Probability density function estimation using orthogonal forward regression

Using the classical Parzen window estimate as the target function, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density estimates. The proposed algorithm incrementally minimises a leave-one-out test error score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights are finally updated using the multiplicative nonnegative quadratic programming algorithm, which has the ability to reduce the model size further. Except for the kernel width, the proposed algorithm has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Two examples are used to demonstrate the ability of this regression-based approach to effectively construct a sparse kernel density estimate with comparable accuracy to that of the full-sample optimised Parzen window density estimate.

Expression and regulation of 80K/MARCKS, a major substrate of protein kinase C, in the developing rat heart

Objective: Protein kinase C (PKC) plays a pivotal role in modulating the growth and differentiation of many cell types including the cardiac myocyte. However, little is known about molecules that act immediately downstream of PKC in the heart. In this study we have investigated the expression of 80K/MARCKS, a major PKC substrate, in whole ventricles and in cardiac myocytes from developing rat hearts. Methods: Poly A+ RNA was prepared from neonatal (2-day) and adult (42-day) cardiac myocytes and whole ventricular tissue and mRNA expression determined by reverse transcription-polymerase chain reaction (RT-PCR) using primers designed to identify a 420 bp fragment in the 80K/MARCKS gene. Protein extracts were prepared from either 2-day and 42-day cardiac myocytes or from whole ventricular tissue at 2, 5–11, 14, 17, 21, 28 and 42 days of age. Protein expression was determined by immunoblotting with an 80K/MARCKS antipeptide antibody and PKC activity was determined by measuring the amount of γ32P-ATP transferred to a specific peptide substrate. Results: RT-PCR analysis of 80K/MARCKS mRNA in neonatal (2-day) and adult (42-day) cardiac myocytes showed the expression of this gene in both cell types. Immunoblotting revealed maximum 80K/MARCKS protein expression in whole ventricular tissue at 5 days (a 75% increase above values at 2 days), followed by a transient decrease in expression during the 6–8-day period (61% of the protein expressed at 2 days for 8-day tissue) with levels returning to 5 day levels by 11 days of age. 80K/MARCKS protein was present in cardiac myocytes at 2 days of age whereas it was not detectable in adult cells. In addition, PKC activity levels increased to 160% of levels present at 2 days in 8-day-old ventricles with PKC activity levels returning to 5-day levels by 9 days of age. This was then followed by a steady decline in both 80K/MARCKS protein expression and PKC activity through to adulthood. Conclusions: Expression of the PKC substrate, 80K/MARCKS, in cardiac myocytes changes significantly during development and the transient loss of immunoreactive protein during the 6–8-day developmental period may reflect 80K/MARCKS phosphorylation and subsequent down-regulation as a result of the concomitant up-regulation of PKC activity at this time.

Probability density estimation with tunable kernels using orthogonal forward regression

A generalized or tunable-kernel model is proposed for probability density function estimation based on an orthogonal forward regression procedure. Each stage of the density estimation process determines a tunable kernel, namely, its center vector and diagonal covariance matrix, by minimizing a leave-one-out test criterion. The kernel mixing weights of the constructed sparse density estimate are finally updated using the multiplicative nonnegative quadratic programming algorithm to ensure the nonnegative and unity constraints, and this weight-updating process additionally has the desired ability to further reduce the model size. The proposed tunable-kernel model has advantages, in terms of model generalization capability and model sparsity, over the standard fixed-kernel model that restricts kernel centers to the training data points and employs a single common kernel variance for every kernel. On the other hand, it does not optimize all the model parameters together and thus avoids the problems of high-dimensional ill-conditioned nonlinear optimization associated with the conventional finite mixture model. Several examples are included to demonstrate the ability of the proposed novel tunable-kernel model to effectively construct a very compact density estimate accurately.

A two-locus forensic match probability for subdivided populations

A two-locus match probability is presented that incorporates the effects of within-subpopulation inbreeding (consanguinity) in addition to population subdivision. The usual practice of calculating multi-locus match probabilities as the product of single-locus probabilities assumes independence between loci. There are a number of population genetics phenomena that can violate this assumption: in addition to consanguinity, which increases homozygosity at all loci simultaneously, gametic disequilibrium will introduce dependence into DNA profiles. However, in forensics the latter problem is usually addressed in part by the careful choice of unlinked loci. Hence, as is conventional, we assume gametic equilibrium here, and focus instead on between-locus dependence due to consanguinity. The resulting match probability formulae are an extension of existing methods in the literature, and are shown to be more conservative than these methods in the case of double homozygote matches. For two-locus profiles involving one or more heterozygous genotypes, results are similar to, or smaller than, the existing approaches.

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.

The solar influence on the probability of relatively cold UK winters in the future

Recent research has suggested that relatively cold UK winters are more common when solar activity is low (Lockwood et al 2010 Environ. Res. Lett. 5 024001). Solar activity during the current sunspot minimum has fallen to levels unknown since the start of the 20th century (Lockwood 2010 Proc. R. Soc. A 466 303–29) and records of past solar variations inferred from cosmogenic isotopes (Abreu et al 2008 Geophys. Res. Lett. 35 L20109) and geomagnetic activity data (Lockwood et al 2009 Astrophys. J. 700 937–44) suggest that the current grand solar maximum is coming to an end and hence that solar activity can be expected to continue to decline. Combining cosmogenic isotope data with the long record of temperatures measured in central England, we estimate how solar change could influence the probability in the future of further UK winters that are cold, relative to the hemispheric mean temperature, if all other factors remain constant. Global warming is taken into account only through the detrending using mean hemispheric temperatures. We show that some predictive skill may be obtained by including the solar effect.

An improved lesion detection approach based on similarity measurement between fuzzy intensity segmentation and spatial probability maps

The application of automatic segmentation methods in lesion detection is desirable. However, such methods are restricted by intensity similarities between lesioned and healthy brain tissue. Using multi-spectral magnetic resonance imaging (MRI) modalities may overcome this problem but it is not always practicable. In this article, a lesion detection approach requiring a single MRI modality is presented, which is an improved method based on a recent publication. This new method assumes that a low similarity should be found in the regions of lesions when the likeness between an intensity based fuzzy segmentation and a location based tissue probabilities is measured. The usage of a normalized similarity measurement enables the current method to fine-tune the threshold for lesion detection, thus maximizing the possibility of reaching high detection accuracy. Importantly, an extra cleaning step is included in the current approach which removes enlarged ventricles from detected lesions. The performance investigation using simulated lesions demonstrated that not only the majority of lesions were well detected but also normal tissues were identified effectively. Tests on images acquired in stroke patients further confirmed the strength of the method in lesion detection. When compared with the previous version, the current approach showed a higher sensitivity in detecting small lesions and had less false positives around the ventricle and the edge of the brain

Holocene environmental changes in the lower Thames Valley, London, UK: implications for our understanding of the history of Taxus woodland

A radiocarbon-dated multiproxy palaeoenvironmental record from the Lower Thames Valley at Hornchurch Marshes has provided a reconstruction of the timing and nature of vegetation succession against a background of Holocene climate change, relative sea level movement and human activities. The investigation recorded widespread peat formation between c. 6300 and 3900 cal. yr BP (marine ‘regression’), succeeded by evidence for marine incursion. The multiproxy analyses of these sediments, comprising pollen, Coleoptera, diatoms, and plant and wood macrofossils, have indicated significant changes in both the wetland and dryland environment, including the establishment of Alnus (Alder) carr woodland, and the decline of both Ulmus (Elm; c. 5740 cal. yr BP) and Tilia (Lime; c. 5600 cal. yr BP, and 4160–3710 cal. yr BP). The beetle faunas from the peat also suggest a thermal climate similar to that of the present day. At c. 4900 cal. yr BP, Taxus (L.; Yew) woodland colonised the peatland forming a plant community that has no known modern analogue in the UK. The precise reason, or reasons, for this event remain unclear, although changes in peatland hydrology seem most likely. The growth of Taxus on peatland not only has considerable importance for our knowledge of the vegetation history of southeast England, and NW Europe generally, but also has wider implications for the interpretation of Holocene palaeobotanical records. At c. 3900 cal. yr BP, Taxus declined on the peatland surface during a period of major hydrological change (marine incursion), an event also strongly associated with the decline of dryland woodland taxa, including Tilia and Quercus, and the appearance of anthropogenic indicators.