IMPLEMENTATION OF THE FDTD METHOD BASED ON LORENTZ-DRUDE DISPERSIVE MODEL ON GPU FOR PLASMONICS APPLICATIONS

Abstract—We present a three-dimensional finite difference time domain (FDTD) method on graphics processing unit (GPU) for plasmonics applications. For the simulation of plasmonics devices, the Lorentz-Drude (LD) dispersive model is incorporated into Maxwell equations, while the auxiliary differential equation (ADE) technique is applied to the LD model. Our numerical experiments based on typical domain sizes as well as plasmonics environment demonstrate that our implementation of the FDTD method on GPU offers significant speed up as compared to the traditional CPU implementations. 1

The Emergence of Urban Land Use Patterns Driven by Dispersion and Aggregation Mechanisms

<div><p>We employ a cellular-automata to reconstruct the land use patterns of cities that we characterize by two measures of spatial heterogeneity: (a) a variant of <i>spatial entropy</i>, which measures the spread of residential, business, and industrial activity sectors, and (b) an <i>index of dissimilarity</i>, which quantifies the degree of spatial mixing of these land use activity parcels. A minimalist and bottom-up approach is adopted that utilizes a limited set of three parameters which represent the forces which determine the extent to which each of these sectors spatially aggregate into clusters. The dispersion degrees of the land uses are governed by a fixed pre-specified power-law distribution based on empirical observations in other cities. Our method is then used to reconstruct land use patterns for the city state of Singapore and a selection of North American cities. We demonstrate the emergence of land use patterns that exhibit comparable visual features to the actual city maps defining our case studies whilst sharing similar spatial characteristics. Our work provides a complementary approach to other measures of urban spatial structure that differentiate cities by their land use patterns resulting from bottom-up dispersion and aggregation processes.</p></div

Smart Robust Feature Selection (SoFt) for imbalanced and heterogeneous data

Designing a smart and robust predictive model that can deal with imbalanced data and a heterogeneous set of features is paramount to its widespread adoption by practitioners. By smart, we mean the model is either parameter-free or works well with default parameters, avoiding the challenge of parameter tuning. Furthermore, a robust model should consistently achieve high accuracy regardless of any dataset (imbalance, heterogeneous set of features) or domain (such as medical, financial). To this end, a computationally inexpensive and yet robust predictive model named smart robust feature selection (SoFt) is proposed. SoFt involves selecting a learning algorithm and designing a filtering-based feature selection algorithm named multi evaluation criteria and Pareto (MECP). Two state-of-the-art gradient boosting methods (GBMs), CatBoost and H2O GBM, are considered potential candidates for learning algorithms. CatBoost is selected over H2O GBM due to its robustness with both default and tuned parameters. The MECP uses multiple parameter-free feature scores to rank the features. SoFt is validated against CatBoost with a full feature set and wrapper-based CatBoost. SoFt is robust and consistent for imbalanced datasets, i.e., average value and standard deviation of log loss are low across different folds of K-fold cross-validation. Features selected by MECP are also consistent, i.e., features selected by SoFt and wrapper-based CatBoost are consistent across different folds, demonstrating the effectiveness of MECP. For balanced datasets, MECP selects too few features, and hence, the log loss of SoFt is significantly higher than CatBoost with a full feature set

Parameter screening for the Singapore model for the range of influence for residential/business and industrial areas (Left column: unconstrained; Right column: constrained).

<p>Preliminary experiments were conducted to identify potentially suitable range values (highlighted in coloured text in the figures) for the respective ranges of influence for the three land use sectors (residential - blue, business - green and industrial - red) for the city state of Singapore. These experiments assisted in limiting the search space to find the best-fit parameters to match the actual spatial entropy values given the specific number of land use cells (pixels), i.e , and for business, residential and industrial pixels respectively in Singapore. Similar experiments were conducted for our selection of North American cities but these are not reported here.</p

Dynamics of spatial entropy and dissimilarity index against number of cells.

<p>These results were extracted from a single illustrative simulation run.</p

The Singapore model.

<p>Highlighted in the right figure are the areas that remains (yellow color) after non-developable lands are removed.</p

Simulation fitting results summary.

<p>The error column reports the sum of squared residuals over the spatial entropy for each land use type and dissimilarity indexes between the actual city map and best-fit reconstructed maps. The base column details the fitted results using the constrained models and a random uniform distribution of the land use sectors throughout the city maps. Thus the base column reports controlled experimental results which highlight the differences when no dispersion and aggregation mechanisms are implemented. The above result shows that the model reported is three orders of magnitude statistically more accurate than a random growth model.</p

Simulation results summary - spatial entropy.

<p>The mean and standard deviation values were computed over 10 individual repeat simulation runs using unique seeds. Results for all cities are based using the compartmental constrained models, except for Singapore land use which was also reconstructed using the unconstrained approach. Note that the standard deviations of the different trial measurements in the average is 2.67% of the mean value (0.74%, 1.37%, 5.89% for , , respectively), indicative of the robustness of the evolved patterns.</p

The Singapore master plan.

<p>The actual land use map depicted in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080309#pone-0080309-g003" target="_blank">Fig. 3</a> was extracted from the URA ((Urban Redevelopment Authority)) Singapore master plan 2008 where the residential, business and industrial land use sectors are the aggregations of relevant sub-categories. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080309#pone.0080309.s001" target="_blank">Appendix S1</a> for details and data sources.</p

Reconstructed versus actual city land use maps.

<p>Simulated figures is randomly chosen representative sample of 10 runs whose statistical resemblance to actual land use is reported in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080309#pone-0080309-t001" target="_blank">Tables 1</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080309#pone-0080309-t003" target="_blank">3</a>.</p