title: N-gram models of agreement in language

authors: Smith, Anthony Clive

abstract: Conventional n-gram language models are well-established as powerful yet simple mechanisms for characterising language structure when low data complexity is the primary objective. Much of their predictive power can be traced to a relatively small number of common word sequences usually comprised of grammatical terms, and a large number of infrequent word patterns comprised of thematic terms with high mutual information. The drawback for conventional approaches is an exceedingly large number of other n-grams which waste probability mass without making a reciprocal contribution in the formulation of accurate probability estimates. 

This thesis describes a simple modification to the n-gram approach which attempts to preserve and enhance the most useful characteristics of conventional models while mitigating their weaknesses by eradicating low utility contexts. If one divides the vocabulary of a language into two broad classes - one comprised solely of contents words (nouns, verbs, adjectives, etc) and the other of grammatical words (determiners, prepositions, modal auxiliaries, etc.) - then language can be viewed as the interlacing of two lexical streams: a content word sequence and a grammatical word sequence. Two words are said to be “super-adjacent” if they are next to each other in one of the two streams. 

It is shown that an n-gram model of super-adjacent terms is better able to exploit the high mutual information of close proximity semantic words and the strong syntactic dependencies exhibited in patterns of grammatical words, while many low-utility n-grams that include words from both classes are eliminated. In addition, by reducing regularly inflected words to their base forms and moving inflectional suffixes to the grammatical stream, large numbers of low frequency content bigrams are collapsed into many fewer more general cases, and morphological agreement is made accessible in abstraction. The result is a more compact model that gives better complexity estimates than is possible from the conventional approach.

text: N-gram models of agreement in language Conventional n-gram language models are well-established as powerful yet simple mechanisms for characterising language structure when low data complexity is the primary objective. Much of their predictive power can be traced to a relatively small number of common word sequences usually comprised of grammatical terms, and a large number of infrequent word patterns comprised of thematic terms with high mutual information. The drawback for conventional approaches is an exceedingly large number of other n-grams which waste probability mass without making a reciprocal contribution in the formulation of accurate probability estimates. 

This thesis describes a simple modification to the n-gram approach which attempts to preserve and enhance the most useful characteristics of conventional models while mitigating their weaknesses by eradicating low utility contexts. If one divides the vocabulary of a language into two broad classes - one comprised solely of contents words (nouns, verbs, adjectives, etc) and the other of grammatical words (determiners, prepositions, modal auxiliaries, etc.) - then language can be viewed as the interlacing of two lexical streams: a content word sequence and a grammatical word sequence. Two words are said to be “super-adjacent” if they are next to each other in one of the two streams. 

It is shown that an n-gram model of super-adjacent terms is better able to exploit the high mutual information of close proximity semantic words and the strong syntactic dependencies exhibited in patterns of grammatical words, while many low-utility n-grams that include words from both classes are eliminated. In addition, by reducing regularly inflected words to their base forms and moving inflectional suffixes to the grammatical stream, large numbers of low frequency content bigrams are collapsed into many fewer more general cases, and morphological agreement is made accessible in abstraction. The result is a more compact model that gives better complexity estimates than is possible from the conventional approach.

year: 2000

title: Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere

authors: Kalnins, Ernie G.

subjects: superintegrability

abstract: We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). Further there is an algebraic relation at order 8 expressing the fact that there are only 5 algebraically independent generators. We work out the details of modeling physically relevant irreducible representations of the quadratic algebra in terms of divided difference operators in two variables. We determine several ON bases for this model including spherical and cylindrical bases. These bases are expressed in terms of two variable Wilson and Racah polynomials with arbitrary parameters, as defined by Tratnik. The generators for the quadratic algebra are expressed in terms of recurrence operators for the one-variable Wilson polynomials. The quadratic algebra structure breaks the degeneracy of the space of these polynomials. In an earlier paper the authors found a similar characterization of one variable Wilson and Racah polynomials in terms of irreducible representations of the quadratic algebra for the quantum superintegrable system on the 2-sphere with generic 3-parameter potential. This indicates a general relationship between 2nd order superintegrable systems and discrete orthogonal polynomials.

text: Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). Further there is an algebraic relation at order 8 expressing the fact that there are only 5 algebraically independent generators. We work out the details of modeling physically relevant irreducible representations of the quadratic algebra in terms of divided difference operators in two variables. We determine several ON bases for this model including spherical and cylindrical bases. These bases are expressed in terms of two variable Wilson and Racah polynomials with arbitrary parameters, as defined by Tratnik. The generators for the quadratic algebra are expressed in terms of recurrence operators for the one-variable Wilson polynomials. The quadratic algebra structure breaks the degeneracy of the space of these polynomials. In an earlier paper the authors found a similar characterization of one variable Wilson and Racah polynomials in terms of irreducible representations of the quadratic algebra for the quantum superintegrable system on the 2-sphere with generic 3-parameter potential. This indicates a general relationship between 2nd order superintegrable systems and discrete orthogonal polynomials.

year: 2011

title: Social deprivation in New Zealand

authors: Harcourt, Brian James

subjects: Deprivation

abstract: The purpose of the thesis was to better understand the phenomenon of social deprivation, world-wide and in particular in New Zealand. Social deprivation has been defined in many ways with multiple surrogates used to ‘measure’ its prevalence. The aim of this research was to provide examples of the lived experiences of social deprivation.

Social constructivist and interpretive lenses were used to portray the voices of those living in deprivation, as well as those people tasked to assist them. A narrative case study approach was employed with participants from Whānau Ora. This social and health initiative offered a holistic approach to assistance in contrast to the usual State agencies operating in a silo fashion, with separate agencies providing for different aspects of social deprivation such as housing, employment, mental health and other services. The approach of Whānau Ora is to support clients’ needs holistically and encourage people to develop their own plans for self- improvement. Navigators help people develop their plans and assist in their interactions with the various State agencies whose services they require. This approach allowed a better understanding of ways to overcome people’s feelings of powerlessness and desperation.

The findings from the study lead to suggestions for the application of evidence-based, complementary, integrated assistance programmes rather than having segregated public service agencies acting independently. The recommendations are simple yet require profound changes in public service operations when attempting to ameliorate or prevent social deprivation among citizens.

text: Social deprivation in New Zealand The purpose of the thesis was to better understand the phenomenon of social deprivation, world-wide and in particular in New Zealand. Social deprivation has been defined in many ways with multiple surrogates used to ‘measure’ its prevalence. The aim of this research was to provide examples of the lived experiences of social deprivation.

Social constructivist and interpretive lenses were used to portray the voices of those living in deprivation, as well as those people tasked to assist them. A narrative case study approach was employed with participants from Whānau Ora. This social and health initiative offered a holistic approach to assistance in contrast to the usual State agencies operating in a silo fashion, with separate agencies providing for different aspects of social deprivation such as housing, employment, mental health and other services. The approach of Whānau Ora is to support clients’ needs holistically and encourage people to develop their own plans for self- improvement. Navigators help people develop their plans and assist in their interactions with the various State agencies whose services they require. This approach allowed a better understanding of ways to overcome people’s feelings of powerlessness and desperation.

The findings from the study lead to suggestions for the application of evidence-based, complementary, integrated assistance programmes rather than having segregated public service agencies acting independently. The recommendations are simple yet require profound changes in public service operations when attempting to ameliorate or prevent social deprivation among citizens.

year: 2019