Using zero-norm constraint for sparse probability density function estimation

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

Association between dietary phyto-oestrogens and bone density in men and postmenopausal women

Phyto-oestrogens have been associated with a decreased risk for osteoporosis, but results from intervention and observational studies in Western countries have been inconsistent. In the present study, we investigated the association between habitual phyto-oestrogen intake and broadband ultrasound attenuation (BUA) of the calcanaeum as a marker of bone density. We collected 7 d records of diet, medical history and demographic and anthropometric data from participants (aged 45–75 years) in the European Prospective Investigation into Cancer-Norfolk study. Phyto-oestrogen (biochanin A, daidzein, formononetin; genistein, glycitein; matairesinol; secoisolariciresinol; enterolactone; equol) intake was determined using a newly developed food composition database. Bone density was assessed using BUA of the calcanaeum. Associations between bone density and phyto-oestrogen intake were investigated in 2580 postmenopausal women who were not on hormone replacement therapy and 4973 men. Median intake of total phyto-oestrogens was 876 (interquartile range 412) μg/d in postmenopausal women and 1212 (interquartile range 604) μg/d in men. The non-soya isoflavones formononetin and biochanin A were marginally significant or significantly associated with BUA in postmenopausal women (β = 1·2; P < 0·1) and men (β = 1·2; P < 0·05), respectively; enterolignans and equol were positively associated with bone density in postmenopausal women, but this association became non-significant when dietary Ca was added to the model. In the lowest quintile of Ca intake, soya isoflavones were positively associated with bone density in postmenopausal women (β = 1·4; P < 0·1). The present results therefore suggest that non-soya isoflavones are associated with bone density independent of Ca, whereas the association with soya or soya isoflavones is affected by dietary Ca.

Stomatal conductance and not stomatal density determines the long-term reduction in leaf transpiration of poplar in elevated CO2

Using a free-air CO2 enrichment (FACE) experiment, poplar trees (Populus · euramericana clone I214) were exposed to either ambient or elevated [CO2] from planting, for a 5-year period during canopy development, closure, coppice and re-growth. In each year, measurements were taken of stomatal density (SD, number mm2) and stomatal index (SI, the proportion of epidermal cells forming stomata). In year 5, measurements were also taken of leaf stomatal conductance (gs, lmol m2 s1), photosynthetic CO2 fixation (A, mmol m2 s1), instantaneous water-use efficiency (A/E) and the ratio of intercellular to atmospheric CO2 (Ci:Ca). Elevated [CO2] caused reductions in SI in the first year, and in SD in the first 2 years, when the canopy was largely open. In following years, when the canopy had closed, elevated [CO2] had no detectable effects on stomatal numbers or index. In contrast, even after 5 years of exposure to elevated [CO2], gs was reduced, A/E was stimulated, and Ci:Ca was reduced relative to ambient [CO2]. These outcomes from the long-term realistic field conditions of this forest FACE experiment suggest that stomatal numbers (SD and SI) had no role in determining the improved instantaneous leaf-level efficiency of water use under elevated [CO2]. We propose that altered cuticular development during canopy closure may partially explain the changing response of stomata to elevated [CO2], although the mechanism for this remains obscure.

Recommendations for the viability assessment of probiotics as concentrated cultures and in food matrices

Due to the fact that probiotic cells need to be alive when they are consumed, culture-based analysis (plate count) is critical in ascertaining the quality (numbers of viable cells) of probiotic products. Since probiotic cells are typically stressed, due to various factors related to their production, processing and formulation, the standard methodology for total plate counts tends to underestimate the cell numbers of these products. Furthermore, products such as microencapsulated cultures require modifications in the release and sampling procedure in order to correctly estimate viable counts. This review examines the enumeration of probiotic bacteria in the following commercial products: powders, microencapsulated cultures, frozen concentrates, capsules, foods and beverages. The parameters which are specifically examined include: sample preparation (rehydration, thawing), dilutions (homogenization, media) and plating (media, incubation) procedures. Recommendations are provided for each of these analytical steps to improve the accuracy of the analysis. Although the recommendations specifically target the analysis of probiotics, many will apply to the analysis of commercial lactic starter cultures used in food fermentations as well.

Initial distribution spread: A density forecasting approach

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model error limits the value of such efforts. This paper argues for choosing the initial ensemble in order to optimise forecasting performance rather than estimate the true state of the system. Density forecasting and choosing the initial ensemble are treated as one problem. Forecasting performance can be quantified by some scoring rule. In the case of the logarithmic scoring rule, theoretical arguments and empirical results are presented. It turns out that, if the underlying noise dominates model error, we can diagnose the noise spread.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Determination of the density of the multiple access interference of a CDMA system from its moments

A standard CDMA system is considered and an extension of Pearson's results is used to determine the density function of the interference. The method is shown to work well in some cases, but not so in others. However this approach can be useful in further determining the probability of error of the system with minimal computational requirements.

Sampling series for determination of probability density of CDMA multiple access interference

Consideration is given to a standard CDMA system and determination of the density function of the interference with and without Gaussian noise using sampling theory concepts. The formula derived provides fast and accurate results and is a simple, useful alternative to other methods

Oxidation of low density lipoprotein by iron at lysosomal pH: implications for atherosclerosis

Low density lipoprotein (LDL) has recently been shown to be oxidised by iron within the lysosomes of macrophages and this is a novel potential mechanism for LDL oxidation in atherosclerosis. Our aim was to characterise the chemical and physical changes induced in LDL by iron at lysosomal pH and to investigate the effects of iron chelators and α-tocopherol on this process. LDL was oxidised by iron at pH 4.5 and 37°C and its oxidation monitored by spectrophotometry and HPLC. LDL was oxidised effectively by FeSO4 (5-50 µM) and became highly aggregated at pH 4.5, but not at pH 7.4. Cholesteryl esters decreased and after a pronounced lag 7-ketocholesterol increased greatly. Total hydroperoxides (measured by tri-iodide assay) increased up to 24 h and then decreased only slowly. The lipid composition after 12 h at pH 4.5 and 37°C was similar to that of LDL oxidised by copper at pH 7.4 and 4°C, i.e. rich in hydroperoxides but low in oxysterols. Previously oxidised LDL aggregated rapidly and spontaneously at pH 4.5, but not at pH 7.4. Ferrous was much more effective than ferric iron at oxidising LDL when added after the oxidation was already underway. The iron chelators diethylenetriaminepentaacetic acid and, to a lesser extent, desferrioxamine inhibited LDL oxidation when added during its initial stages, but were unable to prevent LDL aggregating after it had been partially oxidised. Surprisingly, desferrioxamine increased the rate of LDL modification when added late in the oxidation process. α-Tocopherol enrichment of LDL initially increased the oxidation of LDL, but inhibited it later. The presence of oxidised and highly aggregated lipid within lysosomes has the potential to perturb the function of these organelles and to promote atherosclerosis.