Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem

Sirtuins and proteolytic systems: implications for pathogenesis of synucleinopathies

Insoluble and fibrillar forms of a-synuclein are the major components of Lewy bodies, a hallmark of several sporadic and inherited neurodegenerative diseases known as synucleinopathies. a-Synuclein is a natural unfolded and aggregation-prone protein that can be degraded by the ubiquitin-proteasomal system and the lysosomal degradation pathways. a-Synuclein is a target of the main cellular proteolytic systems, but it is also able to alter their function further, contributing to the progression of neurodegeneration. Aging, a major risk for synucleinopathies, is associated with a decrease activity of the proteolytic systems, further aggravating this toxic looping cycle. Here, the current literature on the basic aspects of the routes for a-synuclein clearance, as well as the consequences of the proteolytic systems collapse, will be discussed. Finally, particular focus will be given to the sirtuins's role on proteostasis regulation, since their modulation emerged as a promising therapeutic strategy to rescue cells from a-synuclein toxicity. The controversial reports on the potential role of sirtuins in the degradation of a-synuclein will be discussed. Connection between sirtuins and proteolytic systems is definitely worth of further studies to increase the knowledge that will allow its proper exploration as new avenue to fight synucleinopathies.

Longitudinal evaluation, acceptability and long-term retention of knowledge on a horizontally integrated organic and functional systems course

Undergraduate medical education is moving from traditional disciplinary basic science courses into more integrated curricula. Integration models based on organ systems originated in the 1950s, but few longitudinal studies have evaluated their effectiveness. This article outlines the development and implementation of the Organic and Functional Systems (OFS) courses at the University of Minho in Portugal, using evidence collected over 10 years. It describes the organization of content, student academic performance and acceptability of the courses, the evaluation of preparedness for future courses and the retention of knowledge on basic sciences. Students consistently rated the OFS courses highly. Physician tutors in subsequent clinical attachments considered that students were appropriately prepared. Performance in the International Foundations of Medicine examination of a self-selected sample of students revealed similar performances in basic science items after the last OFS course and 4 years later, at the moment of graduation. In conclusion, the organizational and pedagogical approaches of the OFS courses achieve high acceptability by students and result in positive outcomes in terms of preparedness for subsequent training and long-term retention of basic science knowledge.

Numerical methods in multibody system dynamics

"Series: Solid mechanics and its applications, vol. 226"

Measurement of the correlation between flow harmonics of different order in lead-lead collisions at root S-NN=2.76 TeV with the ATLAS detector

Correlations between the elliptic or triangular flow coefficients vm (m=2 or 3) and other flow harmonics vn (n=2 to 5) are measured using sNN−−−−√=2.76 TeV Pb+Pb collision data collected in 2010 by the ATLAS experiment at the LHC, corresponding to an integrated lumonisity of 7 μb−1. The vm-vn correlations are measured in midrapidity as a function of centrality, and, for events within the same centrality interval, as a function of event ellipticity or triangularity defined in a forward rapidity region. For events within the same centrality interval, v3 is found to be anticorrelated with v2 and this anticorrelation is consistent with similar anticorrelations between the corresponding eccentricities ϵ2 and ϵ3. On the other hand, it is observed that v4 increases strongly with v2, and v5 increases strongly with both v2 and v3. The trend and strength of the vm-vn correlations for n=4 and 5 are found to disagree with ϵm-ϵn correlations predicted by initial-geometry models. Instead, these correlations are found to be consistent with the combined effects of a linear contribution to vn and a nonlinear term that is a function of v22 or of v2v3, as predicted by hydrodynamic models. A simple two-component fit is used to separate these two contributions. The extracted linear and nonlinear contributions to v4 and v5 are found to be consistent with previously measured event-plane correlations.

Sex differences in the fetal heart rate variability indices of twins

Aims: To evaluate the differences in linear and complex heart rate dynamics in twin pairs according to fetal sex combination [male-female (MF), male-male (MM), and female-female (FF)]. Methods: Fourteen twin pairs (6 MF, 3 MM, and 5 FF) were monitored between 31 and 36.4 weeks of gestation. Twenty-six fetal heart rate (FHR) recordings of both twins were simultaneously acquired and analyzed with a system for computerized analysis of cardiotocograms. Linear and nonlinear FHR indices were calculated. Results: Overall, MM twins presented higher intrapair average in linear indices than the other pairs, whereas FF twins showed higher sympathetic-vagal balance. MF twins exhibited higher intrapair average in entropy indices and MM twins presented lower entropy values than FF twins considering the (automatically selected) threshold rLu. MM twin pairs showed higher intrapair differences in linear heart rate indices than MF and FF twins, whereas FF twins exhibited lower intrapair differences in entropy indices. Conclusions: The results of this exploratory study suggest that twins have sex-specific differences in linear and nonlinear indices of FHR. MM twins expressed signs of a more active autonomic nervous system and MF twins showed the most active complexity control system. These results suggest that fetal sex combination should be taken into consideration when performing detailed evaluation of the FHR in twins.

The potential field method and the nonlinear attractor dynamics approach: what are the differences?

One of the most popular approaches to path planning and control is the potential field method. This method is particularly attractive because it is suitable for on-line feedback control. In this approach the gradient of a potential field is used to generate the robot's trajectory. Thus, the path is generated by the transient solutions of a dynamical system. On the other hand, in the nonlinear attractor dynamic approach the path is generated by a sequence of attractor solutions. This way the transient solutions of the potential field method are replaced by a sequence of attractor solutions (i.e., asymptotically stable states) of a dynamical system. We discuss at a theoretical level some of the main differences of these two approaches.