Existence and regularity of solution for a Stochastic CahnHilliard / Allen-Cahn equation with unbounded noise diffusion

The Cahn-Hilliard/Allen-Cahn equation with noise is a simplified mean field model of stochastic microscopic dynamics associated with adsorption and desorption-spin flip mechanisms in the context of surface processes. For such an equation we consider a multiplicative space-time white noise with diffusion coefficient of linear growth. Applying technics from semigroup theory, we prove local existence and uniqueness in dimensions d = 1,2,3. Moreover, when the diffusion coefficient satisfies a sub-linear growth condition of order α bounded by 1 3, which is the inverse of the polynomial order of the nonlinearity used, we prove for d = 1 global existence of solution. Path regularity of stochastic solution, depending on that of the initial condition, is obtained a.s. up to the explosion time. The path regularity is identical to that proved for the stochastic Cahn-Hilliard equation in the case of bounded noise diffusion. Our results are also valid for the stochastic Cahn-Hilliard equation with unbounded noise diffusion, for which previous results were established only in the framework of a bounded diffusion coefficient. As expected from the theory of parabolic operators in the sense of Petrovsk˘ıı, the bi-Laplacian operator seems to be dominant in the combined model

Supplementing food for health: Practices amongst French adults aged 60 to 75 years

The use of food supplements continues to grow in France, even though it is being discouraged by the main health and medical authorities. The ambiguous definitions surrounding these products make it difficult to measure their consumption. Using a qualitative survey based on interviews (n = 31) of consumers aged 60 to 75 years, this paper explores the ways in which this consumption is increasing. It traces the adoption of food supplementation in this age group back to life-course events, relating to health in particular. Using the practice theory, three forms of supplementation are identified according to the norms, products, sources of medical prescription and purposes at play. The first form is dependent on orthodox medical prescription having been taken; the supplements are prescribed by a doctor and considered by the consumer to be almost like medicinal products. The second form is linked to heterodox 'natural' therapies; products are most often based on plants and considered to be traditional remedies. The third form is related to a heterodox micronutritional approach, claiming to be scientifically advanced; products are identified as food supplements, and their consumption reflected a strategy of prevention, or even health optimisation in ageing. The affinities between these supplementation forms and the individuals' social characteristics are discussed. Results suggest that common consumer categories should be better integrated in the measurement of food supplement consumption

To formalize or not to formalize: women entrepreneurs’ sensemaking of business registration in the context of Nepal

Despite the depiction of decisions to formalize informal firms as rational and ethical, many entrepreneurs in developing countries continue to operate informally regardless of its perceived illicit status. While existing research on why entrepreneurs choose informality emphasizes the economic costs and benefits of such decisions, this often overlooks the realities of the informal economy and the constraints which marginal populations—particularly women—face. In this paper, we use institutional theory and sensemaking to understand the experiences of women in the informal economy and what formalization means to them. We use a qualitative approach to collect data from 90 women entrepreneurs in three different cities in Nepal. In our findings, we identify three groups of women with distinctive understandings of formalization—business sustainability, livelihood sufficiency and strategic alignment. Their interpretation of formalization reveals the complex, dynamic, and cyclical nature of formalization decisions. Decisions are also guided by the optimization of social and emotional logics, whereby formalization is conceived differently depending on different life stages, experiences within the informal economy and wider socio-cultural contexts. Our findings highlight the ethical implications of formalization where being a ‘good citizen’, rather than complying with formal rules and regulations, is about attuning to and fitting in with socially prescribed roles. Our research provides a nuanced view of formalization decisions, challenging idealized and ethical notions of formalization as a desired end state

Epistatic Module Detection for Case-Control Studies: A Bayesian Model with a Gibbs Sampling Strategy

The detection of epistatic interactive effects of multiple genetic variants on the susceptibility of human complex diseases is a great challenge in genome-wide association studies (GWAS). Although methods have been proposed to identify such interactions, the lack of an explicit definition of epistatic effects, together with computational difficulties, makes the development of new methods indispensable. In this paper, we introduce epistatic modules to describe epistatic interactive effects of multiple loci on diseases. On the basis of this notion, we put forward a Bayesian marker partition model to explain observed case-control data, and we develop a Gibbs sampling strategy to facilitate the detection of epistatic modules. Comparisons of the proposed approach with three existing methods on seven simulated disease models demonstrate the superior performance of our approach. When applied to a genome-wide case-control data set for Age-related Macular Degeneration (AMD), the proposed approach successfully identifies two known susceptible loci and suggests that a combination of two other loci—one in the gene SGCD and the other in SCAPER—is associated with the disease. Further functional analysis supports the speculation that the interaction of these two genetic variants may be responsible for the susceptibility of AMD. When applied to a genome-wide case-control data set for Parkinson's disease, the proposed method identifies seven suspicious loci that may contribute independently to the disease

Genetic approaches to human renal agenesis/hypoplasia and dysplasia

Congenital abnormalities of the kidney and urinary tract are frequently observed in children and represent a significant cause of morbidity and mortality. These conditions are phenotypically variable, often affecting several segments of the urinary tract simultaneously, making clinical classification and diagnosis difficult. Renal agenesis/hypoplasia and dysplasia account for a significant portion of these anomalies, and a genetic contribution to its cause is being increasingly recognized. Nevertheless, overlap between diseases and challenges in clinical diagnosis complicate studies attempting to discover new genes underlying this anomaly. Most of the insights in kidney development derive from studies in mouse models or from rare, syndromic forms of human developmental disorders of the kidney and urinary tract. The genes implicated have been shown to regulate the reciprocal induction between the ureteric bud and the metanephric mesenchyme. Strategies to find genes causing renal agenesis/hypoplasia and dysplasia vary depending on the characteristics of the study population available. The approaches range from candidate gene association or resequencing studies to traditional linkage studies, using outbred pedigrees or genetic isolates, to search for structural variation in the genome. Each of these strategies has advantages and pitfalls and some have led to significant discoveries in human disease. However, renal agenesis/hypoplasia and dysplasia still represents a challenge, both for the clinicians who attempt a precise diagnosis and for the geneticist who tries to unravel the genetic basis, and a better classification requires molecular definition to be retrospectively improved. The goal appears to be feasible with the large multicentric collaborative groups that share the same objectives and resources

On strongly Petrovskii's parabolic SPDEs in arbitrary dimension

In this paper we show that the Cahn-Hilliard stochastic SPDE has a function valued solution in dimension 4 and 5 when the perturbation is driven by a space-correlated Gaussian noise. This is done proving general results on SPDEs with globally Lipschitz coefficients associated with operators on smooth domains of R^d which are parabolic in the sense of Petrovskii, and do not necessarily de ne a semi-group of operators. We study the regularity of the trajectories of the solutions and the absolute continuity of the law at some given time and position