Representational information: a new general notion and measure\ud of information

In what follows, we introduce the notion of representational information (information conveyed by sets of dimensionally defined objects about their superset of origin) as well as an\ud original deterministic mathematical framework for its analysis and measurement. The framework, based in part on categorical invariance theory [Vigo, 2009], unifies three key constructsof universal science – invariance, complexity, and information. From this unification we define the amount of information that a well-defined set of objects R carries about its finite superset of origin S, as the rate of change in the structural complexity of S (as determined by its degree of categorical invariance), whenever the objects in R are removed from the set S. The measure captures deterministically the significant role that context and category structure play in determining the relative quantity and quality of subjective information conveyed by particular objects in multi-object stimuli

Normalized Information Distance

The normalized information distance is a universal distance measure for objects of all kinds. It is based on Kolmogorov complexity and thus uncomputable, but there are ways to utilize it. First, compression algorithms can be used to approximate the Kolmogorov complexity if the objects have a string representation. Second, for names and abstract concepts, page count statistics from the World Wide Web can be used. These practical realizations of the normalized information distance can then be applied to machine learning tasks, expecially clustering, to perform feature-free and parameter-free data mining. This chapter discusses the theoretical foundations of the normalized information distance and both practical realizations. It presents numerous examples of successful real-world applications based on these distance measures, ranging from bioinformatics to music clustering to machine translation.Comment: 33 pages, 12 figures, pdf, in: Normalized information distance, in: Information Theory and Statistical Learning, Eds. M. Dehmer, F. Emmert-Streib, Springer-Verlag, New-York, To appea

The descriptive theory of represented spaces

This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented spaces. Most material is from work-in-progress, and thus there may be a stronger focus on projects involving the author than an objective survey would merit.Comment: survey of work-in-progres

An analytic framework to assess organizational resilience

Background: Resilience Engineering is a paradigm for safety management that focuses on coping with complexity to achieve success, even considering several conflicting goals. Modern socio-technical systems have to be resilient to comply with the variability of everyday activities, the tight-coupled and underspecified nature of work and the nonlinear interactions among agents. At organizational level, resilience can be described as a combination of four cornerstones: monitoring, responding, learning and anticipating. Methods: Starting from these four categories, this paper aims at defining a semi-quantitative analytic framework to measure organizational resilience in complex socio-technical systems, combining the Resilience Analysis Grid (RAG) and the Analytic Hierarchy Process (AHP). Results: This paper presents an approach for defining resilience abilities of an organization, creating a structured domain-dependent framework to define a resilience profile at different levels of abstraction, to identify weaknesses and strengths of the system and thus potential actions to increase system’s adaptive capacity. An illustrative example in an anaesthesia department clarifies the outcomes of the approach. Conclusions: The outcome of the RAG, i.e. a weighted set of probing questions, can be used in different domains, as a support tool in a wider Safety-II oriented managerial action to bring safety management into the core business of the organization

Renormalization and Computation II: Time Cut-off and the Halting Problem

This is the second installment to the project initiated in [Ma3]. In the first Part, I argued that both philosophy and technique of the perturbative renormalization in quantum field theory could be meaningfully transplanted to the theory of computation, and sketched several contexts supporting this view. In this second part, I address some of the issues raised in [Ma3] and provide their development in three contexts: a categorification of the algorithmic computations; time cut--off and Anytime Algorithms; and finally, a Hopf algebra renormalization of the Halting Problem.Comment: 28 page

Assessing schematic knowledge of introductory probability theory

[Abstract]: The ability to identify schematic knowledge is an important goal for both assessment and instruction. In the current paper, schematic knowledge of statistical probability theory is explored from the declarative-procedural framework using multiple methods of assessment. A sample of 90 undergraduate introductory statistics students was required to classify 10 pairs of probability problems as similar or different; to identify whether 15 problems contained sufficient, irrelevant, or missing information (text-edit); and to solve 10 additional problems. The complexity of the schema on which the problems were based was also manipulated. Detailed analyses compared text-editing and solution accuracy as a function of text-editing category and schema complexity. Results showed that text-editing tends to be easier than solution and differentially sensitive to schema complexity. While text-editing and classification were correlated with solution, only text-editing problems with missing information uniquely predicted success. In light of previous research these results suggest that text-editing is suitable for supplementing the assessment of schematic knowledge in development

A model of downward abusive communication: exploring relationships between cognitive complexity, downward communicative adaptability, and downward abusive communication

Thesis (M.A.) University of Alaska Fairbanks, 2013A model was proposed to understand the antecedents of abusive supervision. Relationships were explored between cognitive complexity, downward communicative adaptability, and downward abusive communication. Superiors from various organizations were asked to take an online survey which measured superiors' cognitive complexity, downward communicative adaptability and abusive supervision. There was no evidence to support H1, which linked cognitive complexity to downward communicative adaptability, but there was evidence for H2, which stated that downward communicative adaptability was negatively correlated with downward abusive communication. The RCQ proved to be reliable but its validity was questioned in the present study which is why H1 may not have been supported.Chapter 1. Theory and research -- 1.1. Abusive supervision -- 1.2. Cognitive complexity -- 1.2.1. Constructs -- 1.2.2. Cognitive complexity -- 1.2.3. Effects of cognitive complexity -- 1.2.3.1. Relational compatibility -- 1.2.3.2. Interpersonal problem solving -- 1.2.3.3. Perceptual differentiation -- 1.3. Communicative adaptability -- 1.3.1. Effects of communicative adaptability -- 1.3.1.1. Interpersonal attraction -- 1.3.1.2. Friendship formation -- 1.3.1.3. Conflict management -- 1.4. Linking cognitive complexity to communicative adaptability -- 1.5. Abusive supervision -- 1.5.1. Individual difference variables as causes of abusive supervision -- 1.5.1.1. Personality characteristics -- 1.5.1.2. Demographic characteristics -- 1.5.1.3. Supervisors' beliefs -- 1.6. Linking communicative adaptability to abusive communication -- 1.7. Hypotheses -- 2. Research methodology -- 2.1. Participants -- 2.2. Procedures -- 2.3. Measures -- 2.3.1. Cognitive complexity -- 2.3.2. Downward commicative adaptability -- 2.3.3. Downward abusive communication -- Chapter 3. Results -- 3.1.1. Linking cognitive complexity with downward communicative adaptability -- 3.1.2. Linking downward communicative adaptability and downward abusive commication -- Chapter 4. Discussion -- References