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.

Cholinesterase inhibitors for dementia with Lewy bodies, Parkinson's disease dementia and cognitive impairment in Parkinson's disease

Background - Previous Cochrane reviews have considered the use of cholinesterase inhibitors in both Parkinson's disease with dementia (PDD) and dementia with Lewy bodies (DLB). The clinical features of DLB and PDD have much in common and are distinguished primarily on the basis of whether or not parkinsonism precedes dementia by more than a year. Patients with both conditions have particularly severe deficits in cortical levels of the neurotransmitter acetylcholine. Therefore, blocking its breakdown using cholinesterase inhibitors may lead to clinical improvement. Objectives - To assess the efficacy, safety and tolerability of cholinesterase inhibitors in dementia with Lewy bodies (DLB), Parkinson’s disease with dementia (PDD), and cognitive impairment in Parkinson’s disease falling short of dementia (CIND-PD) (considered as separate phenomena and also grouped together as Lewy body disease). Search methods - The trials were identified from a search of ALOIS, the Specialised Register of the Cochrane Dementia and Cognitive Improvement Group (on 30 August 2011) using the search terms Lewy, Parkinson, PDD, DLB, LBD. This register consists of records from major healthcare databases (MEDLINE, EMBASE, PsycINFO, CINAHL) and many ongoing trial databases and is updated regularly. Reference lists of relevant studies were searched for additional trials. Selection criteria - Randomised, double-blind, placebo-controlled trials assessing the efficacy of treatment with cholinesterase inhibitors in DLB, PDD and cognitive impairment in Parkinson’s disease (CIND-PD). Data collection and analysis - Data were extracted from published reports by one review author (MR). The data for each 'condition' (that is DLB, PDD or CIND-PD) were considered separately and, where possible, also pooled together. Statistical analysis was conducted using Review Manager version 5.0. Main results - Six trials met the inclusion criteria for this review, in which a total of 1236 participants were randomised. Four of the trials were of a parallel group design and two cross-over trials were included. Four of the trials included participants with a diagnosis of Parkinson's disease with dementia (Aarsland 2002a; Dubois 2007; Emre 2004; Ravina 2005), of which Dubois 2007 remains unpublished. Leroi 2004 included patients with cognitive impairment and Parkinson's disease (both with and without dementia). Patients with dementia with Lewy bodies (DLB) were included in only one of the trials (McKeith 2000). For global assessment, three trials comparing cholinesterase inhibitor treatment to placebo in PDD (Aarsland 2002a; Emre 2004; Ravina 2005) reported a difference in the Alzheimer's Disease Cooperative Study-Clinical Global Impression of Change (ADCS-CGIC) score of -0.38, favouring the cholinesterase inhibitors (95% CI -0.56 to -0.24, P < 0.0001). For cognitive function, a pooled estimate of the effect of cholinesterase inhibitors on cognitive function measures was consistent with the presence of a therapeutic benefit (standardised mean difference (SMD) -0.34, 95% CI -0.46 to -0.23, P < 0.00001). There was evidence of a positive effect of cholinesterase inhibitors on the Mini-Mental State Examination (MMSE) in patients with PDD (WMD 1.09, 95% CI 0.45 to 1.73, P = 0.0008) and in the single PDD and CIND-PD trial (WMD 1.05, 95% CI 0.42 to 1.68, P = 0.01) but not in the single DLB trial. For behavioural disturbance, analysis of the pooled continuous data relating to behavioural disturbance rating scales favoured treatment with cholinesterase inhibitors (SMD -0.20, 95% CI -0.36 to -0.04, P = 0.01). For activities of daily living, combined data for the ADCS and the Unified Parkinson's Disease Rating Scale (UPDRS) activities of daily living rating scales favoured treatment with cholinesterase inhibitors (SMD -0.20, 95% CI -0.38 to -0.02, P = 0.03). For safety and tolerability, those taking a cholinesterase inhibitor were more likely to experience an adverse event (318/452 versus 668/842; odds ratio (OR) 1.64, 95% CI 1.26 to 2.15, P = 0.0003) and to drop out (128/465 versus 45/279; OR 1.94, 95% CI 1.33 to 2.84, P = 0.0006). Adverse events were more common amongst those taking rivastigmine (357/421 versus 173/240; OR 2.28, 95% CI 1.53 to 3.38, P < 0.0001) but not those taking donepezil (311/421 versus 145/212; OR 1.24, 95% CI 0.86 to 1.80, P = 0.25). Parkinsonian symptoms in particular tremor (64/739 versus 12/352; OR 2.71, 95% CI 1.44 to 5.09, P = 0.002), but not falls (P = 0.39), were reported more commonly in the treatment group but this did not have a significant impact on the UPDRS (total and motor) scores (P = 0.71). Fewer deaths occurred in the treatment group than in the placebo group (4/465 versus 9/279; OR 0.28, 95% CI 0.09 to 0.84, P = 0.03). Authors' conclusions - The currently available evidence supports the use of cholinesterase inhibitors in patients with PDD, with a positive impact on global assessment, cognitive function, behavioural disturbance and activities of daily living rating scales. The effect in DLB remains unclear. There is no current disaggregated evidence to support their use in CIND-PD.

Superstructure fiber gratings via single step femtosecond laser inscription

We present the development of superstructure fiber gratings (SFG) in Ge-doped, silica optical fiber using femtosecond laser inscription. We apply a simple but extremely effective single step process to inscribe low loss, sampled gratings with minor polarization dependence. The method results in a controlled modulated index change with complete suppression of mode coupling associated with the overlapping LPG structure leading to highly symmetric superstructure spectra, with the grating reflection well within the Fourier design limit. The devices are characterized and compared with numerical modeling by solving Maxwell's equations and calculating the back reflection spectrum using the bidirectional beam propagation method (BiBPM). Experimental results validate our numerical analysis, allowing for the estimation of inscription parameters such as the ac index modulation change, and the wavelength, position and relative strength of each significant resonance peak. We also present results on temperature and refractive index measurements showing potential for sensing applications.

Factors preventing myopia progression with orthokeratology correction

PURPOSE: To examine which baseline measurements constitute predictive factors for axial length growth over 2 years in children wearing orthokeratology contact lenses (OK) and single-vision spectacles (SV). METHODS: Sixty-one children were prospectively assigned to wear either OK (n = 31) or SV (n = 30) for 2 years. The primary outcome measure (dependent variable) was axial length change at 2 years relative to baseline. Other measurements (independent variables) were age, age of myopia onset, gender, myopia progression 2 years before baseline and baseline myopia, anterior chamber depth, corneal power and shape (p value), and iris and pupil diameters as well as parental refraction. The contribution of all independent variables to the 2-year change in axial length was assessed using univariate and multivariate regression analyses. RESULTS: After univariate analyses, smaller increases in axial length were found in the OK group compared to the SV group in children who were older, had earlier onset of myopia, were female, had lower rate of myopia progression before baseline, had less myopia at baseline, had longer anterior chamber depth, had greater corneal power, had more prolate corneal shape, had larger iris diameter, had larger pupil sizes, and had lower levels of parental myopia (all p < 0.05). In multivariate analyses, older age and greater corneal power were associated with smaller increases in axial length in the OK group (both p < 0.05), whereas in SV wearers, smaller iris diameter was associated with smaller increases in axial length (p = 0.021). CONCLUSIONS: Orthokeratology is a successful treatment option in controlling axial elongation compared to SV in children of older age, had earlier onset of myopia, were female, had lower rate of myopia progression before baseline, had lower myopia at baseline, had longer anterior chamber depth, had greater corneal power, had more prolate corneal shape, had larger iris and pupil diameters, and had lower levels of parental myopia. © American Academy of Optometry.

Superstructure fiber gratings via single step femtosecond laser inscription

We present the development of superstructure fiber gratings (SFG) in Ge-doped, silica optical fiber using femtosecond laser inscription. We apply a simple but extremely effective single step process to inscribe low loss, sampled gratings with minor polarization dependence. The method results in a controlled modulated index change with complete suppression of mode coupling associated with the overlapping LPG structure leading to highly symmetric superstructure spectra, with the grating reflection well within the Fourier design limit. The devices are characterized and compared with numerical modeling by solving Maxwell's equations and calculating the back reflection spectrum using the bidirectional beam propagation method (BiBPM). Experimental results validate our numerical analysis, allowing for the estimation of inscription parameters such as the ac index modulation change, and the wavelength, position and relative strength of each significant resonance peak. We also present results on temperature and refractive index measurements showing potential for sensing applications.