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In this paper we consider methods for evaluating both exp(A) and $exp(\tau A)q_1$ where ${\rm exp}(\cdot)$ is the exponential function, A is a sparse skew-symmetric matrix of large dimension, q1 is a given vector, and $\tau$ is a scaling factor. The proposed method is based on two main steps: A is factorized into its tridiagonal form H by the well-known Lanczos iterative process, and then exp(A) is derived making use of an effective Schur decomposition of H. The procedure takes full advantage of the sparsity of A and of the decay behavior of exp(H). Several applications and numerical tests are also reported. [ABSTRACT FROM AUTHOR]

In various applications, data in multidimensional space are normalized to unit length. This paper considers the problem of best fitting given points on the m-dimensional unit sphere Sm-1 by k-dimensional great circles with k much less than m. The task is cast as an algebraically constrained low-rank matrix approximation problem. Using the fidelity of the low-rank approximation to the original data as the cost function, this paper offers an analytic expression of the projected gradient which, on one hand, furnishes the first order optimality condition and, on the other hand, can be used as a numerical means for solving this problem. [ABSTRACT FROM AUTHOR]

A matrix Z∈R2n×2n is said to be in the standard symplectic form if Z enjoys a block LU-decomposition in the sense of A0-HIZ=IG0AT, where A is nonsingular and both G and H are symmetric and positive definite in Rn×n. Such a structure arises naturally in the discrete algebraic Riccati equations. This note contains two results: First, by means of a parameter representation it is shown that the set of all 2n×2n standard symplectic matrices is closed under multiplication and, thus, forms a semigroup. Secondly, block LU-decompositions of powers of Z can be derived in closed form which, in turn, can be employed recursively to induce an effective structure-preserving algorithm for solving the Riccati equations. The computational cost of doubling and tripling of the powers is investigated. It is concluded that doubling is the better strategy. [Copyright &y& Elsevier]

Recently several numerical methods have been proposed for solving isospectral problems which are matrix differential systems whose solutions preserve the spectrum during the evolution. In this paper we consider matrix differential systems called isodynamical flows in which only a component of the matrix solution preserves the eigenvalues during the evolution and we propose procedures for their numerical solution. Applications of such numerical procedures may be found in systems theory, in particular in balancing realization problems. Several numerical tests will be reported. [ABSTRACT FROM AUTHOR]

This paper concerns the study of explicit 4-stage fourth order Runge–Kutta methods which preserve quadratic conservation laws when their weights are made solution dependent. Application to orthogonal and Hamiltonian linear systems and numerical tests are also reported. [Copyright &y& Elsevier]

Studies the geometric integration on manifold of square oblique rotation matrices. Constraints on multivariate analysis; Presence of numerical procedures preserving the structure of the solution; Accounts on the factor analysis for multidimensional scaling techniques.

In this paper we propose numerical methods forsolving ODEs on the Stiefel manifold based on the use of the embedded geodesics.Numerical tests are also provided in order to show the features of our methods. [ABSTRACT FROM AUTHOR]

Background Previous research has revealed a clear relationship between weight gain of persons and their metabolic diseases developing later. These studies have covered only short periods lasting 4-8 years. Our goal was to collect decades' old and often life-long anthropometric data and correlate the figures with the presence of hypertension and diabetes or both. Methods A retrospective international study was planned and organized to compare self-recorded data of lifelong weight gain among 60-70-year-old patients, analyze their correlation with metabolic diseases they developed, with special attention to women's weight gain around pregnancy, delivery and menopause in primary care settings in Germany, Hungary, Italy, Slovakia and the Ukraine. Results Of the recruited 815 participants, 319 men and 496 women presented all the required data. Diabetics of both genders had the highest baseline weight at 20 years of age. The weight and BMI of the whole study population increased steadily until their seventies, but to a lesser extent after their fifties. Compared to the control group, changes over decades were the greatest among diabetics and also greater among patients with hypertension. Weight increase in the first decades (20-30-year-old men and 30-40-year-old women) was a significant risk factor for the development of diabetes (OR = 1.044; p = 0.002; 95 % CI: 1.01-1.07). Among patients with diabetes and hypertension, both diagnoses were set up earlier than among those with a single morbidity. Among females, weight increase around pregnancy and menopause correlated significantly with higher odds for the diagnoses of diabetes and/or hypertension, irrespective of the number of children. Conclusions During their decade-long relationship with their patients, family physicians are expected to identify the higher weight gain of their patients, especially among younger generation and intervene, if necessary. [ABSTRACT FROM AUTHOR]

Background. Identifying and testing all HIV-exposed infants (HEIs) by 2 months of age with rapid antiretroviral therapy (ART) initiation for those infected is critical to survival. Yet in 2009 only 29% of HEIs in need of ART received treatment in Malawi. Objectives. To understand barriers, facilitators and recommendations for five key steps in the early infant diagnosis and treatment (EIDT) cascade: (1) identification of HEIs; (2) infant testing; (3) sample processing and transport; (4) reporting results to mothers; (5) ART initiation for HEI. Methods. Semistructured interviews were conducted through convenience sampling with mothers of infants eligible for EIDT (n=47) and with healthcare workers (HCWs) providing EIDT (n=20) in five facilities, in April 2013. Results. (1) Reliance on the health passport to identify HEIs is both barrier, as women may not attend appointments with their passports, and facilitator, for documentation of HIV-exposure status. Use of trained health surveillance assistants in EIDT enhances cascade steps 1 and 2, but requires increased supervision. (2) Women struggle to accept their own HIV status, yet test results for an HEI is a motivator. Sensitisation through local leadership facilitates EIDT. (3) A reliable transport system is needed. (4) Maintaining appointments to report results to women motivates them. (5) Mothers were reluctant to give ART to young, apparently healthy infants. Conclusion. Both women and healthcare workers are motivated by test results for HEIs. The inclusion of community education can improve all steps in the EIDT cascade, including information that HEIs need ART. [ABSTRACT FROM AUTHOR]

In vitro transmesothelial migration assays of ovarian cancer cells, isolated or aggregated in multicellular spheroids, are reproduced deducing suitable Cellular Potts Models (CPM). We show that the simulations are in good agreement with the experimental evidence and that the overall process is regulated by the activity of matrix metalloproteinases (MMPs) and by the interplay of the adhesive properties of the cells with the extracellular matrix and between cells, both of the same type and of different types. In particular, the process depends on the ability of the cell to induce the loosening of cadherin-mediated junctions. Coherently with experiments, it is found that single cell invasion is more conservative with a crucial role played by MMPs. A similar important role is played in cell spheroid invasion, which in comparison is more disruptive. It achieves monofocal or multifocal characteristics according to the relative adhesion affinity among cells or between them and the mesothelial layer. [ABSTRACT FROM PUBLISHER]