S+Net: extending functional coordination with extra-functional semantics

This technical report introduces S+Net, a compositional coordination language for streaming networks with extra-functional semantics. Compositionality simplifies the specification of complex parallel and distributed applications; extra-functional semantics allow the application designer to reason about and control resource usage, performance and fault handling. The key feature of S+Net is that functional and extra-functional semantics are defined orthogonally from each other. S+Net can be seen as a simultaneous simplification and extension of the existing coordination language S-Net, that gives control of extra-functional behavior to the S-Net programmer. S+Net can also be seen as a transitional research step between S-Net and AstraKahn, another coordination language currently being designed at the University of Hertfordshire. In contrast with AstraKahn which constitutes a re-design from the ground up, S+Net preserves the basic operational semantics of S-Net and thus provides an incremental introduction of extra-functional control in an existing language.Comment: 34 pages, 11 figures, 3 table

Different Methods of Embodied Cognition in Pedagogy and its Effectiveness in Student Learning

The Mathematical Ideas Analysis hypothesizes that abstract mathematical reasoning is unconsciously organized and integrated with sensory-motor experience. Basic research testing movement, language, and perception during math problem solving supports this hypothesis. Applied research primarily measures students’ performance on math tests after they engage in analogous sensory-motor tasks, but findings show mixed results. Sensory-motor tasks are dependent on several moderators (e.g., instructional guidance, developmental stage) known to help students learn, and studies vary in how each moderator is implemented. There is little research on the effectiveness of sensory-motor tasks without these moderators. This study compares different approaches to working with an interactive application designed to emulate how people intrinsically solve algebraic equations. A total of 130 participants (84 females, 54 males) were drawn from a pool of Introductory Psychology students attending San Jose State University. Participants were placed in three different learning environments, and their performance was measured by comparing improvement between a pre-test and a post-test. We found no difference between participants who worked alone with the application, were instructed by the experimenter while using the application, or who instructed the experimenter on how to solve equations using the application. Further research is needed to examine how and whether analogous sensory-motor interfaces are a useful learning tool, and if so, what circumstances are ideal for sensory-motor interfaces to be used

Algebraic optimization of recursive queries

Over the past few years, much attention has been paid to deductive databases. They offer a logic-based interface, and allow formulation of complex recursive queries. However, they do not offer appropriate update facilities, and do not support existing applications. To overcome these problems an SQL-like interface is required besides a logic-based interface.\ud \ud In the PRISMA project we have developed a tightly-coupled distributed database, on a multiprocessor machine, with two user interfaces: SQL and PRISMAlog. Query optimization is localized in one component: the relational query optimizer. Therefore, we have defined an eXtended Relational Algebra that allows recursive query formulation and can also be used for expressing executable schedules, and we have developed algebraic optimization strategies for recursive queries. In this paper we describe an optimization strategy that rewrites regular (in the context of formal grammars) mutually recursive queries into standard Relational Algebra and transitive closure operations. We also describe how to push selections into the resulting transitive closure operations.\ud \ud The reason we focus on algebraic optimization is that, in our opinion, the new generation of advanced database systems will be built starting from existing state-of-the-art relational technology, instead of building a completely new class of systems

Towards an Efficient Evaluation of General Queries

Database applications often require to evaluate queries containing quantifiers or disjunctions, e.g., for handling general integrity constraints. Existing efficient methods for processing quantifiers depart from the relational model as they rely on non-algebraic procedures. Looking at quantified query evaluation from a new angle, we propose an approach to process quantifiers that makes use of relational algebra operators only. Our approach performs in two phases. The first phase normalizes the queries producing a canonical form. This form permits to improve the translation into relational algebra performed during the second phase. The improved translation relies on a new operator - the complement-join - that generalizes the set difference, on algebraic expressions of universal quantifiers that avoid the expensive division operator in many cases, and on a special processing of disjunctions by means of constrained outer-joins. Our method achieves an efficiency at least comparable with that of previous proposals, better in most cases. Furthermore, it is considerably simpler to implement as it completely relies on relational data structures and operators

Encouraging versatile thinking in algebra using the computer

In this article we formulate and analyse some of the obstacles to understanding the notion of a variable, and the use and meaning of algebraic notation, and report empirical evidence to support the hypothesis that an approach using the computer will be more successful in overcoming these obstacles. The computer approach is formulated within a wider framework ofversatile thinking in which global, holistic processing complements local, sequential processing. This is done through a combination of programming in BASIC, physical activities which simulate computer storage and manipulation of variables, and specific software which evaluates expressions in standard mathematical notation. The software is designed to enable the user to explore examples and non-examples of a concept, in this case equivalent and non-equivalent expressions. We call such a piece of software ageneric organizer because if offers examples and non-examples which may be seen not just in specific terms, but as typical, or generic, examples of the algebraic processes, assisting the pupil in the difficult task of abstracting the more general concept which they represent. Empirical evidence from several related studies shows that such an approach significantly improves the understanding of higher order concepts in algebra, and that any initial loss in manipulative facility through lack of practice is more than made up at a later stage

Process Algebras

Process Algebras are mathematically rigorous languages with well defined semantics that permit describing and verifying properties of concurrent communicating systems. They can be seen as models of processes, regarded as agents that act and interact continuously with other similar agents and with their common environment. The agents may be real-world objects (even people), or they may be artifacts, embodied perhaps in computer hardware or software systems. Many different approaches (operational, denotational, algebraic) are taken for describing the meaning of processes. However, the operational approach is the reference one. By relying on the so called Structural Operational Semantics (SOS), labelled transition systems are built and composed by using the different operators of the many different process algebras. Behavioral equivalences are used to abstract from unwanted details and identify those systems that react similarly to external experiments