Beyond the therapeutic: a Habermasian view of self-help groups’ place in the public sphere

Self-help groups in the United Kingdom continue to grow in number and address virtually every conceivable health condition, but they remain the subject of very little theoretical analysis. The literature to date has predominantly focused on their therapeutic effects on individual members. And yet they are widely presumed to fulfil a broader civic role and to encourage democratic citizenship. The article uses Habermas’ model of the public sphere as an analytical tool with which to reconsider the literature on self-help groups in order to increase our knowledge of their civic functions. In doing this it also aims to illustrate the continuing relevance of Habermas’ work to our understanding of issues in health and social care. We consider, within the context of current health policies and practices, the extent to which self-help groups with a range of different forms and functions operate according to the principles of communicative rationality that Habermas deemed key to democratic legitimacy. We conclude that self-help groups’ civic role is more complex than is usually presumed and that various factors including groups’ leadership, organisational structure and links with public agencies can affect their efficacy within the public sphere

From Epigenetic Associations to Biological and Psychosocial Explanations in Mental Health

The development of mental disorders constitutes a complex phenomenon driven by unique social, psychological and biological factors such as genetics and epigenetics, throughout an individual's life course. Both environmental and genetic factors have an impact on mental health phenotypes and act simultaneously to induce changes in brain and behavior. Here, we describe and critically evaluate the current literature on gene-environment interactions and epigenetics on mental health by highlighting recent human and animal studies. We furthermore review some of the main ethical and social implications concerning gene-environment interactions and epigenetics and provide explanations and suggestions on how to move from statistical and epigenetic associations to biological and psychological explanations within a multi-disciplinary and integrative approach of understanding mental health

An a posteriori error analysis of stationary incompressible magnetohydrodynamics

Adjoint based a posteriori error analysis is a technique to produce exact error repre- sentations for quantities of interests that are functions of the solution of systems of partial differential equations (PDE). The tools used in the analysis consist of duality arguments and compatible residuals. In this thesis we apply a posteriori error anal- ysis to the magnetohydrodynamics (MHD) equations . MHD provides a continuum level description of conducting fluids in the presence of electromagnetic fields. The MHD system is therefore a multi-physics system, capturing both fluid and electro- magnetic effects. Mathematically, The equations of MHD are highly nonlinear and fully coupled, adding to the complexity of the a posteriori analysis. Additionally, there is a stabilization necessary to ensure the so called solenoidal constraint (div B = 0) is satisfied in a weak sense. We present the new linearized adjoint system, demon- strate its effectiveness on several numerical examples, and prove its well-posedness

A thread parallel implementation of the equilibrated flux in Julia

In this article, we present a novel implementation of the equilibrated flux, the key ingredient in designing a p-robust error estimator. Our algorithm involves two primary loops: one on mesh cells and one on nodal patches. The loop on cells provides a setup phase that allows to reduce memory allocations for the potentially more costly loop on patches. Both of these loops involve mutually independent operations and are therefore amenable to parallelization strategies. We present numerical results of both the correctness of our implementation as well as evidence of the speedup due to parallelism. Our implementation is available as aregistered Julia package under an MIT open source license

Adaptive regularization, discretization, and linearization for nonsmooth problems based on primal-dual gap estimators

We consider nonsmooth partial differential equations associated to a minimization of an energy functional. We adaptively regularize the nonsmooth nonlinearity so as to be able to apply the usual Newton linearization, which is not always possible otherwise. We apply the finite element method as a discretization. We focus on the choice of the regularization parameter and adjust it on the basis of an a posteriori error estimate for the difference of energies of the exact and approximate solutions. Importantly, our estimates distinguish the different error components, namely those of regularization, linearization, and discretization. This leads to an algorithm that steers the overall procedure by adaptive stopping criteria with parameters for the regularization, linearization, and discretization levels. We prove guaranteed upper bounds for the energy difference and discuss the robustness of the estimates with respect to the magnitude of the nonlinearity when the stopping criteria are satisfied. Numerical results illustrate the theoretical developments

Adaptive regularization for the Richards equation

Richards equation is ubiquitous in the modelling of flows in porous media. It serves as a model in its own right, but also as a stepping stone to more complex models of multiphase flows. Despite its relative simplicity, it provides many challenges from a computational point of view due to the nonsmooth and degenerate nature of the functions that appear in the equation. In this paper, we replace these functions with regularized (smooth and nondegenerate) counterparts where the amount of added regualrization is controlled by a single parameter. We also introduce a set of a posteriori error estimators that we use to construct adaptive stopping criteria. In particular, we use a stopping criterion to reduce the decrease the regularization parameter, which we refer to as adaptive regularization. The full adaptive algorithm is tested on a suite of numerical examples adapted from other recent works on improving the robustness of solvers for the Richards equation

Adaptive regularization for the Richards equation

Richards equation is ubiquitous in the modelling of flows in porous media. It serves as a model in its own right, but also as a stepping stone to more complex models of multiphase flows. Despite its relative simplicity, it provides many challenges from a computational point of view due to the nonsmooth and degenerate nature of the functions that appear in the equation. In this paper, we replace these functions with regularized (smooth and nondegenerate) counterparts where the amount of added regualrization is controlled by a single parameter. We also introduce a set of a posteriori error estimators that we use to construct adaptive stopping criteria. In particular, we use a stopping criterion to reduce the decrease the regularization parameter, which we refer to as adaptive regularization. The full adaptive algorithm is tested on a suite of numerical examples adapted from other recent works on improving the robustness of solvers for the Richards equation

Adaptive regularization, discretization, and linearization for nonsmooth problems based on primal-dual gap estimators

We consider nonsmooth partial differential equations associated to a minimization of an energy functional. We adaptively regularize the nonsmooth nonlinearity so as to be able to apply the usual Newton linearization, which is not always possible otherwise. We apply the finite element method as a discretization. We focus on the choice of the regularization parameter and adjust it on the basis of an a posteriori error estimate for the difference of energies of the exact and approximate solutions. Importantly, our estimates distinguish the different error components, namely those of regularization, linearization, and discretization. This leads to an algorithm that steers the overall procedure by adaptive stopping criteria with parameters for the regularization, linearization, and discretization levels. We prove guaranteed upper bounds for the energy difference and discuss the robustness of the estimates with respect to the magnitude of the nonlinearity when the stopping criteria are satisfied. Numerical results illustrate the theoretical developments

Robust energy a posteriori estimates for nonlinear elliptic problems

In this paper, we design a posteriori estimates for finite element approximations of nonlinear elliptic problems satisfying strong-monotonicity and Lipschitz-continuity properties. These estimates include, and build on, any iterative linearization method that satisfies a few clearly identified assumptions; this encompasses the Picard, Newton, and Zarantonello linearizations. The estimates give a guaranteed upper bound on an augmented energy difference (reliability with constant one), as well as a lower bound (efficiency up to a generic constant). We prove that for the Zarantonello linearization, this generic constant only depends on the space dimension, the mesh shape regularity, and possibly the approximation polynomial degree in four or more space dimensions, making the estimates robust with respect to the strength of the nonlinearity. For the other linearizations, there is only a computable dependence on the local variation of the linearization operators. We also derive similar estimates for the energy difference. Numerical experiments illustrate and validate the theoretical results, for both smooth and singular solutions