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.

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.

Sparse probability density function estimation using the minimum integrated square error

We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of kernels and the estimation of mixing weights. The proposed approach is simple to implement and the associated computational cost is very low. Specifically, the complexity of our algorithm is in the order of the number of training data N, which is much lower than the order of N2 offered by the best existing sparse kernel density estimators. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to those of the classical Parzen window estimate and other existing sparse kernel density estimators.

A fast algorithm for sparse probability density function construction

A new sparse kernel density estimator is introduced. Our main contribution is to develop a recursive algorithm for the selection of significant kernels one at time using the minimum integrated square error (MISE) criterion for both kernel selection. The proposed approach is simple to implement and the associated computational cost is very low. 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.

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.

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

The mean evolution and variability of the Asian summer monsoon: Comparison of ECMWF and NCEP-NCAR reanalyses

The behavior of the Asian summer monsoon is documented and compared using the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA) and the National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) Reanalysis. In terms of seasonal mean climatologies the results suggest that, in several respects, the ERA is superior to the NCEP-NCAR Reanalysis. The overall better simulation of the precipitation and hence the diabatic heating field over the monsoon domain in ERA means that the analyzed circulation is probably nearer reality. In terms of interannual variability, inconsistencies in the definition of weak and strong monsoon years based on typical monsoon indices such as All-India Rainfall (AIR) anomalies and the large-scale wind shear based dynamical monsoon index (DMI) still exist. Two dominant modes of interannual variability have been identified that together explain nearly 50% of the variance. Individually, they have many features in common with the composite flow patterns associated with weak and strong monsoons, when defined in terms of regional AIR anomalies and the large-scale DMI. The reanalyses also show a common dominant mode of intraseasonal variability that describes the latitudinal displacement of the tropical convergence zone from its oceanic-to-continental regime and essentially captures the low-frequency active/break cycles of the monsoon. The relationship between interannual and intraseasonal variability has been investigated by considering the probability density function (PDF) of the principal component of the dominant intraseasonal mode. Based on the DMI, there is an indication that in years with a weaker monsoon circulation, the PDF is skewed toward negative values (i,e., break conditions). Similarly, the PDFs for El Nino and La Nina years suggest that El Nino predisposes the system to more break spells, although the sample size may limit the statistical significance of the results.

Deconvolution method for removing the distortion from time jitter in equivalent-time waveform samplers

A sampling oscilloscope is one of the main units in automatic pulse measurement system (APMS). The time jitter in waveform samplers is an important error source that affect the precision of data acquisition. In this paper, this kind of error is greatly reduced by using the deconvolution method. First, the probability density function (PDF) of time jitter distribution is determined by the statistical approach, then, this PDF is used as convolution kern to deconvolve with the acquired waveform data with additional averaging, and the result is the waveform data in which the effect of time jitter has been removed, and the measurement precision of APMS is greatly improved. In addition, some computer simulations are given which prove the success of the method given in this paper.

A comparison among four different retrieval methods for ice-cloud properties using data from CloudSat, CALIPSO, and MODIS

The A-Train constellation of satellites provides a new capability to measure vertical cloud profiles that leads to more detailed information on ice-cloud microphysical properties than has been possible up to now. A variational radar–lidar ice-cloud retrieval algorithm (VarCloud) takes advantage of the complementary nature of the CloudSat radar and Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar to provide a seamless retrieval of ice water content, effective radius, and extinction coefficient from the thinnest cirrus (seen only by the lidar) to the thickest ice cloud (penetrated only by the radar). In this paper, several versions of the VarCloud retrieval are compared with the CloudSat standard ice-only retrieval of ice water content, two empirical formulas that derive ice water content from radar reflectivity and temperature, and retrievals of vertically integrated properties from the Moderate Resolution Imaging Spectroradiometer (MODIS) radiometer. The retrieved variables typically agree to within a factor of 2, on average, and most of the differences can be explained by the different microphysical assumptions. For example, the ice water content comparison illustrates the sensitivity of the retrievals to assumed ice particle shape. If ice particles are modeled as oblate spheroids rather than spheres for radar scattering then the retrieved ice water content is reduced by on average 50% in clouds with a reflectivity factor larger than 0 dBZ. VarCloud retrieves optical depths that are on average a factor-of-2 lower than those from MODIS, which can be explained by the different assumptions on particle mass and area; if VarCloud mimics the MODIS assumptions then better agreement is found in effective radius and optical depth is overestimated. MODIS predicts the mean vertically integrated ice water content to be around a factor-of-3 lower than that from VarCloud for the same retrievals, however, because the MODIS algorithm assumes that its retrieved effective radius (which is mostly representative of cloud top) is constant throughout the depth of the cloud. These comparisons highlight the need to refine microphysical assumptions in all retrieval algorithms and also for future studies to compare not only the mean values but also the full probability density function.

Protease-activated receptor 2: activation, signalling and function

PARs (protease-activated receptors) are a family of four G-protein-coupled receptors for proteases from the circulation, inflammatory cells and epithelial tissues. This report focuses on PAR(2), which plays an important role in inflammation and pain. Pancreatic (trypsin I and II) and extrapancreatic (trypsin IV) trypsins, mast cell tryptase and coagulation factors VIIa and Xa cleave and activate PAR(2). Proteases cleave PAR(2) to expose a tethered ligand that binds to the cleaved receptor. Despite this irreversible activation, PAR(2) signalling is attenuated by beta-arrestin-mediated desensitization and endocytosis, and by lysosomal targeting and degradation, which requires ubiquitination of PAR(2). beta-Arrestins also act as scaffolds for the assembly of multi-protein signalling complexes that determine the location and function of activated mitogen-activated protein kinases. Observations of PAR(2)-deficient mice support a role for PAR(2) in inflammation, and many of the effects of PAR(2) activators promote inflammation. Inflammation is mediated in part by activation of PAR(2) in the peripheral nervous system, which results in neurogenic inflammation and hyperalgesia.

Adaptive nonlinear equalizer using a mixture of gaussians based on-line density estimator

This paper introduces a new adaptive nonlinear equalizer relying on a radial basis function (RBF) model, which is designed based on the minimum bit error rate (MBER) criterion, in the system setting of the intersymbol interference channel plus a co-channel interference. Our proposed algorithm is referred to as the on-line mixture of Gaussians estimator aided MBER (OMG-MBER) equalizer. Specifically, a mixture of Gaussians based probability density function (PDF) estimator is used to model the PDF of the decision variable, for which a novel on-line PDF update algorithm is derived to track the incoming data. With the aid of this novel on-line mixture of Gaussians based sample-by-sample updated PDF estimator, our adaptive nonlinear equalizer is capable of updating its equalizer’s parameters sample by sample to aim directly at minimizing the RBF nonlinear equalizer’s achievable bit error rate (BER). The proposed OMG-MBER equalizer significantly outperforms the existing on-line nonlinear MBER equalizer, known as the least bit error rate equalizer, in terms of both the convergence speed and the achievable BER, as is confirmed in our simulation study

The importance of vertical velocity variability for estimates of the indirect aerosol effects

The activation of aerosols to form cloud droplets is dependent upon vertical velocities whose local variability is not typically resolved at the GCM grid scale. Consequently, it is necessary to represent the subgrid-scale variability of vertical velocity in the calculation of cloud droplet number concentration. This study uses the UK Chemistry and Aerosols community model (UKCA) within the Hadley Centre Global Environmental Model (HadGEM3), coupled for the first time to an explicit aerosol activation parameterisation, and hence known as UKCA-Activate. We explore the range of uncertainty in estimates of the indirect aerosol effects attributable to the choice of parameterisation of the subgrid-scale variability of vertical velocity in HadGEM-UKCA. Results of simulations demonstrate that the use of a characteristic vertical velocity cannot replicate results derived with a distribution of vertical velocities, and is to be discouraged in GCMs. This study focuses on the effect of the variance (σw2) of a Gaussian pdf (probability density function) of vertical velocity. Fixed values of σw (spanning the range measured in situ by nine flight campaigns found in the literature) and a configuration in which σw depends on turbulent kinetic energy are tested. Results from the mid-range fixed σw and TKE-based configurations both compare well with observed vertical velocity distributions and cloud droplet number concentrations. The radiative flux perturbation due to the total effects of anthropogenic aerosol is estimated at −1.9 W m−2 with σw = 0.1 m s−1, −2.1 W m−2 with σw derived from TKE, −2.25 W m−2 with σw = 0.4 m s−1, and −2.3 W m−2 with σw = 0.7 m s−1. The breadth of this range is 0.4 W m−2, which is comparable to a substantial fraction of the total diversity of current aerosol forcing estimates. Reducing the uncertainty in the parameterisation of σw would therefore be an important step towards reducing the uncertainty in estimates of the indirect aerosol effects. Detailed examination of regional radiative flux perturbations reveals that aerosol microphysics can be responsible for some climate-relevant radiative effects, highlighting the importance of including microphysical aerosol processes in GCMs.

On-line Gaussian mixture density estimator for adaptive minimum bit-error-rate beamforming receivers

We develop an on-line Gaussian mixture density estimator (OGMDE) in the complex-valued domain to facilitate adaptive minimum bit-error-rate (MBER) beamforming receiver for multiple antenna based space-division multiple access systems. Specifically, the novel OGMDE is proposed to adaptively model the probability density function of the beamformer’s output by tracking the incoming data sample by sample. With the aid of the proposed OGMDE, our adaptive beamformer is capable of updating the beamformer’s weights sample by sample to directly minimize the achievable bit error rate (BER). We show that this OGMDE based MBER beamformer outperforms the existing on-line MBER beamformer, known as the least BER beamformer, in terms of both the convergence speed and the achievable BER.

The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.