An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Usability of small crisis data sets in the absence of big data

Big data is big news in almost every sector including crisis communication. However, not everyone has access to big data and even if we have access to big data, we often do not have necessary tools to analyze and cross reference such a large data set. Therefore this paper looks at patterns in small data sets that we have ability to collect with our current tools to understand if we can find actionable information from what we already have. We have analyzed 164390 tweets collected during 2011 earthquake to find out what type of location specific information people mention in their tweet and when do they talk about that. Based on our analysis we find that even a small data set that has far less data than a big data set can be useful to find priority disaster specific areas quickly.

The efficiency of corpus-based distributional models for literature-based discovery on large data sets

This paper evaluates the efficiency of a number of popular corpus-based distributional models in performing discovery on very large document sets, including online collections. Literature-based discovery is the process of identifying previously unknown connections from text, often published literature, that could lead to the development of new techniques or technologies. Literature-based discovery has attracted growing research interest ever since Swanson's serendipitous discovery of the therapeutic effects of fish oil on Raynaud's disease in 1986. The successful application of distributional models in automating the identification of indirect associations underpinning literature-based discovery has been heavily demonstrated in the medical domain. However, we wish to investigate the computational complexity of distributional models for literature-based discovery on much larger document collections, as they may provide computationally tractable solutions to tasks including, predicting future disruptive innovations. In this paper we perform a computational complexity analysis on four successful corpus-based distributional models to evaluate their fit for such tasks. Our results indicate that corpus-based distributional models that store their representations in fixed dimensions provide superior efficiency on literature-based discovery tasks.

Fractal dimension of dried foods : a correlation between microstructure and porosity

The quality of dried food is affected by a number of factors including quality of raw material, initial microstructure, and drying conditions. The structure of the food materials goes through deformations due to the simultaneous effect of heat and mass transfer during the drying process. Shrinkage and changes in porosity, microstructure and appearance are some of the most remarkable features that directly influence overall product quality. Porosity and microstructure are the important material properties in relation to the quality attributes of dried foods. Fractal dimension (FD) is a quantitative approach of measuring surface, pore characteristics, and microstructural changes [1]. However, in the field of fractal analysis, there is a lack of research in developing relationship between porosity, shrinkage and microstructure of different solid food materials in different drying process and conditions [2-4]. Establishing a correlation between microstructure and porosity through fractal dimension during convective drying is the main objective of this work.

A RBF meshless approach for modeling a fractal mobile/immobile transport model

A fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBFs) to discretize the space variable. In contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example which is presented to describe a fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating fractional differential equations, and it has good potential in the development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

The Marulan data sets: multi-sensor perception in a natural environment with challenging conditions

In this paper we present large, accurately calibrated and time-synchronized data sets, gathered outdoors in controlled and variable environmental conditions, using an unmanned ground vehicle (UGV), equipped with a wide variety of sensors. These include four 2D laser scanners, a radar scanner, a color camera and an infrared camera. It provides a full description of the system used for data collection and the types of environments and conditions in which these data sets have been gathered, which include the presence of airborne dust, smoke and rain.

Monitoring phase behavior of sub- and supercritical CO2 confined in porous fractal silica with 85% porosity

Phase behavior of CO2 confined in porous fractal silica with volume fraction of SiO2 φs = 0.15 was investigated using small-angle neutron scattering (SANS) and ultrasmall-angle neutron scattering (USANS) techniques. The range of fluid densities (0<(FCO2)bulk<0.977 g/cm3) and temperatures (T=22 °C, 35 and 60 °C) corresponded to gaseous, liquid, near critical and supercritical conditions of the bulk fluid. The results revealed formation of a dense adsorbed phase in small pores with sizes D<40 A° at all temperatures. At low pressure (P <55 bar, (FCO2)bulk <0.2 g/cm3) the average fluid density in pores may exceed the density of bulk fluid by a factor up to 6.5 at T=22 °C. This “enrichment factor” gradually decreases with temperature, however significant fluid densification in small pores still exists at temperature T=60°C, i.e., far above the liquid-gas critical temperature of bulk CO2 (TC=31.1 °C). Larger pores are only partially filled with liquid-like adsorbed layer which coexists with unadsorbed fluid in the pore core. With increasing pressure, all pores become uniformly filled with the fluid, showing no measurable enrichment or depletion of the porous matrix with CO2.

Matching image sets via adaptive multi convex hull

Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image set. Existing multi-model approaches extract local models by clustering each image set individually only once, with fixed clusters used for matching with various image sets. This may not be optimal for discrimination, as undesirable environmental conditions (eg. illumination and pose variations) may result in the two closest clusters representing different characteristics of an object (eg. frontal face being compared to non-frontal face). To address the above problem, we propose a novel approach to enhance nearest points based methods by integrating affine/convex hull classification with an adapted multi-model approach. We first extract multiple local convex hulls from a query image set via maximum margin clustering to diminish the artificial variations and constrain the noise in local convex hulls. We then propose adaptive reference clustering (ARC) to constrain the clustering of each gallery image set by forcing the clusters to have resemblance to the clusters in the query image set. By applying ARC, noisy clusters in the query set can be discarded. Experiments on Honda, MoBo and ETH-80 datasets show that the proposed method outperforms single model approaches and other recent techniques, such as Sparse Approximated Nearest Points, Mutual Subspace Method and Manifold Discriminant Analysis.

Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1–28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

Quantitative characterization of kaolinite dispersibility in styrene–butadiene rubber composites by fractal dimension

A fractal method was introduced to quantitatively characterize the dispersibility of modified kaolinite (MK) and precipitated silica (PS) in styrene–butadiene rubber (SBR) matrix based on the lower magnification transmission electron microscopic images. The fractal dimension (FD) is greater, and the dispersion is worse. The fractal results showed that the dispersibility of MK in the latex blending sample is better than that in the mill blending samples. With the increase of kaolinite content, the FD increases from 1.713 to 1.800, and the dispersibility of kaolinite gradually decreases. There is a negative correlation between the dispersibility and loading content. With the decrease of MK and increase of PS, the FD significantly decreases from 1.735 to 1.496 and the dipersibility of kaolinite remarkably increases. The hybridization can improve the dispersibility of fillers in polymer matrix. The FD can be used to quantitatively characterize the aggregation and dispersion of kaolinite sheets in rubber matrix.