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.

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.

The island-scale internal wave climate of Moorea, French Polynesia

Analysis of five-year records of temperatures and currents collected at Moorea reveal strong internal wave activity at predominantly semi-diurnal frequencies impacting reef slopes at depths 30m around the entire island. Temperature changes of 1.5C to 3C are accompanied by surges of upward and onshore flow and vertical shear in onshore currents. Superimposed on annual temperature changes of approximately 3C, internal wave activity is high from Oct-May and markedly lower from Jun-Sep. The offshore pycnocline is broadly distributed with continuous stratification to at least 500m depth, and a subsurface fluorescence maximum above the strong nutricline at approximately 200m. Minimum buoyancy periods range from 4.8 to 6min, with the maximum density gradient occurring at 50 to 60m depth in summer and deepening to approximately 150 to 200m in winter. The bottom slope angle around all of Moorea is super-critical relative to the vertical stratification angle suggesting that energy propagating into shallow water is only a portion of total incident internal wave energy. Vertical gradient Richardson numbers indicate dominance by density stability relative to current shear with relatively limited diapycnal mixing. Coherence and lagged cross-correlation of semi-diurnal temperature variation indicate complex patterns of inter-site arrival of internal waves and no clear coherence or lagged correlation relationships among island sides. Semi-diurnal and high frequency internal wave packets likely arrive on Moorea from a combination of local and distant sources and may have important impacts for nutrient and particle fluxes in deep reef environments. © 2012 American Geophysical Union. All Rights Reserved.

Inversion of light scattering data by singular system analysis

We consider the problem of inverting experimental data obtained in light scattering experiments described by linear theories. We discuss applications to particle sizing and we describe fast and easy-to-implement algorithms which permit the extraction, from noisy measurements, of reliable information about the particle size distribution. © 1987, SPIE.

Continuous-wave operation of a modulational instability laser

post-deadline paper

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.

Spaces of observation and obscurity: cinematic prisons of light and dark

In The Eye of Power, Foucault delineated the key concerns surrounding hospital architecture in the latter half of the eighteenth century as being the ‘visibility of bodies, individuals and things'. As such, the ‘new form of hospital' that came to be developed ‘was at once the effect and support of a new type of gaze'. This was a gaze that was not simply concerned with ways of minimising overcrowding or cross-contamination. Rather, this was a surveillance intended to produce knowledge about the pathological bodies contained within the hospital walls. This would then allow for their appropriate classification. Foucault went on to describe how these principles came to be applied to the architecture of prisons. This was exemplified for him in the distinct shape of Bentham's panopticon. This circular design, which has subsequently become an often misused synonym for a contemporary culture of surveillance, was premised on a binary of the seen and the not-seen. An individual observer could stand at the central point of the circle and observe the cells (and their occupants) on the perimeter whilst themselves remaining unseen. The panopticon in its purest form was never constructed, yet it conveys the significance of the production of knowledge through observation that became central to institutional design at this time and modern thought more broadly. What is curious though is that whilst the aim of those late eighteenth century buildings was to produce wellventilated spaces suffused with light, this provoked an interest in its opposite. The gothic movement in literature that was developing in parallel conversely took a ‘fantasy world of stone walls, darkness, hideouts and dungeons…' as its landscape (Vidler, 1992: 162). Curiously, despite these modern developments in prison design, the façade took on these characteristics. The gothic imagination came to describe that unseen world that lay behind the outer wall. This is what Evans refers to as an architectural ‘hoax'. The façade was taken to represent the world within the prison walls and it was the façade that came to inform the popular imagination about what occurred behind it. The rational, modern principles ordering the prison became conflated with the meanings projected by and onto the façade. This confusion of meanings have then been repeated and reenforced in the subsequent representations of the prison. This is of paramount importance since it is the cinematic and televisual representation of the prison, as I argue here and elsewhere, that maintain this erroneous set of meanings, this ‘hoax'.

Paying the price for loss of light

Considers the Court of Appeal ruling in Forsyth-Grant v Allen on the principles to be applied in assessing damages for the loss of light. Outlines the method for calculating damages for loss of right to light, the type of amenity which will be included in calculations for loss of amenity and the process applied in this case for assessing damages arising from the loss of profits that would have been made by the owner of the right to light if they had negotiated to relax the covenant, with reference to case law. Notes the limits to damages available for hypothetical loss and the difference between this award of profits and an account of profits.

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.