“Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplitudes you told me about, they’re so complicated and absurd, what makes you think those are right? Maybe they aren’t right. ’ Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out.” —Richard Feynman [1, p.161]

Gödel's theorem may be demonstrated using arguments having an information-theoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast with the traditional proof based on the paradox of the liar, this new viewpoint suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread rather than pathological and unusual.

this paper we describe several such processes and present simple formulas for the velocity and force they generate. We shall call these machines "Brownian Ratchets" (BR) because rectified Brownian motion is fundamental to their operation.

Quantum entanglement lies at the heart of new proposals for quantum communication and computation. Here we describe the recent experimental realization of quantum teleportation.

This paper presents a technique for blindly estimating the amount of gamma correction in the absence of any calibration information or knowledge of the imaging device. The basic approach exploits the fact that gamma correction introduces specific higher-order correlations in the frequency domain. These correlations can be detected using tools from polyspectral analysis. The amount of gamma correction is then estimated by minimizing these correlations

This paper describes attempts to model the modules of early vision in terms of minimizing energy functions, in particular energy functions allowing discontinuities in the solution. It examines the success of using Hopfield-style analog networks for solving such problems. Finally it discusses the limitations of the energy function approach.

This paper presents a new algorithm for planning the time-optimal motion of a robot traveling with limited velocity from a given location to a given destination on a surface in the presence of moving obstacles. Additional constraints such as space variant terrain traversability and fuel economy can be accommodated. A multivalued distance map is defined and applied in computing optimal trajectories. The multivalued distance map incorporates constraints imposed by the moving obstacles, surface topography, and terrain traversability. It is generated by an efficient numerical curve propagation technique.

The statistical mechanics of neocortical interactions (SMNI) approach derives a theoretical model for aggregated neuronal activity that defines the “dipole” assumed by many EEG researchers. This defines a nonlinear stochastic filter to extract EEG signals.

Introduction As one of us has already repeatedly stressed ([10], [12], [13], [15]), we believe, together with Hermann von Helmholtz [23], that the central and the most pressing issue confronting cognitive science and artificial intelligence is the development of a satisfactory unified inductive learning model (see also [5], [34], [43]). Unfortunately, this issue was not perceived to be the central issue by the three leading (and founding) schools of AI, which had a very negative effect on the development of AI up to now. In particular, due only to the difference between the formal models used originally in some areas of AI and pattern recognition, AI had severed practically all ties with pattern recognition, which was very counter-productive to the development of both areas and particularly to AI. 1 With the recent rise of connectionism, this situation has begun to change, which is reflected in the content of the recent AI textbooks ([39], [4

Schneider, T. D. (1991). Theory of molecular machines. I. Channel capacity