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This chapter describes various approaches to concurrency, or “parallel programming”. An overview of high performance computing is followed with a review of Flynn’s taxonomy of parallel computing. Three methods for implementing parallel code using the frameworks provided by MPI, openMP, and C++ threads are presented. The use of the C++ constructs mutex and future to resolve issues of synchronization are discussed. All methods are illustrated with an embarrassingly parallel application to a Monte Carlo integral and common pitfalls are presented. The chapter closes with a discussion and example of the utility of forking processes and the use of C++ sockets and their application in a client/server environment.

The chapter deals with multiple scales in both space and time. First, the state-of-the-art is presented. Then, we discuss a family of computational approaches using time-space homogenization. Emphasis is put on the time aspects.

Can we say anything about the specific speeds at which ems can run? Because of brain parallelism, the cost of running an em should be nearly proportional to speed over a wide range of speeds. The upper limit of this proportional-cost em speed range is the “top cheap” speed, that is, the highest speed at which the cost is still nearly proportional to speed. To estimate this speed, we must consider how simulated neurons in em brains might both send faster signals, and more quickly compute what signals to send. Human brain neuron fibers send signals at speeds ranging from 0.5 to 120 meters per second. In contrast, signal speeds in electronic circuit boards today are typically about half the speed of light. If signals in em brains move at electronics speeds, that would be between one million and 300 million times faster than neuron signals. If signal delays are the limiting factor in em brain speed, then this ratio gives an estimate of the maximum speedup possible, at least if em brains have the same spatial size as human brains. proportionally larger speedups are possible if em brains can be made proportionally smaller. Regarding the computation of when to fire a simulated neuron, note that real neurons usually seem to take at least 20 milliseconds to react ( Tovee 1994 ), while even today electronic circuits can switch 10 billion times faster, in one-and-a-half trillionths of a second ( deal et al. 2010 ). A key question is thus: how many electronic circuit cycles does it take to execute a parallel computer program that emulates the firing of a single neuron? For example, if there were an algorithm that could compute a neuron firing in 10 000 of these fastest-known circuit cycles, then an emulation based on this algorithm would run a million times faster than the human brain. As quite complex parallel computer programs can be run in 10 000 cycles, em speedups of at least one million times seem feasible, provided that energy and cooling are cheap enough to profitably allow the use of these fastest electronic circuits. When energy and cooling are more strongly limiting factors, however, the top cheap speed could be slower.

The topic of this chapter may seem like a digression from methods and approaches to reaction mechanisms, but it is not; it is an introduction to it. We worked on both topics for some time and there is a basic connection. Think of an electronic device and ask: how are the logic functions of this device determined? Electronic inputs (voltages and currents) are applied and outputs are measured. A truth table is constructed and from this table the logic functions of the device, and at times some of its components, may be inferred. The device is not subjected to the approach toward a chemical mechanism described in the previous chapter, of taking the device apart and testing its simplest components. (That may have to be done sometimes but is to be avoided if possible.) Can such an approach be applicable to chemical systems? We show this to be the case by discussing the implementation of logic and computational devices, both sequential machines such as a universal Turing machine (hand computers, laptops) and parallel machines, by means of macroscopic kinetics; by giving a brief comparison with neural networks; by showing the presence of such devices in chemical and biochemical reaction systems; and by presenting some confirming experiments. The next step is clear: if macroscopic chemical kinetics can carry out these electronic functions, then there are likely to be new approaches possible for the determination of complex reaction mechanisms, analogs of such determinations for electronic components. The discussion in the remainder of this chapter is devoted to illustrations of these topics; it can be skipped, except the last paragraph, without loss of continuity with chapter 5 and beyond. A neuron is either on or off depending on the signals it has received. A chemical neuron is a similar device.