Instantaneous gelation in Smoluchowski’s coagulation equation revisited

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreasesas M increases, consistent with the expectation that the gelation time is zero in the unregularized system. This decrease appears to be a logarithmically slow function of M, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, K(m1,m2)=max{m1,m2}ν, which gels instantaneously when M→∞ if ν>1. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent ν for large cluster sizes. The total particle density in the stationary state slowly vanishes as [(ν−1)logM]−1/2 when M→∞. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, M, which decay very slowly when M is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.

Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P. However, there are many situations for which it is impractical or impossible to draw from the transition kernel P. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace P by an approximation Pˆ. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ’close’ the chain given by the transition kernel Pˆ is to the chain given by P . We apply these results to several examples from spatial statistics and network analysis.

A pilot study investigating the effects of a single dose of a flavonoid-rich blueberry drink on memory in 8-10 year old children

Recent evidence from animal and adult human subjects has demonstrated potential benefits to cognition from flavonoid supplementation. This study aimed to investigate whether these cognitive benefits extended to a sample of school-aged children. Using a cross-over design, with a wash out of at least seven days between drinks, fourteen 8-10 year old children consumed either a flavonoid-rich blueberry drink or matched vehicle. Two hours after consumption, subjects completed a battery of five cognitive tests comprising the Go-NoGo, Stroop, Rey’s Auditory Verbal Learning Task, Object Location Task, and a Visual N-back. In comparison to vehicle, the blueberry drink produced significant improvements in the delayed recall of a previously learned list of words, showing for the first time a cognitive benefit for acute flavonoid intervention in children. However, performance on a measure of proactive interference indicated that the blueberry intervention led to a greater negative impact of previously memorised words on the encoding of a set of new words. There was no benefit of our blueberry intervention for measures of attention, response inhibition or visuo-spatial memory. While findings are mixed, the improvements in delayed recall found in this pilot study suggest that, following acute flavonoid-rich blueberry interventions, school aged children encode memory items more effectively.

A benchmark-driven modelling approach for evaluating deployment choices on a multi-core architecture

The complexity of current and emerging architectures provides users with options about how best to use the available resources, but makes predicting performance challenging. In this work a benchmark-driven model is developed for a simple shallow water code on a Cray XE6 system, to explore how deployment choices such as domain decomposition and core affinity affect performance. The resource sharing present in modern multi-core architectures adds various levels of heterogeneity to the system. Shared resources often includes cache, memory, network controllers and in some cases floating point units (as in the AMD Bulldozer), which mean that the access time depends on the mapping of application tasks, and the core's location within the system. Heterogeneity further increases with the use of hardware-accelerators such as GPUs and the Intel Xeon Phi, where many specialist cores are attached to general-purpose cores. This trend for shared resources and non-uniform cores is expected to continue into the exascale era. The complexity of these systems means that various runtime scenarios are possible, and it has been found that under-populating nodes, altering the domain decomposition and non-standard task to core mappings can dramatically alter performance. To find this out, however, is often a process of trial and error. To better inform this process, a performance model was developed for a simple regular grid-based kernel code, shallow. The code comprises two distinct types of work, loop-based array updates and nearest-neighbour halo-exchanges. Separate performance models were developed for each part, both based on a similar methodology. Application specific benchmarks were run to measure performance for different problem sizes under different execution scenarios. These results were then fed into a performance model that derives resource usage for a given deployment scenario, with interpolation between results as necessary.

Rainfall estimation by rain gauge-radar combination: a concurrent multiplicative-additive approach

A procedure (concurrent multiplicative-additive objective analysis scheme [CMA-OAS]) is proposed for operational rainfall estimation using rain gauges and radar data. On the basis of a concurrent multiplicative-additive (CMA) decomposition of the spatially nonuniform radar bias, within-storm variability of rainfall and fractional coverage of rainfall are taken into account. Thus both spatially nonuniform radar bias, given that rainfall is detected, and bias in radar detection of rainfall are handled. The interpolation procedure of CMA-OAS is built on Barnes' objective analysis scheme (OAS), whose purpose is to estimate a filtered spatial field of the variable of interest through a successive correction of residuals resulting from a Gaussian kernel smoother applied on spatial samples. The CMA-OAS, first, poses an optimization problem at each gauge-radar support point to obtain both a local multiplicative-additive radar bias decomposition and a regionalization parameter. Second, local biases and regionalization parameters are integrated into an OAS to estimate the multisensor rainfall at the ground level. The procedure is suited to relatively sparse rain gauge networks. To show the procedure, six storms are analyzed at hourly steps over 10,663 km2. Results generally indicated an improved quality with respect to other methods evaluated: a standard mean-field bias adjustment, a spatially variable adjustment with multiplicative factors, and ordinary cokriging.

Application of complex extreme learning machine to multiclass classification problems with high dimensionality: a THz spectra classification problem

We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

Nonlinear identification using orthogonal forward regression with nested optimal regularization

An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm.

Sparse density estimation on the multinomial manifold

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators.

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.

Generalized convective quasi-equilibrium principle

A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection. The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity.

Climate variability and socio-environmental changes in the northern Aegean (NE Mediterranean) during the last 1500 years

We provide new evidence on sea surface temperature (SST) variations and paleoceanographic/paleoenvironmental changes over the past 1500 years for the north Aegean Sea (NE Mediterranean). The reconstructions are based on multiproxy analyses, obtained from the high resolution (decadal to multidecadal) marine record M2 retrieved from the Athos basin. Reconstructed SSTs show an increase from ca. 850 to 950 AD and from ca. 1100 to 1300 AD. A cooling phase of almost 1.5 �C is observed from ca. 1600 AD to 1700 AD. This seems to have been the starting point of a continuous SST warming trend until the end of the reconstructed period, interrupted by two prominent cooling events at 1832 ± 15 AD and 1995 ± 1 AD. Application of an adaptive Kernel smoothing suggests that the current warming in the reconstructed SSTs of the north Aegean might be unprecedented in the context of the past 1500 years. Internal variability in atmospheric/oceanic circulations systems as well as external forcing as solar radiation and volcanic activity could have affected temperature variations in the north Aegean Sea over the past 1500 years. The marked temperature drop of approximately ~2 �C at 1832 ± 15 yr AD could be related to the 1809 АD ‘unknown’ and the 1815 AD Tambora volcanic eruptions. Paleoenvironmental proxy-indices of the M2 record show enhanced riverine/continental inputs in the northern Aegean after ca. 1450 AD. The paleoclimatic evidence derived from the M2 record is combined with a socio-environmental study of the history of the north Aegean region. We show that the cultivation of temperature-sensitive crops, i.e. walnut, vine and olive, co-occurred with stable and warmer temperatures, while its end coincided with a significant episode of cooler temperatures. Periods of agricultural growth in Macedonia coincide with periods of warmer and more stable SSTs, but further exploration is required in order to identify the causal links behind the observed phenomena. The Black Death likely caused major changes in agricultural activity in the north Aegean region, as reflected in the pollen data from land sites of Macedonia and the M2 proxy-reconstructions. Finally, we conclude that the early modern peaks in mountain vegetation in the Rhodope and Macedonia highlands, visible also in the M2 record, were very likely climate-driven.

Sparse density estimator with tunable kernels

A new sparse kernel density estimator with tunable kernels is introduced within a forward constrained regression framework whereby the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Based on the minimum integrated square error criterion, a recursive algorithm is developed to select significant kernels one at time, and the kernel width of the selected kernel is then tuned using the gradient descent algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing very sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Sparse density estimation on multinomial manifold combining local component analysis

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion combining local component analysis for the finite mixture model. We start with a Parzen window estimator which has the Gaussian kernels with a common covariance matrix, the local component analysis is initially applied to find the covariance matrix using expectation maximization algorithm. Since the constraint on the mixing coefficients of a finite mixture model is on the multinomial manifold, we then use the well-known Riemannian trust-region algorithm to find the set of sparse mixing coefficients. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Amaranth bars enriched with fructans: acceptability and nutritional value

Amaranth bars enriched with fructans: acceptability and nutritional value. There is an increasing appeal for convenience foods with potential health benefits to the consumer. Raw materials with high nutritional value and functional properties must be used on the development of these food products. Amaranth is a gluten-free grain with high nutrition value. Inulin and oligofructose are prebiotic ingredients presenting effects as the enhancement of calcium absorption. Amaranth bars enriched with inulin and oligofructose were developed in the flavors: banana, Brazilian nuts and dried grape, coconut, peach, strawberry and wall nut. The proximate composition were determined and compared to commercial cereal bars, available in traditional (n=59), light (n=60), diet (n=8), with soy (n=10) and quinoa (n=1) categories. Amaranth bars present mean global acceptance values from 6.3 to 7.6 on a 9-point hedonic scale, nutritional advantages as compared to commercial cereal bars (caloric reduction and higher levels of dietary fiber). Although amaranth is an unknown raw material in Brazil, it shows good potential to be used in the manufacturing of ready-to-eat products. As they are gluten free, these amaranth bars are also an alternative product for celiacs, also contributing to the enhancement of calcium absorption, a problem frequently observed in these patients.

Dietary omega-3 fatty acid and omega-3: omega-6 fatty acid ratio predict improvement in glucose disturbances in Japanese Brazilians

Objective: We investigated whether lifestyle-induced changes in dietary fat quality are related to Improvements on glucose metabolism disturbances in Japanese Brazilians at high risk of type 2 diabetes Methods: One hundred forty-eight first- and second-generation subjects with impaired glucose tolerance or impaired fasting glycemia who attended a lifestyle intervention program for 12 mo were studied in the city of Bauru. State of Sao Paulo, Brazil Dietary fatty acid intakes at baseline and after 12 mo were estimated using three 24-h recalls. The effect of dietary fat intake on glucose metabolism was investigated by multiple logistic regression models Results: At baseline, mean standard deviation age and body mass index were 60 II y and 25 5 4.2 kg/m2, respectively After 12 mo. 92 subjects had normal plasma glucose levels and 56 remained in prediabetic conditions. Using logistic regression models adjusted for age, gender, generation, basal intake of explanatory nutrient, energy intake, physical activity, and waist circumference, the odds ratios (95% confidence intervals) for reversion to normoglycemia were 3 14 (1 22-8 10) in the second wrote of total w-3 fatty acid, 4 26 (1.34-13 57) in the second tunic of eicosapentaenoic acid, and 280 (1 10-7.10) in the second tertile of linolenic acid. Similarly. subjects in the highest wrote of w-3.w-6 fatty acid ratio showed a higher chance of improving glucose disturbances (2 51, 1.01-6.37) Conclusions: Our findings support the evidence of an independent protective effect of omega-3 fatty acid and of a higher omega-3:omega-6 fatty acid ratio on the glucose metabolism of high-risk individuals (C) 2010 Elsevier Inc All rights reserved.