We i n vestigate the outsourcing of numerical and scienti c computations using the following framework: A customer who needs computations done but lacks the computational resources computing power, appropriate software, or programming expertise to do these locally, w ould like to use an external agent to perform these computations. This currently arises in many practical situations, including the nancial services and petroleum services industries. The outsourcing is secure if it is done without revealing to the external agent either the actual data or the actual answer to the computations. The general idea is for the customer to do some carefully designed local preprocessing disguising of the problem and or data before sending it to the agent, and also some local postprocessing of the answer returned to extract the true answer. The disguise process should be as lightweight as possible, e.g., take time proportional to the size of the input and answer. The disguise preprocessing that the customer performs locally to hide" the real computation can change the numerical properties of the computation so that numerical stability m ust be considered as well as security and computational performance. We present a framework for disguising scienti c computations and discuss their costs, numerical properties, and levels of security. We show that no single disguise technique is suitable for a broad range of scienti c computations but their is an array of disguise techniques available so that almost any scienti c computation could be disguised at a reasonable cost and with very high levels of security. These disguise techniques can be embedded in a very high level, easy-to-use system problem solving environment that hides their complexity.

Neurofuzzy approaches for predicting financial time series are investigated and shown to perform well in the context of various trading strategies involving stocks and options. The horizon of prediction is typically a few days and trading strategies are examined using historical data. Two methodologies are presented wherein neural predictors are used to anticipate the general behavior of financial indexes (moving up, down, or staying constant) in the context of stocks and options trading. The methodologies are tested with actual financial data and show considerable promise as a decision making and planning tool.

Til t!lis study, we are cOlleemed with the parallelizatiollof finite elemem mesh gellerariol! alld its decomposition, and tlie parallel solution of sparse algebraic equations w/lich are obtainedfrom the parallel discretization of second order ellipticparcial differelltial equations (PDEs) usillgfillire difference ondfinite eleme1lt fec/miques. For this we use the Parallel ELLPACK (lfELLPACK) problem solving environmellt (PSE) which sttppons PDE computations 011 several MIMD platforms. We have considered the ITPACK library o[ stationary iterative solvers which we have parallelized and integrated into the IIEILPACK PSE. This ParaliellTPACK package has been implemellted using the MPl, PVM, PICL, PARMACS, nCUBE Vertex w'd Illtel NX message passing communication libraries. It peiforms very efficiently on a variety of hardware alld communication plat/onl/s. To study the efficiency of three MPI library implementations. the peifomlOnce of the ParallellTPACK solvers was meamred on several distributed memory architectllres and 011 clusters of workslationsfor a testbed of elliptic boundary value PDE problems. We present a comparison of these MPI library implementalionswith PVM and the native com-mUllication libraries, based on their performance on these lests. Moreover we have implemented ill MPI, a parallel mesh generalor that concurremly produces a semi-optimal partitionillg ofthe mesh to SIlpport variol/s domain decol/Iposition solution strategies across the above pla/[onl/s. The results illdicate that the MPI overhead varies amollg the various implementalions without significantly affecting the algorithmic speedllp even all clllsters ofworkstatioTlS.

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