Mermera: Non-Coherent Distributed Shared Memory for Parallel Computing

The proliferation of inexpensive workstations and networks has prompted several researchers to use such distributed systems for parallel computing. Attempts have been made to offer a shared-memory programming model on such distributed memory computers. Most systems provide a shared-memory that is coherent in that all processes that use it agree on the order of all memory events. This dissertation explores the possibility of a significant improvement in the performance of some applications when they use non-coherent memory. First, a new formal model to describe existing non-coherent memories is developed. I use this model to prove that certain problems can be solved using asynchronous iterative algorithms on shared-memory in which the coherence constraints are substantially relaxed. In the course of the development of the model I discovered a new type of non-coherent behavior called Local Consistency. Second, a programming model, Mermera, is proposed. It provides programmers with a choice of hierarchically related non-coherent behaviors along with one coherent behavior. Thus, one can trade-off the ease of programming with coherent memory for improved performance with non-coherent memory. As an example, I present a program to solve a linear system of equations using an asynchronous iterative algorithm. This program uses all the behaviors offered by Mermera. Third, I describe the implementation of Mermera on a BBN Butterfly TC2000 and on a network of workstations. The performance of a version of the equation solving program that uses all the behaviors of Mermera is compared with that of a version that uses coherent behavior only. For a system of 1000 equations the former exhibits at least a 5-fold improvement in convergence time over the latter. The version using coherent behavior only does not benefit from employing more than one workstation to solve the problem while the program using non-coherent behavior continues to achieve improved performance as the number of workstations is increased from 1 to 6. This measurement corroborates our belief that non-coherent shared memory can be a performance boon for some applications.

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.