Scientific and artistic investigation of multi-dimensional fractals on the AT & T pixel machine

The pipelined architecture and parallel organization of the AT&T Pixel Machine image computer are described and demonstrated with applications for the visualization of multidimensional fractals, particularly linear fractals and quaternion/ stacked Julia sets. Techniques for pushing the Pixel Machine to its peak abilities are described and apply to more recent parallel image computers as well.     

Partitioned encoding schemes for algorithm-based fault tolerance inmassively parallel systems

Considers the applicability of algorithm based fault tolerance (ABET) to massively parallel scientific computation. Existing ABET schemes can provide effective fault tolerance at a low cost For computation on matrices of moderate size; however, the methods do not scale well to floating-point operations on large systems. This short note proposes the use of a partitioned linear encoding scheme to provide scalability. Matrix algorithms employing this scheme are presented and compared to current ABET schemes. It is shown that the partitioned scheme provides scalable linear codes with improved numerical properties with only a small increase in hardware and time overhead     

Parallel architecture for fast transforms with trigonometric kernel

We present an unified parallel architecture for four of the most important fast orthogonal transforms with trigonometric kernel: Complex Valued Fourier (CFFT), Real Valued Fourier (RFFT), Hartley (FHT), and Cosine (FCT). Out of these, only the CFFT has a data flow coinciding with the one generated by the successive doubling method, which can be transformed on a constant geometry flow using perfect unshuffle or shuffle permutations. The other three require some type of hardware modification to guarantee the constant geometry of the successive doubling method. We have defined a generalized processing section (PS), based on a circular CORDIC rotator, for the four transforms. This PS section permits the evaluation of the CFFT and FCT transforms in n data recirculations and the RFFT and FHT transforms in n-1 data recirculations, with n being the number of stages of a transform of length N=rⁿ. Also, the efficiency of the partitioned parallel architecture is optimum because there is no cycle loss in the systolic computation of all the butterflies for each of the four transforms     

Weight smoothing to improve network generalization

A weight smoothing algorithm is proposed in this paper to improve a neural network's generalization capability. The algorithm can be used when the data patterns to be classified are presented on an n-dimensional grid (n>/=1) and there exists some correlations among neighboring data points within a pattern. For a fully-interconnected feedforward net, no such correlation information is embedded into the architecture. Consequently, the correlations can only be extracted through sufficient amount of network training. With the proposed algorithm, a smoothing constraint is incorporated into the objective function of backpropagation to reflect the neighborhood correlations and to seek those solutions that have smooth connection weights. Experiments were performed on problems of waveform classification, multifont alphanumeric character recognition, and handwritten numeral recognition. The results indicate that (1) networks trained with the algorithm do have smooth connection weights, and (2) they generalize better.     

Hierarchical models for analysis and recognition of handwritten characters

Different hierarchical models in pattern analysis and recognition are proposed, based on occurrence probability of patterns. As an important application of recognizing handprinted characters, three typical kinds of hierarchical models such asM _89-89,M _89-36 andM _36-36 have been presented, accompanied by the computer algorithms for computing recognition rates of pattern parts. Moreover, a comparative study of their recognition rates has been conducted theoretically; and numerical experiments have been carried out to verify the analytical conclusions made. Various hierarchical models deliberated in this paper can provide users more or better choices of pattern models in practical application, and lead to a uniform computational scheme (or code). The recognition rates of parts can be improved remarkably by a suitable hierarchical model. For the modelM _89-36 in which case some of the Canadian standard handprinted characters have multiple occurrence probabilities, the total mean recognition rates of the given sample may reach 120% of that by the model proposed by Li et al., and 156% of that obtained from the subjective experiments reported by Suen.     

On loop transformations for generalized cycle shrinking

This paper describes several loop transformation techniques for extracting parallelism from nested loop structures. Nested loops can then be scheduled to run in parallel so that execution time is minimized. One technique is called selective cycle shrinking, and the other is called true dependence cycle shrinking. It is shown how selective shrinking is related to linear scheduling of nested loops and how true dependence shrinking is related to conflict-free mappings of higher dimensional algorithms into lower dimensional processor arrays. Methods are proposed in this paper to find the selective and true dependence shrinkings with minimum total execution time by applying the techniques of finding optimal linear schedules and optimal and conflict-free mappings proposed by W. Shang and A.B. Fortes     

The fault-tolerant extension problem for complete multipartitenetworks

We develop a characterization for m-fault-tolerant extensions, and for optimal m-fault-tolerant extensions, of a complete multipartite graph. Our formulation shows that this problem is equivalent to an interesting combinatorial problem on the partitioning of integers. This characterization leads to a new procedure for constructing an optimal m-fault-tolerant extension of any complete multipartite graph, for any m⩾0. The proposed procedure is mainly useful when the size of the graph is relatively small, because the search time required is exponential. This exponential search, however, is not always necessary. We prove several necessary conditions that help us, in several cases, to identify some optimal m-fault-tolerant extensions without performing any search     

Neural network control of communications systems

Neural networks appear well suited to applications in the control of communications systems for two reasons: adaptivity and high speed. This paper describes application of neural networks to two problems, admission control and switch control, which exploit the adaptivity and speed property, respectively. The admission control problem is the selective admission of a set of calls from a number of inhomogeneous call classes, which may have widely differing characteristics as to their rate and variability of traffic, onto a network. It is usually unknown in advance which combinations of calls can be simultaneously accepted so as to ensure satisfactory performance. The approach adopted is that key network performance parameters are observed while carrying various combinations of calls, and their relationship is learned by a neural network structure. The network model chosen has the ability to interpolate or extrapolate from the past results and the ability to adapt to new and changing conditions. The switch control problem is the service policy used by a switch controller in transmitting packets. In a crossbar switch with input queueing, significant loss of throughput can occur when head-of-line service order is employed. A solution can be based on an algorithm which maximizes throughput. However since this solution is typically required in less than one microsecond, software implementation policy is infeasible. We will carry out an analysis of the benefits of such a policy, describe some existing proposed schemes for its implementation, and propose a further scheme that provides this submicrosecond optimization.     

A delta transform approach to loop gain-phase shaping design of robust digital control systems

This paper addresses the existence of loop gain-phase shaping (LGPS) solutions for the design of robust digital control systems for SISO, minimum-phase, continuous-time processes with parametric uncertainty. We develop the frequency response properties of LGPS for discrete-time systems using the Δ-transform, a transform method that applies to both continuous-time and discrete-time systems. A theorem is presented which demonstrates that for reasonable specifications there always exists a sampling period such that the robust digital control problem has a solution. Finally, we offer a procedure for estimating the maximum feasible sampling period for LGPS solutions to robust digital control problems.