On the spectral gap of Brownian motion with jump boundary

In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are dierent and mainly probabilistic relying on coupling methods adapted to the special situation under investigation. Moreover we answer a question raised by Ben-Ari and Pinsky concerning the dependence of the spectral gap from the jump distribution in a multi-dimensional setting.

Formal theory building for the avalanche game: explaining counter-intuitive behaviour of a complex system using geometrical and human behavioural/physiological effects

In 'Avalanche', an object is lowered, players staying in contact throughout. Normally the task is easily accomplished. However, with larger groups counter-intuitive behaviours appear. The paper proposes a formal theory for the underlying causal mechanisms. The aim is to not only provide an explicit, testable hypothesis for the source of the observed modes of behaviour-but also to exemplify the contribution that formal theory building can make to understanding complex social phenomena. Mapping reveals the importance of geometry to the Avalanche game; each player has a pair of balancing loops, one involved in lowering the object, the other ensuring contact. For more players, sets of balancing loops interact and these can allow dominance by reinforcing loops, causing the system to chase upwards towards an ever-increasing goal. However, a series of other effects concerning human physiology and behaviour (HPB) is posited as playing a role. The hypothesis is therefore rigorously tested using simulation. For simplicity a 'One Degree of Freedom' case is examined, allowing all of the effects to be included whilst rendering the analysis more transparent. Formulation and experimentation with the model gives insight into the behaviours. Multi-dimensional rate/level analysis indicates that there is only a narrow region in which the system is able to move downwards. Model runs reproduce the single 'desired' mode of behaviour and all three of the observed 'problematic' ones. Sensitivity analysis gives further insight into the system's modes and their causes. Behaviour is seen to arise only when the geometric effects apply (number of players greater than degrees of freedom of object) in combination with a range of HPB effects. An analogy exists between the co-operative behaviour required here and various examples: conflicting strategic objectives in organizations; Prisoners' Dilemma and integrated bargaining situations. Additionally, the game may be relatable in more direct algebraic terms to situations involving companies in which the resulting behaviours are mediated by market regulations. Finally, comment is offered on the inadequacy of some forms of theory building and the case is made for formal theory building involving the use of models, analysis and plausible explanations to create deep understanding of social phenomena.

Efficient group communication for large-scale parallel clustering

Global communication requirements and load imbalance of some parallel data mining algorithms are the major obstacles to exploit the computational power of large-scale systems. This work investigates how non-uniform data distributions can be exploited to remove the global communication requirement and to reduce the communication cost in iterative parallel data mining algorithms. In particular, the analysis focuses on one of the most influential and popular data mining methods, the k-means algorithm for cluster analysis. The straightforward parallel formulation of the k-means algorithm requires a global reduction operation at each iteration step, which hinders its scalability. This work studies a different parallel formulation of the algorithm where the requirement of global communication can be relaxed while still providing the exact solution of the centralised k-means algorithm. The proposed approach exploits a non-uniform data distribution which can be either found in real world distributed applications or can be induced by means of multi-dimensional binary search trees. The approach can also be extended to accommodate an approximation error which allows a further reduction of the communication costs.

Derivation of an urban materials spectral library through emittance and reflectance spectroscopy

Recent advances in thermal infrared remote sensing include the increased availability of airborne hyperspectral imagers (such as the Hyperspectral Thermal Emission Spectrometer, HyTES, or the Telops HyperCam and the Specim aisaOWL), and it is planned that an increased number spectral bands in the long-wave infrared (LWIR) region will soon be measured from space at reasonably high spatial resolution (by imagers such as HyspIRI). Detailed LWIR emissivity spectra are required to best interpret the observations from such systems. This includes the highly heterogeneous urban environment, whose construction materials are not yet particularly well represented in spectral libraries. Here, we present a new online spectral library of urban construction materials including LWIR emissivity spectra of 74 samples of impervious surfaces derived using measurements made by a portable Fourier Transform InfraRed (FTIR) spectrometer. FTIR emissivity measurements need to be carefully made, else they are prone to a series of errors relating to instrumental setup and radiometric calibration, which here relies on external blackbody sources. The performance of the laboratory-based emissivity measurement approach applied here, that in future can also be deployed in the field (e.g. to examine urban materials in situ), is evaluated herein. Our spectral library also contains matching short-wave (VIS–SWIR) reflectance spectra observed for each urban sample. This allows us to examine which characteristic (LWIR and) spectral signatures may in future best allow for the identification and discrimination of the various urban construction materials, that often overlap with respect to their chemical/mineralogical constituents. Hyperspectral or even strongly multi-spectral LWIR information appears especially useful, given that many urban materials are composed of minerals exhibiting notable reststrahlen/absorption effects in this spectral region. The final spectra and interpretations are included in the London Urban Micromet data Archive (LUMA; http://LondonClimate.info/LUMA/SLUM.html).

Are we there yet? Exploring empowerment at the microscale in the South African wine industry

Empowerment is a standard but ambiguous element of development rhetoric and so, through the socially complex and contested terrain of South Africa, this paper explores its potential to contribute to inclusive development. Investigating micro-level engagements with the national strategy of Broad-Based Black Economic Empowerment (B-BBEE) in the South African wine industry highlights the limitations, but also potential, of this single domain approach. However, latent paternalism, entrenched interests and a ‘dislocated blackness’ maintain a complex racial politics that shapes both power relations and the opportunities for transformation within the industry. Nonetheless, while B-BBEE may not, in reality, be broad-based its manifestations are contributing to challenging racist structures and normalising changing attitudes. This paper concludes that, to be transformative, empowerment needs to be re-embedded within South Africa as a multi-scalar, multi-dimensional dialogue and, despite the continuation of structural constraints, positions the local as a critical scale at which to initiate broader social change.

Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

Large deviations of Rouse polymer chain: first passage problem

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations, and measure the mean first-passage time $\tau(z)$ for the free end to reach a certain distance $z$ away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of $\tau(z)$ are observed, with transition between them varying as a function of chain length. We use these simulations results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations lead us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more.

Coordinated management of intelligent pervasive spaces

The content of this paper is a snapshot of a current project looking at producing a real-time sensor-based building assessment tool, and a system that personalises workspaces using multi-agent technology. Both systems derive physical environment information from a wireless sensor network that allows clients to subscribe to real-time sensed data. The principal ideologies behind this project are energy efficiency and well-being of occupants; in the context of leveraging the current state-of-the-art in agent technology, wireless sensor networks and building assessment systems to enable the optimisation and assessment of buildings. Participants of this project are from both industry (construction and research) and academia.

Co-ordinated management of intelligent pervasive spaces

The content of this paper is a snapshot of a current project looking at producing a real-time sensor-based building assessment tool, and a system that personalises work-spaces using multi-agent technology. Both systems derive physical environment information from a wireless sensor network that allows clients to subscribe to real-time sensed data. The principal ideologies behind this project are energy efficiency and well-being of occupants; in the context of leveraging the current state-of-the-art in agent technology, wireless sensor networks and building assessment systems to enable the optimisation and assessment of buildings. Participants of this project are from both industry (construction and research) and academia.

Probabilistic downscaling of remote sensing data with applications for multi-scale biogeochemical flux modeling

Upscaling ecological information to larger scales in space and downscaling remote sensing observations or model simulations to finer scales remain grand challenges in Earth system science. Downscaling often involves inferring subgrid information from coarse-scale data, and such ill-posed problems are classically addressed using regularization. Here, we apply two-dimensional Tikhonov Regularization (2DTR) to simulate subgrid surface patterns for ecological applications. Specifically, we test the ability of 2DTR to simulate the spatial statistics of high-resolution (4 m) remote sensing observations of the normalized difference vegetation index (NDVI) in a tundra landscape. We find that the 2DTR approach as applied here can capture the major mode of spatial variability of the high-resolution information, but not multiple modes of spatial variability, and that the Lagrange multiplier (γ) used to impose the condition of smoothness across space is related to the range of the experimental semivariogram. We used observed and 2DTR-simulated maps of NDVI to estimate landscape-level leaf area index (LAI) and gross primary productivity (GPP). NDVI maps simulated using a γ value that approximates the range of observed NDVI result in a landscape-level GPP estimate that differs by ca 2% from those created using observed NDVI. Following findings that GPP per unit LAI is lower near vegetation patch edges, we simulated vegetation patch edges using multiple approaches and found that simulated GPP declined by up to 12% as a result. 2DTR can generate random landscapes rapidly and can be applied to disaggregate ecological information and compare of spatial observations against simulated landscapes.

Aspects of particle filtering in high-dimensional spaces

Nonlinear data assimilation is high on the agenda in all fields of the geosciences as with ever increasing model resolution and inclusion of more physical (biological etc.) processes, and more complex observation operators the data-assimilation problem becomes more and more nonlinear. The suitability of particle filters to solve the nonlinear data assimilation problem in high-dimensional geophysical problems will be discussed. Several existing and new schemes will be presented and it is shown that at least one of them, the Equivalent-Weights Particle Filter, does indeed beat the curse of dimensionality and provides a way forward to solve the problem of nonlinear data assimilation in high-dimensional systems.