Data compression and prediction in neural networks

We study the relationship between data compression and prediction in single-layer neural networks of limited complexity. Quantifying the intuitive notion of Occam's razor using Rissanen's minimum complexity framework, we investigate the model-selection criterion advocated by this principle. While we find that the criterion works well for large sample sizes (as it must for consistency), the behavior for finite sample sizes is rather complex, depending intricately on the relationship between the complexity of the hypothesis space and the target space. We also show that the limited networks studied perform efficient data compression, even in the error full regime.     

Processes with no standard extension

Using an example of A. Vershik, a class of processes is introduced with the property that they do not admit astandard extension. This provides a simple proof that Vershik's example process does not admit a standard extension. Supported in part by The Israel Science Foundation.     

Adaptive optics for airborne platforms—Part 1: modeling

Adaptive optics systems mitigate the atmospheric turbulence-induced distortion of a propagating light wavefront. The use of adaptive optics entails the design of a feedback controller, which requires the development of a model of the plant to be controlled. In adaptive optics, the plant consists of the atmosphere through which light is traveling. Moreover, a distinct feature of the adaptive optics control application is the presence of random signals in the plant. In optics, Zernike orthonormal polynomials are commonly used as a basis set for the expansion of wavefront phase distortions. Due to the atmospheric turbulence-induced random nature of the underlying physical process, the spatial-temporal correlation functions of the Zernike polynomial phase distortion expansion coefficients must be evaluated if a proper stochastic model of the plant is to be developed and adaptive optics is to be employed. In Part 1 of this paper, these correlation functions are developed using a layered atmospheric model and calculations for the first few low-order Zernike modes are performed. Using these correlation functions, an underlying stochastic linear dynamical system, which is adequate for control design, is synthesized. This system models the plant and, in turn, provides the basis for the employment of advanced model-based control and estimation concepts in an adaptive optics system for an airborne platform application.     

On random mapping patterns

Random mapping patterns may be represented by unlabelled directed graphs in which each point has out-degree one. We determine the asymptotic behaviour of various parameters associated with such graphs, such as the expected number of points belonging to cycles and the expected number of components. Dedicated to Paul Erdős on his seventieth birthday     

Optimal control problem for an automatic transmission

Attention is given to the control-theoretic aspects of the operation of an automatic transmission for a road vehicle. A differential game model for vehicle control is presented and analyzed; furthermore, the approach leads to a synthesis of the optimal feedback strategy for the selection of the transmission ratio of the automatic gearbox.This work was partially supported by a grant from Control Data.     

Electronic structure for sliding charge density waves

We present a model for the electron system in NbSe₃ based on its quasi one-dimensional metallic properties. In a one-dimensional metal phonon drag of 2K_F-phonons takes place at temperatures higher than θ_D, since the phonon-electron scattering rate τ^?1_ph?el is greater than the phonon-phonon rate τ^?1_ph?ph. this situation is in contrast to the situation in three dimensional metals, where phonon drag takes place only at very low temperatures. Our model explains the transport properties of the material including the electrical conductivity anistropy, the conductivity in a strong electric field, and the Hall effect data.     

The Avidin-Biotin complex in solid phase radioimmunoassays

A solid-phase radioimmunoassay is described in which biotin conjugated antibodies are used to replace¹²⁵I labeled antibodies to individual antigens. The amount of antigen present is subsequently determined by the binding of¹²⁵I-labeled avidin. This method is appealing for a variety of reasons. (a) Only one¹²⁵I-labeled protein (avidin) need be prepared and characterized for all affinity systems, (b) There is no need to purify individual antibodies. (c) Biotin can be attached to antibodies under mild conditions. (d) The size, physical characteristics, and biological activity of the biotin-derived antibody are only nominally affected. (e) The biotin-avidin complex is of exceptionally high affinity and stability, (f) Introduction of biotin groups into the antibodies leads to amplified radioactive tracer binding, (g) Avidin and biotin are commercially available.     

On state restrained linear-quadratic control problems

A finite dimensional linear autonomous control process with subspace state restraint is considered from the controllability and minimum quadratic cost points of view. The problem of holding in a subspace on an infinite time interval with finite total control energy is also considered.