Fast Computation of Smith Forms of Sparse Matrices Over Local Rings

We present algorithms to compute the Smith Normal Form of matrices over two families of local rings. The algorithms use the \emph{black-box} model which is suitable for sparse and structured matrices. The algorithms depend on a number of tools, such as matrix rank computation over finite fields, for which the best-known time- and memory-efficient algorithms are probabilistic. For an \nxn matrix $A$ over the ring \Fzfe, where $f^e$ is a power of an irreducible polynomial f \in \Fz of degree $d$, our algorithm requires \bigO(\eta de^2n) operations in \F, where our black-box is assumed to require \bigO(\eta) operations in \F to compute a matrix-vector product by a vector over \Fzfe (and $\eta$ is assumed greater than \Pden). The algorithm only requires additional storage for \bigO(\Pden) elements of \F. In particular, if \eta=\softO(\Pden), then our algorithm requires only \softO(n^2d^2e^3) operations in \F, which is an improvement on known dense methods for small $d$ and $e$. For the ring \ZZ/p^e\ZZ, where $p$ is a prime, we give an algorithm which is time- and memory-efficient when the number of nontrivial invariant factors is small. We describe a method for dimension reduction while preserving the invariant factors. The time complexity is essentially linear in $\mu n r e \log p,$ where $\mu$ is the number of operations in \ZZ/p\ZZ to evaluate the black-box (assumed greater than $n$) and $r$ is the total number of non-zero invariant factors. To avoid the practical cost of conditioning, we give a Monte Carlo certificate, which at low cost, provides either a high probability of success or a proof of failure. The quest for a time- and memory-efficient solution without restrictions on the number of nontrivial invariant factors remains open. We offer a conjecture which may contribute toward that end.Comment: Preliminary version to appear at ISSAC 201

Seasonal variations of hydrographic parameters off the Sudanese coast of the Red Sea, 2009–2015

© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Regional Studies in Marine Science 18 (2018): 1-10, doi:10.1016/j.rsma.2017.12.004.The variations of temperature and salinity in the Sudanese coastal zone of the Red Sea are studied for the first time using measurements acquired from survey cruises during 2009–2013 and from a mooring during 2014–2015. The measurements show that temperature and salinity variability above the permanent pycnocline is dominated by seasonal signals, similar in character to seasonal temperature and salinity oscillations observed further north on the eastern side of the Red Sea. Using estimates of heat flux, circulation and horizontal temperature/salinity gradients derived from a number of sources, we determined that the observed seasonal signals of temperature and salinity are not the product of local heat and mass flux alone, but are also due to alongshore advection of waters with spatially varying temperature and salinity. As the temperature and salinity gradients, characterized by warmer and less saline water to the south, exhibit little seasonal variation, the seasonal salinity and temperature variations are closely linked to an observed seasonal oscillation in the along-shore flow, which also has a mean northward component. We find that the inclusion of the advection terms in the heat and mass balance has two principal effects on the computed temperature and salinity series. One is that the steady influx of warmer and less saline water from the south counteracts the long-term trend of declining temperatures and rising salinities computed with only the local surface flux terms, and produces a long-term steady state in temperature and salinity. The second effect is produced by the seasonal alongshore velocity oscillation and most profoundly affects the computed salinity, which shows no seasonal signal without the inclusion of the advective term. In both the observations and computed results, the seasonal salinity signal lags that of temperature by roughly 3 months.The SPS surveys were funded by the Norwegian Norad’s Program for Master Studies and organized by IMR–RSU in Port Sudan. The central Red Sea mooring data were acquired as part of a WHOI–KAUST collaboration funded by Award Nos. USA00001, USA00002, and KSA00011 to the WHOI by the KAUST in the Kingdom of Saudi Arabia. The work of I. Skjelvan and A.M. Omar was partly supported by the Research Council of Norway through the MIMT Center for Research-based Innovation. This work is part of a Ph.D. project at GFI–UiB funded by the Norwegian Quota program

A full-field 3D digital image correlation and modelling technique to characterise anterior cruciate ligament mechanics ex vivo

It is limiting to use conventional methods when characterising material properties of complex biological tissues with inhomogeneous and anisotropic structure, such as the anterior cruciate ligament (ACL) in the knee joint. This study aims to develop and utilise a three-dimensional digital image correlation method (3D DIC) for the purpose of determining material properties of femur-ACL-tibia complex across the surface without any contact between the tissue and the loading equipment. A full-field (360° view) 3D DIC test setup consisting of six digital single-lens reflex cameras was developed and ACL specimens from skeletally mature dog knee joints were tested. The six cameras were arranged into three pairs and the cameras within each pair were positioned with 25° in between to obtain the desired stereovision output. The test setup was calibrated twice: first to obtain the intrinsic and extrinsic parameters within camera pairs, and second to align the 3D surfaces from each camera pair in order to generate the full view of the ACLs. Using the undeformed 3D surfaces of the ligaments, ACL-specific finite element models were generated. Longitudinal deformation of ligaments under tensile loads obtained from the 3D DIC, and this was analysed to serve as input for the inverse finite element analysis. As a result, hyperelastic coefficients from the first-order Ogden model that characterise ACL behaviour were determined with a marginal error of <1.5%. This test setup and methodology provides a means to accurately determine inhomogeneous and anisotropic material properties of ACL. The methodology described in this study could be adopted to investigate other biological and cultured tissues with complex structure

Viscoelastic characteristics of the canine cranial cruciate ligament complex at slow strain rates

Ligaments including the cruciate ligaments support and transfer loads between bones applied to the knee joint organ. The functions of these ligaments can get compromised due to changes to their viscoelastic material properties. Currently there are discrepancies in the literature on the viscoelastic characteristics of knee ligaments which are thought to be due to tissue variability and different testing protocols. The aim of this study was to characterise the viscoelastic properties of healthy cranial cruciate ligaments (CCLs), from the canine knee (stifle) joint, with a focus on the toe region of the stress-strain properties where any alterations in the extracellular matrix which would affect viscoelastic properties would be seen. Six paired CCLs, from skeletally mature and disease-free Staffordshire bull terrier stifle joints were retrieved as a femur-CCL-tibia complex and mechanically tested under uniaxial cyclic loading up to 10 N at three strain rates, namely 0.1%, 1% and 10%/min, to assess the viscoelastic property of strain rate dependency. The effect of strain history was also investigated by subjecting contralateral CCLs to an ascending (0.1%, 1% and 10%/min) or descending (10%, 1% and 0.1%/min) strain rate protocol. The differences between strain rates were not statistically significant. However, hysteresis and recovery of ligament lengths showed some dependency on strain rate. Only hysteresis was affected by the test protocol and lower strain rates resulted in higher hysteresis and lower recovery. These findings could be explained by the slow process of uncrimping of collagen fibres and the contribution of proteoglycans in the ligament extracellular matrix to intra-fibrillar gliding, which results in more tissue elongations and higher energy dissipation. This study further expands our understanding of canine CCL behaviour, providing data for material models of femur-CCL-tibia complexes, and demonstrating the challenges for engineering complex biomaterials such as knee joint ligaments

Shear Wave Splitting Analyses in Tian Shan: Geodynamic Implications of Complex Seismic Anisotropy

The Tian Shan is a tectonically complex intracontinental orogenic belt situated between the Tarim Basin and the Kazakh Shield. The vast majority of the previous shear wave splitting (SWS) measurements were presented as station averages, which are only valid when the anisotropy structure can be approximated by a single layer of anisotropy with a horizontal axis of symmetry, i.e., a model of simple anisotropy. A variety of anisotropy-forming hypotheses have been proposed based on the station-averaged measurements. In this study, we measure the splitting parameters at 25 stations that recorded high-quality data from a wide back azimuthal range for the purpose of identifying and characterizing complex anisotropy. Among the 25 stations, 15 of them show systematic azimuthal variations in the observed splitting parameters with a 90° periodicity that is consistent with a model of two-layered anisotropy. The fast orientations of the upper layer range from 50° to 90° measured clockwise from the north, which are subparallel to the strike of the orogenic belt, and the splitting times are between 0.9 and 1.9 s. The corresponding values for the lower layer are -45° to -85° and 1.2-2.2 s, respectively. The remaining 10 stations demonstrate azimuthally invariant splitting parameters with strike-parallel fast orientations, and can be represented by a single layer of anisotropy with a horizontal axis of symmetry. We propose that the strike-parallel anisotropy is caused by lithospheric shortening, and anisotropy in the lower layer is associated with WNW-ward flow of asthenospheric material sandwiched between the subducting Tarim lithosphere and the thick Kazakh lithospheric root

Seismic Anisotropy and Mantle Flow beneath the Northern Great Plains of North America

A diverse set of tectonic features and the recent availability of high-quality broadband seismic data from the USArray and other stations on the northern Great Plains of North America provide a distinct opportunity to test different anisotropy-forming mechanisms. A total of 4138 pairs of well-defined splitting parameters observed at 445 stations show systematic spatial variations of anisotropic characteristics. Azimuthally invariant fast orientations subparallel to the absolute plate motion (APM) direction are observed at most of the stations on the Superior Craton and the southern Yavapai province, indicating that a single layer of anisotropy with a horizontal axis of symmetry is sufficient to explain the anisotropic structure. For areas with simple anisotropy, the application of a procedure for estimating the depth of anisotropy using spatial coherency of splitting parameters results in a depth of 200–250 km, suggesting that the observed anisotropy mostly resides in the upper asthenosphere. In the vicinity of the northern boundary of the Yavapai province and the Wyoming Craton, the splitting parameters can be adequately explained by a two-horizontal layer model. The lower layer has an APM-parallel fast orientation, and the upper layer has a fast orientation that is mostly consistent with the regional strike of the boundary. Based on the splitting measurements and previous results from seismic tomography and geodynamic modeling, we propose a model involving deflecting of asthenosphere flow by the bottom of the lithosphere and channeling of flow by a zone of thinned lithosphere approximately along the northern boundary of the Yavapai province

Repeatability of Corneal Elevation Maps in Keratoconus Patients Using the Tomography Matching Method

To assess repeatability of corneal tomography in successive measurements by Pentacam in keratoconus (KC) and normal eyes based on the Iterative Closest Point (ICP) algorithm. The study involved 143 keratoconic and 143 matched normal eyes. ICP algorithm was used to estimate six single and combined misalignment (CM) parameters, the root mean square (RMS) of the difference in elevation data pre (PreICP-RMS) and post (PosICP-RMS) tomography matching. Corneal keratometry, expressed in the form of M, J0 and J45 (power vector analysis parameters), was used to evaluate the effect of misalignment on corneal curvature measurements. The PreICP-RMS and PosICP-RMS were statistically higher (P < 0.01) in KC than normal eyes. CM increased significantly (p = 0.00), more in KC (16.76 ± 20.88 μm) than in normal eyes (5.43 ± 4.08 μm). PreICP-RMS, PosICP-RMS and CM were correlated with keratoconus grade (p < 0.05). Corneal astigmatism J0 was different (p = 0.01) for the second tomography measurements with misalignment consideration (−1.11 ± 2.35 D) or not (−1.18 ± 2.35 D), while M and J45 kept similar. KC corneas consistently show higher misalignments between successive tomography measurements and lower repeatability compared with healthy eyes. The influence of misalignment is evidently clearer in the estimation of astigmatism than spherical curvature. These higher errors appear correlated with KC progression

Impact of COVID-19 pandemic on eye cancer care in United Kingdom

The COVID-19 pandemic has had an unprecedented impact on the National Health Service in United Kingdom. The UK Ocular Oncology Services evaluated the impact on the adult eye cancer care in the UK. All four adult Ocular Oncology centres participated in a multicentre retrospective review comparing uveal melanoma referral patterns and treatments in a 4-month period during the national lockdown and first wave of the COVID-19 pandemic in 2020 with corresponding periods in previous 2 years. During the national lockdown, referral numbers and confirmed uveal melanoma cases reduced considerably, equalling to ~120 fewer diagnosed uveal melanoma cases compared to previous 2 years. Contrary to the recent trend, increased caseloads of enucleation and stereotactic radiosurgery (p > 0.05), in comparison to fewer proton beam therapy (p < 0.05), were performed. In the 4-month period following lockdown, there was a surge in clinical activities with more advanced diseases (p < 0.05) presenting to the services. As the COVID-19 pandemic continues to mount pressure and reveal its hidden impact on the eye cancer care, it is imperative for the Ocular Oncology Services to plan recovery strategies and innovative ways of working

Carbon-supported trimetallic catalysts (PdAuNi/C) for borohydride oxidation reaction

The synthesis of palladium-based trimetallic catalysts via a facile and scalable synthesis procedure was shown to yield highly promising materials for borohydride-based fuel cells, which are attractive for use in compact environments. This, thereby, provides a route to more environmentally friendly energy storage and generation systems. Carbon-supported trimetallic catalysts were herein prepared by three different routes: using a NaBH4-ethylene glycol complex (PdAuNi/CSBEG), a NaBH4-2-propanol complex (PdAuNi/CSBIPA), and a three-step route (PdAuNi/C3-step). Notably, PdAuNi/CSBIPA yielded highly dispersed trimetallic alloy particles, as determined by XRD, EDX, ICP-OES, XPS, and TEM. The activity of the catalysts for borohydride oxidation reaction was assessed by cyclic voltammetry and RDE-based procedures, with results referenced to a Pd/C catalyst. A number of exchanged electrons close to eight was obtained for PdAuNi/C3-step and PdAuNi/CSBIPA (7.4 and 7.1, respectively), while the others, PdAuNi/CSBEG and Pd/CSBIPA, presented lower values, 2.8 and 1.2, respectively. A direct borohydride-peroxide fuel cell employing PdAuNi/CSBIPA catalyst in the anode attained a power density of 47.5 mW cm−2 at room temperature, while the elevation of temperature to 75 °C led to an approximately four-fold increase in power density to 175 mW cm−2. Trimetallic catalysts prepared via this synthesis route have significant potential for future development