Biological in forma tion TWO TECHNOLOGIESHistorically, the cost of computation has been directly related to the energy used in that computation. Today's electronic wristwatch does far more computation than the Eniac did when it was built. It is not the computation itself that costs-it is the energy consumed, and the system overhead required to supply that energy and to get rid of the heat: the boxes, the connectors, the circuit boards, the power supply, the fans, all of the superstructure that makes the system work. As the technology has evolved, it has always moved in the direction of lower energy per unitcomputation. That trend took us from vacuum tubes to transisitors, and from transistors to integrated circuits. It was the force behind the transition from n-MOS to CMOS technology that happened less than ten years ago. Today, it still is pushing us down to submicron sizes in semiconductor technology.So it pays to look at just how much capability the nervous system has in computation.There is a myth that the nervous system is slow, is built out of slimy stuff, uses ions instead of electrons, and is therefore ineffective. When the Whirlwind computer was first built back at M.I.T., they made a movie about it, which was called "Faster than Thought." The Whirwind did less computation than your wristwatch does. We have evolved by a factor of about 10 million in the cost of computation since the Whirlwind. Yet we still cannot begin to do the simplest computations that can be done by the brains of insects, let alone handle the tasks routinely performed by the brains of humans. So we have finally come to the point where we can see what is difficult and what is easy. Multiplying numbers to balance a bank account is not that difficult. What is difficult is processing the poorly conditioned sensory information that comes in through the lens of an eye or through the eardrum.A typical microprocessor does about 10 million operations/s, and uses about 1 W. In round numbers, it cost us about l O -' J to do one operation, the way we do it today, on a single chip. If we go off the chip to the box level, a whole computer uses about 10-5J/operation. Awhole computer is thus about two orders of magnitude less efficient than is a single chip.Back in the late 1960's we analyzed what would limit the electronic device technology as we know it; those calculations have held up quite well to the present [I]. The standard i ntegrated-ci rcu it fabricat ion processes available today allow usto build transistorsthat have minimum dimensions of about 1 p m). By ten years from now, we will have reduced these dimensions by another factor of 10, and we will be getting close to the fundamental physical limits: if we make the devices any smaller, they will stop working. It is conceiveable that a whole new class of devices will be invented-devices that are not subject to the same limitations. But certainly the ones we have thought of up to now-including the superconducting ones-will not make our circuits more than abouttwoordersof magnitude more den...

A strictly diabatic electronic basis is defined as one for which all components of the nuclear momentum coupling vanish. We examine the possibility that such a basis may exist, and we find that, in general, it does not. The only important exception is for diatomic states of the same symmetry. We also consider some conditions for the definition of an approximately diabatic electronic basis. For molecular systems with three or more nuclei, one can obtain useful approximate diabatic basis sets if the transverse (solenoidal) part of the coupling is negligible; this may occur, for example, if the part of the coupling due to the internuclear-distance dependence of the configurational wave functions is negligible as compared to that due to the internuclear-distance dependence of the configurational coefficients. We derive a criterion showing that such approximations may be useful and accurate if the role of the coupling is important over regions of sufficiently small linear dimensions.

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We show how the presence of a conical intersection in the adiabatic potential energy hypersurface can be handled by including a new vector potential in the nuclear-motion Schrödinger equation. We show how permutational symmetry of the total wave function with respect to interchange of nuclei can be enforced in the Born–Oppenheimer approximation both in the absence and the presence of conical intersections. The treatment of nuclear-motion wave functions in the presence of conical intersections and the treatment of nuclear-interchange symmetry in general both require careful consideration of the phases of the electronic and nuclear-motion wave functions, and this is discussed in detail.

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ABSTRAClNeural systems found in the brains of even very simple animals are amazingly effective at performing computations on information arising in the natural world. Neural structures expend less than a millionth of the power required by our most advanced digital signal processing technology for a similar task. At the level of a single device, however, our silicon technology can much more closely approach the energy requirements of structures in the brain. The nervous system achieves its remarkable effectiveness by using the fundamental device physics to define its computational primitives. In addition, algorithmic structures that emphasize spatial locality make best use of limited wiring resources. A deeper understanding of the design approach used by neural systems may make possible a new, and very powerful, engineering discipline.

Summary. Alamethicin induces a conductance in black lipid films which increases exponentially with voltage. At low conductance the increase occurs in discrete steps which form a pattern of five levels, the second and third being most likely. The conductance of each level is directly proportional to salt concentration, inversely proportional to solution viscosity, and nearly independent of voltage.The probability distribution of the five steps is not a function of voltage, but as the voltage is increased, more levels begin to appear. These can be explained as superpositions of the original five, both in position and relative probability.This suggests that the five levels are associated with a physical entity which we call a pore. This point of view is confirmed by the following measurements. The kinetic response of the current to a voltage step is first order, and shows an exponential increase in rate of pore formation and an exponential decrease in rate of pore disappearance with voltage. If these rates are statistical, the number of pores should fluctuate about a voltage-dependent mean. High conductance current fluctuations are too large to be explained by fluctuation in the number of pores alone. But if fluctuations among the five levels are included, the magnitude of the fluctuations at high conductance is accurately predicted.Alamethicin adsorbs reversibly to the membrane surface, and the conductance at a fixed voltage depends on the ninth power of alamethicin concentration and on the fourth power of salt concentration, in the aqueous phase. In our bacterial phosphatidyl ethanolamine membranes, alamethicin added to one side of the membrane produces elevated conductance only when the voltage on that side is increased.