A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

Assessing the viability of studying motion indicators of autism spectrum disorders in infants at high and low risk for ASD using a passive motion capture system

Gemstone Team AMIRA

Event memory: A theory of memory for laboratory, autobiographical, and fictional events.

An event memory is a mental construction of a scene recalled as a single occurrence. It therefore requires the hippocampus and ventral visual stream needed for all scene construction. The construction need not come with a sense of reliving or be made by a participant in the event, and it can be a summary of occurrences from more than one encoding. The mental construction, or physical rendering, of any scene must be done from a specific location and time; this introduces a "self" located in space and time, which is a necessary, but need not be a sufficient, condition for a sense of reliving. We base our theory on scene construction rather than reliving because this allows the integration of many literatures and because there is more accumulated knowledge about scene construction's phenomenology, behavior, and neural basis. Event memory differs from episodic memory in that it does not conflate the independent dimensions of whether or not a memory is relived, is about the self, is recalled voluntarily, or is based on a single encoding with whether it is recalled as a single occurrence of a scene. Thus, we argue that event memory provides a clearer contrast to semantic memory, which also can be about the self, be recalled voluntarily, and be from a unique encoding; allows for a more comprehensive dimensional account of the structure of explicit memory; and better accounts for laboratory and real-world behavioral and neural results, including those from neuropsychology and neuroimaging, than does episodic memory.

Kappa calculus and evidential strength: A note on Åqvist's logical theory of legal evidence

Lennart Åqvist (1992) proposed a logical theory of legal evidence, based on the Bolding-Ekelöf of degrees of evidential strength. This paper reformulates Åqvist's model in terms of the probabilistic version of the kappa calculus. Proving its acceptability in the legal context is beyond the present scope, but the epistemological debate about Bayesian Law isclearly relevant. While the present model is a possible link to that lineof inquiry, we offer some considerations about the broader picture of thepotential of AI & Law in the evidentiary context. Whereas probabilisticreasoning is well-researched in AI, calculations about the threshold ofpersuasion in litigation, whatever their value, are just the tip of theiceberg. The bulk of the modeling desiderata is arguably elsewhere, if one isto ideally make the most of AI's distinctive contribution as envisaged forlegal evidence research.

[Book review] Theory of Games and Economic Behaviour

Tony Mann provides a review of the book: Theory of Games and Economic Behavior, John von Neumann and Oskar Morgenstern, Princeton University Press, 1944.

What is the value of technology? Toward a labour theory of technology change

Economic analysis of technology treats it as given exogenously, while determined endogenously. This paper examines the conceptual conflict. The paper outlines an alternative conceptual framework. This uses a 'General Vertical Division of Labour' into conceptual and executive parts to facilitate a coherent political economic explanation of technological change. The paper suggests that we may acquire rather than impose an understanding of technological change. It also suggests that we may re-define and reassess the efficiency of technological change, through the values inculcated into it.

Grandparents and parenting: towards a theory of grandparenthood

This paper explores the changing role of contemporary grandparents with many demonstrating a willingness and ability to take on parental responsibilities for their grandchildren, where they may face challenges and opportunities in difficult times. Three main forms of grand parenting are identified in the literature, those who have primary responsibility and are raising their grand children as their main carers perhaps in response to crisis situations, those who live in extended families and participate in care, and those who provide day care while the child’s parents work. The latter has increased because of the increasing frequency of divorce, single parenting and the lack of available or subsidised child care in the United Kingdom. When grandparents step into a troubled situation and attempt to offer stability and security for their grandchildren they may have to manage the combined responsibilities of family caregivers and parental figures. Grandparenthood is a tenuous role, lacking clear agreement on behaviour norms. In the culture of advice and parenting support, while care must be taken not to undermine parenting skills or make judgements about the ability to cope with the demands of childcare, an exploration of the impact on grandparents and children must be undertaken. Due to the complex web of interrelated factors the process and outcomes of care giving by grandparents is not well known in the literature. It is proposed therefore that it is timely for research to be undertaken to explore and develop a theory of Grandparenthood.

Latitudinal phytoplankton distribution and the neutral theory of biodiversity

Aim Recent studies have suggested that global diatom distributions are not limited by dispersal, in the case of both extant species and fossil species, but rather that environmental filtering explains their spatial patterns. Hubbell's neutral theory of biodiversity provides a framework in which to test these alternatives. Our aim is to test whether the structure of marine phytoplankton (diatoms, dinoflagellates and coccolithophores) assemblages across the Atlantic agrees with neutral theory predictions. We asked: (1) whether intersite variance in phytoplankton diversity is explained predominantly by dispersal limitation or by environmental conditions; and (2) whether species abundance distributions are consistent with those expected by the neutral model. Location Meridional transect of the Atlantic (50 degrees N50 degrees S). Methods We estimated the relative contributions of environmental factors and geographic distance to phytoplankton composition using similarity matrices, Mantel tests and variation partitioning of the species composition based upon canonical ordination methods. We compared the species abundance distribution of phytoplankton with the neutral model using Etienne's maximum-likelihood inference method. Results Phytoplankton communities are slightly more determined by niche segregation (24%), than by dispersal limitation and ecological drift (17%). In 60% of communities, the assumption of neutrality in species' abundance distributions could not be rejected. In tropical zones, where oceanic gyres enclose large stable water masses, most communities showed low species immigration rates; in contrast, we infer that communities in temperate areas, out of oligotrophic gyres, have higher rates of species immigration. Conclusions Phytoplankton community structure is consistent with partial niche assembly and partial dispersal and drift assembly (neutral processes). The role of dispersal limitation is almost as important as habitat filtering, a fact that has been largely overlooked in previous studies. Furthermore, the polewards increase in immigration rates of species that we have discovered is probably caused by water mixing conditions and productivity.

Dazed and Confused: Accidental Mixtures of Goods and the Theory of Acquisition of Title

This paper explores the law of accidental mixtures of goods. It traces the development of the English rules on mixture from the seminal nineteenth century case of Spence v Union Marine Insurance Co to the present day, and compares their responses to those given by the Roman law, which always has been claimed as an influence on our jurisprudence in this area. It is argued that the different answers given by English and Roman law to essentially the same problems of title result from the differing bases of these legal systems. Roman a priori theory is contrasted with the more practical reasoning of the common law, and while both sets of rules are judged to be coherent on their own terms, it is suggested that the difference between them is reflective of a more general philosophical disagreement about the proper functioning of a legal system, and the relative importance of theoretical and pragmatic considerations.

Explaining binge drinking among adolescent males using the Theory of Planned Behaviour

Binge drinking among adolescents in Northern Ireland is prevalent and has detrimental eff ects on public health. Health education interventions, based on valid explanatory models of health behaviour, are required to reduce binge drinking behaviour among adolescents. " is paper examines the utility of the " eory of Planned Behaviour in explaining binge drinking behaviour among adolescent males. Using questionnaire responses from 94 adolescent boys attending secondary schools in the Belfast area, logistic regression modelling suggested that the " eory of Planned Behaviour explained 36% of the variance in self-reported binge drinking behaviour. Attitudes towards binge drinking were the strongest predictor of binge drinking behaviour. Tackling attitudes about binge drinking is a challenge to be considered when designing interventions to reduce binge drinking among this population