Low rank representation on Riemannian manifold of symmetric positive definite matrices

Sparse coding aims to find a more compact representation based on a set of dictionary atoms. A well-known technique looking at 2D sparsity is the low rank representation (LRR). However, in many computer vision applications, data often originate from a manifold, which is equipped with some Riemannian geometry. In this case, the existing LRR becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to applications. In this paper, we generalize the LRR over the Euclidean space to the LRR model over a specific Rimannian manifold—the manifold of symmetric positive matrices (SPD). Experiments on several computer vision datasets showcase its noise robustness and superior performance on classification and segmentation compared with state-of-the-art approaches.

Boundary integral methods for singularly perturbed boundary value problems

In this paper we consider boundary integral methods applied to boundary value problems for the positive definite Helmholtz-type problem -DeltaU + alpha U-2 = 0 in a bounded or unbounded domain, with the parameter alpha real and possibly large. Applications arise in the implementation of space-time boundary integral methods for the heat equation, where alpha is proportional to 1/root deltat, and deltat is the time step. The corresponding layer potentials arising from this problem depend nonlinearly on the parameter alpha and have kernels which become highly peaked as alpha --> infinity, causing standard discretization schemes to fail. We propose a new collocation method with a robust convergence rate as alpha --> infinity. Numerical experiments on a model problem verify the theoretical results.

Sparse kernel density estimation technique based on zero-norm constraint

A sparse kernel density estimator is derived based on the zero-norm constraint, in which the zero-norm of the kernel weights is incorporated to enhance model sparsity. The classical Parzen window estimate is adopted as the desired response for density estimation, and an approximate function of the zero-norm is used for achieving mathemtical tractability and algorithmic efficiency. Under the mild condition of the positive definite design matrix, the kernel weights of the proposed density estimator based on the zero-norm approximation can be obtained using the multiplicative nonnegative quadratic programming algorithm. Using the -optimality based selection algorithm as the preprocessing to select a small significant subset design matrix, the proposed zero-norm based approach offers an effective means for constructing very sparse kernel density estimates with excellent generalisation performance.

Simplified recursive identifier for ARMA processes

Symmetrical behaviour of the covariance matrix and the positive-definite criterion are used to simplify identification of single-input/single-output systems using recursive least squares. Simulation results are obtained and these are compared with ordinary recursive least squares. The adaptive nature of the identifier is verified by varying the system parameters on convergence.

Nonlinear symmetric stability of planetary atmospheres

The energy–Casimir method is applied to the problem of symmetric stability in the context of a compressible, hydrostatic planetary atmosphere with a general equation of state. Formal stability criteria for symmetric disturbances to a zonally symmetric baroclinic flow are obtained. In the special case of a perfect gas the results of Stevens (1983) are recovered. Finite-amplitude stability conditions are also obtained that provide an upper bound on a certain positive-definite measure of disturbance amplitude.

A unified theory of available potential energy

Traditional derivations of available potential energy, in a variety of contexts, involve combining some form of mass conservation together with energy conservation. This raises the questions of why such constructions are required in the first place, and whether there is some general method of deriving the available potential energy for an arbitrary fluid system. By appealing to the underlying Hamiltonian structure of geophysical fluid dynamics, it becomes clear why energy conservation is not enough, and why other conservation laws such as mass conservation need to be incorporated in order to construct an invariant, known as the pseudoenergy, that is a positive‐definite functional of disturbance quantities. The available potential energy is just the non‐kinetic part of the pseudoenergy, the construction of which follows a well defined algorithm. Two notable features of the available potential energy defined thereby are first, that it is a locally defined quantity, and second, that it is inherently definable at finite amplitude (though one may of course always take the small‐amplitude limit if this is appropriate). The general theory is made concrete by systematic derivations of available potential energy in a number of different contexts. All the well known expressions are recovered, and some new expressions are obtained. The possibility of generalizing the concept of available potential energy to dynamically stable basic flows (as opposed to statically stable basic states) is also discussed.

Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = cgA where cg is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum. The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ0(z) so long as the variation in θ0(z) over the depth of the fluid is small compared with θ0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., dθ0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow. The counterparts to results for the two-dimensional Boussinesq equations are also noted.

Extension of spherical nonparametric estimators to nonisotropic kernels: An oceanographic application

In a recently published paper. spherical nonparametric estimators were applied to feature-track ensembles to determine a range of statistics for the atmospheric features considered. This approach obviates the types of bias normally introduced with traditional estimators. New spherical isotropic kernels with local support were introduced. Ln this paper the extension to spherical nonisotropic kernels with local support is introduced, together with a means of obtaining the shape and smoothing parameters in an objective way. The usefulness of spherical nonparametric estimators based on nonisotropic kernels is demonstrated with an application to an oceanographic feature-track ensemble.

The Upper Valanginian (Early Cretaceous) positive carbon-isotope event recorded in terrestrial plants

Our understanding of the ancient ocean-atmosphere system has focused on oceanic proxies. However, the study of terrestrial proxies is equally necessary to constrain our understanding of ancient climates and linkages between the terrestrial and oceanic carbon reservoirs. We have analyzed carbon-isotope ratios from fossil plant material through the Valanginian and Lower Hauterivian from a shallow-marine, ammonite-constrained succession in the Crimean Peninsula of the southern Ukraine in order to determine if the Upper Valanginian positive carbon-isotope excursion is expressed in the atmosphere. delta(13)C(plant) values fluctuate around -23% to -22% for the Valanginian-Hauterivian, except during the Upper Valanginian where delta(13)C(plant) values record a positive excursion to similar to-18%. Based upon ammonite biostratigraphy from Crimea, and in conjunction with a composite Tethyan marine delta(13)C(carb) curve, several conclusions can be drawn: (1) the delta(13)C(plant) record indicates that the atmospheric carbon reservoir was affected; (2) the defined ammonite correlations between Europe and Crimea are synchronous; and (3) a change in photosynthetic carbon-isotope fractionation, caused by a decrease in atmospheric PCO2, occurred during the Upper Valanginian Positive delta(13)C excursion. Our new data, combined with other paleoenvironmental and paleoclimatic information, indicate that the Upper Valanginian was a cool period (icehouse) and highlights that the Cretaceous period was interrupted by periods of cooling and was not an equable climate as previously thought. (C) 2005 Elsevier B.V. All rights reserved.

Spin spaces and positive decomposition of linear maps on ordered Banach spaces

Spin factors and generalizations are used to revisit positive generation of B(E, F), where E and F are ordered Banach spaces. Interior points of B(E, F)+ are discussed and in many cases it is seen that positive generation of B(E, F) is controlled by spin structure in F when F is a JBW-algebra.

Reduced capacity to sustain positive emotion in major depression reflects diminished maintenance of fronto-striatal brain activation

Anhedonia, the loss of pleasure or interest in previously rewarding stimuli, is a core feature of major depression. While theorists have argued that anhedonia reflects a reduced capacity to experience pleasure, evidence is mixed as to whether anhedonia is caused by a reduction in hedonic capacity. An alternative explanation is that anhedonia is due to the inability to sustain positive affect across time. Using positive images, we used an emotion regulation task to test whether individuals with depression are unable to sustain activation in neural circuits underlying positive affect and reward. While up-regulating positive affect, depressed individuals failed to sustain nucleus accumbens activity over time compared with controls. This decreased capacity was related to individual differences in self-reported positive affect. Connectivity analyses further implicated the fronto-striatal network in anhedonia. These findings support the hypothesis that anhedonia in depressed patients reflects the inability to sustain engagement of structures involved in positive affect and reward.

Aging is associated with positive responding to neutral information but reduced recovery from negative information

Studies on aging and emotion suggest an increase in reported positive affect, a processing bias of positive over negative information, as well as increasingly adaptive regulation in response to negative events with advancing age. These findings imply that older individuals evaluate information differently, resulting in lowered reactivity to, and/or faster recovery from, negative information, while maintaining more positive responding to positive information. We examined this hypothesis in an ongoing study on Midlife in the US (MIDUS II) where emotional reactivity and recovery were assessed in a large number of respondents (N = 159) from a wide age range (36–84 years). We recorded eye-blink startle magnitudes and corrugator activity during and after the presentation of positive, neutral and negative pictures. The most robust age effect was found in response to neutral stimuli, where increasing age is associated with a decreased corrugator and eyeblink startle response to neutral stimuli. These data suggest that an age-related positivity effect does not essentially alter the response to emotion-laden information, but is reflected in a more positive interpretation of affectively ambiguous information. Furthermore, older women showed reduced corrugator recovery from negative pictures relative to the younger women and men, suggesting that an age-related prioritization of well-being is not necessarily reflected in adaptive regulation of negative affect.

Student-teachers' perspectives on positive and negative social processes in schools

In recent years, the Standards for Qualified Teacher Status in England have placed new emphasis on student-teachers' ability to become integrated into the 'corporate life of the school' and to work with other professionals. Little research, however, has been carried out into how student-teachers perceive the social processes and interactions that are central to such integration during their initial teacher education school placements. This study aims to shed light on these perceptions. The data, gathered from 23 student-teachers through interviews and reflective writing, illustrate the extent to which the participants perceived such social processes as supporting or obstructing their development as teachers. Signals of inclusion, the degree of match or mismatch in students' and school colleagues' role expectations, and the social awareness of both school and student-teacher emerged as crucial factors in this respect. The student-teachers' accounts show their social interactions with school staff to be meaningful in developing their 'teacher self' and to be profoundly emotionally charged. The implications for mentor and student-teacher role preparation are discussed in this article.