Application of the direct Liapunov method to the problem of symmetric stability in the atmosphere

The problem of symmetric stability is examined within the context of the direct Liapunov method. The sufficient conditions for stability derived by Fjørtoft are shown to imply finite-amplitude, normed stability. This finite-amplitude stability theorem is then used to obtain rigorous upper bounds on the saturation amplitude of disturbances to symmetrically unstable flows.By employing a virial functional, the necessary conditions for instability implied by the stability theorem are shown to be in fact sufficient for instability. The results of Ooyama are improved upon insofar as a tight two-sided (upper and lower) estimate is obtained of the growth rate of (modal or nonmodal) symmetric instabilities.The case of moist adiabatic systems is also considered.

Gaming and social interactions in the rehabilitation of brain injuries: a pilot study

Physical rehabilitation of brain injuries and strokes is a time consuming and costly process. Over the past decade several studies have emerged looking at the use of highly sophisticated technologies, such as robotics and virtual reality to tap into the needs of clinicians and patients. While such technologies can be a valuable tool to facilitate intensive movement practice in a motivating and engaging environment, success of therapy also depends on self-administered therapy beyond hospital stay. With the emergence of low-cost gaming consoles such as the Nintendo Wii, new opportunities arise for home-therapy paradigms centred on social interactions and values, which could reduce the sense of isolation and other depression related complications. In this paper we examine the potential, user acceptance and usability of an unmodified Nintendo Wii gaming console as a low-cost treatment alternative to complement current rehabilitation programmes.

Global asymptotic stability in a class of Putnam-type equations

In this paper, we initiate the study of a class of Putnam-type equation of the form x(n-1) = A(1)x(n) + A(2)x(n-1) + A(3)x(n-2)x(n-3) + A(4)/B(1)x(n)x(n-1) + B(2)x(n-2) + B(3)x(n-3) + B-4 n = 0, 1, 2,..., where A(1), A(2), A(3), A(4), B-1, B-2, B-3, B-4 are positive constants with A(1) + A(2) + A(3) + A(4) = B-1 + B-2 + B-3 + B-4, x(-3), x(-2), x(-1), x(0) are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point c = 1 of such equations. (c) 2005 Elsevier Ltd. All rights reserved.

Lorrie Moore collection, 'A Little Ethnic Kink Is Always Good to See”: Jewish performance anxiety and anti-passing in the fiction of Lorrie Moore

This essay explores the ways in which the performance of Jewish identity (in the sense both of representing Jewish characters and of writing about those characters’ conscious and unconscious renditions of their Jewishness) is a particular concern (in both senses of the word) for Lorrie Moore. Tracing Moore's representations of Jewishness over the course of her career, from the early story “The Jewish Hunter” through to her most recent novel, A Gate at the Stairs, I argue that it is characterized by (borrowing a phrase from Moore herself) “performance anxiety,” an anxiety that manifests itself in awkward comedy and that can be read both in biographical terms and as an oblique commentary on, or reworking of, the passing narrative, which I call “anti-passing.” Just as passing narratives complicate conventional ethno-racial definitions so Moore's anti-passing narratives, by representing Jews who represent themselves as other to themselves, as well as to WASP America, destabilize the category of Jewishness and, by implication, deconstruct the very notion of ethnic categorization.

House in the Shape of a Stretcher

In an essay from 1910 the architect and critic Adolf Loos distinguishes between buildings that are for everyday practical use and buildings made for contemplation. The latter type he asserts may be considered as both architecture and works of art. He refers to only two types of contemplative architecture namely the tomb and the monument. There are certain paintings made in the early part of the twentieth century that do not observe this separation such as certain works by Hopper and de Chirico. Here the commonplace is simultaneously experienced in the way a tomb might be. This mortifying gaze condemns building by inducing a sense that space has become inhospitable and alienating. It could be argued that these and other paintings made around this time such as Carlo Carra The Abandoned House 1916 are like premonitions of what will occur when building observes the prescription laid down by Loos and omit an aesthetic dimension. However it might also suggest that buildings need their tombs or at least some space that is not completely assimilable by the daily, practical and functional needs of an inhabitant.

The surprising role of orography in the initiation of an isolated thunderstorm in southern England

Many factors, both mesoscale and larger scale, often come together in order for a particular convective initiation to take place. The authors describe a modeling study of a case from the Convective Storms Initiation Project (CSIP) in which a single thunderstorm formed behind a front in the southern United Kingdom. The key features of the case were a tongue of low-level high θw air associated with a forward-sloping split front (overrunning lower θw air above), a convergence line, and a “lid” of high static stability air, which the shower was initially constrained below but later broke through. In this paper, the authors analyze the initiation of the storm, which can be traced back to a region of high ground (Dartmoor) at around 0700 UTC, in more detail using model sensitivity studies with the Met Office Unified Model (MetUM). It is established that the convergence line was initially caused by roughness effects but had a significant thermal component later. Dartmoor had a key role in the development of the thunderstorm. A period of asymmetric flow over the high ground, with stronger low-level descent in the lee, led to a hole in a layer of low-level clouds downstream. The surface solar heating through this hole, in combination with the tongue of low-level high θw air associated with the front, caused the shower to initiate with sufficient lifting to enable it later to break through the lid.

Nonlinear stability of continuously stratified quasi-geostrophic flow

Nonlinear stability theorems analogous to Arnol'd's second stability theorem are established for continuously stratified quasi-geostrophic flow with general nonlinear boundary conditions in a vertically and horizontally confined domain. Both the standard quasi-geostrophic model and the modified quasi-geostrophic model (incorporating effects of hydrostatic compressibility) are treated. The results establish explicit upper bounds on the disturbance energy, the disturbance potential enstrophy, and the disturbance available potential energy on the horizontal boundaries, in terms of the initial disturbance fields. Nonlinear stability in the sense of Liapunov is also established.

Nonlinear stability and the saturation of instabilities to axisymmetric vortices

Nonlinear stability theorems are presented for axisymmetric vortices under the restriction that the disturbance is independent of either the azimuthal or the axial coordinate. These stability theorems are then used, in both cases, to derive rigorous upper bounds on the saturation amplitudes of instabilities. Explicit examples of such bounds are worked out for some canonical profiles. The results establish a minimum order for the dependence of saturation amplitude on supercriticality, and are thereby suggestive as to the nature of the bifurcation at the stability threshold.

Social equality in the number of choice options is represented in the ventromedial prefrontal cortex

A distinct aspect of the sense of fairness in humans is that we care not only about equality in material rewards but also about equality in non-material values. One such value is the opportunity to choose freely among many options, often regarded as a fundamental right to economic freedom. In modern developed societies, equal opportunities in work, living, and lifestyle are enforced by anti-discrimination laws. Despite the widespread endorsement of equal opportunity, no studies have explored how people assign value to it. We used functional magnetic resonance imaging to identify the neural substrates for subjective valuation of equality in choice opportunity. Participants performed a two-person choice task in which the number of choices available was varied across trials independently of choice outcomes. By using this procedure, we manipulated the degree of equality in choice opportunity between players and dissociated it from the value of reward outcomes and their equality. We found that activation in the ventromedial prefrontal cortex tracked the degree to which the number of options between the two players was equal. In contrast, activation in the ventral striatum tracked the number of options available to participants themselves but not the equality between players. Our results demonstrate that the vmPFC, a key brain region previously implicated in the processing of social values, is also involved in valuation of equality in choice opportunity between individuals. These findings may provide valuable insight into the human ability to value equal opportunity, a characteristic long emphasized in politics, economics, and philosophy.

The notions of 'restriction' and 'discrimination' in the context of the free movement of persons provisions: from a relationship of interdependence to one of (almost complete) independence

This article aims to analyse how the meaning of the notions of ‘restrictions’ and ‘discrimination’ in EU free movement law has developed through the years, and to explore how the relationship between them has evolved. It is explained that the two concepts under examination had originally been closely intertwined, in the sense that one defined the other, the element holding them together being the aim of the relevant provisions to liberalise the inter-State movement of persons in the EU, as part of the process of establishing an internal market. Yet, more recently, the way that the Court has chosen to delimit their scope, illustrates that each of these notions can now have a life of its own, meaning that ‘discrimination’ can include discriminatory measures which do not lead to restrictions that are contrary to the free movement provisions, and ‘restriction’ can cover national measures that are not discriminatory.

Gap junctions and connexin hemichannels in the regulation of haemostasis and thrombosis

Platelets are involved in the maintenance of haemostasis but their inappropriate activation leads to thrombosis, a principal trigger for heart attack and ischemic stroke. Although platelets circulate in isolation, upon activation they accumulate or aggregate together to form a thrombus, where they function in a coordinated manner to prevent loss of blood and control wound repair. Recent reports indicate that the stability and functions of a thrombus are maintained through sustained, contact dependent signalling between platelets. Given the role of gap junctions in the coordination of tissue responses, it was hypothesized that gap junctions may be present within a thrombus and mediate intercellular communication between platelets. Therefore studies were performed to explore the presence and functions of connexins in platelets. In this brief review, the roles of hemichannels and gap junctions in the control of thrombosis and haemostasis and the future directions for this research will be discussed.

Parental responsibility beliefs: associations with parental anxiety and behaviours in the context of childhood anxiety disorders

Background: High levels of parental anxiety are associated with poor treatment outcomes for children with anxiety disorders. Associated parental cognitions and behaviours have been implicated as impediments to successful treatment. We examined the association between parental responsibility beliefs, maternal anxiety and parenting behaviours in the context of childhood anxiety disorders. Methods: Anxious and non-anxious mothers of 7-12 year old children with a current anxiety disorder reported their parental responsibility beliefs using a questionnaire measure. Parental behaviours towards their child during a stressor task were measured. Results: Parents with a current anxiety disorder reported a greater sense of responsibility for their child’s actions and wellbeing than parents who scored within the normal range for anxiety. Furthermore, higher parental responsibility was associated with more intrusive and less warm behaviours in parent-child interactions and there was an indirect effect between maternal anxiety and maternal intrusive behaviours via parental responsibility beliefs. Limitations: The sample was limited to a treatment-seeking, relatively high socio-economic population and only mothers were included so replication with more diverse groups is needed. The use of a range of stressor tasks may have allowed for a more comprehensive assessment of parental behaviours. Conclusions: The findings suggest that parental anxiety disorder is associated with an elevated sense of parental responsibility and may promote parental behaviours likely to inhibit optimum child treatment outcomes. Parental responsibility beliefs may therefore be important to target in child anxiety treatments in the context of parental anxiety disorders.

Intuitions in the Face of Diversity

In recent decades, intuitions' role in philosophy has been hotly debated. Many claim intuitions play an important role. Others, some armed with data, challenge the use of intuitions. This thesis reflects on this debate and advances the debate in two main ways. Having a clear understanding of the challenge which intuition-use in philosophy faces is important. Part I focuses on this. Chapters 1-2 introduce the topic of intuitions, motivate the methodological study of intuitions, and present the historical background to recent empirical challenges to intuition-use. Chapters 3-5 concern the contemporary challenge. I present the empirical evidence the challenge uses, present what I argue to be the strongest version of the challenge, and defend that challenge against some objections. How one characterises intuitions is incredibly important in philosophical methodology. If we are to properly evaluate philosophical methods vis-a-vis their use of something called intuitions { if we are to assess the empirical challenge { it is important to be clear exactly what we mean by `intuitions'. Part II focuses on this. Chapter 6 argues there is little consensus among philosophers as to what intuitions are and their role in philosophy. Chapter 7 questions whether philosophers have developed an idiolect in which `intuition' has distinctive meaning | as frequently supposed. Chapter 8 points out a common misunderstanding about intuitions in philosophy; using quantitative tools to challenge the idea that an increased use of `intuition' in philosophy is the result of an increased use of intuition. So, the developing picture is one of confusion, without a clear idea of what sense of `intuition' is important. Fortunately, Chapter 9 sets us back on the right track. It sets out a positive programme for evaluative methodology: methodologists should adopt a permissive conception of intuitions and make fine distinctions between different intuitions, so long as we can track those distinctions while philosophising.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.