In praise of partially interpretable predictors

Often there is an uninterpretable model that is statistically as good as, if not better than, a successful interpretable model. Accordingly, if one restricts attention to interpretable models, then one may sacrifice predictive power or other desirable properties. A minimal condition for an interpretable, usually parametric, model to be better than another model is that the first should have smallermean-squared error or integratedmean-squared error.We show through a series of examples that this is often not the case and give the asymptotic forms of a variety of interpretable, partially interpretable, and noninterpretable methods. We find techniques that combine aspects of both interpretability and noninterpretability in models seem to give the best results

Polarized Raman Scattering Studies of Orientational Order in Uniaxial Liquid Crystalline Phases

The measurement of vibrational Raman depolarization ratios has been used to study molecular orientational order in uniaxial single domain nematic and smectic liquid crystal samples. This technique is demonstrated to obtain the same microscopic order parameter $\langle P_2 \rangle =1/2 \langle 3 cos^2\theta −1 \rangle$, where $\theta$ is the angle between a molecular long axis and the uniaxial direction, as other existing methods. In addition, the next higher moment of the orientational distribution function $\langle P_4 \rangle=1/8 \langle 35 cos^4 \theta−30 cos^2 \theta+3 \rangle$ has been measured for the first time. The physical basis, theoretical apparatus, and experimental methods necessary for the application of this technique are thoroughly detailed in this paper. Measurements are presented of the temperature dependence of $\langle P_2 \rangle$ and $\langle P_4 \rangle$ of N‐(p'‐butoxybenzylidene)‐p‐cyanoaniline (BBCA) dissolved in N‐(p'‐methoxybenzylidene)‐p‐cyanoaniline (MBBA) and of pure MBBA in the isotropic and nematic phases, and in the isotropic, nematic, smectic A, and smectic B phases of N‐(p'‐butoxybenzylidene)‐p‐n‐octylaniline (40.8). In the nematic phases the new quantitative information marks significant discrepancies with existing theories of nematic ordering. In the smectic phases the results show unambiguously the anticipated high degree of molecular orientational order.Engineering and Applied Science

Using a prisoner advisory group to develop diversity research in a maximum-security prison

This paper addresses groupwork processes with a group of prisoners advising a research project in a maximum-security prison in England. The research project (Appreciative Inquiry into the Diversity Strategy of HMP Wakefield. RES-000-22-3441) was funded by the Economic and Social Research Council (ESRC) and lasted 9 months. The research explored the experiences of prisoners in diverse minority groupings and the strategies of the prison to accommodate the complex needs of these groups. The Prisoner Advisory Group (PAG) was made up of representatives from Black and Minority Ethnic (BME) prisoners; older prisoners (over 60s); Disabled prisoners (with physical disabilities, learning difficulties; and mental health problems); Gay, Bi-sexual and Transgender prisoners; and prisoners affiliated to Faith groups. It met regularly during the research. The paper considers the forming norming and performing aspects of establishing an effective participant voice in a prison-based project. It considers the contribution of the PAG to developing a research strategy that engaged prisoners in the research. It reflects on the nature of ‘participative research’ in general and whether such research is possible within a high-security prison environment

Performativity, fabrication and trust: exploring computer-mediated moderation

Based on research conducted in an English secondary school, this paper explores computer mediated moderation as a performative tool. The Module Assessment Meeting (MAM) was the moderation approach under investigation. I mobilise ethnographic data generated by a key informant, and triangulated with that from other actors in the setting, in order to examine some of the meanings underpinning moderation within a performative environment. Drawing on the work of Ball (2003), Lyotard (1979) and Foucault (1977, 1979), I argue that in this particular case performativity has become entrenched in teachers’ day-to-day practices, and not only affects those practices but also teachers’ sense of self. I suggest that MAM represented performative and fabricated conditions and (re)defined what the key participant experienced as a vital constituent of her educational identities - trust. From examining the case in point, I hope to have illustrated for those interested in teachers’ work some of the implications of the interface between technology and performativity

Error estimation and reduction with cross correlations

Besides the well-known effect of autocorrelations in time series of Monte Carlo simulation data resulting from the underlying Markov process, using the same data pool for computing various estimates entails additional cross correlations. This effect, if not properly taken into account, leads to systematically wrong error estimates for combined quantities. Using a straightforward recipe of data analysis employing the jackknife or similar resampling techniques, such problems can be avoided. In addition, a covariance analysis allows for the formulation of optimal estimators with often significantly reduced variance as compared to more conventional averages.Comment: 16 pages, RevTEX4, 4 figures, 6 tables, published versio

Identifying phase synchronization clusters in spatially extended dynamical systems

We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of both techniques is a matrix whose entries are the mean phase coherence values measured between pairs of time series. The first method is a mean field approach which allows to define the strength of participation of a subsystem in a single synchronization cluster. The second method is based on an eigenvalue decomposition from which a participation index is derived that characterizes the degree of involvement of a subsystem within multiple synchronization clusters. Simulating multiple clusters within a lattice of coupled Lorenz oscillators we explore the limitations and pitfalls of both methods and demonstrate (a) that the mean field approach is relatively robust even in configurations where the single cluster assumption is not entirely fulfilled, and (b) that the eigenvalue decomposition approach correctly identifies the simulated clusters even for low coupling strengths. Using the eigenvalue decomposition approach we studied spatiotemporal synchronization clusters in long-lasting multichannel EEG recordings from epilepsy patients and obtained results that fully confirm findings from well established neurophysiological examination techniques. Multivariate time series analysis methods such as synchronization cluster analysis that account for nonlinearities in the data are expected to provide complementary information which allows to gain deeper insights into the collective dynamics of spatially extended complex systems

Point process model of 1/f noise versus a sum of Lorentzians

We present a simple point process model of $1/f^{\beta}$ noise, covering different values of the exponent $\beta$. The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some interval resulting in the power-law distribution. Our model is free from the requirement of a wide distribution of relaxation times and from the power-law forms of the pulses. It contains only one relaxation rate and yields $1/f^ {\beta}$ spectra in a wide range of frequency. We obtain explicit expressions for the power spectra and present numerical illustrations of the model. Further we analyze the relation of the point process model of $1/f$ noise with the Bernamont-Surdin-McWhorter model, representing the signals as a sum of the uncorrelated components. We show that the point process model is complementary to the model based on the sum of signals with a wide-range distribution of the relaxation times. In contrast to the Gaussian distribution of the signal intensity of the sum of the uncorrelated components, the point process exhibits asymptotically a power-law distribution of the signal intensity. The developed multiplicative point process model of $1/f^{\beta}$ noise may be used for modeling and analysis of stochastic processes in different systems with the power-law distribution of the intensity of pulsing signals.Comment: 23 pages, 10 figures, to be published in Phys. Rev.

Curriculum is - or should be - at the heart of educational practice

First paragraph: We write our first Editorial as Lead Editors of The Curriculum Journal against the political backdrop of turbulent scenes in the UK Parliament. On 12 March 2019, Members of Parliament voted (for a second time) to categorically reject the Prime Minister’s ‘deal’ for exiting the European Union. The following day, they voted almost as decisively to reject a ‘no deal’ exit from the EU. Despite this, at the time of writing it is still quite possible that the UK is spiralling inexorably towards a chaotic (some would say catastrophic) no deal Brexit, with long term effects on the prosperity and wellbeing of its citizens, on its future trading relations with the rest of the world, and ultimately upon its international standing and reputation.Editoria

Raman Scattering from a Nematic Liquid Crystal: Orientational Statistics

Raman-scattering techniques have been used to obtain a new quantitative measure of orientational statistics of individual molecules in a nematic liquid crystal. A marked discrepancy is observed between these measurements and the predictions of existing theories of nematic ordering.Engineering and Applied Science