Composite control of non-linear singularly perturbed systems: meeting a design objective

Using the integral manifold approach, a composite control—the sum of a fast control and a slow control—is derived for a particular class of non-linear singularly perturbed systems. The fast control is designed completely at the outset, thus ensuring the stability of the fast transients of the system and, furthermore, the existence of the integral manifold. A new method is then presented which simplifies the derivation of a slow control such that the singularly perturbed system meets a preselected design objective to within some specified order of accuracy. Though this approach is, by its very nature, ad hoc, the underlying procedure is easily extended to more general classes of singularly perturbed systems by way of three examples.

A three-regime model of speculative behaviour: modelling the evolution of the S&P 500 composite index

We examine whether a three-regime model that allows for dormant, explosive and collapsing speculative behaviour can explain the dynamics of the S&P 500. We extend existing models of speculative behaviour by including a third regime that allows a bubble to grow at a steady rate, and propose abnormal volume as an indicator of the probable time of bubble collapse. We also examine the financial usefulness of the three-regime model by studying a trading rule formed using inferences from it, whose use leads to higher Sharpe ratios and end of period wealth than from employing existing models or a buy-and-hold strategy.

Dimensionalising on- and off-line brands' composite equity

This paper approaches the subject of brand equity measurement on and offline. The existing body of research knowledge on brand equity measurement has derived from classical contexts; however, the majority of today's brands prosper simultaneously online and offline. Since branding on the Web needs to address the unique characteristics of computer-mediated environments, it was posited that classical measures of brand equity were inadequate for this category of brands. Aaker's guidelines for building a brand equity measurement system were thus followed and his brand equity ten was employed as a point of departure. The main challenge was complementing traditional measures of brand equity with new measures pertinent to the Web. Following 16 semi-structured interviews with experts, ten additional measures were identified.

Better cross hedges with composite hedging? Hedging equity portfolios using financial and commodity futures

Unless a direct hedge is available, cross hedging must be used. In such circumstances portfolio theory implies that a composite hedge (the use of two or more hedging instruments to hedge a single spot position) will be beneficial. The study and use of composite hedging has been neglected; possibly because it requires the estimation of two or more hedge ratios. This paper demonstrates a statistically significant increase in out-of-sample effectiveness from the composite hedging of the Amex Oil Index using S&P500 and New York Mercantile Exchange crude oil futures. This conclusion is robust to the technique used to estimate the hedge ratios, and to allowance for transactions costs, dividends and the maturity of the futures contracts.

Design of a biomimetic skin for an octopus-inspired robot - Part II: Development of the skin artefact

In order to develop skin artefact for an octopus-inspired robot arm, which is designed to be able to elongate 60% of its original length, silicone rubber and knitted nylon sheet were selected to manufacture an artificial skin, due to their higher elastic strain and high flexibility. Tensile and scissors cutting tests were conducted to characterise the matrix and reinforcing materials and the skin artefact. Material properties of the individual and the composite materials were compared with the measured properties of real octopus skin presented in Part I. The Young’s modulus of the skin should be below 20 MPa and the elastic strain range should be over 60%. The fracture toughness should be at least 0.9 kJ·m−2. Tubes made of the skin artefact filled with liquid were tested to study volume change under deformation. Finite element analysis model was developed to simulate the material and arm structure under tensile loading. Results show that the skin artefact developed has similar mechanical properties as the real octopus skin and satisfies all the design specifications of the OCTOPUS robot.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Prebiotics and the health benefits of fiber: current regulatory status, future research, and goals.

First defined in the mid-1990s, prebiotics, which alter the composition and activity of gastrointestinal (GI) microbiota to improve health and well-being, have generated scientific and consumer interest and regulatory debate. The Life Sciences Research Organization, Inc. (LSRO) held a workshop, Prebiotics and the Health Benefits of Fiber: Future Research and Goals, in February 2011 to assess the current state of the science and the international regulatory environment for prebiotics, identify research gaps, and create a strategy for future research. A developing body of evidence supports a role for prebiotics in reducing the risk and severity of GI infection and inflammation, including diarrhea, inflammatory bowel disease, and ulcerative colitis as well as bowel function disorders, including irritable bowel syndrome. Prebiotics also increase the bioavailability and uptake of minerals and data suggest that they reduce the risk of obesity by promoting satiety and weight loss. Additional research is needed to define the relationship between the consumption of different prebiotics and improvement of human health. New information derived from the characterization of the composition and function of different prebiotics as well as the interactions among and between gut microbiota and the human host would improve our understanding of the effects of prebiotics on health and disease and could assist in surmounting regulatory issues related to prebiotic use.

Developing sensorized arm skin for an octopus inspired robot

Soft skin artefacts made of knitted nylon reinforced silicon rubber were fabricated mimicking octopus skin. A combination of ecoflex 0030 and 0010 were used as matrix of the composite to obtain the right stiffness for the skin artefacts. Material properties were characterised using static uniaxial tension and scissors cutting tests. Two types of tactile sensors were developed to detect normal contact; one used quantum tunnelling composite materials and the second was fabricated from silicone rubber and a conductive textile. Sensitivities of the sensors were tested by applying different modes of loading and the soft sensors were incorporated into the skin prototype. Passive suckers were developed and tested against squid suckers. An integrated skin prototype with embedded deformable sensors and attached suckers developed for the arm of an octopus inspired robot is also presented.

Developing skin analogues for a robotic octopus

In order to fabricate a biomimetic skin for an octopus inspired robot, a new process was developed based on mechanical properties measured from real octopus skin. Various knitted nylon textiles were tested and the one of 10-denier nylon was chosen as reinforcement. A combination of Ecoflex 0030 and 0010 silicone rubbers was used as matrix of the composite to obtain the right stiffness for the skin-analogue system. The open mould fabrication process developed allows air bubble to escape easily and the artificial skin produced was thin and waterproof. Material properties of the biomimetic skin were characterised using static tensile and instrumented scissors cutting tests. The Young’s moduli of the artificial skin are 0.08 MPa and 0.13 MPa in the longitudinal and transverse directions, which are much lower than those of the octopus skin. The strength and fracture toughness of the artificial skin, on the other hand are higher than those of real octopus skins. Conically-shaped skin prototypes to be used to cover the robotic arm unit were manufactured and tested. The biomimetic skin prototype was stiff enough to maintain it conical shape when filled with water. The driving force for elongation was reduced significantly compared with previous prototypes.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

Terahertz pulse imaging of stratified architectural materials for cultural heritage studies

Terahertz pulse imaging (TPI) is a novel noncontact, nondestructive technique for the examination of cultural heritage artifacts. It has the advantage of broadband spectral range, time-of-flight depth resolution, and penetration through optically opaque materials. Fiber-coupled, portable, time-domain terahertz systems have enabled this technique to move out of the laboratory and into the field. Much like the rings of a tree, stratified architectural materials give the chronology of their environmental and aesthetic history. This work concentrates on laboratory models of stratified mosaics and fresco paintings, specimens extracted from a neolithic excavation site in Catalhoyuk, Turkey, and specimens measured at the medieval Eglise de Saint Jean-Baptiste in Vif, France. Preparatory spectroscopic studies of various composite materials, including lime, gypsum and clay plasters are presented to enhance the interpretation of results and with the intent to aid future computer simulations of the TPI of stratified architectural material. The breadth of the sample range is a demonstration of the cultural demand and public interest in the life history of buildings. The results are an illustration of the potential role of TPI in providing both a chronological history of buildings and in the visualization of obscured wall paintings and mosaics.