Two-way Flow Networks with Small Decay

The set of equilibrium networks in the two-way flow model of network formation (Bala and Goyal, 2000) is very sensitive to the introduction of decay. Even if decay is small enough so that equilibrium networks are minimal, the set of equilibrium architectures becomes much richer, especially when the benefit functions are nonlinear. However, not much is known about these architectures. In this paper we remedy this gap in the literature. We characterize the equilibrium architectures. Moreover, we show results on the relative stability of different types of architectures. Three of the results are that (i) at most one players receives multiple links, (ii) the absolute diameter of equilibrium networks can be arbitrarily large, and (iii) large (small) diameter networks are relatively stable under concave (convex) benefit functions.Network formation, two-way flow model, decay, non-linear benefits

Moving the shared memory closer to the processors: DDM

Multiprocessors with shared memory are considered more general and easier to program than message-passing machines. The scalability is, however, in favor of the latter. There are a number of proposals showing how the poor scalability of shared memory multiprocessors can be improved by the introduction of private caches attached to the processors. These caches are kept consistent with each other by cache-coherence protocols. In this paper we introduce a new class of architectures called Cache Only Memory Architectures (COMA). These architectures provide the programming paradigm of the shared-memory architectures, but are believed to be more scal- able. COMAs have no physically shared memory; instead, the caches attached to the processors contain all the memory in the system, and their size is therefore large. A datum is allowed to be in any or many of the caches, and will automatically be moved to where it is needed by a cache-coherence protocol, which also ensures that the last copy of a datum is never lost. The location of a datum in the machine is completely decoupled from its address. We also introduce one example of COMA: the Data Diffusion Machine (DDM). The DDM is based on a hierarchical network structure, with processor/memory pairs at its tips. Remote accesses generally cause only a limited amount of traffic over a limited part of the machine. The architecture is scalable in that there can be any number of levels in the hierarchy, and that the root bus of the hierarchy can be implemented by several buses, increasing the bandwidth

Introduction to a system for implementing neural net connections on SIMD architectures

Neural networks have attracted much interest recently, and using parallel architectures to simulate neural networks is a natural and necessary application. The SIMD model of parallel computation is chosen, because systems of this type can be built with large numbers of processing elements. However, such systems are not naturally suited to generalized communication. A method is proposed that allows an implementation of neural network connections on massively parallel SIMD architectures. The key to this system is an algorithm permitting the formation of arbitrary connections between the neurons. A feature is the ability to add new connections quickly. It also has error recovery ability and is robust over a variety of network topologies. Simulations of the general connection system, and its implementation on the Connection Machine, indicate that the time and space requirements are proportional to the product of the average number of connections per neuron and the diameter of the interconnection network