Koopman Operator and its Approximations for Systems with Symmetries

Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and to simplify their analysis. The Koopman operator is an infinite dimensional linear operator that fully captures a system's nonlinear dynamics through the linear evolution of functions of the state space. Importantly, in contrast with local linearization, it preserves a system's global nonlinear features. We demonstrate how the presence of symmetries affects the Koopman operator structure and its spectral properties. In fact, we show that symmetry considerations can also simplify finding the Koopman operator approximations using the extended and kernel dynamic mode decomposition methods (EDMD and kernel DMD). Specifically, representation theory allows us to demonstrate that an isotypic component basis induces block diagonal structure in operator approximations, revealing hidden organization. Practically, if the data is symmetric, the EDMD and kernel DMD methods can be modified to give more efficient computation of the Koopman operator approximation and its eigenvalues, eigenfunctions, and eigenmodes. Rounding out the development, we discuss the effect of measurement noise

PI-FLAME: A parallel immune system simulator using the FLAME graphic processing unit environment

Agent-based models (ABMs) are increasingly being used to study population dynamics in complex systems, such as the human immune system. Previously, Folcik et al. (The basic immune simulator: an agent-based model to study the interactions between innate and adaptive immunity. Theor Biol Med Model 2007; 4: 39) developed a Basic Immune Simulator (BIS) and implemented it using the Recursive Porous Agent Simulation Toolkit (RePast) ABM simulation framework. However, frameworks such as RePast are designed to execute serially on central processing units and therefore cannot efficiently handle large model sizes. In this paper, we report on our implementation of the BIS using FLAME GPU, a parallel computing ABM simulator designed to execute on graphics processing units. To benchmark our implementation, we simulate the response of the immune system to a viral infection of generic tissue cells. We compared our results with those obtained from the original RePast implementation for statistical accuracy. We observe that our implementation has a 13× performance advantage over the original RePast implementation

Integration of Evidence-Based Practice in Nursing Education

Evidence based practice (EBP) has gained momentum globally, to provide effective and efficient health care. Although EBP has evolved to a great extent over the last two decades and is accepted as an important concept by all health care professionals, its integration in practice is still challenging. Integration of EBP in nursing profession both in nursing practice and nursing education is an important issue. This article describes the experience of the authors in integrating evidence based practice in nursing education in Manipal University. It focuses on the training of nurse educators in EBP, alignment of EBP in curriculum and EBP practicum in curriculum so as to enable a nurse to identify evidences, make appropriate clinical decisions and utilize EBP in rendering scientific and quality patient care

Rubrics in Nursing Education

Evaluating assignments or course work is a challenging job for faculty of nursing. In order to avoid the dilemmas of evaluation, nurse educators use rubrics as an evaluation tool. In educational technology, rubric refers to „performance standard‟ for a student population. A rubric is defined as an assessment tool that lays out the set standards and criteria to assess a performance, assignment or behavior. The four essential components of a rubric are task description, scale of achievement, dimensions & description of dimensions. Various types of scoring rubrics are available. The type of rubric chosen for assessment depends on the task being evaluated and the needs of the assessor. Holistic rubrics, analytic rubrics, generic rubrics, specific rubrics are the different types of rubrics. In nursing education, rubrics has got wide range of applications such as to; assess clinical skills, grade assignments, evaluate clinical competency and analyze presentations. Rubrics helps to define "quality performance” and promote awareness on critical components in a performance. Rubrics not only act as an evaluation tool for instructors, but also act as a feedback proforma for students. Rubrics are vital tools that can be utilized to solve the problem of subjectivity in evaluation. Rubrics provide consistency in evaluation, reduces subjectivity and enhances objectivity

Galactic accretion and the outer structure of galaxies in the CDM model

We have combined the semi-analytic galaxy formation model of Guo et al. (2011) with the particle-tagging technique of Cooper et al. (2010) to predict galaxy surface brightness profiles in a representative sample of ~1900 massive dark matter haloes (10^12--10^14 M_sol) from the Millennium II Lambda-CDM N-body simulation. Here we present our method and basic results focusing on the outer regions of galaxies, consisting of stars accreted in mergers. These simulations cover scales from the stellar haloes of Milky Way-like galaxies to the 'cD envelopes' of groups and clusters, and resolve low surface brightness substructure such as tidal streams. We find that the surface density of accreted stellar mass around the central galaxies of dark matter haloes is well described by a Sersic profile, the radial scale and amplitude of which vary systematically with halo mass (M_200). The total stellar mass surface density profile breaks at the radius where accreted stars start to dominate over stars formed in the galaxy itself. This break disappears with increasing M_200 because accreted stars contribute more of the total mass of galaxies, and is less distinct when the same galaxies are averaged in bins of stellar mass, because of scatter in the relation between M_star and M_200. To test our model we have derived average stellar mass surface density profiles for massive galaxies at z~0.08 by stacking SDSS images. Our model agrees well with these stacked profiles and with other data from the literature, and makes predictions that can be more rigorously tested by future surveys that extend the analysis of the outer structure of galaxies to fainter isophotes. We conclude that it is likely that the outer structure of the spheroidal components of galaxies is largely determined by collisionless merging during their hierarchical assemblyComment: Accepted by MNRAS. Shortened following referee's report, conclusions unchanged. 21 pages, 15 figure

Robust Bain distortion in the premartensite phase of platinum substituted Ni2MnGa magnetic shape memory alloy

The premartensite phase of shape memory and magnetic shape memory alloys (MSMAs) is believed to be a precursor state of the martensite phase with preserved austenite phase symmetry. The thermodynamic stability of the premartensite phase and its relation to the martensitic phase is still an unresolved issue, even though it is critical to the understanding of the functional properties of MSMAs. We present here unambiguous evidence for macroscopic symmetry breaking leading to robust Bain distortion in the premartensite phase of 10% Pt substituted Ni2MnGa. We show that the robust Bain distorted premartensite (T2) phase results from another premartensite (T1) phase with preserved cubic-like symmetry through an isostructural phase transition. The T2 phase finally transforms to the martensite phase with additional Bain distortion on further cooling. Our results demonstrate that the premartensite phase should not be considered as a precursor state with the preserved symmetry of the cubic austenite phase