A System of Multivariable Krawtchouk Polynomials and a Probabilistic Application

The one variable Krawtchouk polynomials, a special case of the $_2F_1$ function did appear in the spectral representation of the transition kernel for a Markov chain studied a long time ago by M. Hoare and M. Rahman. A multivariable extension of this Markov chain was considered in a later paper by these authors where a certain two variable extension of the $F_1$ Appel function shows up in the spectral analysis of the corresponding transition kernel. Independently of any probabilistic consideration a certain multivariable version of the Gelfand-Aomoto hypergeometric function was considered in papers by H. Mizukawa and H. Tanaka. These authors and others such as P. Iliev and P. Tertwilliger treat the two-dimensional version of the Hoare-Rahman work from a Lie-theoretic point of view. P. Iliev then treats the general $n$-dimensional case. All of these authors proved several properties of these functions. Here we show that these functions play a crucial role in the spectral analysis of the transition kernel that comes from pushing the work of Hoare-Rahman to the multivariable case. The methods employed here to prove this as well as several properties of these functions are completely different to those used by the authors mentioned above

Challenges to describe QoS requirements for web services quality prediction to support web services interoperability in electronic commerce

Quality of service (QoS) is significant and necessary for web service applications quality assurance. Furthermore, web services quality has contributed to the successful implementation of Electronic Commerce (EC) applications. However, QoS is still the big issue for web services research and remains one of the main research questions that need to be explored. We believe that QoS should not only be measured but should also be predicted during the development and implementation stages. However, there are challenges and constraints to determine and choose QoS requirements for high quality web services. Therefore, this paper highlights the challenges for the QoS requirements prediction as they are not easy to identify. Moreover, there are many different perspectives and purposes of web services, and various prediction techniques to describe QoS requirements. Additionally, the paper introduces a metamodel as a concept of what makes a good web service

The Role of Economic Factors, Including the Level of Tuition, in Individual University Participation Decisions in Canada

The study uses individual data from the Canadian Labour Force Survey to consider economic factors in university participation decisions by persons aged 17-24 from 1976 to 2003. The level of real tuition is one economic factor that may affect the university participation decision. There is also regional variation in the opportunity cost of university attendance; in the reduction in the probability of unemployment after obtaining a university degree; and in the proportion of university budgets used for financial support of students. In addition, there is some national variation by gender and over time in the return to a university education. This study finds that higher tuition levels in the 1990s did reduce the probability of university participation by persons aged 17,18 or 19 relative to a province-specific trend increase in university participation. Before drawing a policy conclusion from this result, it would be necessary to consider what the trend terms represent in the university participation decision.tuition fees; enrollment

How Vulnerable are Bangladesh’s Indigenous People to Climate Change?

This paper compares the vulnerabilities to climate change and climate variability of the indigenous people with the Bengali population of Bangladesh. It distinguishes between (a) individual vulnerabilities that are related to an individual’s capability to adapt to climate change and; (b) spatial vulnerabilities, that is, vulnerabilities that are related to the location of a person (like the exposure to climate change-induced disasters). While an individual’s capability to adapt to climate change is determined by many factors, some relatively simple approximation is to look at poverty, landlessness, and illiteracy. Spatial vulnerabilities are reviewed by looking at drought hazard maps, flood hazard maps, landslide hazard maps, and cyclone hazard maps. Hence, the paper compares levels of poverty, landlessness, illiteracy, and the more direct though also more subjective exposures to increased droughts, floods, landslides, and cyclones across the two population groups. The paper concludes with some broad suggestions on adaptation strategies of indigenous people as well as suggestions for policy interventions to reduce climate change-induced vulnerabilities for indigenous people in the Chittagong Hill Tracts (CHT).Bangladesh, climate change, vulnerability

Computing Covers Using Prefix Tables

An \emph{indeterminate string} $x = x[1..n]$ on an alphabet $\Sigma$ is a sequence of nonempty subsets of $\Sigma$; $x$ is said to be \emph{regular} if every subset is of size one. A proper substring $u$ of regular $x$ is said to be a \emph{cover} of $x$ iff for every $i \in 1..n$, an occurrence of $u$ in $x$ includes $x[i]$. The \emph{cover array} $\gamma = \gamma[1..n]$ of $x$ is an integer array such that $\gamma[i]$ is the longest cover of $x[1..i]$. Fifteen years ago a complex, though nevertheless linear-time, algorithm was proposed to compute the cover array of regular $x$ based on prior computation of the border array of $x$. In this paper we first describe a linear-time algorithm to compute the cover array of regular string $x$ based on the prefix table of $x$. We then extend this result to indeterminate strings.Comment: 14 pages, 1 figur

Inferring an Indeterminate String from a Prefix Graph

An \itbf{indeterminate string} (or, more simply, just a \itbf{string}) \s{x} = \s{x}[1..n] on an alphabet $\Sigma$ is a sequence of nonempty subsets of $\Sigma$. We say that \s{x}[i_1] and \s{x}[i_2] \itbf{match} (written \s{x}[i_1] \match \s{x}[i_2]) if and only if \s{x}[i_1] \cap \s{x}[i_2] \ne \emptyset. A \itbf{feasible array} is an array \s{y} = \s{y}[1..n] of integers such that \s{y}[1] = n and for every $i \in 2..n$, \s{y}[i] \in 0..n\- i\+ 1. A \itbf{prefix table} of a string \s{x} is an array \s{\pi} = \s{\pi}[1..n] of integers such that, for every $i \in 1..n$, \s{\pi}[i] = j if and only if \s{x}[i..i\+ j\- 1] is the longest substring at position $i$ of \s{x} that matches a prefix of \s{x}. It is known from \cite{CRSW13} that every feasible array is a prefix table of some indetermintate string. A \itbf{prefix graph} \mathcal{P} = \mathcal{P}_{\s{y}} is a labelled simple graph whose structure is determined by a feasible array \s{y}. In this paper we show, given a feasible array \s{y}, how to use \mathcal{P}_{\s{y}} to construct a lexicographically least indeterminate string on a minimum alphabet whose prefix table \s{\pi} = \s{y}.Comment: 13 pages, 1 figur