title: Embedding negative structures to model holes and cut-outs

authors: Ilanko, Sinniah

subjects: negative structure

abstract: It has now been established that geometric boundary conditions and continuity conditions can be modelled by using either positive or negative stiffness or inertia type penalty term [1-5]. The experience of working with negative stiffness and inertial parameters has led to the question: what if both stiffness and mass were to be taken as negative? Changing the sign of all stiffness and inertial terms of a structure is simply equivalent to multiplying both sides of an eigenvalue equation by minus one, which does not change its frequencies or modes. Basically, a negative structure in such a sense has the same vibratory properties as that of its positive counterpart, although the structure itself may not have a physical meaning.

text: Embedding negative structures to model holes and cut-outs It has now been established that geometric boundary conditions and continuity conditions can be modelled by using either positive or negative stiffness or inertia type penalty term [1-5]. The experience of working with negative stiffness and inertial parameters has led to the question: what if both stiffness and mass were to be taken as negative? Changing the sign of all stiffness and inertial terms of a structure is simply equivalent to multiplying both sides of an eigenvalue equation by minus one, which does not change its frequencies or modes. Basically, a negative structure in such a sense has the same vibratory properties as that of its positive counterpart, although the structure itself may not have a physical meaning.

year: 2009

title: The average order of the Dirichlet series of the gcd-sum function

authors: Broughan, Kevin A.

subjects: mathematics

abstract: Using a result of Bordellès, we derive the second term and improved error expressions for the partial sums of the Dirichlet series of the gcd-sum function, for all real values of the parameter.

text: The average order of the Dirichlet series of the gcd-sum function Using a result of Bordellès, we derive the second term and improved error expressions for the partial sums of the Dirichlet series of the gcd-sum function, for all real values of the parameter.

year: 2007

title: A hybrid architecture for labelling bilingual Māori-English tweets

authors: Trye, David

subjects: borrowing

abstract: Most large-scale language detection tools perform poorly at identifying Māori text. Moreover, rule-based and machine learning-based techniques devised specifically for the Māori-English language pair struggle with interlingual homographs. We develop a hybrid architecture that couples Māori-language orthography with machine learning models in order to annotate mixed Māori-English text. This architecture is used to label a new bilingual Twitter corpus at both the token (word) and tweet (sentence) levels. We use the collected tweets to show that the hybrid approach outperforms existing systems with respect to language detection of interlingual homographs and overall accuracy. We also evaluate its performance on out-of-domain data. Two interactive visualisations are provided for exploring the Twitter corpus and comparing errors across the new and existing techniques. The architecture code and visualisations are available online, and the corpus is available on request.

text: A hybrid architecture for labelling bilingual Māori-English tweets Most large-scale language detection tools perform poorly at identifying Māori text. Moreover, rule-based and machine learning-based techniques devised specifically for the Māori-English language pair struggle with interlingual homographs. We develop a hybrid architecture that couples Māori-language orthography with machine learning models in order to annotate mixed Māori-English text. This architecture is used to label a new bilingual Twitter corpus at both the token (word) and tweet (sentence) levels. We use the collected tweets to show that the hybrid approach outperforms existing systems with respect to language detection of interlingual homographs and overall accuracy. We also evaluate its performance on out-of-domain data. Two interactive visualisations are provided for exploring the Twitter corpus and comparing errors across the new and existing techniques. The architecture code and visualisations are available online, and the corpus is available on request.

year: 2022