Taking the logarithm of binomial type sequences: linear approach

In this paper we obtain the formal asymptotic expansion of the logarithms $\ln p_s(\alpha)$ of $p_s(\alpha)$, which are canonical continuations of polynomials of binomial type $p_n(\alpha)$. Our approach is based on linear methods which do not require the calculation of expansions $(p_s(\alpha)\alpha^{-s}-1)^k$, as opposed to the direct logarithmization.Comment: Typos correcte

Shot noise of interference between independent atomic systems

We study shot (counting) noise of the amplitude of interference between independent atomic systems. In particular, for the two interfering systems the variance of the fringe amplitude decreases as the inverse power of the number of particles per system with the coefficient being a non-universal number. This number depends on the details of the initial state of each system so that the shot noise measurements can be used to distinguish between such states. We explicitly evaluate this coefficient for the two cases of the interference between bosons in number states and in broken symmetry states. We generalize our analysis to the interference of multiple independent atomic systems. We show that the variance of the interference contrast vanishes as the inverse power of the number of the interfering systems. This result, implying high signal to noise ratio in the interference experiments, holds both for bosons and for fermions.Comment: 5 pages, 1 figure, final version, added a simple quantum-mechanical argument why two independent condensates with fixed number of particles in each must interfere in a generic experimental setu

Computational Models of Visual Hyperacuity

The process of visual hyperacuity is described and analyzed in the terms of informative theory. It is shown that in principle, the detection and representation of both luminance and edge features can be performed with a precision commensurate with human abilities. Algorithms are formulated in accord with the different representational methods, and are implemented as distinct computer models, which are tested with vernier acuity tasks. The results indicate that edge information, encoded either in the manner proposed by Marr and his col1eagucs (as zero-crossings in the Laplacian of a Gaussian convolved with the image) or when encoded as a simple filtered difference allows finer spatial localization than does the centroid of the intensity distribution. In particular it is shown that to judge changes of relative positions with a precision of 0.1 sec arc in two and three dimensions, it is sufficient to represent the displacement of an edge by the difference of two Laplacian-Gaussian filters rather than by the difference between interpolated zero-crossings in them. This method entails no loss of relative position information (sign), allows recovery of the magnitude of the change, and provides significant economies of computation

Integrating Multiple Uncertain Views of a Static Scene Acquired by an Agile Camera System

This paper addresses the problem of merging multiple views of a static scene into a common coordinate frame, explicitly considering uncertainty. It assumes that a static world is observed by an agile vision system, whose movements are known with a limited precision, and whose observations are inaccurate and incomplete. It concentrates on acquiring uncertain three-dimensional information from multiple views, rather than on modeling or representing the information at higher levels of abstraction. Two particular problems receive attention: identifying the transformation between two viewing positions; and understanding how errors and uncertainties propagate as a result of applying the transformation. The first is solved by identifying the forward kinematics of the agile camera system. The second is solved by first treating a measurement of camera position and orientation as a uniformly distributed random vector whose component variances are related to the resolution of the encoding potentiometers, then treating an object position measurement as a normally distributed random vector whose component variances are experimentally derived, and finally determining the uncertainty of the merged points as functions of these variances