Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.

Experimental study of modulational instability and vector solitons in optical fibers

info:eu-repo/semantics/published

An extension of Purcell's vector method with applications to panel element equations

The classical Purcell's vector method, for the construction of solutions to dense systems of linear equations is extended to a flexible orthogonalisation procedure. Some properties are revealed of the orthogonalisation procedure in relation to the classical Gauss-Jordan elimination with or without pivoting. Additional properties that are not shared by the classical Gauss-Jordan elimination are exploited. Further properties related to distributed computing are discussed with applications to panel element equations in subsonic compressible aerodynamics. Using an orthogonalisation procedure within panel methods enables a functional decomposition of the sequential panel methods and leads to a two-level parallelism.

A higher order Hopfield network for vector quantisation

A higher order version of the Hopfield neural network is presented which will perform a simple vector quantisation or clustering function. This model requires no penalty terms to impose constraints in the Hopfield energy, in contrast to the usual one where the energy involves only terms quadratic in the state vector. The energy function is shown to have no local minima within the unit hypercube of the state vector so the network only converges to valid final states. Optimisation trials show that the network can consistently find optimal clusterings for small, trial problems and near optimal ones for a large data set consisting of the intensity values from the digitised, grey-level image.

Support vector machines for regression and applications to software quality prediction

Software metrics are the key tool in software quality management. In this paper, we propose to use support vector machines for regression applied to software metrics to predict software quality. In experiments we compare this method with other regression techniques such as Multivariate Linear Regression, Conjunctive Rule and Locally Weighted Regression. Results on benchmark dataset MIS, using mean absolute error, and correlation coefficient as regression performance measures, indicate that support vector machines regression is a promising technique for software quality prediction. In addition, our investigation of PCA based metrics extraction shows that using the first few Principal Components (PC) we can still get relatively good performance.

A clear direction

Comments on the House of Lords decision in Thorner v Curtis, also referred to as Thorner v Major, on whether an unpaid farm labourer could rely on assurances made by the farmer that he would inherit the farm, to establish proprietary estoppel when the farmer died intestate. Considers whether the assurances had been clear and whether the property to be inherited could be specifically identified. Notes the Lords' consideration of the possible existence of a constructive trust. [From Legal Journals Index]

Mode shape expansion using perturbed force vector approach

A new technique for mode shape expansion in structural dynamic applications is presented based on the perturbed force vector approach. The proposed technique can directly adopt the measured incomplete modal data and include the effect of the perturbation between the analytical and test models. The results show that the proposed technique can provide very accurate expanded mode shapes, especially in cases when significant modelling error exists in the analytical model and limited measurements are available.

Exploring multi-sensor satellite synergies to provide direction to high-resolution along-track altimtery currents

A new approach to compute along-track velocity components by combining altimetry-based across-track components and front directions from remote sensing maps of surface chlorophyll concentration is proposed. The analysis focuses on the South Madagascar region characterized by the strong East Madagascar Current and sharp gradients of surface tracers. The results are compared against in-situ observations from three moorings along the Jason-1 track 196. Accurate information on the total velocity direction is the key factor for obtaining accurate estimates of along-track velocities. Although with some limitations, surface tracer fronts can be successfully used to retrieve such information.

Direction repulsion goes global

When viewing two superimposed, translating sets of dots moving in different directions, one overestimates the direction difference. This phenomenon of direction repulsion is thought to be driven by inhibitory interactions between directionally tuned motion detectors [1, 2]. However, there is disagreement on where this occurs — at early stages of motion processing [1, 3], or at the later, global motion-processing stage following “pooling” of these measures [4–6]. These two stages of motion pro - cessing have been identified as occurring in area V1 and the human homolog of macaque MT/V5, respectively[7, 8]. We designed experiments in which local and global predictions of repulsion are pitted against one another. Our stimuli contained a target set of dots, moving at a uniform speed, superimposed on a “mixed-speed” distractor set. Because the perceived speed of a mixed-speed stimulus is equal to the dots’ average speed [9], a global-processing account of direction repulsion predicts that repulsion magnitude induced by a mixed-speed distractor will be indistinguishable from that induced by a single-speed distractor moving at the same mean speed. This is exactly what we found. These results provide compelling evidence that global-motion interactions play a major role in driving direction repulsion.

Speed tuning of direction repulsion describes an inverted U-function

Direction repulsion describes the phenomenon in which observers typically overestimate the direction difference between two superimposed motions moving in different directions (Marshak & Sekuler, Science 205(1979) 1399). Previous research has found that, when a relatively narrow range of distractor speeds is considered, direction repulsion of a target motion increases monotonically with increasing speed of the distractor motion. We sought to obtain a more complete measurement of this speed-tuning function by considering a wider range of distractor speeds than has previously been used. Our results show that, contrary to previous reports, direction repulsion as a function of distractor speed describes an inverted U-function. For a target of 2.5deg/s, we demonstrate that the attenuation of repulsion magnitude with high-speed disractors can be largely explained in terms of the reduced apparent contrast of the distractor. However, when we reduce target motion speed, this no longer holds. When considered from the perspective of Edwards et al.s (Edwards, Badcock, & Smith, Vision Research 38 (1998) 1573) two global-motion channels, our results suggest that direction repulsion is speed dependent when the distractor and target motions are processed by different globalmotion channels, but is not speed dependent when both motions are processed by the same, high-speed channel. The implications of these results for models of direction repulsion are discussed.

The direction aftereffect is driven by adaptation of local motion detectors

The processing of motion information by the visual system can be decomposed into two general stages; point-by-point local motion extraction, followed by global motion extraction through the pooling of the local motion signals. The direction aftereVect (DAE) is a well known phenomenon in which prior adaptation to a unidirectional moving pattern results in an exaggerated perceived direction diVerence between the adapted direction and a subsequently viewed stimulus moving in a diVerent direction. The experiments in this paper sought to identify where the adaptation underlying the DAE occurs within the motion processing hierarchy. We found that the DAE exhibits interocular transfer, thus demonstrating that the underlying adapted neural mechanisms are binocularly driven and must, therefore, reside in the visual cortex. The remaining experiments measured the speed tuning of the DAE, and used the derived function to test a number of local and global models of the phenomenon. Our data provide compelling evidence that the DAE is driven by the adaptation of motion-sensitive neurons at the local-processing stage of motion encoding. This is in contrast to earlier research showing that direction repulsion, which can be viewed as a simultaneous presentation counterpart to the DAE, is a global motion process. This leads us to conclude that the DAE and direction repulsion reflect interactions between motion-sensitive neural mechanisms at different levels of the motion-processing hierarchy.

Transfer ionization process p+He -> H-0+He2++e(-) with the ejected electron detected in the plane perpendicular to the incident beam direction

A joint experimental and theoretical study of the transfer ionization process p+He→ H-0+He2++e(-) is presented for 630-keV proton impact energy, where the electron is detected in a plane perpendicular to the proton beam direction. With this choice of kinematics we find the triple-differential cross section to be particularly sensitive to angular correlation in the helium target. There is a good agreement between the experimental data and theoretical calculations.