The relative order and inverses of recurrent networks

Differential geometry is used to investigate the structure of neural-network-based control systems. The key aspect is relative order—an invariant property of dynamic systems. Finite relative order allows the specification of a minimal architecture for a recurrent network. Any system with finite relative order has a left inverse. It is shown that a recurrent network with finite relative order has a local inverse that is also a recurrent network with the same weights. The results have implications for the use of recurrent networks in the inverse-model-based control of nonlinear systems.

The strength of the system and my experiences of it, was that in fact, oddly enough, it was actually a very collaborative enterprise already

Video:35 mins, 2006. The video shows a group of performers in a studio and seminar situation. Individually addressing the camera they offer personal views and experiences of their own art production in relation to the institution, while reflecting on their role as teachers. The performance scripts mainly originate from a series of real interviews with a diverse group of artist teachers, who emphasise the collaborative, performative and subversive nature of teaching. These views may seems symptomatic for contemporary art practices, but are ultimately antagonistic to the ongoing commodification of the system of art education.

Low-order dynamical behavior in the martian atmosphere: Diagnosis of general circulation model results

The hypothesis of a low dimensional martian climate attractor is investigated by the application of the proper orthogonal decomposition (POD) to a simulation of martian atmospheric circulation using the UK Mars general circulation model (UK-MGCM). In this article we focus on a time series of the interval between autumn and winter in the northern hemisphere, when baroclinic activity is intense. The POD is a statistical technique that allows the attribution of total energy (TE) to particular structures embedded in the UK-MGCM time-evolving circulation. These structures are called empirical orthogonal functions (EOFs). Ordering the EOFs according to their associated energy content, we were able to determine the necessary number to account for a chosen amount of atmospheric TE. We show that for Mars a large fraction of TE is explained by just a few EOFs (with 90% TE in 23 EOFs), which apparently support the initial hypothesis. We also show that the resulting EOFs represent classical types of atmospheric motion, such as thermal tides and transient waves. Thus, POD is shown to be an efficient method for the identification of different classes of atmospheric modes. It also provides insight into the non-linear interaction of these modes.

Effects of polydispersity on the order-disorder transition of diblock copolymer melts

The effect of polydispersity on an AB diblock copolymer melt is investigated using latticebased Monte Carlo simulations. We consider melts of symmetric composition, where the B blocks are monodisperse and the A blocks are polydisperse with a Schultz-Zimm distribution. In agreement with experiment and self-consistent field theory (SCFT), we find that polydispersity causes a significant increase in domain size. It also induces a transition from flat to curved interfaces, with the polydisperse blocks residing on the inside of the interfacial curvature. Most importantly, the simulations show a relatively small shift in the order-disorder transition (ODT) in agreement with experiment, whereas SCFT incorrectly predicts a sizable shift towards higher temperatures.

Randomized controlled trial of full and brief cognitive-behaviour therapy and wait-list for paediatric obsessive-compulsive disorder

Background: Reviews and practice guidelines for paediatric obsessive-compulsive disorder (OCD) recommend cognitive-behaviour therapy (CBT) as the psychological treatment of choice, but note that it has not been sufficiently evaluated for children and adolescents and that more randomized controlled trials are needed. The aim of this trial was to evaluate effectiveness and optimal delivery of CBT, emphasizing cognitive interventions. Methods: A total of 96 children and adolescents with OCD were randomly allocated to the three conditions each of approximately 12 weeks duration: full CBT (average therapist contact: 12 sessions) and brief CBT (average contact: 5 sessions, with use of therapist-guided workbooks), and wait-list/delayed treatment. The primary outcome measure was the child version of the semi-structured interviewer-based Yale-Brown Obsessive Compulsive Scale. Clinical Trial registration: http://www.controlled-trials.com/ISRCTN/; unique identifier: ISRCTN29092580. Results: There was statistically significant symptomatic improvement in both treatment groups compared with the wait-list group, with no significant differences in outcomes between the two treatment groups. Controlled treatment effect sizes in intention-to-treat analyses were 2.2 for full CBT and 1.6 for brief CBT. Improvements were maintained at follow-up an average of 14 weeks later. Conclusions: The findings demonstrate the benefits of CBT emphasizing cognitive interventions for children and adolescents with OCD and suggest that relatively lower therapist intensity delivery with use of therapist-guided workbooks is an efficient mode of delivery.

Stable reduced-order models for discrete-time systems

The Routh-stability method is employed to reduce the order of discrete-time system transfer functions. It is shown that the Routh approximant is well suited to reduce both the denominator and the numerator polynomials, although alternative methods, such as PadÃ�Â(c)-Markov approximation, are also used to fit the model numerator coefficients.

A new approach to reduced-order modelling

An error polynomial is defined, the coefficients of which indicate the difference at any instant between a system and a model of lower order approximating the system. It is shown how Markov parameters and time series proportionals of the model can be matched with those of the system by setting error polynomial coefficients to zero. Also discussed is the way in which the error between system and model can be considered as being a filtered form of an error input function specified by means of model parameter selection.

State estimation using model order reduction for unstable systems

The problem of state estimation occurs in many applications of fluid flow. For example, to produce a reliable weather forecast it is essential to find the best possible estimate of the true state of the atmosphere. To find this best estimate a nonlinear least squares problem has to be solved subject to dynamical system constraints. Usually this is solved iteratively by an approximate Gauss–Newton method where the underlying discrete linear system is in general unstable. In this paper we propose a new method for deriving low order approximations to the problem based on a recently developed model reduction method for unstable systems. To illustrate the theoretical results, numerical experiments are performed using a two-dimensional Eady model – a simple model of baroclinic instability, which is the dominant mechanism for the growth of storms at mid-latitudes. It is a suitable test model to show the benefit that may be obtained by using model reduction techniques to approximate unstable systems within the state estimation problem.

Exploring the construction of social class in educational discourse: the rational order of the nation state vs. global uncertainties

This article aims to create intellectual space in which issues of social inequality and education can be analyzed and discussed in relation to the multifaceted and multi-levelled complexities of the modern world. It is divided into three sections. Section One locates the concept of social class in the context of the modern nation state during the period after the Second World War. Focusing particularly on the impact of ‘Fordism’ on social organization and cultural relations, it revisits the articulation of social justice issues in the United Kingdom, and the structures put into place at the time to alleviate educational and social inequalities. Section Two problematizes the traditional concept of social class in relation to economic, technological and sociocultural changes that have taken place around the world since the mid-1980s. In particular, it charts some of the changes to the international labour market and global patterns of consumption, and their collective impact on the re-constitution of class boundaries in ‘developed countries’. This is juxtaposed with some of the major social effects of neo-classical economic policies in recent years on the sociocultural base in developing countries. It discusses some of the ways these inequalities are reflected in education. Section Three explores tensions between the educational ideals of the ‘knowledge economy’ and the discursive range of social inequalities that are emerging within and beyond the nation state. Drawing on key motifs identified throughout, the article concludes with a reassessment of the concept of social class within the global cultural economy. This is discussed in relation to some of the major equity and human rights issues in education today.

Electro-optical properties of liquid crystal copolymers and their relationship to structural order

A range of side chain liquid crystal copolymers have been prepared using mesogenic and non-mesogenic units. It is found that high levels of the non-mesogenic moieties may be introduced without completely disrupting the organization of the liquid crystal phase. Incorporation of this comonomer causes a marked reduction in the glass transition temperature (Tg), presumably as a result of enhanced backbone mobility and a corresponding lowering of the nematic transition temperature, thereby restricting the temperature range for stability of the liquid crystal phase. The effect of the interactions between the various components of these side-chain polymers on their electro-optic responses is described. Infrared (i.r.) dichroism measurements have been made to determine the order parameters of the liquid crystalline side-chain polymers. By identifying a certain band (CN stretching) in the i.r. absorption spectrum, the order parameter of the mesogenic groups can be obtained. The temperature and composition dependence of the observed order parameter are related to the liquid crystal phase transitions and to the electro-optic response. It is found that the introduction of the non-mesogenic units into the polymer chain lowers the threshold voltage of the electro-optic response over and above that due to the reduction in the order parameter. The dynamic electro-optic responses are dominated by the temperature-dependent viscosity and evidence is presented for relaxation processes involving the polymer backbone which are on a time scale greater than that for the mesogenic side-chain units.

Making robust policy decision using global biodiversity indicators

In order to influence global policy effectively, conservation scientists need to be able to provide robust predictions of the impact of alternative policies on biodiversity and measure progress towards goals using reliable indicators. We present a framework for using biodiversity indicators predictively to inform policy choices at a global level. The approach is illustrated with two case studies in which we project forwards the impacts of feasible policies on trends in biodiversity and in relevant indicators. The policies are based on targets agreed at the Convention on Biological Diversity (CBD) meeting in Nagoya in October 2010. The first case study compares protected area policies for African mammals, assessed using the Red List Index; the second example uses the Living Planet Index to assess the impact of a complete halt, versus a reduction, in bottom trawling. In the protected areas example, we find that the indicator can aid in decision-making because it is able to differentiate between the impacts of the different policies. In the bottom trawling example, the indicator exhibits some counter-intuitive behaviour, due to over-representation of some taxonomic and functional groups in the indicator, and contrasting impacts of the policies on different groups caused by trophic interactions. Our results support the need for further research on how to use predictive models and indicators to credibly track trends and inform policy. To be useful and relevant, scientists must make testable predictions about the impact of global policy on biodiversity to ensure that targets such as those set at Nagoya catalyse effective and measurable change.

Rights, the environment and Part V of the Criminal Justice and Public Order Act 1994

Using figures derived from the UK Home Office, this paper analyses and reviews the impact and deployment of Part V of the Criminal Justice and Public Order Act 1994 since its enactment. This is done with special reference to its impact on citizenship and the regulation of ‘the environment’ and associated rural spaces. It is argued that, notwithstanding the actual use of the public order clauses in Part V of the Act, its underlying meanings are largely of a symbolic nature. Such symbolism is, however, a powerful indication of the defence of particularist constructions of rural space. It can also open out new conditions of possibility, providing a useful ‘oppressed’ status and media spectacle for a range of protesters and activists.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

A low-order model investigation of the analysis of gravity waves in the ensemble Kalman filter.

The behavior of the ensemble Kalman filter (EnKF) is examined in the context of a model that exhibits a nonlinear chaotic (slow) vortical mode coupled to a linear (fast) gravity wave of a given amplitude and frequency. It is shown that accurate recovery of both modes is enhanced when covariances between fast and slow normal-mode variables (which reflect the slaving relations inherent in balanced dynamics) are modeled correctly. More ensemble members are needed to recover the fast, linear gravity wave than the slow, vortical motion. Although the EnKF tends to diverge in the analysis of the gravity wave, the filter divergence is stable and does not lead to a great loss of accuracy. Consequently, provided the ensemble is large enough and observations are made that reflect both time scales, the EnKF is able to recover both time scales more accurately than optimal interpolation (OI), which uses a static error covariance matrix. For OI it is also found to be problematic to observe the state at a frequency that is a subharmonic of the gravity wave frequency, a problem that is in part overcome by the EnKF.However, error in themodeled gravity wave parameters can be detrimental to the performance of the EnKF and remove its implied advantages, suggesting that a modified algorithm or a method for accounting for model error is needed.