Observation impact in data assimilation: the effect of non-Gaussian observation error.

Data assimilation methods which avoid the assumption of Gaussian error statistics are being developed for geoscience applications. We investigate how the relaxation of the Gaussian assumption affects the impact observations have within the assimilation process. The effect of non-Gaussian observation error (described by the likelihood) is compared to previously published work studying the effect of a non-Gaussian prior. The observation impact is measured in three ways: the sensitivity of the analysis to the observations, the mutual information, and the relative entropy. These three measures have all been studied in the case of Gaussian data assimilation and, in this case, have a known analytical form. It is shown that the analysis sensitivity can also be derived analytically when at least one of the prior or likelihood is Gaussian. This derivation shows an interesting asymmetry in the relationship between analysis sensitivity and analysis error covariance when the two different sources of non-Gaussian structure are considered (likelihood vs. prior). This is illustrated for a simple scalar case and used to infer the effect of the non-Gaussian structure on mutual information and relative entropy, which are more natural choices of metric in non-Gaussian data assimilation. It is concluded that approximating non-Gaussian error distributions as Gaussian can give significantly erroneous estimates of observation impact. The degree of the error depends not only on the nature of the non-Gaussian structure, but also on the metric used to measure the observation impact and the source of the non-Gaussian structure.

Gaussian anamorphosis in the analysis step of the EnKF: a joint state-variable/observation approach

The analysis step of the (ensemble) Kalman filter is optimal when (1) the distribution of the background is Gaussian, (2) state variables and observations are related via a linear operator, and (3) the observational error is of additive nature and has Gaussian distribution. When these conditions are largely violated, a pre-processing step known as Gaussian anamorphosis (GA) can be applied. The objective of this procedure is to obtain state variables and observations that better fulfil the Gaussianity conditions in some sense. In this work we analyse GA from a joint perspective, paying attention to the effects of transformations in the joint state variable/observation space. First, we study transformations for state variables and observations that are independent from each other. Then, we introduce a targeted joint transformation with the objective to obtain joint Gaussianity in the transformed space. We focus primarily in the univariate case, and briefly comment on the multivariate one. A key point of this paper is that, when (1)-(3) are violated, using the analysis step of the EnKF will not recover the exact posterior density in spite of any transformations one may perform. These transformations, however, provide approximations of different quality to the Bayesian solution of the problem. Using an example in which the Bayesian posterior can be analytically computed, we assess the quality of the analysis distributions generated after applying the EnKF analysis step in conjunction with different GA options. The value of the targeted joint transformation is particularly clear for the case when the prior is Gaussian, the marginal density for the observations is close to Gaussian, and the likelihood is a Gaussian mixture.

Hydrogen sulfide inhibits Cav3.2 T-type Ca2+ channels

The importance of H2S as a physiological signaling molecule continues to develop, and ion channels are emerging as a major family of target proteins through which H2S exerts many actions. The purpose of the present study was to investigate its effects on T-type Ca2+ channels. Using patch-clamp electrophysiology, we demonstrate that the H2S donor, NaHS (10 μM-1 mM) selectively inhibits Cav3.2 T-type channels heterologously expressed in HEK293 cells, whereas Cav3.1 and Cav3.3 channels were unaffected. The sensitivity of Cav3.2 channels to H2S required the presence of the redox-sensitive extracellular residue H191, which is also required for tonic binding of Zn2+ to this channel. Chelation of Zn2+ with N,N,N',N'-tetra-2-picolylethylenediamine prevented channel inhibition by H2S and also reversed H2S inhibition when applied after H2S exposure, suggesting that H2S may act via increasing the affinity of the channel for extracellular Zn2+ binding. Inhibition of native T-type channels in 3 cell lines correlated with expression of Cav3.2 and not Cav3.1 channels. Notably, H2S also inhibited native T-type (primarily Cav3.2) channels in sensory dorsal root ganglion neurons. Our data demonstrate a novel target for H2S regulation, the T-type Ca2+ channel Cav3.2, and suggest that such modulation cannot account for the pronociceptive effects of this gasotransmitter.

Diverse mechanisms underlying the regulation of ion channels by carbon monoxide

Carbon monoxide (CO) is firmly established as an important, physiological signalling molecule as well as a potent toxin. Through its ability to bind metal-containing proteins, it is known to interfere with a number of intracellular signalling pathways, and such actions can account for its physiological and pathological effects. In particular, CO can modulate the intracellular production of reactive oxygen species, NO and cGMP levels, as well as regulate MAPK signalling. In this review, we consider ion channels as more recently discovered effectors of CO signalling. CO is now known to regulate a growing number of different ion channel types, and detailed studies of the underlying mechanisms of action are revealing unexpected findings. For example, there are clear areas of contention surrounding its ability to increase the activity of high conductance, Ca2+ -sensitive K+ channels. More recent studies have revealed the ability of CO to inhibit T-type Ca2+ channels and have unveiled a novel signalling pathway underlying tonic regulation of this channel. It is clear that the investigation of ion channels as effectors of CO signalling is in its infancy, and much more work is required to fully understand both the physiological and the toxic actions of this gas. Only then can its emerging use as a therapeutic tool be fully and safely exploited.

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.

B-spline neural network based single-carrier frequency domain equalisation for Hammerstein channels

A practical single-carrier (SC) block transmission with frequency domain equalisation (FDE) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such Hammerstein channels, the standard SC-FDE scheme no longer works. We propose a novel Bspline neural network based nonlinear SC-FDE scheme for Hammerstein channels. In particular, we model the nonlinear HPA, which represents the complex-valued static nonlinearity of the Hammerstein channel, by two real-valued B-spline neural networks, one for modelling the nonlinear amplitude response of the HPA and the other for the nonlinear phase response of the HPA. We then develop an efficient alternating least squares algorithm for estimating the parameters of the Hammerstein channel, including the channel impulse response coefficients and the parameters of the two B-spline models. Moreover, we also use another real-valued B-spline neural network to model the inversion of the HPA’s nonlinear amplitude response, and the parameters of this inverting B-spline model can be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse Bspline neural network model obtained in time domain. The effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels is demonstrated in a simulation study.

Gaussian processes autoencoder for dimensionality reduction

Learning low dimensional manifold from highly nonlinear data of high dimensionality has become increasingly important for discovering intrinsic representation that can be utilized for data visualization and preprocessing. The autoencoder is a powerful dimensionality reduction technique based on minimizing reconstruction error, and it has regained popularity because it has been efficiently used for greedy pretraining of deep neural networks. Compared to Neural Network (NN), the superiority of Gaussian Process (GP) has been shown in model inference, optimization and performance. GP has been successfully applied in nonlinear Dimensionality Reduction (DR) algorithms, such as Gaussian Process Latent Variable Model (GPLVM). In this paper we propose the Gaussian Processes Autoencoder Model (GPAM) for dimensionality reduction by extending the classic NN based autoencoder to GP based autoencoder. More interestingly, the novel model can also be viewed as back constrained GPLVM (BC-GPLVM) where the back constraint smooth function is represented by a GP. Experiments verify the performance of the newly proposed model.

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.

Low complexity equalization of HCM systems with DPFFT demodulation over doubly-selective channels

To mitigate the inter-carrier interference (ICI) of doubly-selective (DS) fading channels, we consider a hybrid carrier modulation (HCM) system employing the discrete partial fast Fourier transform (DPFFT) demodulation and the banded minimum mean square error (MMSE) equalization in this letter. We first provide the discrete form of partial FFT demodulation, then apply the banded MMSE equalization to suppress the residual interference at the receiver. The proposed algorithm has been demonstrated, via numerical simulations, to be its superior over the single carrier modulation (SCM) system and circularly prefixed orthogonal frequency division multiplexing (OFDM) system over a typical DS channel. Moreover, it represents a good trade-off between computational complexity and performance.

Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities

We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation principle (LDP) for capacities for such Gaussian rough paths. Together with Lyons' universal limit theorem, our results yield immediately the corresponding results for pathwise solutions to stochastic differential equations driven by such Gaussian process in the sense of rough paths. Moreover, our LDP result implies the result of Yoshida on the LDP for capacities over the abstract Wiener space associated with such Gaussian process.

Monitoring scan asymmetry of microwave humidity sounding channels using simultaneous all angle collocations (SAACs)

Simultaneous all angle collocations (SAACs) of microwave humidity sounders (AMSU-B and MHS) on-board polar orbiting satellites are used to estimate scan-dependent biases. This method has distinct advantages over previous methods, such as that the estimated scan-dependent biases are not influenced by diurnal differences between the edges of the scan and the biases can be estimated for both sides of the scan. We find the results are robust in the sense that biases estimated for one satellite pair can be reproduced by double differencing biases of these satellites with a third satellite. Channel 1 of these instruments shows the least bias for all satellites. Channel 2 has biases greater than 5 K, thus needs to be corrected. Channel 3 has biases of about 2 K and more and they are time varying for some of the satellites. Channel 4 has the largest bias which is about 15 K when the data are averaged for 5 years, but biases of individual months can be as large as 30 K. Channel 5 also has large and time varying biases for two of the AMSU-Bs. NOAA-15 (N15) channels are found to be affected the most, mainly due to radio frequency interference (RFI) from onboard data transmitters. Channel 4 of N15 shows the largest and time varying biases, so data of this channel should only be used with caution for climate applications. The two MHS instruments show the best agreement for all channels. Our estimates may be used to correct for scan-dependent biases of these instruments, or at least used as a guideline for excluding channels with large scan asymmetries from scientific analyses.

Modulation of potassium channels inhibits bunyavirus infection

Bunyaviruses are considered to be emerging pathogens facilitated by the segmented nature of their genome that allows reassortment between different species to generate novel viruses with altered pathogenicity. Bunyaviruses are transmitted via a diverse range of arthropod vectors, as well as rodents, and have established a global disease range with massive importance in healthcare, animal welfare and economics. There are no vaccines or anti-viral therapies available to treat human bunyavirus infections and so development of new anti-viral strategies is urgently required. Bunyamwera virus (BUNV; genus Orthobunyavirus) is the model bunyavirus, sharing aspects of its molecular and cellular biology with all Bunyaviridae family members. Here, we show for the first time that BUNV activates and requires cellular potassium (K+) channels to infect cells. Time of addition assays using K+ channel modulating agents demonstrated that K+ channel function is critical to events shortly after virus entry but prior to viral RNA synthesis/replication. A similar K+ channel dependence was identified for other bunyaviruses namely Schmallenberg virus (Orthobunyavirus) as well as the more distantly related Hazara virus (Nairovirus). Using a rational pharmacological screening regimen, twin-pore domain K+ channels (K2P) were identified as the K+ channel family mediating BUNV K+ channel dependence. As several K2P channel modulators are currently in clinical use, our work suggests they may represent a new and safe drug class for the treatment of potentially lethal bunyavirus disease.

High-precision measurements of the co-polar correlation coefficient: non-Gaussian errors and retrieval of the dispersion parameter µ in rainfall

The co-polar correlation coefficient (ρhv) has many applications, including hydrometeor classification, ground clutter and melting layer identification, interpretation of ice microphysics and the retrieval of rain drop size distributions (DSDs). However, we currently lack the quantitative error estimates that are necessary if these applications are to be fully exploited. Previous error estimates of ρhv rely on knowledge of the unknown "true" ρhv and implicitly assume a Gaussian probability distribution function of ρhv samples. We show that frequency distributions of ρhv estimates are in fact highly negatively skewed. A new variable: L = -log10(1 - ρhv) is defined, which does have Gaussian error statistics, and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of ρhv. In addition, we demonstrate how the imperfect co-location of the horizontal and vertical polarisation sample volumes may be accounted for. The possibility of using L to estimate the dispersion parameter (µ) in the gamma drop size distribution is investigated. We find that including drop oscillations is essential for this application, otherwise there could be biases in retrieved µ of up to ~8. Preliminary results in rainfall are presented. In a convective rain case study, our estimates show µ to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.