Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned

Constructing the frequency and wave normal distribution of whistler-mode wave power

We introduce a new methodology that allows the construction of wave frequency distributions due to growing incoherent whistler-mode waves in the magnetosphere. The technique combines the equations of geometric optics (i.e. raytracing) with the equation of transfer of radiation in an anisotropic lossy medium to obtain spectral energy density as a function of frequency and wavenormal angle. We describe the method in detail, and then demonstrate how it could be used in an idealised magnetosphere during quiet geomagnetic conditions. For a specific set of plasma conditions, we predict that the wave power peaks off the equator at ~15 degrees magnetic latitude. The new calculations predict that wave power as a function of frequency can be adequately described using a Gaussian function, but as a function of wavenormal angle, it more closely resembles a skew normal distribution. The technique described in this paper is the first known estimate of the parallel and oblique incoherent wave spectrum as a result of growing whistler-mode waves, and provides a means to incorporate self-consistent wave-particle interactions in a kinetic model of the magnetosphere over a large volume.

Model simulations and aircraft measurements of vertical, seasonal and latitudinal O3 and CO distributions over Europe

During a series of 8 measurement campaigns within the SPURT project (2001-2003), vertical profiles of CO and O3 have been obtained at subtropical, middle and high latitudes over western Europe, covering the troposphere and lowermost stratosphere up to ~14 km altitude during all seasons. The seasonal and latitudinal variation of the measured trace gas profiles are compared to simulations with the chemical transport model MATCH. In the troposphere reasonable agreement between observations and model predictions is achieved for CO and O3, in particular at subtropical and mid-latitudes, while the model overestimates (underestimates) CO (O3 in the lowermost stratosphere particularly at high latitudes, indicating too strong simulated bi-directional exchange across the tropopause. By the use of tagged tracers in the model, long-range transport of Asian air masses is identified as the dominant source of CO pollution over Europe in the free troposphere.

Evaluating the Survey of Professional Forecasters probability distributions of expected inflation based on derived event probability forecasts

Techniques are proposed for evaluating forecast probabilities of events. The tools are especially useful when, as in the case of the Survey of Professional Forecasters (SPF) expected probability distributions of inflation, recourse cannot be made to the method of construction in the evaluation of the forecasts. The tests of efficiency and conditional efficiency are applied to the forecast probabilities of events of interest derived from the SPF distributions, and supplement a whole-density evaluation of the SPF distributions based on the probability integral transform approach.

Probability distributions or point predictions? Survey forecasts of US output growth and inflation

We consider whether survey respondents’ probability distributions, reported as histograms, provide reliable and coherent point predictions, when viewed through the lens of a Bayesian learning model. We argue that a role remains for eliciting directly-reported point predictions in surveys of professional forecasters.

Pollen-based reconstructions of biome distributions for Australia, Southeast Asia and the Pacific (SEAPAC region) at 0,6000 and 18,000 14C yr B.P.

Aim  This paper documents reconstructions of the vegetation patterns in Australia, Southeast Asia and the Pacific (SEAPAC region) in the mid-Holocene and at the last glacial maximum (LGM). Methods  Vegetation patterns were reconstructed from pollen data using an objective biomization scheme based on plant functional types. The biomization scheme was first tested using 535 modern pollen samples from 377 sites, and then applied unchanged to fossil pollen samples dating to 6000 ± 500 or 18,000 ± 1000 14C yr bp. Results  1. Tests using surface pollen sample sites showed that the biomization scheme is capable of reproducing the modern broad-scale patterns of vegetation distribution. The north–south gradient in temperature, reflected in transitions from cool evergreen needleleaf forest in the extreme south through temperate rain forest or wet sclerophyll forest (WSFW) and into tropical forests, is well reconstructed. The transitions from xerophytic through sclerophyll woodlands and open forests to closed-canopy forests, which reflect the gradient in plant available moisture from the continental interior towards the coast, are reconstructed with less geographical precision but nevertheless the broad-scale pattern emerges. 2. Differences between the modern and mid-Holocene vegetation patterns in mainland Australia are comparatively small and reflect changes in moisture availability rather than temperature. In south-eastern Australia some sites show a shift towards more moisture-stressed vegetation in the mid-Holocene with xerophytic woods/scrub and temperate sclerophyll woodland and shrubland at sites characterized today by WSFW or warm-temperate rain forest (WTRF). However, sites in the Snowy Mountains, on the Southern Tablelands and east of the Great Dividing Range have more moisture-demanding vegetation in the mid-Holocene than today. South-western Australia was slightly drier than today. The single site in north-western Australia also shows conditions drier than today in the mid-Holocene. Changes in the tropics are also comparatively small, but the presence of WTRF and tropical deciduous broadleaf forest and woodland in the mid-Holocene, in sites occupied today by cool-temperate rain forest, indicate warmer conditions. 3. Expansion of xerophytic vegetation in the south and tropical deciduous broadleaf forest and woodland in the north indicate drier conditions across mainland Australia at the LGM. None of these changes are informative about the degree of cooling. However the evidence from the tropics, showing lowering of the treeline and forest belts, indicates that conditions were between 1 and 9 °C (depending on elevation) colder. The encroachment of tropical deciduous broadleaf forest and woodland into lowland evergreen broadleaf forest implies greater aridity. Main conclusions  This study provides the first continental-scale reconstruction of mid-Holocene and LGM vegetation patterns from Australia, Southeast Asia and the Pacific (SEAPAC region) using an objective biomization scheme. These data will provide a benchmark for evaluation of palaeoclimate simulations within the framework of the Palaeoclimate Modelling Intercomparison Project.

Autobiographical memory distributions for negative self-images: memories are organised around negative as well as positive aspects of identity

The relationship between developmental experiences, and an individual’s emerging beliefs about themselves and the world, is central to many forms of psychotherapy. People suffering from a variety of mental health problems have been shown to use negative memories when defining the self, however little is known about how these negative memories might be organised and relate to negative self-images. In two online studies with middle-aged (N = 18; Study 1) and young (N = 56; Study 2) adults, we found that participants’ negative self-images (e.g., I am a failure) were associated with sets of autobiographical memories that formed clustered distributions around times of self-formation, in much the same pattern as for positive self-images (e.g., I am talented). This novel result shows that highly organised sets of salient memories may be responsible for perpetuating negative beliefs about the self. Implications for therapy are discussed.

Fast identification algorithms for Gaussian process model

A class identification algorithms is introduced for Gaussian process(GP)models.The fundamental approach is to propose a new kernel function which leads to a covariance matrix with low rank,a property that is consequently exploited for computational efficiency for both model parameter estimation and model predictions.The objective of either maximizing the marginal likelihood or the Kullback–Leibler (K–L) divergence between the estimated output probability density function(pdf)and the true pdf has been used as respective cost functions.For each cost function,an efficient coordinate descent algorithm is proposed to estimate the kernel parameters using a one dimensional derivative free search, and noise variance using a fast gradient descent algorithm. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

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.

Incoherent scatter radar observations of non-Maxwellian ion velocity distributions in the auroral F-region

Observations by the EISCAT experiments “POLAR” and Common Programme CP-3 reveal non-Maxwellian ion velocity distributions in the auroral F-region ionosphere. Analysis of data from three periods is presented. During the first period, convection velocities are large (≈2 km s-1) and constant over part of a CP-3 latitude scan; the second period is one of POLAR data containing a short-lived (<1 min.) burst of rapid (>1.5 km s-1) flow. We concentrate on these two periods as they allow the study of a great many features of the ion-neutral interactions which drive the plasma non-thermal and provide the best available experimental test for models of the 3-dimensional ion velocity distribution function. The third period is included to illustrate the fact that non-thermal plasma frequently exists in the auroral ionosphere: the data, also from the POLAR experiment, cover a three-hour period of typical auroral zone flow and analysis reveals that the ion distribution varies from Maxwellian to the threshold of a toroidal form.

The influence of anisotropic F region ion velocity distributions on ionospheric ion outflows into the magnetosphere

The contribution to the field-aligned ionospheric ion momentum equation, due to coupling between pressure anisotropy and the inhomogeneous geomagnetic field, is investigated. We term this contribution the “hydrodynamic mirror force” and investigate its dependence on the ion drift and the resulting deformations of the ion velocity distribution function from an isotropic form. It is shown that this extra upforce increases rapidly with ion drift relative to the neutral gas but is not highly dependent on the ion-neutral collision model employed. An example of a burst of flow observed by EISCAT, thought to be the ionospheric signature of a flux transfer event at the magnetopause, is studied in detail and it is shown that the nonthermal plasma which results is subject to a hydrodynamic mirror force which is roughly 10% of the gravitational downforce. In addition, predictions by the coupled University College London-Sheffield University model of the ionosphere and thermosphere show that the hydrodynamic mirror force in the auroral oval is up to 3% of the gravitational force for Kp of about 3, rising to 10% following a sudden increase in cross-cap potential. The spatial distribution of the upforce shows peaks in the cusp region and in the post-midnight auroral oval, similar to that of observed low-energy heavy ion flows from the ionosphere into the magnetosphere. We suggest the hydrodynamic mirror force may modulate these outflows by controlling the supply of heavy ions to regions of ion acceleration and that future simulations of the effects of Joule heating on ion outflows should make allowance for it.

Non-Maxwellian ion velocity distributions observed using EISCAT

Recent observations from the EISCAT incoherent scatter radar have revealed bursts of poleward ion flow in the dayside auroral ionosphere which are consistent with the ionospheric signature of flux transfer events at the magnetopause. These bursts frequently contain ion drifts which exceed the neutral thermal speed and, because the neutral thermospheric wind is incapable of responding sufficiently rapidly, toroidal, non-Maxwellian ion velocity distributions are expected. The EISCAT observations are made with high time resolution (15 seconds) and at a large angle to the geomagnetic field (73.5°), allowing the non-Maxwellian nature of the distribution to be observed remotely for the first time. The observed features are also strongly suggestive of a toroidal distribution: characteristic spectral shape, increased scattered power (both consistent with reduced Landau damping and enhanced electric field fluctuations) and excessively high line-of-sight ion temperatures deduced if a Maxwellian distribution is assumed. These remote sensing observations allow the evolution of the distributions to be observed. They are found to be non-Maxwellian whenever the ion drift exceeds the neutral thermal speed, indicating that such distributions can exist over the time scale of the flow burst events (several minutes).

Subdiffraction fluorescence imaging of biomolecular structure and distributions with quantum dots

We introduce semiconductor quantum dot-based fluorescence imaging with approximately 2-fold increased optical resolution in three dimensions as a method that allows both studying cellular structures and spatial organization of biomolecules in membranes and subcellular organelles. Target biomolecules are labelled with quantum dots via immunocytochemistry. The resolution enhancement is achieved by three-photon absorption of quantum dots and subsequent fluorescence emission from a higher-order excitonic state. Different from conventional multiphoton microscopy, this approach can be realized on any confocal microscope without the need for pulsed excitation light. We demonstrate quantum dot triexciton imaging (QDTI) of the microtubule network of U373 cells, 3D imaging of TNF receptor 2 on the plasma membrane of HeLa cells, and multicolor 3D imaging of mitochondrial cytochrome c oxidase and actin in COS-7 cells.

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.

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.