title: Generalized Stäckel matrices

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: Stäckel and differential-Stäckel matrices are generalized so that the matrix elements may be functions of the derivatives of the dependent variable as well as the independent variable. The inverses of these matrices are characterized and it is shown that for significant classes of linear and nonlinear partial differential equations, variable separation is accomplished via this generalized Stäckel mechanism.

text: Generalized Stäckel matrices Stäckel and differential-Stäckel matrices are generalized so that the matrix elements may be functions of the derivatives of the dependent variable as well as the independent variable. The inverses of these matrices are characterized and it is shown that for significant classes of linear and nonlinear partial differential equations, variable separation is accomplished via this generalized Stäckel mechanism.

year: 1985-09

title: Cyber security visualization effectiveness

authors: Garae, Jeffery

subjects: Cyber Security

abstract: Security visualization utilises predefined data attributes and translates them into visual nodes to form images for the purpose of communicating critical security information to targeted audiences. It is commonly used for two reasons: exploring and reporting purposes thus, sharing insights on suspected security events. However, the challenge of selecting the best visualization out of two or more visualization samples, regardless of existing limitations such as screen dimensions and visual complexities, required users to utilise certain measurement criteria. These criteria urge security visualization researchers, developers and users (viewers) to ask themselves the following two questions: What makes a security visualization effective? How do we measure visualization effectiveness in the context of investigating, analysing, understanding and reporting cyber security incidents?

This thesis explores a range of effectiveness measurement techniques for web and mobile platforms. We investigated existing effectiveness methods for the design, implementation and user observation phases in security visualizations. Consequently, we identified effectiveness criteria and metrics in applications include visual clarity, visibility, distortion rates and user cognitive response (viewing) times. With the goal of aiding decision making in cyber security operations, we provided a distinctive security visualization paradigm of a full-scale effectiveness measurement (SvEm framework) approach for both theoretical and user-centric visualization techniques. Our framework facilitates effectiveness through our SvEm algorithm thus, providing various interactive three-dimensional (3D) visualization applications to enhance both single and multi-user collaboration.

The SvEm framework involves several key components: (1) web/mobile display dimensions and resolution, (2) security incident entities, (3) user cognitive activators and alerts, (4) working memory load, (5) threat scoring system and (6) the colour usage management. To evaluate effectiveness in our framework, we developed several use cases: (1) VisualProgger - a real-time security visualization analytic application (web and mobile platforms), (2) a security visualization with augmented reality and (3) a security visualization for intelligence tracking and monitoring. In addition, we developed and documented a new security visualization guideline (a SCeeVis pre-standard) as part of the SvEm framework to aid with the design, implementation and observation environments.

This pre-standard further allowed us to develop our SCeeVis colour chaining standard and a new cognition and working memory (SvEm-CWML) instruction set to enhance the user’s cognition and perception process for security visualizations. As a result, our visualization application outputs effectiveness measurement by capturing and increasing the user's attention span through the process of reducing cognitive load, while increasing the viewer’s memory efficiency. Thus, users have a high potential to gain security insights from a given visualization. Our evaluation shows that, viewers perform better with the existence of prior knowledge of security events and if they operate in a comfortable visual environment. It has also indicated that circular visualization designs attracted and maintained the viewer’s attention. Finally, these discoveries have revealed new research directions for future work relating to effectiveness measurement in security visualization.

text: Cyber security visualization effectiveness Security visualization utilises predefined data attributes and translates them into visual nodes to form images for the purpose of communicating critical security information to targeted audiences. It is commonly used for two reasons: exploring and reporting purposes thus, sharing insights on suspected security events. However, the challenge of selecting the best visualization out of two or more visualization samples, regardless of existing limitations such as screen dimensions and visual complexities, required users to utilise certain measurement criteria. These criteria urge security visualization researchers, developers and users (viewers) to ask themselves the following two questions: What makes a security visualization effective? How do we measure visualization effectiveness in the context of investigating, analysing, understanding and reporting cyber security incidents?

This thesis explores a range of effectiveness measurement techniques for web and mobile platforms. We investigated existing effectiveness methods for the design, implementation and user observation phases in security visualizations. Consequently, we identified effectiveness criteria and metrics in applications include visual clarity, visibility, distortion rates and user cognitive response (viewing) times. With the goal of aiding decision making in cyber security operations, we provided a distinctive security visualization paradigm of a full-scale effectiveness measurement (SvEm framework) approach for both theoretical and user-centric visualization techniques. Our framework facilitates effectiveness through our SvEm algorithm thus, providing various interactive three-dimensional (3D) visualization applications to enhance both single and multi-user collaboration.

The SvEm framework involves several key components: (1) web/mobile display dimensions and resolution, (2) security incident entities, (3) user cognitive activators and alerts, (4) working memory load, (5) threat scoring system and (6) the colour usage management. To evaluate effectiveness in our framework, we developed several use cases: (1) VisualProgger - a real-time security visualization analytic application (web and mobile platforms), (2) a security visualization with augmented reality and (3) a security visualization for intelligence tracking and monitoring. In addition, we developed and documented a new security visualization guideline (a SCeeVis pre-standard) as part of the SvEm framework to aid with the design, implementation and observation environments.

This pre-standard further allowed us to develop our SCeeVis colour chaining standard and a new cognition and working memory (SvEm-CWML) instruction set to enhance the user’s cognition and perception process for security visualizations. As a result, our visualization application outputs effectiveness measurement by capturing and increasing the user's attention span through the process of reducing cognitive load, while increasing the viewer’s memory efficiency. Thus, users have a high potential to gain security insights from a given visualization. Our evaluation shows that, viewers perform better with the existence of prior knowledge of security events and if they operate in a comfortable visual environment. It has also indicated that circular visualization designs attracted and maintained the viewer’s attention. Finally, these discoveries have revealed new research directions for future work relating to effectiveness measurement in security visualization.

year: 2019

title: Prismatic storying: Making visible multi coloured codes

authors: Stuart, Margaret J.

abstract: Language is a casement into cultures' deepest meanings. As children acquire languages, they implicitly adopt the mores of people around them; read the symbols, artefacts and codes. In this article, we examine the importance of language and literacy in the early childhood curriculum Te Whariki: He Whariki Matauranga mo nga Mokopuna o Aotearoa/Early Childhood Curriculum (Ministry of Education, 1996). The focus of the article is on literacy from a bicultural perspective. Adults support children in finding out about both their social and physical worlds. They use their 'imaginations to explore their own and others' identities' (MoE, 1996, p. 25). Our aim is to offer teachers in mainstream early childhood centres (ECE) strategies to apply, practise and situate literacy approaches that reflect Te Ao Maori through stories reflecting symbolic representations of people, places and things.

text: Prismatic storying: Making visible multi coloured codes Language is a casement into cultures' deepest meanings. As children acquire languages, they implicitly adopt the mores of people around them; read the symbols, artefacts and codes. In this article, we examine the importance of language and literacy in the early childhood curriculum Te Whariki: He Whariki Matauranga mo nga Mokopuna o Aotearoa/Early Childhood Curriculum (Ministry of Education, 1996). The focus of the article is on literacy from a bicultural perspective. Adults support children in finding out about both their social and physical worlds. They use their 'imaginations to explore their own and others' identities' (MoE, 1996, p. 25). Our aim is to offer teachers in mainstream early childhood centres (ECE) strategies to apply, practise and situate literacy approaches that reflect Te Ao Maori through stories reflecting symbolic representations of people, places and things.

year: 2018