A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems

Constraining the provenance of the Stonehenge 'Altar Stone': Evidence from automated mineralogy and U–Pb zircon age dating

The Altar Stone at Stonehenge is a greenish sandstone thought to be of Late Silurian-Devonian (‘Old Red Sandstone’) age. It is classed as one of the bluestone lithologies which are considered to be exotic to the Salisbury Plain environ, most of which are derived from the Mynydd Preseli, in west Wales. However, no Old Red Sandstone rocks crop out in the Preseli; instead a source in the Lower Old Red Sandstone Cosheston Subgroup at Mill Bay to the south of the Preseli, has been proposed. More recently, on the basis of detailed petrography, a source for the Altar Stone much further to the east, towards the Wales-England border, has been suggested. Quantitative analyses presented here compare mineralogical data from proposed Stonehenge Altar Stone debris with samples from Milford Haven at Mill Bay, as well as with a second sandstone type found at Stonehenge which is Lower Palaeozoic in age. The Altar Stone samples have contrasting modal mineralogies to the other two sandstone types, especially in relation to the percentages of its calcite, kaolinite and barite cements. Further differences between the Altar Stone sandstone and the Cosheston Subgroup sandstone are seen when their contained zircons are compared, showing differing morphologies and U-Pb age dates having contrasting populations. These data confirm that Mill Bay is not the source of the Altar Stone with the abundance of kaolinite in the Altar Stone sample suggesting a source further east, towards the Wales-England border. The disassociation of the Altar Stone and Milford Haven undermines the hypothesis that the bluestones, including the Altar Stone, were transported from west Wales by sea up the Bristol Channel and adds further credence to a totally land-based route, possibly along a natural routeway leading from west Wales to the Severn estuary and beyond. This route may well have been significant in prehistory, raising the possibility that the Altar Stone was added en route to the assemblage of Preseli bluestones taken to Stonehenge around or shortly before 3000 BC. Recent strontium isotope analysis of human and animal bones from Stonehenge, dating to the beginning of its first construction stage around 3000 BC, are consistent with the suggestion of connectivity between this western region of Britain and Salisbury Plain.This study appears to be the first application of quantitative automated mineralogy in the provenancing of archaeological lithic material and highlights the potential value of automated mineralogy in archaeological provenancing investigations, especially when combined with complementary techniques, in the present case zircon age dating

Seasonal variations in vitamin D do not change the musculoskeletal health of physically active ambulatory men with cerebral palsy: a longitudinal cross-sectional comparison study

Increased levels of vitamin D in the summer months from natural seasonal variations in sun exposure have been linked to improvements in musculoskeletal health and function in UK populations; however, studies have shown that differences in lifestyles because of disability can inhibit the natural vitamin D increase in these populations. We hypothesized that men with cerebral palsy (CP) will experience smaller increases in 25-hydroxyvitamin D (25(OH)D) from winter to summer and men with CP will not experience any improvements in musculoskeletal health and function during the summer. A longitudinal observational study in 16 ambulant men with CP aged 21.0 ± 1.3 years and 16 healthy, physical activity matched, typically developed controls aged 25.4 ± 2.6 years, completed assessments of serum 25(OH)D and parathyroid hormone during winter and summer. Neuromuscular outcomes included vastus lateralis size, knee extensor strength, 10-m sprint, vertical jumps, and grip strength. Bone ultrasounds were performed to obtain radius and tibia T and Z scores. Men with CP and typically developed controls showed a 70.5% and 85.7% increase in serum 25(OH)D from winter to summer months, respectively. Neither group showed seasonal effect on neuromuscular outcomes muscle strength, size, vertical jump, or tibia and radius T and Z scores. A seasonal interaction effect was seen in the tibia T and Z scores (P < .05). In conclusion, there were similar seasonal increases in 25(OH)D observed in men with CP and typically developed controls, but serum 25(OH)D levels were still considered insufficient to improve bone or neuromuscular outcomes

Improved model identification for non-linear systems using a random subsampling and multifold modelling (RSMM) approach

In non-linear system identification, the available observed data are conventionally partitioned into two parts: the training data that are used for model identification and the test data that are used for model performance testing. This sort of 'hold-out' or 'split-sample' data partitioning method is convenient and the associated model identification procedure is in general easy to implement. The resultant model obtained from such a once-partitioned single training dataset, however, may occasionally lack robustness and generalisation to represent future unseen data, because the performance of the identified model may be highly dependent on how the data partition is made. To overcome the drawback of the hold-out data partitioning method, this study presents a new random subsampling and multifold modelling (RSMM) approach to produce less biased or preferably unbiased models. The basic idea and the associated procedure are as follows. First, generate K training datasets (and also K validation datasets), using a K-fold random subsampling method. Secondly, detect significant model terms and identify a common model structure that fits all the K datasets using a new proposed common model selection approach, called the multiple orthogonal search algorithm. Finally, estimate and refine the model parameters for the identified common-structured model using a multifold parameter estimation method. The proposed method can produce robust models with better generalisation performance

The wavelet-NARMAX representation : a hybrid model structure combining polynomial models with multiresolution wavelet decompositions

A new hybrid model structure combing polynomial models with multiresolution wavelet decompositions is introduced for nonlinear system identification. Polynomial models play an important role in approximation theory, and have been extensively used in linear and nonlinear system identification. Wavelet decompositions, in which the basis functions have the property of localization in both time and frequency, outperform many other approximation schemes and offer a flexible solution for approximating arbitrary functions. Although wavelet representations can approximate even severe nonlinearities in a given signal very well, the advantage of these representations can be lost when wavelets are used to capture linear or low-order nonlinear behaviour in a signal. In order to sufficiently utilise the global property of polynomials and the local property of wavelet representations simultaneously, in this study polynomial models and wavelet decompositions are combined together in a parallel structure to represent nonlinear input-output systems. As a special form of the NARMAX model, this hybrid model structure will be referred to as the WAvelet-NARMAX model, or simply WANARMAX. Generally, such a WANARMAX representation for an input-output system might involve a large number of basis functions and therefore a great number of model terms. Experience reveals that only a small number of these model terms are significant to the system output. A new fast orthogonal least squares algorithm, called the matching pursuit orthogonal least squares (MPOLS) algorithm, is also introduced in this study to determine which terms should be included in the final model

Taxonomy, biostratigraphy, and phylogeny of Oligocene and lower Miocene Dentoglobigerina and Globoquadrina

The taxonomy, phylogeny, and biostratigraphy of Oligocene and lower Miocene Dentoglobigerina and Globoquadrina are reviewed. Because of the discovery of spine holes in various species assigned to these genera, the entire group is now considered to have been fully or sparsely spinose in life and hence part of Family Globigerinidae. One new species, Dentoglobigerina eotripartita Pearson, Wade, and Olsson n. sp., is named. Dentoglobigerina includes forms with and without umbilical teeth and species for which the presence or absence of a tooth is a variable feature. A significant finding has been the triple synonymy of Globigerina tripartita Koch, Globigerina rohri Bolli, and Globoquadrina dehiscens praedehiscens Blow, which greatly simplifies part of the taxonomy. The genus Globoquadrina is restricted to its type species, Globigerina dehiscens Chapman and others. The following species from the time interval of interest are regarded as valid: Dentoglobigerina altispira (Cushman and Jarvis), Dentoglobigerina baroemoenensis (LeRoy), Dentoglobigerina binaiensis (Koch), Dentoglobigerina eotripartita Pearson, Wade, and Olsson n. sp., Dentoglobigerina galavisi (Bermúdez), Dentoglobigerina globosa (Bolli), Dentoglobigerina globularis (Bermúdez), Dentoglobigerina juxtabinaiensis Fox and Wade, Dentoglobigerina larmeui (Akers), Dentoglobigerina prasaepis (Blow), Dentoglobigerina pseudovenezuelana (Blow and Banner), Dentoglobigerina sellii (Borsetti), Dentoglobigerina taci Pearson and Wade, Dentoglobigerina tapuriensis (Blow and Banner), Dentoglobigerina tripartita (Koch), Dentoglobigerina venezuelana (Hedberg), and Globoquadrina dehiscens (Chapman, Parr, and Collins). The genus Dentoglobigerina also comprises other Neogene/Quaternary species not listed, including the living species Dentoglobigerina cf. conglomerata (Schwager)

Predicting Remaining Useful Life with Similarity-Based Priors

Prognostics is the area of research that is concerned with predicting the remaining useful life of machines and machine parts. The remaining useful life is the time during which a machine or part can be used, before it must be replaced or repaired. To create accurate predictions, predictive techniques must take external data into account on the operating conditions of the part and events that occurred during its lifetime. However, such data is often not available. Similarity-based techniques can help in such cases. They are based on the hypothesis that if a curve developed similarly to other curves up to a point, it will probably continue to do so. This paper presents a novel technique for similarity-based remaining useful life prediction. In particular, it combines Bayesian updating with priors that are based on similarity estimation. The paper shows that this technique outperforms other techniques on long-term predictions by a large margin, although other techniques still perform better on short-term predictions.</p

Focusing and Compression of Ultrashort Pulses through Scattering Media

Light scattering in inhomogeneous media induces wavefront distortions which pose an inherent limitation in many optical applications. Examples range from microscopy and nanosurgery to astronomy. In recent years, ongoing efforts have made the correction of spatial distortions possible by wavefront shaping techniques. However, when ultrashort pulses are employed scattering induces temporal distortions which hinder their use in nonlinear processes such as in multiphoton microscopy and quantum control experiments. Here we show that correction of both spatial and temporal distortions can be attained by manipulating only the spatial degrees of freedom of the incident wavefront. Moreover, by optimizing a nonlinear signal the refocused pulse can be shorter than the input pulse. We demonstrate focusing of 100fs pulses through a 1mm thick brain tissue, and 1000-fold enhancement of a localized two-photon fluorescence signal. Our results open up new possibilities for optical manipulation and nonlinear imaging in scattering media

Do MRI findings identify patients with chronic low back pain and Modic changes who respond best to rest or exercise: A subgroup analysis of a randomised controlled trial

Background: No previous clinical trials have investigated MRI findings as effect modifiers for conservative treatment of low back pain. This hypothesis-setting study investigated if MRI findings modified response to rest compared with exercise in patients with chronic low back pain and Modic changes. Methods: This study is a secondary analysis of a randomised controlled trial comparing rest with exercise. Patients were recruited from a specialised outpatient spine clinic and included in a clinical trial if they had chronic low back pain and an MRI showing Modic changes. All patients received conservative treatment while participating in the trial. Five baseline MRI findings were investigated as effect modifiers: Modic changes Type 1 (any size), large Modic changes (any type), large Modic changes Type 1, severe disc degeneration and large disc herniation. The outcome measure was change in low back pain intensity measured on a 0-10 point numerical rating scale at 14-month follow-up (n = 96). An interaction = 1.0 point (0-10 scale) between treatment group and MRI findings in linear regression was considered clinically important. Results: The interactions for Modic Type 1, with large Modic changes or with large Modic changes Type 1 were all potentially important in size (-0.99 (95% CI -3.28 to 1.29), -1.49 (-3.73 to 0.75), -1.49 (-3.57 to 0.58), respectively) but the direction of the effect was the opposite to what we had hypothesized-that people with these findings would benefit more from rest than from exercise. The interactions for severe disc degeneration (0.74 (-1.40 to 2.88)) and large disc herniation (-0.92 (3.15 to 1.31)) were less than the 1.0-point threshold for clinical importance. As expected, because of the lack of statistical power, no interaction term for any of the MRI findings was statistically significant. Conclusions: Three of the five MRI predictors showed potentially important effect modification, although the direction of the effect was surprising and confidence intervals were wide so very cautious interpretation is required. Further studies with adequate power are warranted to study these and additional MRI findings as potential effect modifiers for common interventions

Adipose energy stores, physical work, and the metabolic syndrome: lessons from hummingbirds

Hummingbirds and other nectar-feeding, migratory birds possess unusual adaptive traits that offer important lessons concerning obesity, diabetes and the metabolic syndrome. Hummingbirds consume a high sugar diet and have fasting glucose levels that would be severely hyperglycemic in humans, yet these nectar-fed birds recover most glucose that is filtered into the urine. Hummingbirds accumulate over 40% body fat shortly before migrations in the spring and autumn. Despite hyperglycemia and seasonally elevated body fat, the birds are not known to become diabetic in the sense of developing polyuria (glucosuria), polydipsia and polyphagia. The tiny (3–4 g) Ruby-throated hummingbird has among the highest mass-specific metabolic rates known, and loses most of its stored fat in 20 h by flying up to 600 miles across the Gulf of Mexico. During the breeding season, it becomes lean and maintains an extremely accurate energy balance. In addition, hummingbirds can quickly enter torpor and reduce resting metabolic rates by 10-fold. Thus, hummingbirds are wonderful examples of the adaptive nature of fat tissue, and may offer lessons concerning prevention of metabolic syndrome in humans