General relativistic hydrodynamics in curvilinear coordinates

In this paper we report on what we believe is the first successful implementation of relativistic hydrodynamics, coupled to dynamical spacetimes, in spherical polar coordinates without symmetry assumptions. We employ a high-resolution shock-capturing scheme, which requires that the equations be cast in flux-conservative form. One example of such a form is the :Valencia" formulation, which has been adopted in numerous applications, in particular in Cartesian coordinates. Here we generalize this formulation to allow for a reference-metric approach, which provides a natural framework for calculations in curvilinear coordinates. In spherical polar coordinates, for example, it allows for an analytical treatment of the singular r and sin(\theta) terms that appear in the equations. We experiment with different versions of our generalized Valencia formulation in numerical implementations of relativistic hydrodynamics for both fixed and dynamical spacetimes. We consider a number of different tests -- non-rotating and rotating relativistic stars, as well as gravitational collapse to a black hole -- to demonstrate that our formulation provides a promising approach to performing fully relativistic astrophysics simulations in spherical polar coordinates.Comment: 14 pages, 8 figures, version to be published in PR

Numerical Relativity in Spherical Polar Coordinates: Off-center Simulations

We have recently presented a new approach for numerical relativity simulations in spherical polar coordinates, both for vacuum and for relativistic hydrodynamics. Our approach is based on a reference-metric formulation of the BSSN equations, a factoring of all tensor components, as well as a partially implicit Runge-Kutta method, and does not rely on a regularization of the equations, nor does it make any assumptions about the symmetry across the origin. In order to demonstrate this feature we present here several off-centered simulations, including simulations of single black holes and neutron stars whose center is placed away from the origin of the coordinate system, as well as the asymmetric head-on collision of two black holes. We also revisit our implementation of relativistic hydrodynamics and demonstrate that a reference-metric formulation of hydrodynamics together with a factoring of all tensor components avoids problems related to the coordinate singularities at the origin and on the axes. As a particularly demanding test we present results for a shock wave propagating through the origin of the spherical polar coordinate system.Comment: 13 pages, 11 figures; matches version published in PR

Trumpet Slices in Kerr Spacetimes

We introduce a new time-independent family of analytical coordinate systems for the Kerr spacetime representing rotating black holes. We also propose a (2+1)+1 formalism for the characterization of trumpet geometries. Applying this formalism to our new family of coordinate systems we identify, for the first time, analytical and stationary trumpet slices for general rotating black holes, even for charged black holes in the presence of a cosmological constant. We present results for metric functions in this slicing and analyze the geometry of the rotating trumpet surface.Comment: 5 pages, 2 figures; version published in PR

How to reduce the number of rating scale items without predictability loss?

Rating scales are used to elicit data about qualitative entities (e.g., research collaboration). This study presents an innovative method for reducing the number of rating scale items without the predictability loss. The "area under the receiver operator curve method" (AUC ROC) is used. The presented method has reduced the number of rating scale items (variables) to 28.57\% (from 21 to 6) making over 70\% of collected data unnecessary. Results have been verified by two methods of analysis: Graded Response Model (GRM) and Confirmatory Factor Analysis (CFA). GRM revealed that the new method differentiates observations of high and middle scores. CFA proved that the reliability of the rating scale has not deteriorated by the scale item reduction. Both statistical analysis evidenced usefulness of the AUC ROC reduction method.Comment: 14 pages, 5 figure

Acquisition of anoikis resistance in human osteosarcoma cells does not alter sensitivity to chemotherapeutic agents

BACKGROUND: Chemotherapy-induced cell death can involve the induction of apoptosis. Thus, aberrant function of the pathways involved might result in chemoresistance. Since cell adhesion to the extracellular matrix acts as a survival factor that homeostatically maintains normal tissue architecture, it was tested whether acquisition of resistance to deadhesion-induced apoptosis (anoikis) in human osteosarcoma would result in resistance to chemotherapy. METHODS: Osteosarcoma cell lines (SAOS-2 and TE-85) obtained from ATCC and were maintained in complete Eagle's MEM medium. Suspension culture was established by placing cells in tissue culture wells coated with poly-HEMA. Cell cytotoxicity was determined using a live/dead cytotoxicity assay. Cell cycle/apoptosis analyses were performed using propidium iodide (PI) staining with subsequent FACS analysis. Apoptosis was also assayed by Annexin-FITC/PI staining. RESULTS: Etoposide, adriamycin, vinblastine, cisplatin and paclitaxel were able to induce apoptosis in human osteosarcoma cells SAOS-2 regardless of their anoikis resistance phenotype or the culture conditions (adhered vs. suspended). Moreover, suspended anoikis resistant TE-85 cells (TE-85ar) retained their sensitivity to chemotherapy as well. CONCLUSION: Acquisition of anoikis resistance in human osteosarcoma cells does not result in a generalized resistance to all apoptotic stimuli, including chemotherapy. Moreover, our results suggest that the pathways regulating anoikis resistance and chemotherapy resistance might involve the action of different mediators

Collapse of Nonlinear Gravitational Waves in Moving-Puncture Coordinates

We study numerical evolutions of nonlinear gravitational waves in moving-puncture coordinates. We adopt two different types of initial data -- Brill and Teukolsky waves -- and evolve them with two independent codes producing consistent results. We find that Brill data fail to produce long-term evolutions for common choices of coordinates and parameters, unless the initial amplitude is small, while Teukolsky wave initial data lead to stable evolutions, at least for amplitudes sufficiently far from criticality. The critical amplitude separates initial data whose evolutions leave behind flat space from those that lead to a black hole. For the latter we follow the interaction of the wave, the formation of a horizon, and the settling down into a time-independent trumpet geometry. We explore the differences between Brill and Teukolsky data and show that for less common choices of the parameters -- in particular negative amplitudes -- Brill data can be evolved with moving-puncture coordinates, and behave similarly to Teukolsky waves

The Attentional Demands of Ambulating with an Assistive Device in Older Adults with Alzheimer\u27s Disease

Ambulation with a mobility aid is a unique real-life situation of multi-tasking. These simultaneous motor tasks place increased demands on executive function in healthy young and older adults, but the demands have not been evaluated in people with Alzheimer\u27s disease (AD). Mobility problems are common among adults with AD, leading to provision of a mobility aid to optimize independent activity. The study objectives were: (i) to determine the dual-task cost (DTC) associated with the use of a mobility aid in straight and complex path walking, and (ii) to evaluate the association between executive function and ambulation with a mobility aid in older adults with AD and age-sex matched cognitively normal controls. Fourteen people (mean age±SD, 72.6±9.9years) with a diagnosis of probable AD (MMSE range 12-25) and controls (mean age±SD, 72.9±9.5) walked at a self-selected pace and using a 4-wheeled walker in a 6m straight path and a Figure of 8 Test. Ambulation with the walker in a straight path produced a low DTC that was not different between the groups. Ambulation with the 4-wheeled walker in the complex path produced a significantly different DTC in the group with AD at -38.1±23.5% compared to -19.7±21.4% (p=0.041). Lower scores on executive function were associated with longer times across test conditions. Ambulation with a 4-wheeled walker, in particular maneuvering around obstacles, requires greater attentional costs in dementia. Future research should explore the timing for safely introducing mobility aids in AD and the role of improving executive function

Parrondo-like behavior in continuous-time random walks with memory

The Continuous-Time Random Walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this article we will show how the random combination of two different unbiased CTRWs can give raise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same of the Parrondo's paradox in game theoryComment: 8 pages, 3 figures, revtex; enlarged and revised versio