Graph rigidity for near-coplanar structure from motion

Recent algorithms for monocular motion capture (MoCap) estimate weak-perspective camera matrices between images using a small subset of approximately-rigid points on the human body (i.e. the torso and hip). A problem with this approach, however, is that these points are often close to coplanar, causing canonical linear factorisation algorithms for rigid structure from motion (SFM) to become extremely sensitive to noise. In this paper, we propose an alternative solution to weak-perspective SFM based on a convex relaxation of graph rigidity. We demonstrate the success of our algorithm on both synthetic and real world data, allowing for much improved solutions to marker less MoCap problems on human bodies. Finally, we propose an approach to solve the two-fold ambiguity over bone direction using a k-nearest neighbour kernel density estimator.

Coordination of UAV path planning in 2D and 3D in environmental/bio sensing applications

This paper is concerned with the optimal path planning and initialization interval of one or two UAVs in presence of a constant wind. The method compares previous literature results on synchronization of UAVs along convex curves, path planning and sampling in 2D and extends it to 3D. This method can be applied to observe gas/particle emissions inside a control volume during sampling loops. The flight pattern is composed of two phases: a start-up interval and a sampling interval which is represented by a semi-circular path. The methods were tested in four complex model test cases in 2D and 3D as well as one simulated real world scenario in 2D and one in 3D.

Which dissimilarity is to be used when extracting typologies in sequence analysis? A comparative study

Originally developed in bioinformatics, sequence analysis is being increasingly used in social sciences for the study of life-course processes. The methodology generally employed consists in computing dissimilarities between the trajectories and, if typologies are sought, in clustering the trajectories according to their similarities or dissemblances. The choice of an appropriate dissimilarity measure is a major issue when dealing with sequence analysis for life sequences. Several dissimilarities are available in the literature, but neither of them succeeds to become indisputable. In this paper, instead of deciding upon one dissimilarity measure, we propose to use an optimal convex combination of different dissimilarities. The optimality is automatically determined by the clustering procedure and is defined with respect to the within-class variance.

Using GPS technology to (re)-examine operational definitions of 'neighbourhood' in place-based health research

BACKGROUND Inconsistencies in research findings on the impact of the built environment on walking across the life course may be methodologically driven. Commonly used methods to define 'neighbourhood', from which built environment variables are measured, may not accurately represent the spatial extent to which the behaviour in question occurs. This paper aims to provide new methods for spatially defining 'neighbourhood' based on how people use their surrounding environment. RESULTS Informed by Global Positioning Systems (GPS) tracking data, several alternative neighbourhood delineation techniques were examined (i.e., variable width, convex hull and standard deviation buffers). Compared with traditionally used buffers (i.e., circular and polygon network), differences were found in built environment characteristics within the newly created 'neighbourhoods'. Model fit statistics indicated that exposure measures derived from alternative buffering techniques provided a better fit when examining the relationship between land-use and walking for transport or leisure. CONCLUSIONS This research identifies how changes in the spatial extent from which built environment measures are derived may influence walking behaviour. Buffer size and orientation influences the relationship between built environment measures and walking for leisure in older adults. The use of GPS data proved suitable for re-examining operational definitions of neighbourhood.

Intervertebral staple grading system with micro-CT

Introduction Intervertebral stapling is a leading method of fusionless scoliosis treatment which attempts to control growth by applying pressure to the convex side of a scoliotic curve in accordance with the Hueter-Volkmann principle. In addition to that, staples have the potential to damage surrounding bone during insertion and subsequent loading. The aim of this study was to assess the extent of bony structural damage including epiphyseal injury as a result of intervertebral stapling using an in vitro bovine model. Materials and Methods Thoracic spines from 6-8 week old calves were dissected and divided into motion segments including levels T4-T11 (n=14). Each segment was potted in polymethylemethacrylate. An Instron Biaxial materials testing machine with a custom made jig was used for testing. The segments were tested in flexion/extension, lateral bending and axial rotation at 37⁰C and 100% humidity, using moment control to a maximum 1.75 Nm with a loading rate of 0.3 Nm per second for 10 cycles. The segments were initially tested uninstrumented with data collected from the tenth load cycle. Next an anterolateral 4-prong Shape Memory Alloy (SMA) staple (Medtronic Sofamor Danek, USA) was inserted into each segment. Biomechanical testing was repeated as before. The staples were cut in half with a diamond saw and carefully removed. Micro-CT scans were performed and sagittal, transverse and coronal reformatted images were produced using ImageJ (NIH, USA).The specimens were divided into 3 grades (0, 1 and 2) according to the number of epiphyses damaged by the staple prongs. Results: There were 9 (65%) segments with grade 1 staple insertions and 5 (35%) segments with grade 2 insertions. There were no grade 0 staples. Grade 2 spines had a higher stiffness level than grade 1 spines, in all axes of movement, by 28% (p=0.004). This was most noted in flexion/extension with an increase of 49% (p=0.042), followed by non-significant change in lateral bending 19% (p=0.129) and axial rotation 8% (p=0.456) stiffness. The cross sectional area of bone destruction from the prongs was only 0.4% larger in the grade 2 group compared to the grade 1 group (p=0.961). Conclusion Intervertebral staples cause epiphyseal damage. There is a difference in stiffness between grade 1 and grade 2 staple insertion segments in flexion/extension only. There is no difference in the cross section of bone destruction as a result of prong insertion and segment motion.

Total factor productivity growth and convergence in the petroleum industry : empirical analysis testing for convexity

While economic theory acknowledges that some features of technology (e.g., indivisibilities, economies of scale and specialization) can fundamentally violate the traditional convexity assumption, almost all empirical studies accept the convexity property on faith. In this contribution, we apply two alternative flexible production technologies to measure total factor productivity growth and test the significance of the convexity axiom using a nonparametric test of closeness between unknown distributions. Based on unique field level data on the petroleum industry, the empirical results reveal significant differences, indicating that this production technology is most likely non-convex. Furthermore, we also show the impact of convexity on answers to traditional convergence questions in the productivity growth literature.

Mapping Hydrophobicity on the Protein Molecular Surface at Atom-Level Resolution

A precise representation of the spatial distribution of hydrophobicity, hydrophilicity and charges on the molecular surface of proteins is critical for the understanding of the interaction with small molecules and larger systems. The representation of hydrophobicity is rarely done at atom-level, as this property is generally assigned to residues. A new methodology for the derivation of atomic hydrophobicity from any amino acid-based hydrophobicity scale was used to derive 8 sets of atomic hydrophobicities, one of which was used to generate the molecular surfaces for 35 proteins with convex structures, 5 of which, i.e., lysozyme, ribonuclease, hemoglobin, albumin and IgG, have been analyzed in more detail. Sets of the molecular surfaces of the model proteins have been constructed using spherical probes with increasingly large radii, from 1.4 to 20 A˚, followed by the quantification of (i) the surface hydrophobicity; (ii) their respective molecular surface areas, i.e., total, hydrophilic and hydrophobic area; and (iii) their relative densities, i.e., divided by the total molecular area; or specific densities, i.e., divided by property-specific area. Compared with the amino acid-based formalism, the atom-level description reveals molecular surfaces which (i) present an approximately two times more hydrophilic areas; with (ii) less extended, but between 2 to 5 times more intense hydrophilic patches; and (iii) 3 to 20 times more extended hydrophobic areas. The hydrophobic areas are also approximately 2 times more hydrophobicity-intense. This, more pronounced "leopard skin"-like, design of the protein molecular surface has been confirmed by comparing the results for a restricted set of homologous proteins, i.e., hemoglobins diverging by only one residue (Trp37). These results suggest that the representation of hydrophobicity on the protein molecular surfaces at atom-level resolution, coupled with the probing of the molecular surface at different geometric resolutions, can capture processes that are otherwise obscured to the amino acid-based formalism.

Adaptive online gradient descent

We study the rates of growth of the regret in online convex optimization. First, we show that a simple extension of the algorithm of Hazan et al eliminates the need for a priori knowledge of the lower bound on the second derivatives of the observed functions. We then provide an algorithm, Adaptive Online Gradient Descent, which interpolates between the results of Zinkevich for linear functions and of Hazan et al for strongly convex functions, achieving intermediate rates between [square root T] and [log T]. Furthermore, we show strong optimality of the algorithm. Finally, we provide an extension of our results to general norms.

Edge-weighting of gene expression graphs

In recent years, considerable research efforts have been directed to micro-array technologies and their role in providing simultaneous information on expression profiles for thousands of genes. These data, when subjected to clustering and classification procedures, can assist in identifying patterns and providing insight on biological processes. To understand the properties of complex gene expression datasets, graphical representations can be used. Intuitively, the data can be represented in terms of a bipartite graph, with weighted edges corresponding to gene-sample node couples in the dataset. Biologically meaningful subgraphs can be sought, but performance can be influenced both by the search algorithm, and, by the graph-weighting scheme and both merit rigorous investigation. In this paper, we focus on edge-weighting schemes for bipartite graphical representation of gene expression. Two novel methods are presented: the first is based on empirical evidence; the second on a geometric distribution. The schemes are compared for several real datasets, assessing efficiency of performance based on four essential properties: robustness to noise and missing values, discrimination, parameter influence on scheme efficiency and reusability. Recommendations and limitations are briefly discussed. Keywords: Edge-weighting; weighted graphs; gene expression; bi-clustering

Estimating link-dependent origin-destination matrices from sample trajectories and traffic counts

In transport networks, Origin-Destination matrices (ODM) are classically estimated from road traffic counts whereas recent technologies grant also access to sample car trajectories. One example is the deployment in cities of Bluetooth scanners that measure the trajectories of Bluetooth equipped cars. Exploiting such sample trajectory information, the classical ODM estimation problem is here extended into a link-dependent ODM (LODM) one. This much larger size estimation problem is formulated here in a variational form as an inverse problem. We develop a convex optimization resolution algorithm that incorporates network constraints. We study the result of the proposed algorithm on simulated network traffic.

Discrete families of Saffman–Taylor fingers with exotic shapes

The mathematical problem of determining the shape of a steadily propagating Saffman–Taylor finger in a rectangular Hele-Shaw cell is known to have a countably infinite number of solutions for each fixed surface tension value. For sufficiently large surface tension values, we find that fingers on higher solution branches are non-convex. The tips of the fingers have increasingly exotic shapes as the branch number increases.

Persistent anterior chamber silicone oil and myopia

A 60-year-old male experienced a marked unilateral myopic shift of 20 D following attempted removal of intravitreal heavy silicone oil (HSO) used in the treatment of inferior proliferative vitreous retinopathy following retinal detachment. Examination revealed HSO adherent to the corneal endothelium forming a convex interface with the aqueous, obscuring the entire pupil, which required surgical intervention to restore visual acuity. This case highlights the potential ocular complications associated with silicone oil migration into the anterior chamber, which include corneal endothelial decompensation and a significant increase in myopia.

Estimating link-dependent origin-destination matrices from sample trajectories and traffic counts

Origin-Destination matrices (ODM) estimation can benefits of the availability of sample trajectories which can be measured thanks to recent technologies. This paper focus on the case of transport networks where traffic counts are measured by magnetic loops and sample trajectories available. An example of such network is the city of Brisbane, where Bluetooth detectors are now operating. This additional data source is used to extend the classical ODM estimation to a link-specific ODM (LODM) one using a convex optimisation resolution that incorporates networks constraints as well. The proposed algorithm is assessed on a simulated network.

Linear programming for large-scale Markov decision problems

We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest goal of competing with a low-dimensional family of policies. We use the dual linear programming formulation of the MDP average cost problem, in which the variable is a stationary distribution over state-action pairs, and we consider a neighborhood of a low-dimensional subset of the set of stationary distributions (defined in terms of state-action features) as the comparison class. We propose a technique based on stochastic convex optimization and give bounds that show that the performance of our algorithm approaches the best achievable by any policy in the comparison class. Most importantly, this result depends on the size of the comparison class, but not on the size of the state space. Preliminary experiments show the effectiveness of the proposed algorithm in a queuing application.

Twist phase in Gaussian-beam optics

The recently discovered twist phase is studied in the context of the full ten-parameter family of partially coherent general anisotropic Gaussian Schell-model beams. It is shown that the nonnegativity requirement on the cross-spectral density of the beam demands that the strength of the twist phase be bounded from above by the inverse of the transverse coherence area of the beam. The twist phase as a two-point function is shown to have the structure of the generalized Huygens kernel or Green's function of a first-order system. The ray-transfer matrix of this system is exhibited. Wolf-type coherent-mode decomposition of the twist phase is carried out. Imposition of the twist phase on an otherwise untwisted beam is shown to result in a linear transformation in the ray phase space of the Wigner distribution. Though this transformation preserves the four-dimensional phase-space volume, it is not symplectic and hence it can, when impressed on a Wigner distribution, push it out of the convex set of all bona fide Wigner distributions unless the original Wigner distribution was sufficiently deep into the interior of the set.