Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

Optimal steady motions for oriented vehicles

Motivated by the motion planning problem for oriented vehicles travelling in a 3-Dimensional space; Euclidean space E3, the sphere S3 and Hyperboloid H3. For such problems the orientation of the vehicle is naturally represented by an orthonormal frame over a point in the underlying manifold. The orthonormal frame bundles of the space forms R3,S3 and H3 correspond with their isometry groups and are the Euclidean group of motion SE(3), the rotation group SO(4) and the Lorentzian group SO(1; 3) respectively. Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. For constant twist motions or helical motions, the corresponding curves g(t) 2 SE(3) are given in closed form by using the well known Rodrigues’ formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw/helical motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

Segmentation-level fusion for iris recognition

This paper investigates the potential of fusion at normalisation/segmentation level prior to feature extraction. While there are several biometric fusion methods at data/feature level, score level and rank/decision level combining raw biometric signals, scores, or ranks/decisions, this type of fusion is still in its infancy. However, the increasing demand to allow for more relaxed and less invasive recording conditions, especially for on-the-move iris recognition, suggests to further investigate fusion at this very low level. This paper focuses on the approach of multi-segmentation fusion for iris biometric systems investigating the benefit of combining the segmentation result of multiple normalisation algorithms, using four methods from two different public iris toolkits (USIT, OSIRIS) on the public CASIA and IITD iris datasets. Evaluations based on recognition accuracy and ground truth segmentation data indicate high sensitivity with regards to the type of errors made by segmentation algorithms.

Document engineering approaches toward scalable and structured multimedia, web and printable documents

Document engineering is the computer science discipline that investigates systems for documents in any form and in all media. As with the relationship between software engineering and software, document engineering is concerned with principles, tools and processes that improve our ability to create, manage, and maintain documents (http://www.documentengineering.org). The ACM Symposium on Document Engineering is an annual meeting of researchers active in document engineering: it is sponsored by ACM by means of the ACM SIGWEB Special Interest Group. In this editorial, we first point to work carried out in the context of document engineering, which are directly related to multimedia tools and applications. We conclude with a summary of the papers presented in this special issue.

A Systems-Level Approach to Human Epileptic Seizures

Epileptic seizures are due to the pathological collective activity of large cellular assemblies. A better understanding of this collective activity is integral to the development of novel diagnostic and therapeutic procedures. In contrast to reductionist analyses, which focus solely on small-scale characteristics of ictogenesis, here we follow a systems-level approach, which combines both small-scale and larger-scale analyses. Peri-ictal dynamics of epileptic networks are assessed by studying correlation within and between different spatial scales of intracranial electroencephalographic recordings (iEEG) of a heterogeneous group of patients suffering from pharmaco-resistant epilepsy. Epileptiform activity as recorded by a single iEEG electrode is determined objectively by the signal derivative and then subjected to a multivariate analysis of correlation between all iEEG channels. We find that during seizure, synchrony increases on the smallest and largest spatial scales probed by iEEG. In addition, a dynamic reorganization of spatial correlation is observed on intermediate scales, which persists after seizure termination. It is proposed that this reorganization may indicate a balancing mechanism that decreases high local correlation. Our findings are consistent with the hypothesis that during epileptic seizures hypercorrelated and therefore functionally segregated brain areas are re-integrated into more collective brain dynamics. In addition, except for a special sub-group, a highly significant association is found between the location of ictal iEEG activity and the location of areas of relative decrease of localised EEG correlation. The latter could serve as a clinically important quantitative marker of the seizure onset zone (SOZ).

Flexible varieties and automorphism groups

Given an irreducible affine algebraic variety X of dimension n≥2 , we let SAut(X) denote the special automorphism group of X , that is, the subgroup of the full automorphism group Aut(X) generated by all one-parameter unipotent subgroups. We show that if SAut(X) is transitive on the smooth locus X reg , then it is infinitely transitive on X reg . In turn, the transitivity is equivalent to the flexibility of X . The latter means that for every smooth point x∈X reg the tangent space T x X is spanned by the velocity vectors at x of one-parameter unipotent subgroups of Aut(X) . We also provide various modifications and applications.

Directives for a Correct Diagnosis

A special Working Group, to study and develop standars related to Building Restoration, Rehabilitation and Maintenance, was formed in January 2001 in AENOR (Spanish Association for Codes and Standars) under the management of the Department of Building Construction of the School of Architecture of Madrid (DCTA-UPM). Three groups were organized to deal with different topics: Diagnosis, Techiques and Materials, and Maintenance. In this paper the differents topics in which the Diagnosis Subgroup is working are described: historical studies, constructive description of the building and building pathology. These will be basic to carry out a correct diagnosis of any type of building, whether it is historic or not. In the development of such topics, the recognizable architectural values are justified as they are prior to the diagnosis stage. As an example of the subgroup work, several pathology cards are shown which include: longitudinal cracks of mechanical origin in beams of concrete structures, façade closings and claddings, and general symptoms of installation services.

Estimating Adaptacion of Dialogue Partners with Different Verbal Intelligence

This work investigates to what degree speakers with different verbal intelligence may adapt to each other. The work is based on a corpus consisting of 100 descriptions of a short film (monologues), 56 discussions about the same topic (dialogues), and verbal intelligence scores of the test participants. Adaptation between two dialogue partners was measured using cross-referencing, proportion of "I", "You" and "We" words, between-subject correlation and similarity of texts. It was shown that lower verbal intelligence speakers repeated more nouns and adjectives from the other and used the same linguistic categories more often than higher verbal intelligence speakers. In dialogues between strangers, participants with higher verbal intelligence showed a greater level of adaptation.