Hyperbolic Fibrations and PDE

2010 Mathematics Subject Classification: 35L10, 35L90.

Perceptually-based Comparison of Image Similarity Metrics

The image comparison operation ??sessing how well one image matches another ??rms a critical component of many image analysis systems and models of human visual processing. Two norms used commonly for this purpose are L1 and L2, which are specific instances of the Minkowski metric. However, there is often not a principled reason for selecting one norm over the other. One way to address this problem is by examining whether one metric better captures the perceptual notion of image similarity than the other. With this goal, we examined perceptual preferences for images retrieved on the basis of the L1 versus the L2 norm. These images were either small fragments without recognizable content, or larger patterns with recognizable content created via vector quantization. In both conditions the subjects showed a consistent preference for images matched using the L1 metric. These results suggest that, in the domain of natural images of the kind we have used, the L1 metric may better capture human notions of image similarity.

Yang-Baxter deformations of Minkowski spacetime

We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincaré group/Lorentz group. Instead we consider a slice of AdS5 by embedding the 4D Poincaré group into the 4D conformal group SO(2, 4) . With this procedure we obtain metrics and B-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS4 and AdS4. Finally we consider a deformation with a classical r-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and B-field which we conjecture to correspond to a new integrable system.

Perceptual quality metrics applied to still image compression

We present a review of perceptual image quality metrics and their application to still image compression. The review describes how image quality metrics can be used to guide an image compression scheme and outlines the advantages, disadvantages and limitations of a number of quality metrics. We examine a broad range of metrics ranging from simple mathematical measures to those which incorporate full perceptual models. We highlight some variation in the models for luminance adaptation and the contrast sensitivity function and discuss what appears to be a lack of a general consensus regarding the models which best describe contrast masking and error summation. We identify how the various perceptual components have been incorporated in quality metrics, and identify a number of psychophysical testing techniques that can be used to validate the metrics. We conclude by illustrating some of the issues discussed throughout the paper with a simple demonstration. (C) 1998 Elsevier Science B.V. All rights reserved.

Spatial and temporal variation in distribution of mangroves in Moreton Bay, subtropical Australia: a comparison of pattern metrics and change detection analyses based on aerial photographs

An assessment of the changes in the distribution and extent of mangroves within Moreton Bay, southeast Queensland, Australia, was carried out. Two assessment methods were evaluated: spatial and temporal pattern metrics analysis, and change detection analysis. Currently, about 15,000 ha of mangroves are present in Moreton Bay. These mangroves are important ecosystems, but are subject to disturbance from a number of sources. Over the past 25 years, there has been a loss of more than 3800 ha, as a result of natural losses and mangrove clearing (e.g. for urban and industrial development, agriculture and aquaculture). However, areas of new mangroves have become established over the same time period, offsetting these losses to create a net loss of about 200 ha. These new mangroves have mainly appeared in the southern bay region and the bay islands, particularly on the landward edge of existing mangroves. In addition, spatial patterns and species composition of mangrove patches have changed. The pattern metrics analysis provided an overview of mangrove distribution and change in the form of single metric values, while the change detection analysis gave a more detailed and spatially explicit description of change. An analysis of the effects of spatial scales on the pattern metrics indicated that they were relatively insensitive to scale at spatial resolutions less than 50 m, but that most metrics became sensitive at coarser resolutions, a finding which has implications for mapping of mangroves based on remotely sensed data. (C) 2003 Elsevier Science B.V. All rights reserved.

Choice of macroinvertebrate metrics to evaluate stream conditions in Atlantic Forest, Brazil

The development of biomonitoring programs based on the macroinvertebrate community requires the understanding of species distribution patterns, as well as of the responses of the community to anthropogenic stressors. In this study, 49 metrics were tested as potential means of assessing the condition of 29 first- and second-order streams located in areas of differing types of land use in So Paulo State, Brazil. Of the sampled streams, 15 were in well-preserved regions in the Atlantic Forest, 5 were among sugarcane cultivations, 5 were in areas of pasture, and 4 were among eucalyptus plantations. The metrics were assessed against the following criteria: (1) predictable response to the impact of human activity; (2) highest taxonomic resolution, and (3) operational and theoretical simplicity. We found that 18 metrics were correlated with the environmental and spatial predictors used, and seven of these satisfied the selection criteria and are thus candidates for inclusion in a multimetric system to assess low-order streams in So Paulo State. These metrics are family richness; Ephemeroptera, Plecoptera and Trichoptera (EPT) richness; proportion of Megaloptera and Hirudinea; proportion of EPT; Shannon diversity index for genus; and adapted Biological Monitoring Work Party biotic index.

Testing landscape metrics as indicators of habitat loss and fragmentation in continuous eucalypt forests (Queensland, Australia)

Landscape metrics are widely applied in landscape ecology to quantify landscape structure. However, many are poorly tested and require rigorous validation if they are to serve as reliable indicators of habitat loss and fragmentation, such as Montreal Process Indicator 1.1e. We apply a landscape ecology theory, supported by exploratory and confirmatory statistical techniques, to empirically test landscape metrics for reporting Montreal Process Indicator 1.1e in continuous dry eucalypt forests of sub-tropical Queensland, Australia. Target biota examined included: the Yellow-bellied Glider (Petaurus australis); the diversity of nectar and sap feeding glider species including P. australis, the Sugar Glider P. breviceps, the Squirrel Glider P. norfolcensis, and the Feathertail Glider Acrobates pygmaeus; six diurnal forest birds species; total diurnal bird species diversity; and the density of nectar-feeding diurnal bird species. Two scales of influence were considered: the stand-scale (2 ha), and a series of radial landscape extents (500 m - 2 km; 78 - 1250 ha) surrounding each fauna transect. For all biota, stand-scale structural and compositional attributes were found to be more influential than landscape metrics. For the Yellow-bellied Glider, the proportion of trace habitats with a residual element of old spotted-gum/ironbark eucalypt trees was a significant landscape metric at the 2 km landscape extent. This is a measure of habitat loss rather than habitat fragmentation. For the diversity of nectar and sap feeding glider species, the proportion of trace habitats with a high coefficient of variation in patch size at the 750 m extent was a significant landscape metric. None of the landscape metrics tested was important for diurnal forest birds. We conclude that no single landscape metric adequately captures the response of the region's forest biota per se. This poses a major challenge to regional reporting of Montreal Process Indicator 1.1e, fragmentation of forest types.

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

Science metrics on fractional calculus development since 1966

During the last fifty years the area of Fractional Calculus verified a considerable progress. This paper analyzes and measures the evolution that occurred since 1966.

Assessment of the quality of brain regions and neuroimaging metrics as biomarkers of Alzheimer’s disease

Alzheimer Disease (AD) is characterized by progressive cognitive decline and dementia. Earlier diagnosis and classification of different stages of the disease are currently the main challenges and can be assessed by neuroimaging. With this work we aim to evaluate the quality of brain regions and neuroimaging metrics as biomarkers of AD. Multimodal Imaging Brain Connectivity Analysis (MIBCA) toolbox functionalities were used to study AD by T1weighted, Diffusion Tensor Imaging and 18FAV45 PET, with data obtained from the AD Neuroimaging Initiative database, specifically 12 healthy controls (CTRL) and 33 patients with early mild cognitive impairment (EMCI), late MCI (LMCI) and AD (11 patients/group). The metrics evaluated were gray-matter volume (GMV), cortical thickness (CThk), mean diffusivity (MD), fractional anisotropy (FA), fiber count (FiberConn), node degree (Deg), cluster coefficient (ClusC) and relative standard-uptake-values (rSUV). Receiver Operating Characteristic (ROC) curves were used to evaluate and compare the diagnostic accuracy of the most significant metrics and brain regions and expressed as area under the curve (AUC). Comparisons were performed between groups. The RH-Accumbens/Deg demonstrated the highest AUC when differentiating between CTRLEMCI (82%), whether rSUV presented it in several brain regions when distinguishing CTRL-LMCI (99%). Regarding CTRL-AD, highest AUC were found with LH-STG/FiberConn and RH-FP/FiberConn (~100%). A larger number of neuroimaging metrics related with cortical atrophy with AUC>70% was found in CTRL-AD in both hemispheres, while in earlier stages, cortical metrics showed in more confined areas of the temporal region and mainly in LH, indicating an increasing of the spread of cortical atrophy that is characteristic of disease progression. In CTRL-EMCI several brain regions and neuroimaging metrics presented AUC>70% with a worst result in later stages suggesting these indicators as biomarkers for an earlier stage of MCI, although further research is necessary.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

Spatial metrics and Landsat data for urban landuse change detection: case of Addis Ababa, Ethiopia.

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies.

A go-to-market strategy for vertebral metrics

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Dynamic stability metrics for the container loading problem

The Container Loading Problem (CLP) literature has traditionally evaluated the dynamic stability of cargo by applying two metrics to box arrangements: the mean number of boxes supporting the items excluding those placed directly on the floor (M1) and the percentage of boxes with insufficient lateral support (M2). However, these metrics, that aim to be proxies for cargo stability during transportation, fail to translate real-world cargo conditions of dynamic stability. In this paper two new performance indicators are proposed to evaluate the dynamic stability of cargo arrangements: the number of fallen boxes (NFB) and the number of boxes within the Damage Boundary Curve fragility test (NB_DBC). Using 1500 solutions for well-known problem instances found in the literature, these new performance indicators are evaluated using a physics simulation tool (StableCargo), replacing the real-world transportation by a truck with a simulation of the dynamic behaviour of container loading arrangements. Two new dynamic stability metrics that can be integrated within any container loading algorithm are also proposed. The metrics are analytical models of the proposed stability performance indicators, computed by multiple linear regression. Pearson’s r correlation coefficient was used as an evaluation parameter for the performance of the models. The extensive computational results show that the proposed metrics are better proxies for dynamic stability in the CLP than the previous widely used metrics.

Smoothing singularities of Riemannian metrics while preserving lower curvature bounds

Magdeburg, Univ., Fak. für Mathematik, Diss., 2014