Cramer-Rao bounds for parametric shape estimation in inverse problems

We address the problem of computing fundamental performance bounds for estimation of object boundaries from noisy measurements in inverse problems, when the boundaries are parameterized by a finite number of unknown variables. Our model applies to multiple unknown objects, each with its own unknown gray level, or color, and boundary parameterization, on an arbitrary known background. While such fundamental bounds on the performance of shape estimation algorithms can in principle be derived from the Cramer-Rao lower bounds, very few results have been reported due to the difficulty of computing the derivatives of a functional with respect to shape deformation. We provide a general formula for computing Cramer-Rao lower bounds in inverse problems where the observations are related to the object by a general linear transform, followed by a possibly nonlinear and noisy measurement system. As an illustration, we derive explicit formulas for computed tomography, Fourier imaging, and deconvolution problems. The bounds reveal that highly accurate parametric reconstructions are possible in these examples, using severely limited and noisy data.     

An efficient return algorithm for non-associated plasticity with linear yield criteria in principal stress space

An efficient return algorithm for stress update in numerical plasticity computations is presented. The yield criterion must be linear in principal stress space and can be composed of any number of yield planes. Each of these yield planes may have an associated or non-associated flow rule. The stress return and the formation of the constitutive matrix is carried out in principal stress space. Here the manipulations simplify and rely on geometrical arguments. The singularities arising at the intersection of yield planes are dealt with in a straightforward way also based on geometrical considerations. The method is exemplified on non-associated Mohr–Coulomb plasticity throughout the paper.     

Skewed symmetry: A nonaccidental property used to perceive visual forms.

Mathematically, skewed symmetry is a nonaccidental property because it can be interpreted as bilateral symmetry in depth viewed from a nonorthogonal angle. To find out whether this is a useful property in the perception of visual forms, 4 experiments were designed in which the Ss had to determine whether 2 symmetric or random patterns were the same regardless of possible affine transformations between them. The results provided mixed evidence: Although there was always a large symmetry advantage, skewed symmetry was only perceived as bilateral symmetry in depth for dot patterns with higher order types of symmetry (Exp 1), when the dots were connected to form closed polygons (Exp 2 and 4), or when they were surrounded by a frame to enhance their planarity (Exp 3). In other cases, Ss relied on local groupings on the basis of proximity or curvilinearity, which are qualitatively affine invariant. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

High‐error approximate dictionary search using estimate hash comparisons

A method for finding all matches in a pre‐processed dictionary for a query string q and with at most k differences is presented. A very fast constant‐time estimate using hashes is presented. A tree structure is used to minimize the number of estimates made. Practical tests are performed, showing that the estimate can filter out 99% of the full comparisons for 40% error rates and dictionaries of up to four million words. The tree is found to be efficient up to a 50% error rate. Copyright © 2006 John Wiley & Sons, Ltd.     

Group codes on certain algebraic curves with many rational points

We construct a series of algebraic geometric codes using a class of curves which have many rational points. We obtain codes of lengthq ² over _q , whereq = 2q ₀ ² andq ₀ = 2 ⁿ , such that dimension + minimal distance q ² + 1 – q ₀ (q – 1). The codes are ideals in the group algebra _q [S], whereS is a Sylow-2-subgroup of orderq ² of the Suzuki-group of orderq ² (q ² + 1)(q – 1). The curves used for construction have in relation to their genera the maximal number of GF _q -rational points. This maximal number is determined by the explicit formulas of Weil and is effectively smaller than the Hasse—Weil bound.Supported by Deutsche Forschungsgemeinschaft while visiting Essen University     

Coverage-biased random exploration of large models and application to testing

This paper presents several randomised algorithms for generating paths in large models according to a given coverage criterion. Using methods for counting combinatorial structures, these algorithms can efficiently explore very large models, based on a graphical representation by an automaton or by a product of several automata. This new approach can be applied to random exploration in order to optimise path coverage and can be generalised to take into account other coverage criteria, via the definition of a notion of randomised coverage satisfaction. Our main contributions are a method for drawing paths uniformly at random in composed models, i.e. models that are given as products of automata, first without and then with synchronisation; a new efficient approach to draw paths at random taking into account some other coverage criterion. Experimental results show promising agreement with theoretical predictions and significant improvement over previous randomised approaches. This work opens new perspectives for future studies of statistical testing and model checking, mainly to fight the combinatorial explosion problem.     

Majority gates vs. general weighted threshold gates

In this paper we study small depth circuits that contain threshold gates (with or without weights) and parity gates. All circuits we consider are of polynomial size. We prove several results which complete the work on characterizing possible inclusions between many classes defined by small depth circuits. These results are the following: