This paper introduces and studies a field theoretic analogue of the Clebsch variational principle of classical mechanics. This principle yields an alternative derivation of the covariant Euler-Poincaré equations that naturally includes covariant Clebsch variables via multisymplectic momentum maps. In the case of diffeomorphism groups, this approach gives a new interpretation of recently derived...

We develop a new class of log-Sobolev inequalities (LSIs) that provide a nonlinear comparison between the entropy and the Dirichlet form. For the hypercube, these LSIs imply a new version of the hypercontractivity for functions of small support. As a consequence, we derive a sharp form of the uncertainty principle for the hypercube: a function whose energy is concentrated on a set of small size...

Categories of relations over a regular category form a family of models of quantum theory. Using regular logic, many properties of relations over sets lift to these models, including the correspondence between Frobenius structures and internal groupoids. Over compact Hausdorff spaces, this lifting gives continuous symmetric encryption. Over a regular Mal’cev category, this correspondence gives ...

This work investigates the effects of uncertainties in a chaotic system. It continues the work of a previous paper in which an uncertain regression model was used to represent a nonlinear system capable of bifurcation. In this case, the two-dimensional Henon map is studied. A possibilistic uncertainty modelling approach is used to estimate the system response subject to uncertain inputs and par...

This paper presents a novel and robust chaos-based cryptosystem for secure transmitted images and four other versions. In the proposed block encryption/decryption algorithm, a 2D chaotic map is used to shuffle the image pixel positions. Then, substitution (confusion) and permutation (diffusion) operations on every block, with multiple rounds, are combined using two perturbed chaotic PWLCM maps....

The study of fixed points of single-valued self-mappings or multivalued self-mappings satisfying certain contraction conditions has a great majority of results inmetric fixed point theory. All these results are mainly generalizations of Banach contraction principle. The Banach contraction principle guarantees the existence and uniqueness of fixed points of certain self-maps in complete metric s...

We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object’s interior is required. We propose an algorithm that can be used to detect grayscale objects of unk...

W e describe techniques to optimally select landmarks in order to perform mobile robot localization by matching terrain maps. The method is based upon a maximum-likelihood robot localization algorithm that efficiently searches the space of possible robot positions. W e u s e a sensor error model to estimate the probability distribution of the terrain expected to be seen from the current robot p...

The evaluation of the measurement uncertainty of a robust all-fiber-based low-coherence interferometer for the measurement of absolute thickness of transparent artifacts is described. The performance of the instrument is evaluated by measuring the length of air-gaps in specially constructed artifacts and the observed measurement errors are discussed in the context of the uncertainty associated ...

Some new Advanced Driver Assistance Systems (ADAS) need on-the-lane vehicle positioning on accurate digital maps, but present applications of vehicle positioning do not justify the surcharge of very accurate equipment such as DGPS or high-cost inertial systems. For this reason, performance of GPS in autonomous mode is analyzed. Although satisfactory results can be found, in some areas GPS signa...