We explore the computational power of formal models for computation with pulses. Such models are motivated by realistic models for biological neurons, and by related new types of VLSI (\pulse stream VLSI"). In preceding work it was shown that the computational power of formal models for computation with pulses is quite high if the pulses arriving at a computational unit have an approximately linearly rising or linearly decreasing initial segment. This property is satis ed by common models for biological neurons. On the other hand several implementations of pulse stream VLSI employ pulses that are approximately piecewise constant (i.e. step functions). In this article we investigate the relevance of the shape of pulses in formal models for computation with pulses. It turns out that the computational power drops signi cantly if one replaces pulses with linearly rising or decreasing initial segments by piecewise constant pulses. We provide an exact characterization of the latter model in terms of a weak version of a random access machine (RAM). We also compare the language recognition capability of a recurrent version of this model with that of deterministic nite automata and Turing machines. 1

The firing of a neuron in a biological neural system causes in certain other neurons excitatory postsynaptic potential changes (EPSP's) that are not "rectangular", but have the form of a smooth hill. We prove in this article for a formal model of a network of spiking neurons, that the rising respectively declining segments of these EPSP's are in fact essential for the computational power of the model. 1 Introduction Apparently all computations in biological neural systems are realized through sequences of firings of neurons as a result of incoming postsynaptic potentials, see e.g. (Kandel et al., 1991). Each firing of a neuron in a biological neural system causes excitatory or inhibitory postsynaptic potentials (EPSP's respectively IPSP's) in those other neurons to which it is connected by synapses. A neuron fires if the sum of its incoming postsynaptic potentials becomes larger than its current threshold (which depends on the time of its last previous firing) . Recently one has also ...

Recently one has started to investigate the computational power of spiking neurons (also called "integrate and fire neurons"). These are neuron models that are substantially more realistic from the biological point of view than the ones which are traditionally employed in artificial neural nets. It has turned out that the computational power of networks of spiking neurons is quite large. In particular they have the ability to communicate and manipulate analog variables in spatio-temporal coding, i.e. encoded in the time points when specific neurons "fire" (and thus send a "spike" to other neurons). These preceding results have motivated the question which details of the firing mechanism of spiking neurons are essential for their computational power, and which details are "accidental" aspects of their realization in biological "wetware". Obviously this question becomes important if one wants to capture some of the advantages of computing and learning with spatio-temporal c...

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Computing the maximum bichromatic discrepancy is an interesting theoretical problem with important applications in computational learning theory, computational geometry and computer graphics. In this paper we give algorithms to compute the maximum bichromatic discrepancy for simple geometric ranges, including rectangles and halfspaces. In addition, we give extensions to other discrepancy problems. 1 Introduction The main theme of this paper is to present efficient algorithms that solve the problem of computing the maximum bichromatic discrepancy for axis oriented rectangles. This problem arises naturally in different areas of computer science, such as computational learning theory, computational geometry and computer graphics ([Ma], [DG]), and has applications in all these areas. In computational learning theory, the problem of agnostic PAC-learning with simple geometric hypotheses can be reduced to the problem of computing the maximum bichromatic discrepancy for simple geometric ra...