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

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 $4k+1$ 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 $k\ge 3$ 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 $k=1$ and superconvergent in the interior (e.g., region excluding the boundary) for $k\ge2$. 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

Blau Syndrome-Associated Uveitis: Preliminary Results From an International Prospective Interventional Case Series

PURPOSE: Provide baseline and preliminary follow-up results in a 5-year longitudinal study of Blau syndrome. DESIGN: Multicenter, prospective interventional case series. METHODS: Baseline data from 50 patients from 25 centers worldwide, and follow-up data for patients followed 1, 2, or 3 years at the end of study enrollment. Ophthalmic data were collected at baseline and yearly visits by means of a standardized collection form. RESULTS: Median age at onset of eye disease was 60 months and duration of eye disease at baseline 145 months. At baseline 38 patients (78%) had uveitis, which was bilateral in 37 (97%). Eight patients (21%) had moderate to severe visual impairment. Panuveitis was found in 38 eyes (51%), with characteristic multifocal choroidal infiltrates in 29 eyes (39%). Optic disc pallor in 9 eyes (12%) and peripapillary nodules in 9 eyes (12%) were the commonest signs of optic nerve involvement. Active anterior chamber inflammation was noted in 30 eyes (40%) at baseline and in 16 (34%), 17 (57%), and 11 (61%) eyes at 1, 2, and 3 years, respectively. Panuveitis was associated with longer disease duration. At baseline, 56 eyes (75%) were on topical corticosteroids. Twenty-six patients (68%) received a combination of systemic corticosteroids and immunomodulatory therapy. CONCLUSIONS: Blau uveitis is characterized by progressive panuveitis with multifocal choroiditis, resulting in severe ocular morbidity despite continuous systemic and local immunomodulatory therapy. The frequency and severity of Blau uveitis highlight the need for close ophthalmologic surveillance as well as a search for more effective therapies