modeled using a non-linear approach based on Support Vector Regression (SVR) and performed better than other approaches based on Linear Regression or Artificial Neural Networks

High speed all-optical switching based on a single-arm interferometer

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaves 125-133).by Naimish S. Patel.M.Eng