Numerical approximations of second-order matrix differential equations using higher-degree splines

Many studies of mechanical systems in engineering are based on second-order matrix models. This work discusses the second-order generalization of previous research on matrix differential equations dealing with the construction of approximate solutions for non-stiff initial problems Y 00(x) = f(x, Y (x), Y 0 (x)) using higher-degree matrix splines without any dimensional increase. An estimation of the approximation error for some illustrative examples are presented by using Mathematica. Several MatLab functions have also been developed, comparing, under equal conditions, accuracy and execution times with built-in MatLab functions. Experimental results show the advantages of solving the above initial problem by using the implemented MatLab functions.The authors wish to thank for financial support by the Universidad Politecnica de Valencia [grant number PAID-06-11-2020].Defez Candel, E.; Tung ., MM.; Solis Lozano, FJ.; Ibáñez González, JJ. (2015). Numerical approximations of second-order matrix differential equations using higher-degree splines. Linear and Multilinear Algebra. 63(3):472-489. https://doi.org/10.1080/03081087.2013.873427S472489633Loscalzo, F. R., & Talbot, T. D. (1967). Spline Function Approximations for Solutions of Ordinary Differential Equations. SIAM Journal on Numerical Analysis, 4(3), 433-445. doi:10.1137/0704038Al-Said, E. A. (2001). The use of cubic splines in the numerical solution of a system of second-order boundary value problems. Computers & Mathematics with Applications, 42(6-7), 861-869. doi:10.1016/s0898-1221(01)00204-8Al-Said, E. A., & Noor, M. A. (2003). Cubic splines method for a system of third-order boundary value problems. Applied Mathematics and Computation, 142(2-3), 195-204. doi:10.1016/s0096-3003(02)00294-1Kadalbajoo, M. K., & Patidar, K. C. (2002). Numerical solution of singularly perturbed two-point boundary value problems by spline in tension. Applied Mathematics and Computation, 131(2-3), 299-320. doi:10.1016/s0096-3003(01)00146-1Micula, G., & Revnic, A. (2000). An implicit numerical spline method for systems for ODEs. Applied Mathematics and Computation, 111(1), 121-132. doi:10.1016/s0096-3003(98)10111-xDefez, E., Soler, L., Hervás, A., & Santamaría, C. (2005). Numerical solution ofmatrix differential models using cubic matrix splines. Computers & Mathematics with Applications, 50(5-6), 693-699. doi:10.1016/j.camwa.2005.04.012Defez, E., Hervás, A., Soler, L., & Tung, M. M. (2007). Numerical solutions of matrix differential models using cubic matrix splines II. Mathematical and Computer Modelling, 46(5-6), 657-669. doi:10.1016/j.mcm.2006.11.027Ascher, U., Pruess, S., & Russell, R. D. (1983). On Spline Basis Selection for Solving Differential Equations. SIAM Journal on Numerical Analysis, 20(1), 121-142. doi:10.1137/0720009Brunner, H. (2004). On the Divergence of Collocation Solutions in Smooth Piecewise Polynomial Spaces for Volterra Integral Equations. BIT Numerical Mathematics, 44(4), 631-650. doi:10.1007/s10543-004-3828-5Tung, M. M., Defez, E., & Sastre, J. (2008). Numerical solutions of second-order matrix models using cubic-matrix splines. Computers & Mathematics with Applications, 56(10), 2561-2571. doi:10.1016/j.camwa.2008.05.022Defez, E., Tung, M. M., Ibáñez, J. J., & Sastre, J. (2012). Approximating and computing nonlinear matrix differential models. Mathematical and Computer Modelling, 55(7-8), 2012-2022. doi:10.1016/j.mcm.2011.11.060Claeyssen, J. R., Canahualpa, G., & Jung, C. (1999). A direct approach to second-order matrix non-classical vibrating equations. Applied Numerical Mathematics, 30(1), 65-78. doi:10.1016/s0168-9274(98)00085-3Froese, C. (1963). NUMERICAL SOLUTION OF THE HARTREE–FOCK EQUATIONS. Canadian Journal of Physics, 41(11), 1895-1910. doi:10.1139/p63-189Marzulli, P. (1991). Global error estimates for the standard parallel shooting method. Journal of Computational and Applied Mathematics, 34(2), 233-241. doi:10.1016/0377-0427(91)90045-lShore, B. W. (1973). Comparison of matrix methods applied to the radial Schrödinger eigenvalue equation: The Morse potential. The Journal of Chemical Physics, 59(12), 6450-6463. doi:10.1063/1.1680025ZHANG, J. F. (2002). OPTIMAL CONTROL FOR MECHANICAL VIBRATION SYSTEMS BASED ON SECOND-ORDER MATRIX EQUATIONS. Mechanical Systems and Signal Processing, 16(1), 61-67. doi:10.1006/mssp.2001.1441Flett, T. M. (1980). Differential Analysis. doi:10.1017/cbo978051189719

Disease flare of ankylosing spondylitis presenting as reactive arthritis with seropositivity: a case report

<p>Abstract</p> <p>Introduction</p> <p>Concurrent rheumatoid factor seropositivity is occasionally detected in ankylosing spondylitis and often causes confusion in clinical routine. Overlap between various seronegative arthritides is a known but uncommon association. Differentiation of spondyloarthropathy from rheumatoid arthritis is important, since the natural history, complications, treatments and prognosis of the two diseases differ significantly.</p> <p>Case presentation</p> <p>Here, we report the case of a 47-year-old Sri Lankan man who had a long history of intermittent joint pains worsening following a recent episode of self-resolving non-bloody diarrhea. Subsequently, he developed a skin rash suggestive of keratoderma blenorrhagica and circinate balanitis. He had classical radiological evidence of ankylosing spondylosis (previously undiagnosed) associated with human leukocyte antigen B27 antigen, but was positive for rheumatoid factor.</p> <p>Conclusions</p> <p>A disease flare of ankylosing spondylitis prompted by a minor diarrheal illness showing well documented features of reactive arthritis is remarkable. The prognostic implications of seropositivity in spondyloarthritis are discussed.</p

Is cell-to-cell scale variability necessary in reservoir models?

Reservoir models typically contain hundreds-of-thousands to millions of grid cells in which petrophysical properties such as porosity and permeability vary on a cell-to-cell basis. However, although the petrophysical properties of rocks do vary on a point-to-point basis, this variability is not equivalent to the cell-to-cell variations in models. We investigate the impact of removing cell-to-cell variability on predictions of fluid flow in reservoir models. We remove cell-to-cell variability from models containing hundreds of thousands of unique porosity and permeability values to yield models containing just a few tens of unique porosity and permeability values grouped into a few internally homogeneous domains. The flow behavior of the original model is used as a reference. We find that the impact of cell-to-cell variability on predicted flow is small. Cell-to-cell variability is not necessary to capture flow in reservoir models; rather, it is the spatially correlated variability in petrophysical properties that is important. Reservoir modelling effort should focus on capturing correlated geologic domains in the most realistic and computationally efficient manner

Challenges in Developing Evidence-Based Recommendations Using the GRADE Approach: The Case of Mental, Neurological, and Substance Use Disorders

Corrado Barbui and colleagues describe their use and adaptation of the GRADE approach in developing the guidelines for the WHO mental health Gap Action Programme (mhGAP)

Engaging national organizations for knowledge translation: Comparative case studies in knowledge value mapping

<p>Abstract</p> <p>Background</p> <p>Government sponsors of research and development, along with their funded investigators, are increasingly tasked with demonstrating evidence of knowledge use by nontraditional audiences. This requires efforts to translate their findings for effective communication. For technology-related knowledge, these audiences include clinicians, consumers, manufacturers, public policy agencies, and knowledge brokers. One potentially efficient approach is to communicate research findings through relevant national organizations. However, this requires an understanding of how such organizations view and treat research knowledge, which can be determined through knowledge-value mapping. Do knowledge values differ between national organizations representing different audiences? Can a deeper understanding of knowledge values help sponsors, investigators, and organizations better communicate research findings to stakeholders?</p> <p>Methods</p> <p>A series of comparative case studies on knowledge-value mapping were derived through interviews with spokespersons for six national organizations. The semi-structured interviews followed a 10-item questionnaire to characterize different ways in which each organization engages with research-based knowledge. Each participating organization represents a particular stakeholder group, while all share a common interest in the research subject matter.</p> <p>Results</p> <p>Each national organization considers the value of the research knowledge in the context of their organization's mission and the interests of their members. All are interested in collaborating with researchers to share relevant findings, while they vary along the following dimensions of knowledge engagement: create, identify, translate, adapt, communicate, use, promote, absorptive capacity, and recommendations for facilitation.</p> <p>Conclusions</p> <p>The principles of knowledge translation suggest that investigators can increase use by tailoring the format and context of their findings to the absorptive capacity of nonscholars. Greater absorption should result in higher levels of knowledge awareness, interest, and use, which can then be documented. National organizations and their members, in turn, can strive to optimize their absorptive capacities regarding the state of the sciences. This combination will ensure the highest possible return on public investment in research activities. This knowledge-value mapping study concludes that national organizations are appropriate channels for communicating research findings and for meeting statutory requirements and general expectations for generating and documenting knowledge use.</p

Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size $N$. We study the behaviour of the process as the population size $N$ tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as $N \to \infty$ but more slowly than $N^{-1/2}$. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.Comment: Revised; 34 pages; 6 figure

Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.Comment: 33 pages, 12 figure

Amyloid β induces early changes in the ribosomal machinery, cytoskeletal organization and oxidative phosphorylation in retinal photoreceptor cells

Amyloid &beta; (A&beta;) accumulation and its aggregation is characteristic molecular feature of the development of Alzheimer&rsquo;s disease (AD). More recently, A&beta; has been suggested to be associated with retinal pathology associated with AD, glaucoma and drusen deposits in age related macular degeneration (AMD). In this study, we investigated the proteins and biochemical networks that are affected by A&beta; in the 661 W photoreceptor cells in culture. Time and dose dependent effects of A&beta; on the photoreceptor cells were determined utilizing tandem mass tag (TMT) labeling-based quantitative mass-spectrometric approach. Bioinformatic analysis of the data revealed concentration and time dependent effects of the A&beta; peptide stimulation on various key biochemical pathways that might be involved in mediating the toxicity effects of the peptide. We identified increased Tau phosphorylation, GSK3&beta; dysregulation and reduced cell viability in cells treated with A&beta; in a dose and time dependent manner. This study has delineated for the first-time molecular networks in photoreceptor cells that are impacted early upon A&beta; treatment and contrasted the findings with a longer-term treatment effect. Proteins associated with ribosomal machinery homeostasis, mitochondrial function and cytoskeletal organization were affected in the initial stages of A&beta; exposure, which may provide key insights into AD effects on the photoreceptors and specific molecular changes induced by A&beta; peptide