Necklace rings and logarithmic functions

In this paper, we develop the theory of the necklace ring and the logarithmic function. Regarding the necklace ring, we introduce the necklace ring functor $Nr$ from the category of special \ld-rings into the category of special \ld-rings and then study the associated Adams operators. As far as the logarithmic function is concerned, we generalize the results in Bryant's paper (J. Algebra. 253 (2002); no.1, 167-188) to the case of graded Lie (super)algebras with a group action by applying the Euler-Poincar\'e principle

Where Theory meets Practice: A Case for an Activity Theory based Methodology to guide Computer System Design

Computer system developers are increasingly being challenged to develop tools that are not only usable, but more importantly useful in the sense of assisting the user to achieve desired goals. This requirement has highlighted the importance of accounting for the social and cultural issues of the computer tool user when developing a computer system. Activity Theory (AT) has emerged as a suitable framework for analysing social and cultural issues because it provides a language to describe what people do in context. However, many computer system developers have failed to benefit from this insight mainly due to lack of established methods to operationalise ideas from this framework for the purpose of guiding the design process. This paper proposes a methodology developed to direct the application of a version of AT based on Engeström’s (1987) conceptualisation in order to support requirements capture during computer system design

Insurance Premia Consistent with the Market.

We consider insurance prices in presence of an incomplete and competitive market. We show that if the insurance price system is internal, sublinear, and consistent with the market, then insurance prices are the maxima of their expected payments with respect to a family of risk neutral probabilities. We also show that under a simple additional assumption it is possible to decompose the obtained price in net premium plus safety loading.

Maximally selected chi-square statistics and umbrella orderings

Binary outcomes that depend on an ordinal predictor in a non-monotonic way are common in medical data analysis. Such patterns can be addressed in terms of cutpoints: for example, one looks for two cutpoints that define an interval in the range of the ordinal predictor for which the probability of a positive outcome is particularly high (or low). A chi-square test may then be performed to compare the proportions of positive outcomes in and outside this interval. However, if the two cutpoints are chosen to maximize the chi-square statistic, referring the obtained chi-square statistic to the standard chi-square distribution is an inappropriate approach. It is then necessary to correct the p-value for multiple comparisons by considering the distribution of the maximally selected chi-square statistic instead of the nominal chi-square distribution. Here, we derive the exact distribution of the chi-square statistic obtained by the optimal two cutpoints. We suggest a combinatorial computation method and illustrate our approach by a simulation study and an application to varicella data

Generalised Moonshine and Abelian Orbifold Constructions

We consider the application of Abelian orbifold constructions in Meromorphic Conformal Field Theory (MCFT) towards an understanding of various aspects of Monstrous Moonshine and Generalised Moonshine. We review some of the basic concepts in MCFT and Abelian orbifold constructions of MCFTs and summarise some of the relevant physics lore surrounding such constructions including aspects of the modular group, the fusion algebra and the notion of a self-dual MCFT. The FLM Moonshine Module, $V^\natural$, is historically the first example of such a construction being a $Z_2$ orbifolding of the Leech lattice MCFT, $V^\Lambda$. We review the usefulness of these ideas in understanding Monstrous Moonshine, the genus zero property for Thompson series which we have shown is equivalent to the property that the only meromorphic $Z_n$ orbifoldings of $V^\natural$ are $V^\Lambda$ and $V^\natural$ itself (assuming that $V^\natural$ is uniquely determined by its characteristic function $J(\tau)$. We show that these constraints on the possible $Z_n$ orbifoldings of $V^\natural$ are also sufficient to demonstrate the genus zero property for Generalised Moonshine functions in the simplest non-trivial prime cases by considering $Z_p\times Z_p$ orbifoldings of $V^\natural$. Thus Monstrous Moonshine implies Generalised Moonshine in these cases.Comment: Talk presented at the AMS meeting on Moonshine, the Monster and related topics, Mt. Holyoke, June 1994, 16 pp, Plain TeX with AMS Font

Model for Human, Artificial & Collective Consciousness (Part I)

Borrowing the functional modeling approach common in systems and software engineering, an implementable model of the functions of human consciousness proposed to have the capacity for general problem solving ability transferable to any domain, or true self-aware intelligence, is presented. Being a functional model that is independent of implementation, this model is proposed to also be applicable to artificial consciousness, and to platforms that organize individuals into what is defined here as a first order collective consciousness, or at higher orders into what is defined here as Nth order collective consciousness. Part I of this two-part article includes: Summary; Introduction; Set of Postulates One; Set of Postulates Two; Overview of the Model; Model of Homeostasis; Model of the Functional Units; Model of the Body System; Model of the Other Basic Life Processes; Model of the Other Functional Systems; Model of Perceptions in the Perceptual Fields; Model of Body Processes as Paths in the Perceptual Field; & Model of Conscious Awarenes

Be vicarious: the challenge for project management in the service economy

Purpose. The paper aims to answer to the following questions: which are the critical dynamic capabilities to survive in the rubber landscape of service economy? Does it exist in service economy a dynamic capabilities provider? Methodology. The paper combines the literature review on dynamic capability perspective and that on vicariance to the Project Management professional services. Findings. Firstly, the paper identifies vicariance as an intriguing dynamic capability, crucial to survive in the rubber landscape of service economy. Secondly, the paper sheds light on Project Management (PM) as a vicarious that provides vicariance. Practical implications. For each critical organizational dimension, the paper identifies the links among the service economy challenges and the vicariance typology required to the project manager to face those challenge. Originality/value.The approach to conceive the PM as a vicarious that provides vicariance is original and leads to new insights on the professional services management. In fact, on one hand, dynamic capabilities cannot easily be bought through a market transaction; on the other hand, they must be built. This building can be achieved internally, by the organization itself (i.e. hierarchy), or through a partnership (i.e. hybrid form among hierarchy and market). PM professional services enrich organizations with additional information variety according to a hybrid (i.e. non- market) coordination model