Direct Analog Computers

Grounding Analog Computers

1.0 Is Cognition Discrete or Continuous? 1.1 Although I hate to haggle over words, Harnad's use ofànalog' confuses a number of issues. The problem begins with the phrasèanalog world' in the title, which does not correspond to any technical or nontechnical usage ofànalog' with which I'm familiar. Although I don't know precisely what he means byànalog', it is clearly related to the distinction be...

Metric Relations among Analog Computers

Brains as analog-model computers

Computational neuroscientists not only employ computer models and simulations in studying brain functions. They also view the modeled nervous system itself as computing. What does it mean to say that the brain computes? And what is the utility of the ‘brain-as-computer’ assumption in studying brain functions? In previous work, I have argued that a structural conception of computation is not ade...

Analog input layer for optical reservoir computers

Reservoir computing is an information processing technique, derived from the theory of neural networks, which is easy to implement in hardware. Several reservoir computer hardware implementations have been realized recently with performance comparable to digital implementations, which demonstrated the potential of reservoir computing for ultrahigh bandwidth signal processing tasks. In all these...

Iteration, Inequalities, and Differentiability in Analog Computers

Shannon's General Purpose Analog Computer (GPAC) is an elegant model of analog computation in continuous time. In this paper, we consider whether the set G of GPAC-computable functions is closed under iteration, that is, whether for any function f(x) 2 G there is a function F (x; t) 2 G such that F (x; t) = f (x) for non-negative integers t. We show that G is not closed under iteration, but a s...