Estimation of Gaussian process regression model using probability distance measures

A new class of parameter estimation algorithms is introduced for Gaussian process regression (GPR) models. It is shown that the integration of the GPR model with probability distance measures of (i) the integrated square error and (ii) Kullback–Leibler (K–L) divergence are analytically tractable. An efficient coordinate descent algorithm is proposed to iteratively estimate the kernel width using golden section search which includes a fast gradient descent algorithm as an inner loop to estimate the noise variance. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

Ecto- and arbuscular mycorrhizal symbiosis can induce tolerance to toxic pulses of phosphorus in jarrah (Eucalyptus marginata) seedlings

In common with many plants native to low P soils, jarrah (Eucalyptus marginata) develops toxicity symptoms upon exposure to elevated phosphorus (P). Jarrah plants can establish arbuscular mycorrhizal (AM) and ectomycorrhizal (ECM) associations, along with a non-colonizing symbiosis described recently. AM colonization is known to influence the pattern of expression of genes required for P uptake of host plants and our aim was to investigate this phenomenon in relation to P sensitivity. Therefore, we examined the effect on hosts of the presence of AM and ECM fungi in combination with toxic pulses of P and assessed possible correlations between the induced tolerance and the shoot P concentration. The P transport dynamics of AM (Rhizophagus irregularis and Scutellospora calospora), ECM (Scleroderma sp.), non-colonizing symbiosis (Austroboletus occidentalis), dual mycorrhizal (R. irregularis and Scleroderma sp.), and non-mycorrhizal (NM) seedlings were monitored following two pulses of P. The ECM and A. occidentalis associations significantly enhanced the shoot P content of jarrah plants growing under P-deficient conditions. In addition, S. calospora, A. occidentalis, and Scleroderma sp. all stimulated plant growth significantly. All inoculated plants had significantly lower phytotoxicity symptoms compared to NM controls 7 days after addition of an elevated P dose (30 mg P kg−1 soil). Following exposure to toxicity-inducing levels of P, the shoot P concentration was significantly lower in R. irregularis-inoculated and dually inoculated plants compared to NM controls. Although all inoculated plants had reduced toxicity symptoms and there was a positive linear relationship between rank and shoot P concentration, the protective effect was not necessarily explained by the type of fungal association or the extent of mycorrhizal colonization.

Energy compensation following consumption of sugar-reduced products: a randomized controlled trial

PURPOSE: Consumption of sugar-reformulated products (commercially available foods and beverages that have been reduced in sugar content through reformulation) is a potential strategy for lowering sugar intake at a population level. The impact of sugar-reformulated products on body weight, energy balance (EB) dynamics and cardiovascular disease risk indicators has yet to be established. The REFORMulated foods (REFORM) study examined the impact of an 8-week sugar-reformulated product exchange on body weight, EB dynamics, blood pressure, arterial stiffness, glycemia and lipemia. METHODS: A randomized, controlled, double-blind, crossover dietary intervention study was performed with fifty healthy normal to overweight men and women (age 32.0 ± 9.8 year, BMI 23.5 ± 3.0 kg/m2) who were randomly assigned to consume either regular sugar or sugar-reduced foods and beverages for 8 weeks, separated by 4-week washout period. Body weight, energy intake (EI), energy expenditure and vascular markers were assessed at baseline and after both interventions. RESULTS: We found that carbohydrate (P < 0.001), total sugars (P < 0.001) and non-milk extrinsic sugars (P < 0.001) (% EI) were lower, whereas fat (P = 0.001) and protein (P = 0.038) intakes (% EI) were higher on the sugar-reduced than the regular diet. No effects on body weight, blood pressure, arterial stiffness, fasting glycemia or lipemia were observed. CONCLUSIONS: Consumption of sugar-reduced products, as part of a blinded dietary exchange for an 8-week period, resulted in a significant reduction in sugar intake. Body weight did not change significantly, which we propose was due to energy compensation.

Low rank representation on Riemannian manifold of symmetric positive definite matrices

Sparse coding aims to find a more compact representation based on a set of dictionary atoms. A well-known technique looking at 2D sparsity is the low rank representation (LRR). However, in many computer vision applications, data often originate from a manifold, which is equipped with some Riemannian geometry. In this case, the existing LRR becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to applications. In this paper, we generalize the LRR over the Euclidean space to the LRR model over a specific Rimannian manifold—the manifold of symmetric positive matrices (SPD). Experiments on several computer vision datasets showcase its noise robustness and superior performance on classification and segmentation compared with state-of-the-art approaches.

Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics

We give an a posteriori analysis of a semidiscrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (2014, SIAM J. Math. Anal., 46, 3518–3539). This framework allows energy-type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions and a set of elliptic reconstructions to apply the reduced relative entropy framework in this setting.

Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics

We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (SIAM J Math Anal 46(5):3518–3539, 2014). The estimate we derive is optimal in the L∞(0,T;dG) norm for the strain and the L2(0,T;dG) norm for the velocity, where dG is an appropriate mesh dependent H1-like space.

Probabilistic wind power forecasts with an inverse power curve transformation and censored regression

Forecasting wind power is an important part of a successful integration of wind power into the power grid. Forecasts with lead times longer than 6 h are generally made by using statistical methods to post-process forecasts from numerical weather prediction systems. Two major problems that complicate this approach are the non-linear relationship between wind speed and power production and the limited range of power production between zero and nominal power of the turbine. In practice, these problems are often tackled by using non-linear non-parametric regression models. However, such an approach ignores valuable and readily available information: the power curve of the turbine's manufacturer. Much of the non-linearity can be directly accounted for by transforming the observed power production into wind speed via the inverse power curve so that simpler linear regression models can be used. Furthermore, the fact that the transformed power production has a limited range can be taken care of by employing censored regression models. In this study, we evaluate quantile forecasts from a range of methods: (i) using parametric and non-parametric models, (ii) with and without the proposed inverse power curve transformation and (iii) with and without censoring. The results show that with our inverse (power-to-wind) transformation, simpler linear regression models with censoring perform equally or better than non-linear models with or without the frequently used wind-to-power transformation.

Tests of sunspot number sequences: 3. Effects of regression procedures on the calibration of historic sunspot data

We use sunspot group observations from the Royal Greenwich Observatory (RGO) to investigate the effects of intercalibrating data from observers with different visual acuities. The tests are made by counting the number of groups RB above a variable cut-off threshold of observed total whole-spot area (uncorrected for foreshortening) to simulate what a lower acuity observer would have seen. The synthesised annual means of RB are then re-scaled to the full observed RGO group number RA using a variety of regression techniques. It is found that a very high correlation between RA and RB (rAB > 0.98) does not prevent large errors in the intercalibration (for example sunspot maximum values can be over 30 % too large even for such levels of rAB). In generating the backbone sunspot number (RBB), Svalgaard and Schatten (2015, this issue) force regression fits to pass through the scatter plot origin which generates unreliable fits (the residuals do not form a normal distribution) and causes sunspot cycle amplitudes to be exaggerated in the intercalibrated data. It is demonstrated that the use of Quantile-Quantile (“Q  Q”) plots to test for a normal distribution is a useful indicator of erroneous and misleading regression fits. Ordinary least squares linear fits, not forced to pass through the origin, are sometimes reliable (although the optimum method used is shown to be different when matching peak and average sunspot group numbers). However, other fits are only reliable if non-linear regression is used. From these results it is entirely possible that the inflation of solar cycle amplitudes in the backbone group sunspot number as one goes back in time, relative to related solar-terrestrial parameters, is entirely caused by the use of inappropriate and non-robust regression techniques to calibrate the sunspot data.

A global empirical system for probabilistic seasonal climate prediction

Preparing for episodes with risks of anomalous weather a month to a year ahead is an important challenge for governments, non-governmental organisations, and private companies and is dependent on the availability of reliable forecasts. The majority of operational seasonal forecasts are made using process-based dynamical models, which are complex, computationally challenging and prone to biases. Empirical forecast approaches built on statistical models to represent physical processes offer an alternative to dynamical systems and can provide either a benchmark for comparison or independent supplementary forecasts. Here, we present a simple empirical system based on multiple linear regression for producing probabilistic forecasts of seasonal surface air temperature and precipitation across the globe. The global CO2-equivalent concentration is taken as the primary predictor; subsequent predictors, including large-scale modes of variability in the climate system and local-scale information, are selected on the basis of their physical relationship with the predictand. The focus given to the climate change signal as a source of skill and the probabilistic nature of the forecasts produced constitute a novel approach to global empirical prediction. Hindcasts for the period 1961–2013 are validated against observations using deterministic (correlation of seasonal means) and probabilistic (continuous rank probability skill scores) metrics. Good skill is found in many regions, particularly for surface air temperature and most notably in much of Europe during the spring and summer seasons. For precipitation, skill is generally limited to regions with known El Niño–Southern Oscillation (ENSO) teleconnections. The system is used in a quasi-operational framework to generate empirical seasonal forecasts on a monthly basis.

An upgrade on the rabbit model of anthracycline-induced cardiomyopathy: shorter protocol, reduced mortality, and higher incidence of overt dilated cardiomyopathy

Current protocols of anthracycline-induced cardiomyopathy in rabbits present with high premature mortality and nephrotoxicity, thus rendering them unsuitable for studies requiring long-term functional evaluation of myocardial function (e.g., stem cell therapy). We compared two previously described protocols to an in-house developed protocol in three groups: Group DOX2 received doxorubicin 2 mg/kg/week (8 weeks); Group DAU3 received daunorubicin 3 mg/kg/week (10 weeks); and Group DAU4 received daunorubicin 4 mg/kg/week (6 weeks). A cohort of rabbits received saline (control). Results of blood tests, cardiac troponin I, echocardiography, and histopathology were analysed. Whilst DOX2 and DAU3 rabbits showed high premature mortality (50% and 33%, resp.), DAU4 rabbits showed 7.6% premature mortality. None of DOX2 rabbits developed overt dilated cardiomyopathy; 66% of DAU3 rabbits developed overt dilated cardiomyopathy and quickly progressed to severe congestive heart failure. Interestingly, 92% of DAU4 rabbits showed overt dilated cardiomyopathy and 67% developed congestive heart failure exhibiting stable disease. DOX2 and DAU3 rabbits showed alterations of renal function, with DAU3 also exhibiting hepatic function compromise. Thus, a shortened protocol of anthracycline-induced cardiomyopathy as in DAU4 group results in high incidence of overt dilated cardiomyopathy, which insidiously progressed to congestive heart failure, associated to reduced systemic compromise and very low premature mortality.

Dysregulation of granulosal bone morphogenetic protein receptor 1B density is associated with reduced ovarian reserve and the age-related decline in human fertility

Reproductive ageing is linked to the depletion of ovarian primordial follicles, which causes an irreversible change to ovarian cellular function and the capacity to reproduce. The current study aimed to profile the expression of bone morphogenetic protein receptor, (BMPR1B) in 53 IVF patients exhibiting different degrees of primordial follicle depletion. The granulosa cell receptor density was measured in 403 follicles via flow cytometry. A decline in BMPR1B density occurred at the time of dominant follicle selection and during the terminal stage of folliculogenesis in the 23-30 y good ovarian reserve patients. The 40+ y poor ovarian reserve patients experienced a reversal of this pattern. The results demonstrate an association between age-induced depletion of the ovarian reserve and BMPR1B receptor density at the two critical time points of dominant follicle selection and pre-ovulatory follicle maturation. Dysregulation of BMP receptor signalling may inhibit the normal steroidogenic differentiation required for maturation in older patients.

A low mortality, high morbidity reduced intensity status epilepticus (RISE) model of epilepsy and epileptogenesis in the rat

Animal models of acquired epilepsies aim to provide researchers with tools for use in understanding the processes underlying the acquisition, development and establishment of the disorder. Typically, following a systemic or local insult, vulnerable brain regions undergo a process leading to the development, over time, of spontaneous recurrent seizures. Many such models make use of a period of intense seizure activity or status epilepticus, and this may be associated with high mortality and/or global damage to large areas of the brain. These undesirable elements have driven improvements in the design of chronic epilepsy models, for example the lithium-pilocarpine epileptogenesis model. Here, we present an optimised model of chronic epilepsy that reduces mortality to 1% whilst retaining features of high epileptogenicity and development of spontaneous seizures. Using local field potential recordings from hippocampus in vitro as a probe, we show that the model does not result in significant loss of neuronal network function in area CA3 and, instead, subtle alterations in network dynamics appear during a process of epileptogenesis, which eventually leads to a chronic seizure state. The model’s features of very low mortality and high morbidity in the absence of global neuronal damage offer the chance to explore the processes underlying epileptogenesis in detail, in a population of animals not defined by their resistance to seizures, whilst acknowledging and being driven by the 3Rs (Replacement, Refinement and Reduction of animal use in scientific procedures) principles.

OX133, a monoclonal antibody recognizing protein-bound N-ethylmaleimide for the identification of reduced disulfide bonds in proteins

In vivo, enzymatic reduction of some protein disulfide bonds, allosteric disulfide bonds, provides an important level of structural and functional regulation. The free cysteine residues generated can be labeled by maleimide reagents, including biotin derivatives, allowing the reduced protein to be detected or purified. During the screening of monoclonal antibodies for those specific for the reduced forms of proteins, we isolated OX133, a unique antibody that recognizes polypeptide resident, N-ethylmaleimide (NEM)-modified cysteine residues in a sequence-independent manner. OX133 offers an alternative to biotin-maleimide reagents for labeling reduced/alkylated antigens and capturing reduced/alkylated proteins with the advantage that NEM-modified proteins are more easily detected in mass spectrometry, and may be more easily recovered than is the case following capture with biotin based reagents.

Emergence dynamics of barnyardgrass and jimsonweed from two depths when switching from conventional to reduced and no-till conditions

A cylinder experiment was conducted in northern Greece during 2005 and 2006 to assess emergence dynamics of barnyardgrass (Echinochloa crus-galli (L.) Beauv.) and jimsonweed (Datura stramonium L.) in the case of a switch from conventional to conservation tillage systems (CT). Emergence was surveyed from two burial depths (5 and 10 cm) and with simulation of reduced tillage (i.e. by soil disturbance) and no-till conditions. Barnyardgrass emergence was significantly affected by burial depth, having greater emergence from 5 cm depth (96%) although even 78% of seedlings emerged from 10 cm depth after the two years of study. Emergence of barnyardgrass was stable across years from the different depths and tillage regimes. Jimsonweed seeds showed lower germination than barnyardgrass during the study period, whereas its emergence was significantly affected by soil disturbance having 41% compared to 28% without disturbance. A burial depth x soil disturbance interaction was also determined, which showed higher emergence from 10 cm depth with soil disturbance. Jimsonweed was found to have significantly higher emergence from 10 cm depth with soil disturbance in Year 2. Seasonal emergence timing of barnyardgrass did not vary between the different burial depth and soil disturbance regimes, as it started in April and lasted until end of May in both years. Jimsonweed showed a bimodal pattern, with first emergence starting end of April until mid-May and the second ranging from mid-June to mid-August from 10 cm burial depth and from mid-July to mid-August from 5 cm depth, irrespective of soil disturbance in both cases.