Inferring the biggest and best: a measurement model for applying recognition to evoke consideration sets and judge between multiple alternatives

It has long been supposed that preference judgments between sets of to-be-considered possibilities are made by means of initially winnowing down the most promising-looking alternatives to form smaller “consideration sets” (Howard, 1963; Wright & Barbour, 1977). In preference choices with >2 options, it is standard to assume that a “consideration set”, based upon some simple criterion, is established to reduce the options available. Inferential judgments, in contrast, have more frequently been investigated in situations in which only two possibilities need to be considered (e.g., which of these two cities is the larger?) Proponents of the “fast and frugal” approach to decision-making suggest that such judgments are also made on the basis of limited, simple criteria. For example, if only one of two cities is recognized and the task is to judge which city has the larger population, the recognition heuristic states that the recognized city should be selected. A multinomial processing tree model is outlined which provides the basis for estimating the extent to which recognition is used as a criterion in establishing a consideration set for inferential judgments between three possible options.

Dynamics of the lower stratospheric circulation response to ENSO

A robust feature of the observed response to El Nin˜o–Southern Oscillation (ENSO) is an altered circulation in the lower stratosphere. When sea surface temperatures (SSTs) in the tropical Pacific are warmer there is enhanced upwelling and cooling in the tropical lower stratosphere and downwelling and warming in the midlatitudes, while the opposite is true of cooler SSTs. The midlatitude lower stratospheric response to ENSO is larger in the Southern Hemisphere (SH) than in the Northern Hemisphere (NH). In this study the dynamical version of the Canadian Middle Atmosphere Model (CMAM) is used to simulate 25 realizations of the atmospheric response to the 1982/83 El Nin˜o and the 1973/74 La Nin˜ a. This version ofCMAMis a comprehensive high-top general circulation model that does not include interactive chemistry. The observed lower stratospheric response to ENSO is well reproduced by the simulations, allowing them to be used to investigate the mechanisms involved. Both the observed and simulated responses maximize in December–March and so this study focuses on understanding the mechanisms involved in that season. The response in tropical upwelling is predominantly driven by anomalous transient synoptic-scale wave drag in the SH subtropical lower stratosphere, which is also responsible for the compensating SH midlatitude response. This altered wave drag stems from an altered upward flux of wave activity from the troposphere into the lower stratosphere between 208 and 408S. The altered flux of wave activity can be divided into two distinct components. In the Pacific, the acceleration of the zonal wind in the subtropics from the warmer tropical SSTs results in a region between the midlatitude and subtropical jets where there is an enhanced source of low phase speed eddies. At other longitudes, an equatorward shift of the midlatitude jet from the extratropical tropospheric response to El Nin˜o results in an enhanced source of waves of higher phase speeds in the subtropics. The altered resolved wave drag is only apparent in the SH and the difference between the two hemispheres can be related to the difference in the climatological jet structures in this season and the projection of the wind anomalies associated with ENSO onto those structures.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain

A representation of the conformal mapping g of the interior or exterior of the unit circle onto a simply-connected domain Ω as a boundary integral in terms ofƒ|∂Ω is obtained, whereƒ :=g -l. A product integration scheme for the approximation of the boundary integral is described and analysed. An ill-conditioning problem related to the domain geometry is discussed. Numerical examples confirm the conclusions of this discussion and support the analysis of the quadrature scheme.

Projection of global wave climate change towards the end of the 21st century

Wind generated waves at the sea surface are of outstanding importance for both their practical relevance in many aspects, such as coastal erosion, protection, or safety of navigation, and for their scientific relevance in modifying fluxes at the air-sea interface. So far long-term changes in ocean wave climate have been studied mostly from a regional perspective with global dynamical studies emerging only recently. Here a global wave climate study is presented, in which a global wave model (WAM) is driven by atmospheric forcing from a global climate model (ECHAM5) for present day and potential future climate conditions represented by the IPCC (Intergovernmental Panel for Climate Change) A1B emission scenario. It is found that changes in mean and extreme wave climate towards the end of the twenty-first century are small to moderate, with the largest signals being a poleward shift in the annual mean and extreme significant wave heights in the mid-latitudes of both hemispheres, more pronounced in the Southern Hemisphere, and most likely associated with a corresponding shift in mid-latitude storm tracks. These changes are broadly consistent with results from the few studies available so far. The projected changes in the mean wave periods, associated with the changes in the wave climate in the mid to high latitudes, are also shown, revealing a moderate increase in the equatorial eastern side of the ocean basins. This study presents a step forward towards a larger ensemble of global wave climate projections required to better assess robustness and uncertainty of potential future wave climate change.

Solution-free sets for sums of binary forms

In this paper, we obtain quantitative estimates for the asymptotic density of subsets of the integer lattice Z2 that contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of Vinogradov’s mean value theorem applicable to binary forms.

A comparative review of dimension reduction methods in approximate Bayesian computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

A high frequency $hp$ boundary element method for scattering by convex polygons

In this paper we propose and analyze a hybrid $hp$ boundary element method for the solution of problems of high frequency acoustic scattering by sound-soft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution. We demonstrate, both theoretically and via numerical examples, exponential convergence with respect to the order of the polynomials, moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern, in which the dependence on the frequency of all constants is explicit. Importantly, these estimates prove that, to achieve any desired accuracy in the computation of these quantities, it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods.

Wave activity in the tropical tropopause layer in seven reanalysis and four chemistry climate model data sets

Sub-seasonal variability including equatorial waves significantly influence the dehydration and transport processes in the tropical tropopause layer (TTL). This study investigates the wave activity in the TTL in 7 reanalysis data sets (RAs; NCEP1, NCEP2, ERA40, ERA-Interim, JRA25, MERRA, and CFSR) and 4 chemistry climate models (CCMs; CCSRNIES, CMAM, MRI, and WACCM) using the zonal wave number-frequency spectral analysis method with equatorially symmetric-antisymmetric decomposition. Analyses are made for temperature and horizontal winds at 100 hPa in the RAs and CCMs and for outgoing longwave radiation (OLR), which is a proxy for convective activity that generates tropopause-level disturbances, in satellite data and the CCMs. Particular focus is placed on equatorial Kelvin waves, mixed Rossby-gravity (MRG) waves, and the Madden-Julian Oscillation (MJO). The wave activity is defined as the variance, i.e., the power spectral density integrated in a particular zonal wave number-frequency region. It is found that the TTL wave activities show significant difference among the RAs, ranging from ∼0.7 (for NCEP1 and NCEP2) to ∼1.4 (for ERA-Interim, MERRA, and CFSR) with respect to the averages from the RAs. The TTL activities in the CCMs lie generally within the range of those in the RAs, with a few exceptions. However, the spectral features in OLR for all the CCMs are very different from those in the observations, and the OLR wave activities are too low for CCSRNIES, CMAM, and MRI. It is concluded that the broad range of wave activity found in the different RAs decreases our confidence in their validity and in particular their value for validation of CCM performance in the TTL, thereby limiting our quantitative understanding of the dehydration and transport processes in the TTL.

Evidence for changes in stratospheric transport and mixing over the past three decades based on multiple data sets and tropical leaky pipe analysis

Variability in the strength of the stratospheric Lagrangian mean meridional or Brewer-Dobson circulation and horizontal mixing into the tropics over the past three decades are examined using observations of stratospheric mean age of air and ozone. We use a simple representation of the stratosphere, the tropical leaky pipe (TLP) model, guided by mean meridional circulation and horizontal mixing changes in several reanalyses data sets and chemistry climate model (CCM) simulations, to help elucidate reasons for the observed changes in stratospheric mean age and ozone. We find that the TLP model is able to accurately simulate multiyear variability in ozone following recent major volcanic eruptions and the early 2000s sea surface temperature changes, as well as the lasting impact on mean age of relatively short-term circulation perturbations. We also find that the best quantitative agreement with the observed mean age and ozone trends over the past three decades is found assuming a small strengthening of the mean circulation in the lower stratosphere, a moderate weakening of the mean circulation in the middle and upper stratosphere, and a moderate increase in the horizontal mixing into the tropics. The mean age trends are strongly sensitive to trends in the horizontal mixing into the tropics, and the uncertainty in the mixing trends causes uncertainty in the mean circulation trends. Comparisons of the mean circulation and mixing changes suggested by the measurements with those from a recent suite of CCM runs reveal significant differences that may have important implications on the accurate simulation of future stratospheric climate.

The accuracy of SST retrievals from AATSR: An initial assessment through geophysical validation against in situ radiometers, buoys and other SST data sets

The Advanced Along-Track Scanning Radiometer (AATSR) was launched on Envisat in March 2002. The AATSR instrument is designed to retrieve precise and accurate global sea surface temperature (SST) that, combined with the large data set collected from its predecessors, ATSR and ATSR-2, will provide a long term record of SST data that is greater than 15 years. This record can be used for independent monitoring and detection of climate change. The AATSR validation programme has successfully completed its initial phase. The programme involves validation of the AATSR derived SST values using in situ radiometers, in situ buoys and global SST fields from other data sets. The results of the initial programme presented here will demonstrate that the AATSR instrument is currently close to meeting its scientific objectives of determining global SST to an accuracy of 0.3 K (one sigma). For night time data, the analysis gives a warm bias of between +0.04 K (0.28 K) for buoys to +0.06 K (0.20 K) for radiometers, with slightly higher errors observed for day time data, showing warm biases of between +0.02 (0.39 K) for buoys to +0.11 K (0.33 K) for radiometers. They show that the ATSR series of instruments continues to be the world leader in delivering accurate space-based observations of SST, which is a key climate parameter.

Complex extreme learning machine applications in terahertz pulsed signals feature sets

This paper presents a novel approach to the automatic classification of very large data sets composed of terahertz pulse transient signals, highlighting their potential use in biochemical, biomedical, pharmaceutical and security applications. Two different types of THz spectra are considered in the classification process. Firstly a binary classification study of poly-A and poly-C ribonucleic acid samples is performed. This is then contrasted with a difficult multi-class classification problem of spectra from six different powder samples that although have fairly indistinguishable features in the optical spectrum, they also possess a few discernable spectral features in the terahertz part of the spectrum. Classification is performed using a complex-valued extreme learning machine algorithm that takes into account features in both the amplitude as well as the phase of the recorded spectra. Classification speed and accuracy are contrasted with that achieved using a support vector machine classifier. The study systematically compares the classifier performance achieved after adopting different Gaussian kernels when separating amplitude and phase signatures. The two signatures are presented as feature vectors for both training and testing purposes. The study confirms the utility of complex-valued extreme learning machine algorithms for classification of the very large data sets generated with current terahertz imaging spectrometers. The classifier can take into consideration heterogeneous layers within an object as would be required within a tomographic setting and is sufficiently robust to detect patterns hidden inside noisy terahertz data sets. The proposed study opens up the opportunity for the establishment of complex-valued extreme learning machine algorithms as new chemometric tools that will assist the wider proliferation of terahertz sensing technology for chemical sensing, quality control, security screening and clinic diagnosis. Furthermore, the proposed algorithm should also be very useful in other applications requiring the classification of very large datasets.

Weighted alpha-rate dominating sets in social networks

We are looking into variants of a domination set problem in social networks. While randomised algorithms for solving the minimum weighted domination set problem and the minimum alpha and alpha-rate domination problem on simple graphs are already present in the literature, we propose here a randomised algorithm for the minimum weighted alpha-rate domination set problem which is, to the best of our knowledge, the first such algorithm. A theoretical approximation bound based on a simple randomised rounding technique is given. The algorithm is implemented in Python and applied to a UK Twitter mentions networks using a measure of individuals’ influence (klout) as weights. We argue that the weights of vertices could be interpreted as the costs of getting those individuals on board for a campaign or a behaviour change intervention. The minimum weighted alpha-rate dominating set problem can therefore be seen as finding a set that minimises the total cost and each individual in a network has at least alpha percentage of its neighbours in the chosen set. We also test our algorithm on generated graphs with several thousand vertices and edges. Our results on this real-life Twitter networks and generated graphs show that the implementation is reasonably efficient and thus can be used for real-life applications when creating social network based interventions, designing social media campaigns and potentially improving users’ social media experience.