Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.

Minimum jerk trajectory control for rehabilitation and haptic applications

Smooth trajectories are essential for safe interaction in between human and a haptic interface. Different methods and strategies have been introduced to create such smooth trajectories. This paper studies the creation of human-like movements in haptic interfaces, based on the study of human arm motion. These motions are intended to retrain the upper limb movements of patients that lose manipulation functions following stroke. We present a model that uses higher degree polynomials to define a trajectory and control the robot arm to achieve minimum jerk movements. It also studies different methods that can be driven from polynomials to create more realistic human-like movements for therapeutic purposes.

Gene-chip technology and its applications

Gene Chips are finding extensive use in animal and plant science. Generally microarrays are of two kind, cDNA or oligonucleotide. cDNA microarrays were developed at Stanford University, whereas oligonucleotide were developed by Affymetrix. The construction of cDNA or oligonucleotide on a glass slide helps to compare the gene expression level of treated and control samples by labeling mRNA with green (Cy3) and red (Cy5) dyes. The hybridized gene chip emit fluorescence whose intensity and colour can be measured. RNA labeling can be done directly or indirectly. Indirect method involves amino allyle modified dUTP instead of pre-labelled nucleotide. Hybridization of gene chip generally occurs in a minimum volume possible and to ensure the hetroduplex formation, a ten fold more DNA is spotted on slide than in the solutions. A confocal or semi confocal laser technologies coupled with CCD camera are used for image acquisition. For standardization, house keeping genes are used or cDNA are spotted in gene chip that are not present in treated or control samples. Moreover, statistical analysis (image analysis) and cluster analysis softwares have been developed by Stanford University. The gene-chip technology has many applications like expression analysis, gene expression signatures (molecular phenotypes) and promoter regulatory element co-expression.

Analysis and modeling of ants’ behavior from single to multi-body

In order to shed light on the collective behavior of social insects, we analyzed the behavior of ants from single to multi-body. In an experimental set-up, ants are placed in hemisphere without a nest and food. Trajectory of ants is recorded. From this bottom-up approach, we found that collective behavior of ants as follows: 1. Activity of single ant increases and decreases periodically. 2. Spontaneous meeting process is observed between two ants and meeting spot of two ants is localized in hemisphere. 3. Result on division of labor is obtained between two ants.

Community engagement and social organization: introducing concepts, policy and practical applications

This chapter provides an introductory overview of how the term ‘community’ has been conceptualized in sociological literatures, noting that there remains considerable uncertainty with regard to the way in which communities could or should be defined. The chapter examines the salience of underlying concepts of social organization that can shape and influence the extent to which programmes of engagement are likely to be successful. Drawing on recent empirical work some of the key opportunities and challenges for local government in translating the concepts into practice are considered.

Terahertz spectroscopy and imaging at the nanoscale for biological and security applications

The chemical specificity of terahertz spectroscopy, when combined with techniques for sub-wavelength sensing, is giving new understanding of processes occurring at the nanometre scale in biological systems and offers the potential for single molecule detection of chemical and biological agents and explosives. In addition, terahertz techniques are enabling the exploration of the fundamental behaviour of light when it interacts with nanoscale optical structures, and are being used to measure ultrafast carrier dynamics, transport and localisation in nanostructures. This chapter will explain how terahertz scale modelling can be used to explore the fundamental physics of nano-optics, it will discuss the terahertz spectroscopy of nanomaterials, terahertz near-field microscopy and other sub-wavelength techniques, and summarise recent developments in the terahertz spectroscopy and imaging of biological systems at the nanoscale. The potential of using these techniques for security applications will be considered.

Forecast, measurement, and modeling of an unprecedented polar ozone filament event over Mauna Loa Observatory, Hawaii

In mid-March 2005 the northern lower stratospheric polar vortex experienced a severe stretching episode, bringing a large polar filament far south of Alaska toward Hawaii. This meridional intrusion of rare extent, coinciding with the polar vortex final warming and breakdown, was followed by a zonal stretching in the wake of the easterly propagating subtropical main flow. This caused polar air to remain over Hawaii for several days before diluting into the subtropics. After being successfully forecasted to pass over Hawaii by the high-resolution potential vorticity advection model Modèle Isentrope du transport Méso-échelle de l'Ozone Stratosphérique par Advection (MIMOSA), the filament was observed on isentropic surfaces between 415 K and 455 K (17–20 km) by the Jet Propulsion Laboratory stratospheric ozone lidar measurements at Mauna Loa Observatory, Hawaii, between 16 and 19 March 2005. It was materialized as a thin layer of enhanced ozone peaking at 1.6 ppmv in a region where the climatological values usually average 1.0 ppmv. These values were compared to those obtained by the three-dimensional Chemistry-Transport Model MIMOSA-CHIM. Agreement between lidar and model was excellent, particularly in the similar appearance of the ozone peak near 435 K (18.5 km) on 16 March, and the persistence of this layer at higher isentropic levels for the following three days. Passive ozone, also modeled by MIMOSA-CHIM, was at about 3–4 ppmv inside the filament while above Hawaii. A detailed history of the modeled chemistry inside the filament suggests that the air mass was still polar ozone–depleted when passing over Hawaii. The filament quickly separated from the main vortex after its Hawaiian overpass. It never reconnected and, in less than 10 days, dispersed entirely in the subtropics

Simultaneous lidar and EOS MLS measurements, and modeling, of a rare polar ozone filament event over Mauna Loa Observatory, Hawaii

In mid-March 2005, a rare lower stratospheric polar vortex filamentation event was observed simultaneously by the JPL lidar at Mauna Loa Observatory, Hawaii, and by the EOS MLS instrument onboard the Aura satellite. The event coincided with the beginning of the spring 2005 final warming. On 16 March, the filament was observed by lidar around 0600 UT between 415 K and 455 K, and by MLS six hours earlier. It was seen on both the lidar and MLS profiles as a layer of enhanced ozone, peaking at 1.7 ppmv in a region where the climatological values are usually around or below 1 ppmv. Ozone profiles measured by lidar and MLS were compared to profiles from the Chemical Transport Model MIMOSA-CHIM. The agreement between lidar, MLS, and the model is excellent considering the difference in the sampling techniques. MLS was also able to identify the filament at another location north of Hawaii.