Instantaneous gelation in Smoluchowski’s coagulation equation revisited

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreasesas M increases, consistent with the expectation that the gelation time is zero in the unregularized system. This decrease appears to be a logarithmically slow function of M, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, K(m1,m2)=max{m1,m2}ν, which gels instantaneously when M→∞ if ν>1. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent ν for large cluster sizes. The total particle density in the stationary state slowly vanishes as [(ν−1)logM]−1/2 when M→∞. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, M, which decay very slowly when M is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.

Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P. However, there are many situations for which it is impractical or impossible to draw from the transition kernel P. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace P by an approximation Pˆ. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ’close’ the chain given by the transition kernel Pˆ is to the chain given by P . We apply these results to several examples from spatial statistics and network analysis.

Towards (more) integrity in academia: transcending neo-liberal assumption of research and knowledge creation and the “rules” supressing academic freedom

European researchers across heterogeneous disciplines voice concerns and argue for new paths towards a brighter future regarding scientific and knowledge creation and communication. Recently, in biological and natural sciences concerns have been expressed that major threats are intentionally ignored. These threats are challenging Europe’s future sustainability towards creating knowledge that effectively deals with emerging social, environmental, health, and economic problems of a planetary scope. Within social science circles however, the root cause regarding the above challenges, have been linked with macro level forces of neo-liberal ways of valuing and relevant rules in academia and beyond which we take for granted. These concerns raised by heterogeneous scholars in natural and the applied social sciences concern the ethics of today’s research and academic integrity. Applying Bourdieu’s sociology may not allow an optimistic lens if change is possible. Rather than attributing the replication of neo-liberal habitus in intentional agent and institutional choices, Bourdieu’s work raises the importance of thoughtlessly internalised habits in human and social action. Accordingly, most action within a given paradigm (in this case, neo-liberalism) is understood as habituated, i.e. unconsciously reproducing external social fields, even ill-defined ways of valuing. This essay analyses these and how they may help critically analyse the current habitus surrounding research and knowledge production, evaluation, and communication and related aspects of academic freedom. Although it is acknowledged that transformation is not easy, the essay presents arguments and recent theory paths to suggest that change nevertheless may be a realistic hope once certain action logics are encouraged.

A benchmark-driven modelling approach for evaluating deployment choices on a multi-core architecture

The complexity of current and emerging architectures provides users with options about how best to use the available resources, but makes predicting performance challenging. In this work a benchmark-driven model is developed for a simple shallow water code on a Cray XE6 system, to explore how deployment choices such as domain decomposition and core affinity affect performance. The resource sharing present in modern multi-core architectures adds various levels of heterogeneity to the system. Shared resources often includes cache, memory, network controllers and in some cases floating point units (as in the AMD Bulldozer), which mean that the access time depends on the mapping of application tasks, and the core's location within the system. Heterogeneity further increases with the use of hardware-accelerators such as GPUs and the Intel Xeon Phi, where many specialist cores are attached to general-purpose cores. This trend for shared resources and non-uniform cores is expected to continue into the exascale era. The complexity of these systems means that various runtime scenarios are possible, and it has been found that under-populating nodes, altering the domain decomposition and non-standard task to core mappings can dramatically alter performance. To find this out, however, is often a process of trial and error. To better inform this process, a performance model was developed for a simple regular grid-based kernel code, shallow. The code comprises two distinct types of work, loop-based array updates and nearest-neighbour halo-exchanges. Separate performance models were developed for each part, both based on a similar methodology. Application specific benchmarks were run to measure performance for different problem sizes under different execution scenarios. These results were then fed into a performance model that derives resource usage for a given deployment scenario, with interpolation between results as necessary.

Rainfall estimation by rain gauge-radar combination: a concurrent multiplicative-additive approach

A procedure (concurrent multiplicative-additive objective analysis scheme [CMA-OAS]) is proposed for operational rainfall estimation using rain gauges and radar data. On the basis of a concurrent multiplicative-additive (CMA) decomposition of the spatially nonuniform radar bias, within-storm variability of rainfall and fractional coverage of rainfall are taken into account. Thus both spatially nonuniform radar bias, given that rainfall is detected, and bias in radar detection of rainfall are handled. The interpolation procedure of CMA-OAS is built on Barnes' objective analysis scheme (OAS), whose purpose is to estimate a filtered spatial field of the variable of interest through a successive correction of residuals resulting from a Gaussian kernel smoother applied on spatial samples. The CMA-OAS, first, poses an optimization problem at each gauge-radar support point to obtain both a local multiplicative-additive radar bias decomposition and a regionalization parameter. Second, local biases and regionalization parameters are integrated into an OAS to estimate the multisensor rainfall at the ground level. The procedure is suited to relatively sparse rain gauge networks. To show the procedure, six storms are analyzed at hourly steps over 10,663 km2. Results generally indicated an improved quality with respect to other methods evaluated: a standard mean-field bias adjustment, a spatially variable adjustment with multiplicative factors, and ordinary cokriging.

Nonlinear identification using orthogonal forward regression with nested optimal regularization

An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm.

Sparse density estimation on the multinomial manifold

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators.

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.

The importance of anisotropic Coulomb interaction in LaMnO3

In low-temperature anti-ferromagnetic LaMnO3, strong and localized electronic interactions among Mn 3d electrons prevent a satisfactory description from standard local density and generalized gradient approximations in density functional theory calculations. Here we show that the strong on-site electronic interactions are described well only by using direct and exchange corrections to the intra-orbital Coulomb potential. Only DFT+U calculations with explicit exchange corrections produce a balanced picture of electronic, magnetic and structural observables in agreement with experiment. To understand the reason, a rewriting of the functional form of the +U corrections is presented that leads to a more physical and transparent understanding of the effect of these correction terms. The approach highlights the importance of Hund’s coupling (intra-orbital exchange) in providing anisotropy across the occupation and energy eigenvalues of the Mn d states. This intra-orbital exchange is the key to fully activating the Jahn-Teller distortion, reproducing the experimental band gap and stabilizing the correct magnetic ground state in LaMnO3. The best parameter values for LaMnO3 within the DFT(PBEsol)+U framework are determined to be U = 8 eV and J = 1.9 eV.

Resilience as transformative capacity: exploring the quadripartite cycle of structuration in a Mozambican resettlement programme

The concept of resilience has emerged out of a complex literature that has sought to make sense of an increasingly interconnected world that appears ever more beset by crises. Resilience’s appeal is reflected by the burgeoning mass of literature that has appeared on the subject in the past five years. However, there is ongoing debate surrounding its usage, with some commentators claiming that the term is inherently too conservative a one to be usefully applied to situations of vulnerability in which more radical social change is required. This article extends existing efforts to formulate more transformative notions of resilience by reframing it as a double-edged outcome of the pre-reflective and critical ways in which actors draw upon their internal structures following the occurrence of a negative event, thus reproducing or changing the external structural context that gave rise to the event in the first place. By employing a structuration-inspired analysis to the study of small-scale farmer responses to a flood-induced resettlement programme in central Mozambique, the article presents a systematic approach to the examination of resilience in light of this reframing. The case study findings suggest that more attention should be paid to the facilitative, as well as constraining, nature of structures if vulnerable populations are to be assisted in their efforts to exert transformative capacity over the wider conditions that give rise to their difficulties.

Investigating the relationship between Eurasian snow and the Arctic Oscillation with data and models

Recent research suggests Eurasian snow-covered area (SCA) influences the Arctic Oscillation (AO) via the polar vortex. This could be important for Northern Hemisphere winter season forecasting. A fairly strong negative correlation between October SCA and the AO, based on both monthly and daily observational data, has been noted in the literature. While reproducing these previous links when using the same data, we find no further evidence of the link when using an independent satellite data source, or when using a climate model.

Generalized convective quasi-equilibrium principle

A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection. The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity.

An ensemble of eddy-permitting global ocean reanalyses from the MyOcean project

A set of four eddy-permitting global ocean reanalyses produced in the framework of the MyOcean project have been compared over the altimetry period 1993–2011. The main differences among the reanalyses used here come from the data assimilation scheme implemented to control the ocean state by inserting reprocessed observations of sea surface temperature (SST), in situ temperature and salinity profiles, sea level anomaly and sea-ice concentration. A first objective of this work includes assessing the interannual variability and trends for a series of parameters, usually considered in the community as essential ocean variables: SST, sea surface salinity, temperature and salinity averaged over meaningful layers of the water column, sea level, transports across pre-defined sections, and sea ice parameters. The eddy-permitting nature of the global reanalyses allows also to estimate eddy kinetic energy. The results show that in general there is a good consistency between the different reanalyses. An intercomparison against experiments without data assimilation was done during the MyOcean project and we conclude that data assimilation is crucial for correctly simulating some quantities such as regional trends of sea level as well as the eddy kinetic energy. A second objective is to show that the ensemble mean of reanalyses can be evaluated as one single system regarding its reliability in reproducing the climate signals, where both variability and uncertainties are assessed through the ensemble spread and signal-to-noise ratio. The main advantage of having access to several reanalyses differing in the way data assimilation is performed is that it becomes possible to assess part of the total uncertainty. Given the fact that we use very similar ocean models and atmospheric forcing, we can conclude that the spread of the ensemble of reanalyses is mainly representative of our ability to gauge uncertainty in the assimilation methods. This uncertainty changes a lot from one ocean parameter to another, especially in global indices. However, despite several caveats in the design of the multi-system ensemble, the main conclusion from this study is that an eddy-permitting multi-system ensemble approach has become mature and our results provide a first step towards a systematic comparison of eddy-permitting global ocean reanalyses aimed at providing robust conclusions on the recent evolution of the oceanic state.

A reappraisal of Baskerville's Greek types

Ιn the eighteenth century the printing of Greek texts continued to be central to scholarship and discourse. The typography of Greek texts could be characterised as a continuation of French models from the sixteenth century, with a gradual dilution of the complexity of ligatures and abbreviations, mostly through printers in the Low Countries. In Britain, Greek printing was dominated by the university presses, which reproduced conservatively the continental models – exemplified by Oxford's Fell types, which were Dutch adaptations of earlier French models. Hindsight allows us to identify a meaningful development in the Greek types cut by Alexander Wilson for the Foulis Press in Glasgow, but we can argue that in the middle of the eighteenth century Baskerville was considering Greek printing the typographic environment was ripe for a new style of Greek types. The opportunity to cut the types for a New Testament (in an twin edition that included a generous octavo and a large quarto version) would seem perfect for showcasing Baskerville's capacity for innovation. His Greek type maintained the cursive ductus of earlier models, but abandoned complex ligatures and any hint of scribal flourish. He homogenised the modulation of the letter strokes and the treatment of terminals, and normalised the horizontal alignments of all letters. Although the strokes are in some letters too delicate, the narrow set of the style composes a consistent, uniform texture that is a clean break from contemporaneous models. The argument is made that this is the first Greek typeface that can be described as fully typographic in the context of the technology of the time. It sets a pattern that was to be followed, without acknowledgement, by Richard Porson nearly a century and a half later. The typeface received little praise by typographic historians, and was condemned by Victor Scholderer in his retrospective of Greek typography. A survey of typeface reviews in the surrounding decades establishes that the commentators were mostly reproducing the views of an arbitrary typographic orthodoxy, for which only types with direct references to Renaissance models were acceptable. In these comments we detect a bias against someone considered an arriviste in the scholarly printing establishment, as well as a conservative attitude to typographic innovation.

Examining the predictability of the Stratospheric Sudden Warming of January 2013 using multiple NWP systems

The first multi-model study to estimate the predictability of a boreal Sudden Stratospheric Warming (SSW) is performed using five NWP systems. During the 2012-2013 boreal winter, anomalous upward propagating planetary wave activity was observed towards the end of December, which followed by a rapid deceleration of the westerly circulation around 2 January 2013, and on 7 January 2013 the zonal mean zonal wind at 60°N and 10 hPa reversed to easterly. This stratospheric dynamical activity was followed by an equatorward shift of the tropospheric jet stream and by a high pressure anomaly over the North Atlantic, which resulted in severe cold conditions in the UK and Northern Europe. In most of the five models, the SSW event was predicted 10 days in advance. However, only some ensemble members in most of the models predicted weakening of westerly wind when the models were initialized 15 days in advance of the SSW. Further dynamical analysis of the SSW shows that this event was characterized by the anomalous planetary wave-1 amplification followed by the anomalous wave-2 amplification in the stratosphere, which resulted in a split vortex occurring between 6 January 2013 and 8 January 2013. The models have some success in reproducing wave-1 activity when initialized 15 days in advance, they but generally failed to produce the wave-2 activity during the final days of the event. Detailed analysis shows that models have reasonably good skill in forecasting tropospheric blocking features that stimulate wave-2 amplification in the troposphere, but they have limited skill in reproducing wave-2 amplification in the stratosphere.