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

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

Corneal Biomechanics in Ectatic Diseases: Refractive Surgery Implications.

BACKGROUND: Ectasia development occurs due to a chronic corneal biomechanical decompensation or weakness, resulting in stromal thinning and corneal protrusion. This leads to corneal steepening, increase in astigmatism, and irregularity. In corneal refractive surgery, the detection of mild forms of ectasia pre-operatively is essential to avoid post-operative progressive ectasia, which also depends on the impact of the procedure on the cornea. METHOD: The advent of 3D tomography is proven as a significant advancement to further characterize corneal shape beyond front surface topography, which is still relevant. While screening tests for ectasia had been limited to corneal shape (geometry) assessment, clinical biomechanical assessment has been possible since the introduction of the Ocular Response Analyzer (Reichert Ophthalmic Instruments, Buffalo, USA) in 2005 and the Corvis ST (Oculus Optikgerate GmbH, Wetzlar, Germany) in 2010. Direct clinical biomechanical evaluation is recognized as paramount, especially in detection of mild ectatic cases and characterization of the susceptibility for ectasia progression for any cornea. CONCLUSIONS: The purpose of this review is to describe the current state of clinical evaluation of corneal biomechanics, focusing on the most recent advances of commercially available instruments and also on future developments, such as Brillouin microscopy.(undefined)info:eu-repo/semantics/publishedVersio

Frailty in End-Stage Liver Disease: Understanding Pathophysiology, Tools for Assessment, and Strategies for Management

Frailty and sarcopenia are frequently observed in patients with end-stage liver disease. Frailty is a complex condition that arises from deteriorations across various physiological systems, including the musculoskeletal, cardiovascular, and immune systems, resulting in a reduced ability of the body to withstand stressors. This condition is associated with declined resilience and increased vulnerability to negative outcomes, including disability, hospitalization, and mortality. In cirrhotic patients, frailty is influenced by multiple factors, such as hyperammonemia, hormonal imbalance, malnutrition, ascites, hepatic encephalopathy, and alcohol intake. Assessing frailty is crucial in predicting morbidity and mortality in cirrhotic patients. It can aid in making critical decisions regarding patients\u27 eligibility for critical care and transplantation. This, in turn, can guide the development of an individualized treatment plan for each patient with cirrhosis, with a focus on prioritizing exercise, proper nutrition, and appropriate treatment of hepatic complications as the primary lines of treatment. In this review, we aim to explore the topic of frailty in liver diseases, with a particular emphasis on pathophysiology, clinical assessment, and discuss strategies for preventing frailty through effective treatment of hepatic complications. Furthermore, we explore novel assessment and management strategies that have emerged in recent years, including the use of wearable technology and telemedicine

The multifunctional solute carrier 3A2 (SLC3A2) confers a poor prognosis in the highly proliferative breast cancer subtypes

Background: Breast cancer (BC) is a heterogeneous disease characterised by variant biology, metabolic activity and patient outcome. This study aimed to evaluate the biological and prognostic value of the membrane solute carrier, SLC3A2 in BC with emphasis on the intrinsic molecular subtypes. Methods: SLC3A2 was assessed at the genomic level, using METABRIC data (n=1,980), and proteomic level, using immunohistochemistry on TMA sections constructed from a large well-characterised primary BC cohort (n=2,500). SLC3A2 expression was correlated with clinicopathological parameters, molecular subtypes, and patient outcome. Results: SLC3A2 mRNA and protein expression were strongly correlated with higher tumour grade and poor Nottingham prognostic index (NPI). High expression of SLC3A2 was observed in triple negative (TN), HER2+, and ER+ high proliferation subtypes. SLC3A2 mRNA and protein expression were significantly associated with the expression of c-MYC in all BC subtypes (p<0.001). High expression of SLC3A2 protein was associated with poor patient outcome (p<0.001)), but only in the ER+ high proliferation (p=0.01) and triple negative (p=0.04) subtypes. In multivariate analysis SLC3A2 protein was an independent risk factor for shorter breast cancer specific survival (p<0.001). Conclusions: SLC3A2 appears to play a role in the aggressive BC subtypes driven by MYC and could act as a potential prognostic marker. Functional assessment is necessary to reveal its potential therapeutic value in the different BC subtypes

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

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

MYC functions are specific in biological subtypes of breast cancer and confers resistance to endocrine therapy in luminal tumours.

BACKGROUND: MYC is amplified in approximately 15% of breast cancers (BCs) and is associated with poor outcome. c-MYC protein is multi-faceted and participates in many aspects of cellular function and is linked with therapeutic response in BCs. We hypothesised that the functional role of c-MYC differs between molecular subtypes of BCs. METHODS: We therefore investigated the correlation between c-MYC protein expression and other proteins involved in different cellular functions together with clinicopathological parameters, patients' outcome and treatments in a large early-stage molecularly characterised series of primary invasive BCs (n=1106) using immunohistochemistry. The METABRIC BC cohort (n=1980) was evaluated for MYC mRNA expression and a systems biology approach utilised to identify genes associated with MYC in the different BC molecular subtypes. RESULTS: High MYC and c-MYC expression was significantly associated with poor prognostic factors, including grade and basal-like BCs. In luminal A tumours, c-MYC was associated with ATM (P=0.005), Cyclin B1 (P=0.002), PIK3CA (P=0.009) and Ki67 (P<0.001). In contrast, in basal-like tumours, c-MYC showed positive association with Cyclin E (P=0.003) and p16 (P=0.042) expression only. c-MYC was an independent predictor of a shorter distant metastases-free survival in luminal A LN+ tumours treated with endocrine therapy (ET; P=0.013). In luminal tumours treated with ET, MYC mRNA expression was associated with BC-specific survival (P=0.001). In ER-positive tumours, MYC was associated with expression of translational genes while in ER-negative tumours it was associated with upregulation of glucose metabolism genes. CONCLUSIONS: c-MYC function is associated with specific molecular subtypes of BCs and its overexpression confers resistance to ET. The diverse mechanisms of c-MYC function in the different molecular classes of BCs warrants further investigation particularly as potential therapeutic targets

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