Numerical aerodynamic simulation facility preliminary study: Executive study

A computing system was designed with the capability of providing an effective throughput of one billion floating point operations per second for three dimensional Navier-Stokes codes. The methodology used in defining the baseline design, and the major elements of the numerical aerodynamic simulation facility are described

The effect of multiple knowledge sources on learning and teaching

Current paradigms for machine-based learning and teaching tend to perform their task in isolation from a rich context of existing knowledge. In contrast, the research project presented here takes the view that bringing multiple sources of knowledge to bear is of central importance to learning in complex domains. As a consequence teaching must both take advantage of and beware of interactions between new and existing knowledge. The central process which connects learning to its context is reasoning by analogy, a primary concern of this research. In teaching, the connection is provided by the explicit use of a learning model to reason about the choice of teaching actions. In this learning paradigm, new concepts are incrementally refined and integrated into a body of expertise, rather than being evaluated against a static notion of correctness. The domain chosen for this experimentation is that of learning to solve "algebra story problems." A model of acquiring problem solving skills in this domain is described, including: representational structures for background knowledge, a problem solving architecture, learning mechanisms, and the role of analogies in applying existing problem solving abilities to novel problems. Examples of learning are given for representative instances of algebra story problems. After relating our views to the psychological literature, we outline the design of a teaching system. Finally, we insist on the interdependence of learning and teaching and on the synergistic effects of conducting both research efforts in parallel

On the numerical stability of Fourier extensions

An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically fast in the truncation parameter. Unfortunately, computing a Fourier extension requires solving an ill-conditioned linear system, and hence one might expect such rapid convergence to be destroyed when carrying out computations in finite precision. The purpose of this paper is to show that this is not the case. Specifically, we show that Fourier extensions are actually numerically stable when implemented in finite arithmetic, and achieve a convergence rate that is at least superalgebraic. Thus, in this instance, ill-conditioning of the linear system does not prohibit a good approximation. In the second part of this paper we consider the issue of computing Fourier extensions from equispaced data. A result of Platte, Trefethen & Kuijlaars states that no method for this problem can be both numerically stable and exponentially convergent. We explain how Fourier extensions relate to this theoretical barrier, and demonstrate that they are particularly well suited for this problem: namely, they obtain at least superalgebraic convergence in a numerically stable manner

A Prolog application for reasoning on maths puzzles with diagrams

open5noDespite the indisputable progresses of artificial intelligence, some tasks that are rather easy for a human being are still challenging for a machine. An emblematic example is the resolution of mathematical puzzles with diagrams. Sub-symbolical approaches have proven successful in fields like image recognition and natural language processing, but the combination of these techniques into a multimodal approach towards the identification of the puzzle’s answer appears to be a matter of reasoning, more suitable for the application of a symbolic technique. In this work, we employ logic programming to perform spatial reasoning on the puzzle’s diagram and integrate the deriving knowledge into the solving process. Analysing the resolution strategies required by the puzzles of an international competition for humans, we draw the design principles of a Prolog reasoning library, which interacts with image processing software to formulate the puzzle’s constraints. The library integrates the knowledge from different sources, and relies on the Prolog inference engine to provide the answer. This work can be considered as a first step towards the ambitious goal of a machine autonomously solving a problem in a generic context starting from its textual-graphical presentation. An ability that can help potentially every human–machine interaction.openBuscaroli, Riccardo; Chesani, Federico; Giuliani, Giulia; Loreti, Daniela; Mello, PaolaBuscaroli, Riccardo; Chesani, Federico; Giuliani, Giulia; Loreti, Daniela; Mello, Paol