Sparse image reconstruction on the sphere: implications of a new sampling theorem.

We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result, we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations, we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.

Different Effects of BORIS/CTCFL on Stemness Gene Expression, Sphere Formation and Cell Survival in Epithelial Cancer Stem Cells.

Cancer stem cells are cancer cells characterized by stem cell properties and represent a small population of tumor cells that drives tumor development, progression, metastasis and drug resistance. To date, the molecular mechanisms that generate and regulate cancer stem cells are not well defined. BORIS (Brother of Regulator of Imprinted Sites) or CTCFL (CTCF-like) is a DNA-binding protein that is expressed in normal tissues only in germ cells and is re-activated in tumors. Recent evidences have highlighted the correlation of BORIS/CTCFL expression with poor overall survival of different cancer patients. We have previously shown an association of BORIS-expressing cells with stemness gene expression in embryonic cancer cells. Here, we studied the role of BORIS in epithelial tumor cells. Using BORIS-molecular beacon that was already validated, we were able to show the presence of BORIS mRNA in cancer stem cell-enriched populations (side population and spheres) of cervical, colon and breast tumor cells. BORIS silencing studies showed a decrease of sphere formation capacity in breast and colon tumor cells. Importantly, BORIS-silencing led to down-regulation of hTERT, stem cell (NANOG, OCT4, SOX2 and BMI1) and cancer stem cell markers (ABCG2, CD44 and ALDH1) genes. Conversely, BORIS-induction led to up-regulation of the same genes. These phenotypes were observed in cervical, colon and invasive breast tumor cells. However, a completely different behavior was observed in the non-invasive breast tumor cells (MCF7). Indeed, these cells acquired an epithelial mesenchymal transition phenotype after BORIS silencing. Our results demonstrate that BORIS is associated with cancer stem cell-enriched populations of several epithelial tumor cells and the different phenotypes depend on the origin of tumor cells.

Space–Time Block Codes and the Complexity of Sphere Decoding

In wireless communications the transmitted signals may be affected by noise. The receiver must decode the received message, which can be mathematically modelled as a search for the closest lattice point to a given vector. This problem is known to be NP-hard in general, but for communications applications there exist algorithms that, for a certain range of system parameters, offer polynomial expected complexity. The purpose of the thesis is to study the sphere decoding algorithm introduced in the article On Maximum-Likelihood Detection and the Search for the Closest Lattice Point, which was published by M.O. Damen, H. El Gamal and G. Caire in 2003. We concentrate especially on its computational complexity when used in space–time coding. Computer simulations are used to study how different system parameters affect the computational complexity of the algorithm. The aim is to find ways to improve the algorithm from the complexity point of view. The main contribution of the thesis is the construction of two new modifications to the sphere decoding algorithm, which are shown to perform faster than the original algorithm within a range of system parameters.

Recovering Euclidean deformable models from stereo-motion

In this paper we present a novel structure from motion (SfM) approach able to infer 3D deformable models from uncalibrated stereo images. Using a stereo setup dramatically improves the 3D model estimation when the observed 3D shape is mostly deforming without undergoing strong rigid motion. Our approach first calibrates the stereo system automatically and then computes a single metric rigid structure for each frame. Afterwards, these 3D shapes are aligned to a reference view using a RANSAC method in order to compute the mean shape of the object and to select the subset of points on the object which have remained rigid throughout the sequence without deforming. The selected rigid points are then used to compute frame-wise shape registration and to extract the motion parameters robustly from frame to frame. Finally, all this information is used in a global optimization stage with bundle adjustment which allows to refine the frame-wise initial solution and also to recover the non-rigid 3D model. We show results on synthetic and real data that prove the performance of the proposed method even when there is no rigid motion in the original sequence

The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

Baroclinic instability of perturbations described by the linearized primitive quations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamiltonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’—potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there. At short wavelengths the upper CRW is focused in the mid-troposphere just above the steering level of the NM, but at longer wavelengths the upper CRW has a second wave-activity maximum at the tropopause. In the absence of meridional shear, CRW behaviour is very similar to that of Charney modes, while shear results in a meridional slant with height of the air-parcel displacement-structures of CRWs in sympathy with basic-state zonal angular-velocity surfaces. A consequence of this slant is that baroclinically growing eddies (on jets broader than the Rossby radius) must tilt downshear in the horizontal, giving rise to up-gradient momentum fluxes that tend to accelerate the barotropic component of the jet.

Feature tracking on the unit-sphere

Techniques used in a previous study of the objective identification and tracking of meteorological features in model data are extended to the unit sphere. An alternative feature detection scheme is described based on cubic interpolation for the sphere and local maximization. The extension of the tracking technique, used in the previous study, to the unit sphere is described. An example of the application of these techniques to a global relative vorticity field from a model integration are presented and discussed.

Voronoi, Delaunay, and Block-Structured Mesh Refinement for Solution of the Shallow-Water Equations on the Sphere

Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing.

A life less ordinary: The ritualization of the domestic sphere in later prehistoric Europe

This article, which is based on the fourteenth McDonald Lecture, considers two tensions in contemporary archaeology. one is between interpretations of specific structures, monuments and deposits as the result of either 'ritual' 'practical' activities in the past, and the other is between an archaeology that focuses on subsistence and adaptation and one that emphasizes cognition, meaning, and agency. It suggests that these tensions arise from an inadequate conception of ritual itself. Drawing on recent studies of ritualization, it suggests that it might be more helpful to consider how aspects of domestic life took on special qualities in later prehistoric Europe. The discussion is based mainly on Neolithic enclosures and other monuments, Bronze Age and Iron Age settlement sites and the Viereckschanzen of central Europe. it may have implications for field archaeology as well as social archaeology, and also for those who study the formation of the archaeological record.

Effect of Stretching on the Structure of Cylinder- and Sphere-Forming Styrene-Isoprene-Styrene Block Copolymers

Two styrene-isoprene-styrene block copolymers Vector 4111 and 4113, exhibiting cylindrical (18 wt % PS) and spherical (16 wt % PS) morphology, respectively, have been examined under uniaxial elongation up to 200% strain. On the basis of stress-strain data, mechanical properties are compared for isotropic and oriented polystyrene domains. The structure at various stages of deformation has been determined from SAXS patterns in three planes and two principal deformation directions with respect to orientation. Samples showed a very high degree of hexagonal packing, resulting in an X-ray pattern taken parallel to the cylinder alignment approaching single crystal ordering. Cylinders were aligned with the closest packed planes parallel to film surface. Particular attention has been paid to a lattice deformation process occurring during the first stretching and relaxation cycle. For a copolymer with oriented cylindrical morphology the deformation was affine up to 120% strain. The microdomain spacing was calculated parallel and perpendicular to the stretching direction. The cylindrical microstructure orientation, quantified by Hermans' orientation factor reduced during elongation of oriented polymer, while the elongation of isotropic sample caused an increase of orientation. Deformation of all studied morphologies was reversible.

Integrating control systems defined on the frame bundles of the space forms

This paper considers left-invariant control systems defined on the orthonormal frame bundles of simply connected manifolds of constant sectional curvature, namely the space forms Euclidean space E-3, the sphere S-3 and Hyperboloid H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1, 3). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. In the Euclidean case the elements of the Lie algebra se(3) are often referred to as twists. For constant twist motions, the corresponding curves g(t) is an element of SE(3) are known as screw motions, given in closed form by using the well known Rodrigues' formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.