Upper and lower bounds on the learning curve for Gaussian processes

In this paper we introduce and illustrate non-trivial upper and lower bounds on the learning curves for one-dimensional Gaussian Processes. The analysis is carried out emphasising the effects induced on the bounds by the smoothness of the random process described by the Modified Bessel and the Squared Exponential covariance functions. We present an explanation of the early, linearly-decreasing behavior of the learning curves and the bounds as well as a study of the asymptotic behavior of the curves. The effects of the noise level and the lengthscale on the tightness of the bounds are also discussed.

Between safety and vulnerability:the exiled other of international relations

Inspired by the idea of safe citizenship this article queries the possibilities of safety in an age of securitization. It challenges the cosmopolitan worldview and its iteration of a global cosmopolitan citizen. It champions an account of affective citizenship, narration and attends to the trauma of exile. It offers an account of exile before suggesting an institutional design premised on politicization. This design, it is argued, facilitates moments of storytelling fostering individual empowerment. This unorthodox rendering of agency allows the traumatized exile to negotiate the world as it is, not as it could be, as a potential ‘safe’ citizen.

A two-factor model of the U.K. yield curve

I model the forward premium in the U.K. gilt-edged market over the period 1982–96 using a two-factor general equilibrium model of the term structure of interest rates. The model permits the decomposition of the forward premium into separate components representing interest rate expectations, the risk premia associated with each of the underlying factors, and terms capturing the direct impact of the variances of the factors on the shape of the forward curve.

Factors determining the growth curve of the foliose lichen Parmelia conspersa

Growth curves of the foliose lichen Parmelia conspersa (Ehrh. Ex Ach.)Ach. Were obtained by plotting radial growth (RGR, mm yr-1) of the fastest measured lobe, the slowest measured lobe, a randomly selected lobe, and by averaging a sample of lobes from each thallus against thallus diameter. Growth curves derived from the fastest-growing lobe and by averaging lobes were asymptotic and could be fitted by the growth model of Aplin and Hill. Mean lobe width increased with thallus size, reaching a maximum at approx. 4.5 cm thallus diameter. In four out of six thalli, radial growth of lobes over four months was positively correlated with initial lobe width or area. The RGR of isolated lobes was unaffected until the base of the lobe was removed to within 1-2 mm of the tip. The concentration (micrograms mg-1 biomass) of ribitol, arabitol and mannitol was greater in the marginal lobes of large than in small thalli. The results suggested that the growth curve of P. conspersa is determined by processes that occur within individual marginal lobes and can be explained by the Aplin and Hill model. Changes in lobe width and in the productive capacity of individual lobes with thallus size are likely to be more important factors than the degree of translocation within the lobe in determining the growth curve.

Growth curve of the lichen Rhizocarpon geographicum

Data on the growth curve of the lichen Rhizocarpon geographicum were obtained by measuring the radial growth rates (mm per 1.5 years) of 39 thalli from 2 to 65 mm in diameter growing in the same environment. An Aplin and Hill plot (r2 – r1 against ln r2 – ln r1) of the data and regression analyses suggested an initial phase of growth (up to a diameter of about 7 mm) in which the relative growth rate increased rapidly. This was followed by a phase in which the relative growth rate fell but the radial growth rate continued to rise (7 to 20 mm in diameter). Radial growth was then relatively constant until about 45 mm diameter and then declined. The Aplin and Hill model did not fit the data as a whole but may apply for a transient period in thalli between about 7 and 16 mm in diameter. The curve shows some similarities to that suggested by lichenometric studies but differs in showing a less steep decline in growth rate after the ‘great’ period.

Statnote 19: non-linear regression: fitting an exponential curve to data

Non-linear relationships are common in microbiological research and often necessitate the use of the statistical techniques of non-linear regression or curve fitting. In some circumstances, the investigator may wish to fit an exponential model to the data, i.e., to test the hypothesis that a quantity Y either increases or decays exponentially with increasing X. This type of model is straight forward to fit as taking logarithms of the Y variable linearises the relationship which can then be treated by the methods of linear regression.

Statnote 20: non-linear regression: fitting a general polynomial curve

In some circumstances, there may be no scientific model of the relationship between X and Y that can be specified in advance and indeed the objective of the investigation may be to provide a ‘curve of best fit’ for predictive purposes. In such an example, the fitting of successive polynomials may be the best approach. There are various strategies to decide on the polynomial of best fit depending on the objectives of the investigation.

Abnormal left and right amygdala-orbitofrontal cortical functional connectivity to emotional faces:state versus trait vulnerability markers of depression in bipolar disorder

Background - Amygdala-orbitofrontal cortical (OFC) functional connectivity (FC) to emotional stimuli and relationships with white matter remain little examined in bipolar disorder individuals (BD). Methods - Thirty-one BD (type I; n = 17 remitted; n = 14 depressed) and 24 age- and gender-ratio-matched healthy individuals (HC) viewed neutral, mild, and intense happy or sad emotional faces in two experiments. The FC was computed as linear and nonlinear dependence measures between amygdala and OFC time series. Effects of group, laterality, and emotion intensity upon amygdala-OFC FC and amygdala-OFC FC white matter fractional anisotropy (FA) relationships were examined. Results - The BD versus HC showed significantly greater right amygdala-OFC FC (p = .001) in the sad experiment and significantly reduced bilateral amygdala-OFC FC (p = .007) in the happy experiment. Depressed but not remitted female BD versus female HC showed significantly greater left amygdala-OFC FC (p = .001) to all faces in the sad experiment and reduced bilateral amygdala-OFC FC to intense happy faces (p = .01). There was a significant nonlinear relationship (p = .001) between left amygdala-OFC FC to sad faces and FA in HC. In BD, antidepressants were associated with significantly reduced left amygdala-OFC FC to mild sad faces (p = .001). Conclusions - In BD, abnormally elevated right amygdala-OFC FC to sad stimuli might represent a trait vulnerability for depression, whereas abnormally elevated left amygdala-OFC FC to sad stimuli and abnormally reduced amygdala-OFC FC to intense happy stimuli might represent a depression state marker. Abnormal FC measures might normalize with antidepressant medications in BD. Nonlinear amygdala-OFC FC–FA relationships in BD and HC require further study.

Perception of risk, feelings of vulnerability and effects on driving behaviour in women drivers across the lifespan.

Sustained driving in older age has implications for quality of life and mental health. Studies have shown that despite the recognised importance of driving in maintaining health and social engagement, many women give up driving prematurely or adopt self-imposed restrictive driving practices. Emotional responses to driving have been implicated in these decisions. This research examined the effect of risk perception and feelings of vulnerability on women’s driving behaviour across the lifespan. It also developed and tested a modified theory of planned behaviour intervention to positively affect driving habits. The first two studies (N=395) used quantitative analysis to model driving behaviours affected by risk perception and feelings of vulnerability, and established that feelings of vulnerability do indeed affect women’s driving behaviour, specifically resulting in increases in driving avoidance and the adoption of maladaptive driving styles. Further, that self-regulation, conceptualised as avoidance, is used by drivers across the lifespan. Qualitative analysis of focus group data (N=48) in the third study provided a deeper understanding of the variations in coping behaviours adopted by sub-groups of drivers and extended the definition of self-regulation to incorporate adaptive coping strategies. The next study (N=64) reported the construction and preliminary validation of the novel self-regulation index (SRI) to measure wider self-regulation behaviours using an objective measure of driving behaviour, a simulated driving task. The understanding gained from the formative research was used in the final study, an extended theory of planned behaviour intervention to promote wider self-regulation behaviour, measured using the previously validated self-regulation index. The intervention achieved moderate success with changes in affective attitude and normative beliefs as well as self-reported behaviour. The results offer promise for self-regulation, incorporating a spectrum of planning and coping behaviours, to be used as a mechanism to assist drivers in achieving their personal mobility goals whilst promoting safe driving.

Evaluating the environmental Kuznets curve

We examine the empirical evidence for an environmental Kuznets curve using a semiparametric smooth coefficient regression model that allows us to incorporate flexibility in the parameter estimates, while maintaining the basic econometric structure that is typically used to estimate the pollution-income relationship. This allows us to assess the sensitivity to parameter heterogeneity of typical parametric models used to estimate the relationship between pollution and income, as well as identify why the results from such models are seldom found to be robust. Our results confirm that the resulting relationship between pollution and income is fragile; we show that the estimated pollution-income relationship depends substantially on the heterogeneity of the slope coefficients and the parameter values at which the relationship is evaluated. Different sets of parameters obtained from the semiparametric model give rise to many different shapes for the pollution-income relationship that are commonly found in the literature.

Watermark-only security attack on DM-QIM watermarking:vulnerability to guided key guessing

This paper addresses the security of a specific class of common watermarking methods based on Dither modulation-quantisation index modulation (DM-QIM) and focusing on watermark-only attacks (WOA). The vulnerabilities of and probable attacks on lattice structure based watermark embedding methods have been presented in the literature. DM-QIM is one of the best known lattice structure based watermarking techniques. In this paper, the authors discuss a watermark-only attack scenario (the attacker has access to a single watermarked content only). In the literature it is an assumption that DM-QIM methods are secure to WOA. However, the authors show that the DM-QIM based embedding method is vulnerable against a guided key guessing attack by exploiting subtle statistical regularities in the feature space embeddings for time series and images. Using a distribution-free algorithm, this paper presents an analysis of the attack and numerical results for multiple examples of image and time series data.

Watermark-only security attack on DM-QIM watermarking:vulnerability to guided key guessing

This paper addresses the security of a specific class of common watermarking methods based on Dither modulation-quantisation index modulation (DM-QIM) and focusing on watermark-only attacks (WOA). The vulnerabilities of and probable attacks on lattice structure based watermark embedding methods have been presented in the literature. DM-QIM is one of the best known lattice structure based watermarking techniques. In this paper, the authors discuss a watermark-only attack scenario (the attacker has access to a single watermarked content only). In the literature it is an assumption that DM-QIM methods are secure to WOA. However, the authors show that the DM-QIM based embedding method is vulnerable against a guided key guessing attack by exploiting subtle statistical regularities in the feature space embeddings for time series and images. Using a distribution-free algorithm, this paper presents an analysis of the attack and numerical results for multiple examples of image and time series data.

Laminar distribution of the pathological changes in sporadic frontotemporal lobar degeneration with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy:a quantitative study using polynomial curve fitting

Aims: Previous data suggest heterogeneity in laminar distribution of the pathology in the molecular disorder frontotemporal lobar degeneration (FTLD) with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy (FTLD-TDP). To study this heterogeneity, we quantified the changes in density across the cortical laminae of neuronal cytoplasmic inclusions, glial inclusions, neuronal intranuclear inclusions, dystrophic neurites, surviving neurones, abnormally enlarged neurones, and vacuoles in regions of the frontal and temporal lobe. Methods: Changes in density of histological features across cortical gyri were studied in 10 sporadic cases of FTLD-TDP using quantitative methods and polynomial curve fitting. Results: Our data suggest that laminar neuropathology in sporadic FTLD-TDP is highly variable. Most commonly, neuronal cytoplasmic inclusions, dystrophic neurites and vacuolation were abundant in the upper laminae and glial inclusions, neuronal intranuclear inclusions, abnormally enlarged neurones, and glial cell nuclei in the lower laminae. TDP-43-immunoreactive inclusions affected more of the cortical profile in longer duration cases; their distribution varied with disease subtype, but was unrelated to Braak tangle score. Different TDP-43-immunoreactive inclusions were not spatially correlated. Conclusions: Laminar distribution of pathological features in 10 sporadic cases of FTLD-TDP is heterogeneous and may be accounted for, in part, by disease subtype and disease duration. In addition, the feedforward and feedback cortico-cortical connections may be compromised in FTLD-TDP. © 2012 The Authors. Neuropathology and Applied Neurobiology © 2012 British Neuropathological Society.