On the elliptic generating region of a tsunami

The surface elevation is calculated for the three-dimensional motion of waves in a fluid of constant depth subject to a given bottom velocity. An example, modeling tsunami generation, with antisymmetric bottom velocity, is considered in detail. The amplitude of the wave front is found to decay much more rapidly than the main wave. The distribution of amplitude with wave number and with angular position is computed for some cases

Elementary bidiagonal factorizations

AbstractAn elementary bidiagonal (EB) matrix has every main diagonal entry equal to 1, and exactly one off-diagonal nonzero entry that is either on the sub- or super-diagonal. If matrix A can be written as a product of EB matrices and at most one diagonal matrix, then this product is an EB factorization of A. Every matrix is shown to have an EB factorization, and this is related to LU factorization and Neville elimination. The minimum number of EB factors needed for various classes of n-by-n matrices is considered. Some exact values for low dimensions and some bounds for general n are proved; improved bounds are conjectured. Generic factorizations that correspond to different orderings of the EB factors are briefly considered

Eigenvalue location for nonnegative and Z-matrices

AbstractLet Lk0 denote the class of n × n Z-matrices A = tl − B with B ⩾ 0 and ϱk(B) ⩽ t < ϱk + 1(B), where ϱk(B) denotes the maximum spectral radius of k × k principal submatrices of B. Bounds are determined on the number of eigenvalues with positive real parts for A ϵ Lk0, where k satisfies, ⌊n2⌋ ⩽ k ⩽ n − 1. For these classes, when k = n − 1 and n − 2, wedges are identified that contain only the unqiue negative eigenvalue of A. These results lead to new eigenvalue location regions for nonnegative matrices

Automated analysis of retinal imaging using machine learning techniques for computer vision

There are almost two million people in the United Kingdom living with sight loss, including around 360,000 people who are registered as blind or partially sighted. Sight threatening diseases, such as diabetic retinopathy and age related macular degeneration have contributed to the 40% increase in outpatient attendances in the last decade but are amenable to early detection and monitoring. With early and appropriate intervention, blindness may be prevented in many cases. Ophthalmic imaging provides a way to diagnose and objectively assess the progression of a number of pathologies including neovascular (“wet”) age-related macular degeneration (wet AMD) and diabetic retinopathy. Two methods of imaging are commonly used: digital photographs of the fundus (the ‘back’ of the eye) and Optical Coherence Tomography (OCT, a modality that uses light waves in a similar way to how ultrasound uses sound waves). Changes in population demographics and expectations and the changing pattern of chronic diseases creates a rising demand for such imaging. Meanwhile, interrogation of such images is time consuming, costly, and prone to human error. The application of novel analysis methods may provide a solution to these challenges. This research will focus on applying novel machine learning algorithms to automatic analysis of both digital fundus photographs and OCT in Moorfields Eye Hospital NHS Foundation Trust patients. Through analysis of the images used in ophthalmology, along with relevant clinical and demographic information, Google DeepMind Health will investigate the feasibility of automated grading of digital fundus photographs and OCT and provide novel quantitative measures for specific disease features and for monitoring the therapeutic success

From regional pulse vaccination to global disease eradication: insights from a mathematical model of Poliomyelitis

Mass-vaccination campaigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region. The effective reproduction number, $R_e$, is defined and proved to be a global threshold for persistence of the disease. Analytical and numerical calculations show the importance of synchronising the pulse vaccinations in connected regions and the timing of the pulses with respect to the pathogen circulation seasonality. Our results indicate that it may be crucial for mass-vaccination programs, such as national immunisation days, to be synchronised across different regions. In addition, simulations show that a migration imbalance can increase $R_e$ and alter how pulse vaccination should be optimally distributed among the patches, similar to results found with constant-rate vaccination. Furthermore, contrary to the case of constant-rate vaccination, the fraction of environmental transmission affects the value of $R_e$ when pulse vaccination is present.Comment: Added section 6.1, made other revisions, changed titl

Modelling and analysis of influenza A (H1N1) on networks

Network modelling is a useful tool for studying the transmission of H1N1 in China, capturing the main features of the spread of H1N1. The paper calculates the basic reproduction number and studies the effects of various immunization schemes. The final size relation is derived for the network epidemic model. While a uniform, mass-immunization strategy helps control the prevalence, a targeted immunization strategy focusing on specific groups with given connectivity may better control an epidemic

Water waves generated by a moving bottom

Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results based on the analytical solutions are shown for the free-surface profiles, the horizontal and vertical velocities as well as the bottom pressure.Comment: 41 pages, 13 figures. Accepted for publication in a book: "Tsunami and Nonlinear Waves", Kundu, Anjan (Editor), Springer 2007, Approx. 325 p., 170 illus., Hardcover, ISBN: 978-3-540-71255-8, available: May 200

A model of HIV/AIDS population dynamics including ARV treatment and pre-exposure prophylaxis

Antiretroviral treatment (ART) and oral pre-exposure prophylaxis (PrEP) have recently been used efficiently in management of HIV infection. Pre-exposure prophylaxis consists in the use of an antiretroviral medication to prevent the acquisition of HIV infection by uninfected individuals. We propose a new model for the transmission of HIV/AIDS including ART and PrEP. Our model can be used to test the effects of ART and of the uptake of PrEP in a given population, as we demonstrate through simulations. The model can also be used to estimate future projections of HIV prevalence. We prove global stability of the disease-free equilibrium. We also prove global stability of the endemic equilibrium for the most general case of the model, i.e., which allows for PrEP individuals to default. We include insightful simulations based on recently published South-African data

Fibromuscular dysplasia presenting as a renal infarction: a case report

<p>Abstract</p> <p>Introduction</p> <p>Fibromuscular dysplasia is a non-atherosclerotic, non-inflammatory disease that most commonly affects the renal and internal carotid arteries.</p> <p>Case presentation</p> <p>We present the case of a 44-year-old Caucasian man who was admitted with complaints of loin pain and hypertension. A computed tomography scan of the abdomen revealed a right renal infarction with a nodular aspect of the right renal artery. Subsequent renal angiography revealed a typical 'string of beads' pattern of the right renal artery with thrombus formation. Oral anticoagulation was started and the secondary hypertension was easily controlled with anti-hypertensive drugs. At follow-up, our patient refused percutaneous transluminal renal angioplasty as a definitive treatment.</p> <p>Conclusions</p> <p>Fibromuscular dysplasia is the most common cause of renovascular hypertension in patients under 50 years of age. Presentation with renal infarction is rare.</p> <p>In fibromuscular dysplasia, angioplasty has been proven to have, at least for some indications, an advantage over anti-hypertensive drugs. Therefore, hypertension secondary to fibromuscular dysplasia is the most common cause of curable hypertension.</p