157 research outputs found
Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes
We present an abstract framework for analyzing the weak error of fully
discrete approximation schemes for linear evolution equations driven by
additive Gaussian noise. First, an abstract representation formula is derived
for sufficiently smooth test functions. The formula is then applied to the wave
equation, where the spatial approximation is done via the standard continuous
finite element method and the time discretization via an I-stable rational
approximation to the exponential function. It is found that the rate of weak
convergence is twice that of strong convergence. Furthermore, in contrast to
the parabolic case, higher order schemes in time, such as the Crank-Nicolson
scheme, are worthwhile to use if the solution is not very regular. Finally we
apply the theory to parabolic equations and detail a weak error estimate for
the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic
heat equation
The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and lubrication-type equations
The cutoff method, which cuts off the values of a function less than a given
number, is studied for the numerical computation of nonnegative solutions of
parabolic partial differential equations. A convergence analysis is given for a
broad class of finite difference methods combined with cutoff for linear
parabolic equations. Two applications are investigated, linear anisotropic
diffusion problems satisfying the setting of the convergence analysis and
nonlinear lubrication-type equations for which it is unclear if the convergence
analysis applies. The numerical results are shown to be consistent with the
theory and in good agreement with existing results in the literature. The
convergence analysis and applications demonstrate that the cutoff method is an
effective tool for use in the computation of nonnegative solutions. Cutoff can
also be used with other discretization methods such as collocation, finite
volume, finite element, and spectral methods and for the computation of
positive solutions.Comment: 19 pages, 41 figure
Attention deficit hyperactivity symptoms predict problematic mobile phone use
Attention-deficit-hyperactivity disorder (ADHD) is the most commonly diagnosed childhood disorder characterised by inattention, hyperactivity/impulsivity, or both. Some of the key traits of ADHD have previously been linked to addictive and problematic behaviours. The aim of the present study was to examine the relationship between problematic mobile phone use, smartphone
addiction risk and ADHD symptoms in an adult population. A sample of 273 healthy adult volunteers completed the Adult
ADHD Self-Report Scale (ASRS), the Mobile Phone Problem Usage Scale (MPPUS), and the Smartphone Addiction Scale
(SAS). A significant positive correlation was found between the ASRS and both scales. More specifically, inattention symptoms
and age predicted smartphone addiction risk and problematic mobile phone use. Our results suggest that there is a positive
relationship between ADHD traits and problematic mobile phone use. In particular, younger adults with higher level of inattention symptoms could be at higher risk of developing smartphone addiction. The implication of our findings for theoretical
frameworks of problematic mobile phone use and clinical practice are discussed
Can disordered mobile phone use be considered a behavioral addiction? An update on current evidence and a comprehensive model for future research
Despite the many positive outcomes, excessive mobile phone use is now often associated with potentially harmful and/or disturbing behaviors (e.g., symptoms of deregulated use, negative impact on various aspects of daily life such as relationship problems, and work intrusion). Problematic mobile phone use (PMPU) has generally been considered as a behavioral addiction that shares many features with more established drug addictions. In light of the most recent data, the current paper reviews the validity of the behavioral addiction model when applied to PMPU. On the whole, it is argued that the evidence supporting PMPU as an addictive behavior is scarce. In particular, it lacks studies that definitively show behavioral and neurobiological similarities between mobile phone addiction and other types of legitimate addictive behaviors. Given this context, an integrative pathway model is proposed that aims to provide a theoretical framework to guide future research in the field of PMPU. This model highlights that PMPU is a heterogeneous and multi-faceted condition
Rapid covariance-based sampling of linear SPDE approximations in the multilevel Monte Carlo method
The efficient simulation of the mean value of a non-linear functional of the
solution to a linear stochastic partial differential equation (SPDE) with
additive Gaussian noise is considered. A Galerkin finite element method is
employed along with an implicit Euler scheme to arrive at a fully discrete
approximation of the mild solution to the equation. A scheme is presented to
compute the covariance of this approximation, which allows for rapid sampling
in a Monte Carlo method. This is then extended to a multilevel Monte Carlo
method, for which a scheme to compute the cross-covariance between the
approximations at different levels is presented. In contrast to traditional
path-based methods it is not assumed that the Galerkin subspaces at these
levels are nested. The computational complexities of the presented schemes are
compared to traditional methods and simulations confirm that, under suitable
assumptions, the costs of the new schemes are significantly lower.Comment: 18 pages, 5 figures; numerical simulations revised, implementation
section added; To appear in Monte Carlo and Quasi-Monte Carlo Methods -
MCQMC, Rennes, France, July 201
Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo
Efficient uncertainty quantification algorithms are key to understand the
propagation of uncertainty -- from uncertain input parameters to uncertain
output quantities -- in high resolution mathematical models of brain
physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and
multilevel Monte Carlo (MLMC) have the potential to dramatically improve upon
standard Monte Carlo (MC) methods, but their applicability and performance in
biomedical applications is underexplored. In this paper, we design and apply
QMC and MLMC methods to quantify uncertainty in a convection-diffusion model of
tracer transport within the brain. We show that QMC outperforms standard MC
simulations when the number of random inputs is small. MLMC considerably
outperforms both QMC and standard MC methods and should therefore be preferred
for brain transport models.Comment: Multilevel Monte Carlo, quasi Monte Carlo, brain simulation, brain
fluids, finite element method, biomedical computing, random fields,
diffusion-convectio
Computers in Secondary Schools: Educational Games
This entry introduces educational games in secondary schools. Educational
games include three main types of educational activities with a playful
learning intention supported by digital technologies: educational serious
games, educational gamification, and learning through game creation.
Educational serious games are digital games that support learning objectives.
Gamification is defined as the use of "game design elements and game thinking
in a non-gaming context" (Deterding et al. 2011, p. 13). Educational
gamification is not developed through a digital game but includes game elements
for supporting the learning objectives. Learning through game creation is
focused on the process of designing and creating a prototype of a game to
support a learning process related to the game creation process or the
knowledge mobilized through the game creation process. Four modalities of
educational games in secondary education are introduced in this entry to
describe educational games in secondary education: educational purpose of
entertainment games, serious games, gamification, and game design
One-Sided Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering Over Uniform and Non-Uniform Meshes
In this paper, we introduce a new position-dependent Smoothness-Increasing Accuracy-Conserving (SIAC) filter that retains the benefits of position dependence while ameliorating some of its shortcomings. As in the previous position-dependent filter, our new filter can be applied near domain boundaries, near a discontinuity in the solution, or at the interface of different mesh sizes; and as before, in general, it numerically enhances the accuracy and increases the smoothness of approximations obtained using the discontinuous Galerkin (dG) method. However, the previously proposed position-dependent one-sided filter had two significant disadvantages: (1) increased computational cost (in terms of function evaluations), brought about by the use of central B-splines near a boundary (leading to increased kernel support) and (2) increased numerical conditioning issues that necessitated the use of quadruple precision for polynomial degrees of for the reported accuracy benefits to be realizable numerically. Our new filter addresses both of these issues --- maintaining the same support size and with similar function evaluation characteristicsas the symmetric filter in a way that has better numerical conditioning --- making it, unlike its predecessor, amenable for GPU computing. Our new filter was conceived by revisiting the original error analysis for superconvergence of SIAC filters and by examining the role of the B-splines and their weights in the SIAC filtering kernel. We demonstrate, in the uniform mesh case, that our new filter is globally superconvergent for and superconvergent in the interior (e.g., region excluding the boundary) for . Furthermore, we present the first theoretical proof of superconvergence for postprocessing over smoothly varying meshes, and explain the accuracy-order conserving nature of this new filter when applied to certain non-uniform meshes cases. We provide numerical examples supporting our theoretical results and demonstrating that our new filter, in general, enhances the smoothness and accuracy of the solution. Numerical results are presented for solutions of both linear and nonlinear equation solved on both uniform and non-uniform one- and two-dimensional meshes
Perceived connections between information and communication technology use and mental symptoms among young adults - a qualitative study
<p>Abstract</p> <p>Background</p> <p>Prospective associations have been found between high use of information and communication technology (ICT) and reported mental symptoms among young adult university students, but the causal mechanisms are unclear. Our aim was to explore possible explanations for associations between high ICT use and symptoms of depression, sleep disorders, and stress among young adults in order to propose a model of possible pathways to mental health effects that can be tested epidemiologically.</p> <p>Methods</p> <p>We conducted a qualitative interview study with 16 women and 16 men (21-28 years), recruited from a cohort of university students on the basis of reporting high computer (n = 28) or mobile phone (n = 20) use at baseline and reporting mental symptoms at the one-year follow-up. Semi-structured interviews were performed, with open-ended questions about possible connections between the use of computers and mobile phones, and stress, depression, and sleep disturbances. The interview data were analyzed with qualitative content analysis and summarized in a model.</p> <p>Results</p> <p>Central factors appearing to explain high quantitative ICT use were personal dependency, and demands for achievement and availability originating from the domains of work, study, social life, and individual aspirations. Consequences included mental overload, neglect of other activities and personal needs, time pressure, role conflicts, guilt feelings, social isolation, physical symptoms, worry about electromagnetic radiation, and economic problems. Qualitative aspects (destructive communication and information) were also reported, with consequences including vulnerability, misunderstandings, altered values, and feelings of inadequacy. User problems were a source of frustration. Altered ICT use as an effect of mental symptoms was reported, as well as possible positive effects of ICT on mental health.</p> <p>Conclusions</p> <p>The concepts and ideas of the young adults with high ICT use and mental symptoms generated a model of possible paths for associations between ICT exposure and mental symptoms. Demands for achievement and availability as well as personal dependency were major causes of high ICT exposure but also direct sources of stress and mental symptoms. The proposed model shows that factors in different domains may have an impact and should be considered in epidemiological and intervention studies.</p
Sparse initial data indentification for parabolic pde and its finite element approximations
We address the problem of inverse source identification for parabolic equations from the optimal control viewpoint employing measures of minimal norm as initial data. We adopt the point of view of approximate controllability so that the target is not required to be achieved exactly but only in an approximate sense. We prove an approximate inversion result and derive a characterization of the optimal initial measures by means of duality and the minimization of a suitable quadratic functional on the solutions of the adjoint system. We prove the sparsity of the optimal initial measures showing that they are supported in sets of null Lebesgue measure. As a consequence, approximate controllability can be achieved efficiently by means of controls that are activated in a finite number of pointwise locations. Moreover, we discuss the finite element numerical approximation of the control problem providing a convergence result of the corresponding optimal measures and states as the discretization parameters tend to zero.The first author was supported by Spanish Ministerio de Economía y Competitividad under project MTM2011-22711. The third author was supported by the Advanced Grant NUMERIWAVES/FP7-246775 of the European Research Council Executive Agency, FA9550-14-1-0214 of the EOARD-AFOSR, FA9550-15-1-0027 of AFOSR, the BERC 2014-2017 program of the Basque Government, the MTM2011-29306 and SEV-2013-0323 Grants of the MINECO, the CIMI-Toulouse Excellence Chair in PDEs, Control and Numerics and a Humboldt Award at the University of Erlangen-Nürnberg
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