Stochastic volatility jump-diffusions for European equity index dynamics

Major research on equity index dynamics has investigated only US indices (usually the S&P 500) and has provided contradictory results. In this paper a clarification and extension of that previous research is given. We find that European equity indices have quite different dynamics from the S&P 500. Each of the European indices considered may be satisfactorily modelled using either an affine model with price and volatility jumps or a GARCH volatility process without jumps. The S&P 500 dynamics are much more difficult to capture in a jump-diffusion framework.

Dynamic input/output linearization using recurrent neural networks

A dynamic recurrent neural network (DRNN) is used to input/output linearize a control affine system in the globally linearizing control (GLC) structure. The network is trained as a part of a closed loop that involves a PI controller, the goal is to use the network, as a dynamic feedback, to cancel the nonlinear terms of the plant. The stability of the configuration is guarantee if the network and the plant are asymptotically stable and the linearizing input is bounded.

Stable linearization using multilayer neural networks

The main limitation of linearization theory that prevents its application in practical problems is the need for an exact knowledge of the plant. This requirement is eliminated and it is shown that a multilayer network can synthesise the state feedback coefficients that linearize a nonlinear control affine plant. The stability of the linearizing closed loop can be guaranteed if the autonomous plant is asymptotically stable and the state feedback is bounded.

Development of orientation during electrospinning of fibres of poly(ε-caprolactone)

We explore the influence of a rotating collector on the internal structure of poly(ε-caprolactone) fibres electrospun from a solution in dichloroethane. We find that above a threshold collector speed, the mean fibre diameter reduces as the speed increases and the fibres are further extended. Small-angle and wide-angle X-ray scattering techniques show a preferred orientation of the lamellar crystals normal to the fibre axis which increases with collector speed to a maximum and then reduces. We have separated out the processes of fibre alignment on the collector and the orientation of crystals within the fibres. There are several stages to this behaviour which correspond to the situations (a) where the collector speed is slower than the fibre spinning rate, (b) the fibre is mechanically extended by the rotating collector and (c) where the deformation leads to fibre fracture. The mechanical deformation leads to a development of preferred orientation with extension which is similar to the prediction of the pseudo-affine deformation model and suggests that the deformation takes place during the spinning process after the crystals have formed.

A wide-angle X-ray study of the development of molecular orientation in crosslinked natural rubber

Molecular orientation parameters have been measured for the non-crystalline component of crosslinked natural rubber samples deformed in uniaxial tension as a function of the extension ratio and of temperature. The orientation parapeters 〈P2(cosα)〉 and 〈P4(cosα)〉 were obtained by an analysis of the anisotropy of the wide-angle X-ray scattering functions. For the measurements made at high temperatures the level of crystallinity detected was negligible and the orientation-strain behaviour could be compared directly with the predictions of molecular models of rubber elasticity. The molecular orientation behaviour with strain was found to be at variance with the estimates of the affine model particularly at low and moderate strains. Extension of the crosslinked rubber at room temperature led to strain-crystallization and measurements of both the molecular orientation of the non-crystalline chains and the degree of crystallinity during extension and relaxation enabled the role of the crystallites in the deformation process to be considered in detail. The intrinsic birefringence of the non-crystalline component was estimated, through the use of the 〈P2(cosα)〉 values obtained from X-ray scattering measurements, to be 0.20±0.02.

Coupling between mesogenic units and polymer backbone in side-chain liquid crystal polymers and elastomers

The levels of alignment of the mesogenic units and of the polymer backbone trajectory for polyacrylate based nematic side-chain liquid crystal polymers and elastomers were evaluated by using wide angle X-ray and small angle neutron scattering procedures. The X-ray scattering measurements show that substantial levels of preferred orientation of the mesogenic units may be introduced through magnetic fields for uncrosslinked polymers and through mechanical extension for liquid crystal elastomers. Small angle neutron scattering measurements show that for highly aligned samples an anisotropic polymer backbone trajectory is observed in which the envelope is slightly extended by ∼ 10% in the direction parallel to the axis of alignment of the mesogenic units. The sense of this coupling differs from that recorded for other uncrosslinked side-chain liquid crystal polymers. Possible mechanisms to account for this anisotropy and its relationship to the properties of liquid crystal elastomers are discussed. The observed deformation behaviour of the liquid crystal elastomer is non-affine and this appears to confirm the dominating influence of the liquid crystal order of the side chains on the mechanical properties of these novel networks.

The determination of molecular orientation in uniaxially compressed PMMA by X-ray scattering

A procedure is presented for obtaining full molecular orientation information from wide angle X-ray scattering patterns of deformed non-crystalline polymers. The method is based on the analysis of experimental and calculated scattering patterns into their spherical harmonics. The results obtained for PMMA are compared with values predicted by the pseudo affine and affine deformation schemes.

From ensemble forecasts to predictive distribution functions

The translation of an ensemble of model runs into a probability distribution is a common task in model-based prediction. Common methods for such ensemble interpretations proceed as if verification and ensemble were draws from the same underlying distribution, an assumption not viable for most, if any, real world ensembles. An alternative is to consider an ensemble as merely a source of information rather than the possible scenarios of reality. This approach, which looks for maps between ensembles and probabilistic distributions, is investigated and extended. Common methods are revisited, and an improvement to standard kernel dressing, called ‘affine kernel dressing’ (AKD), is introduced. AKD assumes an affine mapping between ensemble and verification, typically not acting on individual ensemble members but on the entire ensemble as a whole, the parameters of this mapping are determined in parallel with the other dressing parameters, including a weight assigned to the unconditioned (climatological) distribution. These amendments to standard kernel dressing, albeit simple, can improve performance significantly and are shown to be appropriate for both overdispersive and underdispersive ensembles, unlike standard kernel dressing which exacerbates over dispersion. Studies are presented using operational numerical weather predictions for two locations and data from the Lorenz63 system, demonstrating both effectiveness given operational constraints and statistical significance given a large sample.

Forests of the tropical eastern Andean flank during the middle pleistocene

Inter-bedded volcanic and organic sediments from Erazo (Ecuador) indicate the presence of four different forest assemblages on the eastern Andean flank during the middle Pleistocene. Radiometric dates (40Ar–39Ar) obtained fromthe volcanic ash indicate that deposition occurred between 620,000 and 192,000 years ago. Examination of the organic sediment composition and the fossil pollen, wood and charcoal it contains provides insight into depositional environment, vegetation assemblage and fire history. The high organic content and abundance of macro fossils found throughout the sediment suggest that during the period of deposition the local environment was either a swamp or a shallow water body. The correlation of fire activity (peaks in charcoal abundance) with volcanic ash deposits through most of the record suggests that volcanoes were the main source of ignition. The low abundance of grass (typically b10%) throughout the sedimentary sequence along with the low abundance of other taxa indicative of open vegetation suggests the persistence of forest at Erazo. Four types of forest assemblage were identified (with the first taxa as the most dominant): i) Alnus-Arecaceae, ii) Miconia- Melastomataceae/Combretaceae-Moraceae/Urticaceae, iii) Arecaceae-Alnus, and iv) Podocarpus with Oreopanax sp. and Melastomataceae/Combretaceae. Changes in the forest floristic composition indicate high vegetation turnover and reassortment of taxa between upper and lower montane forests during the middle Pleistocene as well as the persistence of forest cover.

An ASIFT-based local registration method for satellite imagery

Imagery registration is a fundamental step, which greatly affects later processes in image mosaic, multi-spectral image fusion, digital surface modelling, etc., where the final solution needs blending of pixel information from more than one images. It is highly desired to find a way to identify registration regions among input stereo image pairs with high accuracy, particularly in remote sensing applications in which ground control points (GCPs) are not always available, such as in selecting a landing zone on an outer space planet. In this paper, a framework for localization in image registration is developed. It strengthened the local registration accuracy from two aspects: less reprojection error and better feature point distribution. Affine scale-invariant feature transform (ASIFT) was used for acquiring feature points and correspondences on the input images. Then, a homography matrix was estimated as the transformation model by an improved random sample consensus (IM-RANSAC) algorithm. In order to identify a registration region with a better spatial distribution of feature points, the Euclidean distance between the feature points is applied (named the S criterion). Finally, the parameters of the homography matrix were optimized by the Levenberg–Marquardt (LM) algorithm with selective feature points from the chosen registration region. In the experiment section, the Chang’E-2 satellite remote sensing imagery was used for evaluating the performance of the proposed method. The experiment result demonstrates that the proposed method can automatically locate a specific region with high registration accuracy between input images by achieving lower root mean square error (RMSE) and better distribution of feature points.

ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n).

The Bullough-Dodd model coupled to matter fields

The Bullough-Dodd model is an important two-dimensional integrable field theory which finds applications in physics and geometry. We consider a conformally invariant extension of it, and study its integrability properties using a zero curvature condition based on the twisted Kac-Moody algebra A(2)((2)). The one- and two-soliton solutions as well as the breathers are constructed explicitly. We also consider integrable extensions of the Bullough-Dodd model by the introduction of spinor (matter) fields. The resulting theories are conformally invariant and present local internal symmetries. All the one-soliton solutions, for two examples of those models, are constructed using a hybrid of the dressing and Hirota methods. One model is of particular interest because it presents a confinement mechanism for a given conserved charge inside the solitons. (C) 2008 Elsevier B.V. All rights reserved.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point.

Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface (Sigma, g), its tangent bundle T Sigma enjoys a natural pseudo-Kahler structure, that is the combination of a complex structure 2, a pseudo-metric G with neutral signature and a symplectic structure Omega. We give a local classification of those surfaces of T Sigma which are both Lagrangian with respect to Omega and minimal with respect to G. We first show that if g is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R(3) or R(1)(3) induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS(2) or TH(2) respectively. We relate the area of the congruence to a second-order functional F = f root H(2) - K dA on the original surface. (C) 2010 Elsevier B.V. All rights reserved.