New results for the magnitude of flicker noise, considered as resistance fluctuations, in random resistor networks are reported. Near the percolation threshold p c , the magnitude of the relative noise is shown to diverge as (p-p c )~K. The new exponent K is calculated by various methods: Monte Carlo simulations, effective-medium theory, and position-space renormalization group. Exponents pertaining to higher-order cumulants of the resistance fluctuations are also calculated. The possible implications of our results for ongoing experiments on metal-insulator mixtures and cermets are also discussed.

New bounds for the exponent characterizing the amplitude of the resistance noise near the percolation threshold of discrete random networks are found. The difference between the lower and upper bounds is very small, so that an accurate estimate of the noise exponent can be obtained in all dimensions. Continuum corrections to these exponents for the random-void class of systems are then calculated within the nodes-links-blobs model of percolating networks.

Many presume that parsing the shadows out of an image is a high-level task, because of the global nature of the shadow formation process. But shapefrom-shading algorithms are low-level, in the sense that they seek solutions (surface normals or depth values) directly from image intensities. A dilemma arises: since shape-from-shading involves an illumination term, shadows must first be identified. We show that a structure in.termediate between intensitees and surfaces -the shading flow field ~ provides a solution to this dilemma. Our analysis is based on the observation that the geometric information that can be derived froin images supports different inferences than the photometric information, and our specific goal will be to articulate this geometric structure and to show how shading flow fields can be reliably computed.

It is shown that the Negative Eigenvalue Theorem and transfer matrix methods may be considered within a unified framework and generalized to compute projected densities of states or, more generally, any linear combination of matrix elements of the inverse of large symmetric random matrices. As examples of applications, extensive simulations for one- and two-mode behaviour in the Raman spectrum of one-dimensional mixed crystals and a finite-size scaling analysis of critical exponents for the central force percolation universality class are presented

No abstract

The classical approach to shape from shading problems is to find a numerical solution of the image irradianee partial differential equation. It is always assumed that the parameters of this equation (the light source direction and surface albedo) can be estimated in advance. For images which contain shadows and occluding contours, this decoupling of problems is artificial. We develop a new approach to solving these equations. It is based on modern differential geometry, and solves for light source, surface shape, and material changes concurrently. Local scene elements (scenels) are estimated from the shading flow field, and smoothness, material, and light source compatibility conditions resolve them into consistent scene descriptions. Shadows and related difficulties for the classical approach are discussed.

Analogies between critical phenomena and the continuous spectrum of scaling exponents associated with fractal measures are pointed out. The analogies are based first on the Hausdorff-Bernstein reconstruction theorem, which states that the positive integer moments suf5ce to characterize a probability distribution function with finite support, and second on the joint probability distribution for the positive integer moments. This joint probability distribution, which can be considered as a fixed point, is universal and exhibits both gap scaling and the infinite set of exponents. Monte Carlo simulations of the electrical properties of percolation clusters on the square and triangular lattices support this general result. Extensions to other fields where infinite sets of exponents have arisen, such as diAusion-limited aggregation and localization, should be straightforward.

The application of exact and approximate position-space renormalization group techniques to the calculation of densities of states for problems with Gaussian generating functions (such as free tight-binding electrons, harmonic vibrations, spin waves, or random walks on Euclidian or "fractal" lattices) is briefly reviewed. It is also shown that for one-dimensional Gaussian theories with disorder, the approximate recursion relations proposed by Gon<;alves da Silva and Koiller (GK) are exact for problems formulated on Berker-Ostlund lattices. A generalization of the GK scheme which allows one to calculate the optical zone-center density of states is formulated and then applied to the study of one-and two-mode behavior in mixed diatomic crystals.