General local and rectilinear vibrational coordinates consistent with Eckart's conditions

We present a general method to construct a set of local rectilinear vibrational coordinates for a nonlinear molecule whose reference structure does not necessarily correspond to a stationary point of the potential-energy surface. We show both analytically and with a numerical example that the vibrational coordinates satisfy Eckart's conditions. In addition, we find that the Watson Hamiltonian provides a fairly robust description even of highly excited vibrational states of triatomic molecules, except for a few states of large amplitude motion sampling the singular region of the Hamiltonian. These states can be identified through slow convergence.

Forward and backward least angle regression for nonlinear system identification

A forward and backward least angle regression (LAR) algorithm is proposed to construct the nonlinear autoregressive model with exogenous inputs (NARX) that is widely used to describe a large class of nonlinear dynamic systems. The main objective of this paper is to improve model sparsity and generalization performance of the original forward LAR algorithm. This is achieved by introducing a replacement scheme using an additional backward LAR stage. The backward stage replaces insignificant model terms selected by forward LAR with more significant ones, leading to an improved model in terms of the model compactness and performance. A numerical example to construct four types of NARX models, namely polynomials, radial basis function (RBF) networks, neuro fuzzy and wavelet networks, is presented to illustrate the effectiveness of the proposed technique in comparison with some popular methods.

Integrating geophysical data and upscaling techniques to support regional groundwater flow modelling: A practical example of the Lagan Valley, Northern Ireland

When studying heterogeneous aquifer systems, especially at regional scale, a degree of generalization is anticipated. This can be due to sparse sampling regimes, complex depositional environments or lack of accessibility to measure the subsurface. This can lead to an inaccurate conceptualization which can be detrimental when applied to groundwater flow models. It is important that numerical models are based on observed and accurate geological information and do not rely on the distribution of artificial aquifer properties. This can still be problematic as data will be modelled at a different scale to which it was collected. It is proposed here that integrating geophysics and upscaling techniques can assist in a more realistic and deterministic groundwater flow model. In this study, the sedimentary aquifer of the Lagan Valley in Northern Ireland is chosen due to intruding sub-vertical dolerite dykes. These dykes are of a lower permeability than the sandstone aquifer. The use of airborne magnetics allows the delineation of heterogeneities, confirmed by field analysis. Permeability measured at the field scale is then upscaled to different levels using a correlation with the geophysical data, creating equivalent parameters that can be directly imported into numerical groundwater flow models. These parameters include directional equivalent permeabilities and anisotropy. Several stages of upscaling are modelled in finite element. Initial modelling is providing promising results, especially at the intermediate scale, suggesting an accurate distribution of aquifer properties. This deterministic based methodology is being expanded to include stochastic methods of obtaining heterogeneity location based on airborne geophysical data. This is through the Direct Sample method of Multiple-Point Statistics (MPS). This method uses the magnetics as a training image to computationally determine a probabilistic occurrence of heterogeneity. There is also a need to apply the method to alternate geological contexts where the heterogeneity is of a higher permeability than the host rock.

Failure of a numerical quality assessment scale to identify potential risk of bias in a systematic review: a comparison study

BACKGROUND: Assessing methodological quality of primary studies is an essential component of systematic reviews. Following a systematic review which used a domain based system [United States Preventative Services Task Force (USPSTF)] to assess methodological quality, a commonly used numerical rating scale (Downs and Black) was also used to evaluate the included studies and comparisons were made between quality ratings assigned using the two different methods. Both tools were used to assess the 20 randomized and quasi-randomized controlled trials examining an exercise intervention for chronic musculoskeletal pain which were included in the review. Inter-rater reliability and levels of agreement were determined using intraclass correlation coefficients (ICC). Influence of quality on pooled effect size was examined by calculating the between group standardized mean difference (SMD).

RESULTS: Inter-rater reliability indicated at least substantial levels of agreement for the USPSTF system (ICC 0.85; 95% CI 0.66, 0.94) and Downs and Black scale (ICC 0.94; 95% CI 0.84, 0.97). Overall level of agreement between tools (ICC 0.80; 95% CI 0.57, 0.92) was also good. However, the USPSTF system identified a number of studies (n = 3/20) as "poor" due to potential risks of bias. Analysis revealed substantially greater pooled effect sizes in these studies (SMD -2.51; 95% CI -4.21, -0.82) compared to those rated as "fair" (SMD -0.45; 95% CI -0.65, -0.25) or "good" (SMD -0.38; 95% CI -0.69, -0.08).

CONCLUSIONS: In this example, use of a numerical rating scale failed to identify studies at increased risk of bias, and could have potentially led to imprecise estimates of treatment effect. Although based on a small number of included studies within an existing systematic review, we found the domain based system provided a more structured framework by which qualitative decisions concerning overall quality could be made, and was useful for detecting potential sources of bias in the available evidence.

Comprehensive numerical modelling of the performance of a second harmonic generation stage coupled with a low-gain optical parametric amplifier

We present a comprehensive model for predicting the full performance of a second harmonic generation-optical parametric amplification system that aims at enhancing the temporal contrast of laser pulses. The model simultaneously takes into account all the main parameters at play in the system such as the group velocity mismatch, the beam divergence, the spectral content, the pump depletion, and the length of the nonlinear crystals. We monitor the influence of the initial parameters of the input pulse and the interdependence of the two related non-linear processes on the performance of the system and show its optimum configuration. The influence of the initial beam divergence on the spectral and the temporal characteristics of the generated pulse is discussed. In addition, we show that using a crystal slightly longer than the optimum length and introducing small delay between the seed and the pump ensures maximum efficiency and compensates for the spectral shift in the optical parametric amplification stage in case of chirped input pulse. As an example, calculations for bandwidth transform limited and chirped pulses of sub-picosecond duration in beta barium borate crystal are presented.