Lower bounds for dilation, wirelength, and edge congestion of embedding graphs into hypercubes

Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. One of the most efficient interconnection networks is the hypercube due to its structural regularity, potential for parallel computation of various algorithms, and the high degree of fault tolerance. Thus it becomes the first choice of topological structure of parallel processing and computing systems. In this paper, lower bounds for the dilation, wirelength, and edge congestion of an embedding of a graph into a hypercube are proved. Two of these bounds are expressed in terms of the bisection width. Applying these results, the dilation and wirelength of embedding of certain complete multipartite graphs, folded hypercubes, wheels, and specific Cartesian products are computed

Spatial gradient consistency for unsupervised learning of hyperspectral demosaicking: Application to surgical imaging

Hyperspectral imaging has the potential to improve intraoperative decision making if tissue characterisation is performed in real-time and with high-resolution. Hyperspectral snapshot mosaic sensors offer a promising approach due to their fast acquisition speed and compact size. However, a demosaicking algorithm is required to fully recover the spatial and spectral information of the snapshot images. Most state-of-the-art demosaicking algorithms require ground-truth training data with paired snapshot and high-resolution hyperspectral images, but such imagery pairs with the exact same scene are physically impossible to acquire in intraoperative settings. In this work, we present a fully unsupervised hyperspectral image demosaicking algorithm which only requires exemplar snapshot images for training purposes. We regard hyperspectral demosaicking as an ill-posed linear inverse problem which we solve using a deep neural network. We take advantage of the spectral correlation occurring in natural scenes to design a novel inter spectral band regularisation term based on spatial gradient consistency. By combining our proposed term with standard regularisation techniques and exploiting a standard data fidelity term, we obtain an unsupervised loss function for training deep neural networks, which allows us to achieve real-time hyperspectral image demosaicking. Quantitative results on hyperspetral image datasets show that our unsupervised demosaicking approach can achieve similar performance to its supervised counter-part, and significantly outperform linear demosaicking. A qualitative user study on real snapshot hyperspectral surgical images confirms the results from the quantitative analysis. Our results suggest that the proposed unsupervised algorithm can achieve promising hyperspectral demosaicking in real-time thus advancing the suitability of the modality for intraoperative use

Sensitivity of the Eocene climate to CO₂ and orbital variability

The early Eocene, from about 56 Ma, with high atmospheric CO2 levels, offers an analogue for the response of the Earth’s climate system to anthropogenic fossil fuel burning. In this study, we present an ensemble of 50 Earth system model runs with an early Eocene palaeogeography and variation in the forcing values of atmospheric CO2 and the Earth’s orbital parameters. Relationships between simple summary metrics of model outputs and the forcing parameters are identified by linear modelling, providing estimates of the relative magnitudes of the effects of atmospheric CO2 and each of the orbital parameters on important climatic features, including tropical–polar temperature difference, ocean–land temperature contrast, Asian, African and South (S.) American monsoon rains, and climate sensitivity. Our results indicate that although CO2 exerts a dominant control on most of the climatic features examined in this study, the orbital parameters also strongly influence important components of the ocean–atmosphere system in a greenhouse Earth. In our ensemble, atmospheric CO2 spans the range 280–3000 ppm, and this variation accounts for over 90 % of the effects on mean air temperature, southern winter high-latitude ocean– land temperature contrast and northern winter tropical–polar temperature difference. However, the variation of precession accounts for over 80 % of the influence of the forcing parameters on the Asian and African monsoon rainfall, and obliquity variation accounts for over 65 % of the effects on winter ocean–land temperature contrast in high northern latitudes and northern summer tropical–polar temperature difference. Our results indicate a bimodal climate sensitivity, with values of 4.36 and 2.54 ◦C, dependent on low or high states of atmospheric CO2 concentration, respectively, with a threshold at approximately 1000 ppm in this model, and due to a saturated vegetation–albedo feedback. Our method gives a quantitative ranking of the influence of each of the forcing parameters on key climatic model outputs, with additional spatial information from singular value decomposition providing insights into likely physical mechanisms. The results demonstrate the importance of orbital variation as an agent of change in climates of the past, and we demonstrate that emulators derived from our modelling output can be used as rapid and efficient surrogates of the full complexity model to provide estimates of climate conditions from any set of forcing parameters

Diamond-based models for scientific visualization

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes

HCmodelSets: An R package for specifying sets of well-fitting models in high dimensions

In the context of regression with a large number of explanatory variables, Cox and Battey(2017) emphasize that if there are alternative reasonable explanations of the data that are statisticallyindistinguishable, one should aim to specify as many of these explanations as is feasible. The standardpractice, by contrast, is to report a single model effective for prediction. The present paper illustratesthe R implementation of the new ideas in the packageHCmodelSets, using simple reproducibleexamples and real data. Results of some simulation experiments are also reported

Snapshot hyperspectral imaging : near-infrared image replicating imaging spectrometer and achromatisation of Wollaston prisms

Conventional hyperspectral imaging (HSI) techniques are time-sequential and rely on temporal scanning to capture hyperspectral images. This temporal constraint can limit the application of HSI to static scenes and platforms, where transient and dynamic events are not expected during data capture. The Near-Infrared Image Replicating Imaging Spectrometer (N-IRIS) sensor described in this thesis enables snapshot HSI in the short-wave infrared (SWIR), without the requirement for scanning and operates without rejection in polarised light. It operates in eight wavebands from 1.1μm to 1.7μm with a 2.0° diagonal field-of-view. N-IRIS produces spectral images directly, without the need for prior topographic or image reconstruction. Additional benefits include compactness, robustness, static operation, lower processing overheads, higher signal-to-noise ratio and higher optical throughput with respect to other HSI snapshot sensors generally. This thesis covers the IRIS design process from theoretical concepts to quantitative modelling, culminating in the N-IRIS prototype designed for SWIR imaging. This effort formed the logical step in advancing from peer efforts, which focussed upon the visible wavelengths. After acceptance testing to verify optical parameters, empirical laboratory trials were carried out. This testing focussed on discriminating between common materials within a controlled environment as proof-of-concept. Significance tests were used to provide an initial test of N-IRIS capability in distinguishing materials with respect to using a conventional SWIR broadband sensor. Motivated by the design and assembly of a cost-effective visible IRIS, an innovative solution was developed for the problem of chromatic variation in the splitting angle (CVSA) of Wollaston prisms. CVSA introduces spectral blurring of images. Analytical theory is presented and is illustrated with an example N-IRIS application where a sixfold reduction in dispersion is achieved for wavelengths in the region 400nm to 1.7μm, although the principle is applicable from ultraviolet to thermal-IR wavelengths. Experimental proof of concept is demonstrated and the spectral smearing of an achromatised N-IRIS is shown to be reduced by an order of magnitude. These achromatised prisms can provide benefits to areas beyond hyperspectral imaging, such as microscopy, laser pulse control and spectrometry