Fuzzy c-means clustering of incomplete data

The problem of clustering a real s-dimensional data set X={x(1 ),,,,,x(n)} subset R(s) is considered. Usually, each observation (or datum) consists of numerical values for all s features (such as height, length, etc.), but sometimes data sets can contain vectors that are missing one or more of the feature values. For example, a particular datum x(k) might be incomplete, having the form x(k)=(254.3, ?, 333.2, 47.45, ?)(T), where the second and fifth feature values are missing. The fuzzy c-means (FCM) algorithm is a useful tool for clustering real s-dimensional data, but it is not directly applicable to the case of incomplete data. Four strategies for doing FCM clustering of incomplete data sets are given, three of which involve modified versions of the FCM algorithm. Numerical convergence properties of the new algorithms are discussed, and all approaches are tested using real and artificially generated incomplete data sets.     

Autothermal hybridization and controlled production of hydrogen-rich syngas in a molten salt solar gasifier

High efficiency solar steam gasification of biomass is carried out in a prototype molten salt reactor for solar-only and solar-autothermal hybrid operation. Previous demonstration of the prototype 3-kW solar gasifier for steam gasification of cellulose at stoichiometric conditions demonstrated thermal efficiency of 44% during continuous operation at 1200 K. The present work expands the range of operating conditions to consider two challenges. Hybridization between solar and autothermal modes of operation is accomplished by adding oxygen directly to the reactor. Control of the H₂:CO ratio of the product gas is accomplished through in-situ steam shifting. Hybridization stabilized temperatures for variations in radiative input as large as a 30% reduction in power, corresponding to conditions where both sensible and chemical heat demands for the process were fully met by exothermic heat release with no significant challenges. Peak efficiencies and carbon conversion values observed are 45% and 99.5% respectively. The resulting product gas stream composition was shifted from a hydrogen and carbon monoxide ratio of 1:1 with stoichiometric steam delivery to a ratio of 1.7:1 with steam at nine times the stoichiometric amount, only slightly lower than equilibrium predictions. The results demonstrate very favorable attributes for the molten salt reactor in a continuous fuel production process.     

Impact of Storm-Water Runoff on Clogging and Fecal Bacteria Reduction in Sand Columns

Storm-water runoff has been identified as a major cause of coastal water quality degradation. Storm-water outfalls, common in many coastal towns, convey bacteria and other pollutants into the ocean and estuaries. In an effort to minimize this impact, the Town of Kure Beach, North Carolina, installed Dune Infiltration Systems (DIS) at two storm-water outfalls to receive storm-water runoff and allow infiltration beneath the beach dunes. A laboratory column experiment was performed to supplement this installation and determine the potential hydraulic and bacterial removal efficiency of the sand comprising the Kure Beach dunes. Columns constructed using sand collected at different depths of the dune were used to analyze the affect of bacteria application on infiltration and to examine the changes in bacteria removal that occur as infiltration rates are affected by bacteria-laden water application. Sand columns were loaded over a 60-day period with either bacteria-free storm water or storm water spiked with Escherichia coli. The seepage rate for the bacteria-spiked storm-water treatment was significantly lower (p<0.05) than the seepage rate of the bacteria-free treatment, particularly toward the end of the study. Bacteria application likely compounds the impact of sediment clogging at the sand/storm-water interface. This study indicates the need for maintenance when implementing a DIS or similar sand filter to maintain design infiltration rates, especially if reduced infiltration rates are not planned for in the design. However, a decrease in seepage rate was correlated with a decrease in effluent bacteria concentration in the bacteria-spiked storm-water sand columns. Thus, optimization is required to provide maximum infiltration of storm-water while maintaining bacteria removal efficiency.     

A comprehensive CAD system for high-performance 300 K-circuit ASIClogic chips

A computer-aided design (CAD) system has been developed to support design of CMOS application-specific integrated circuit (ASIC) logic chips containing more than 300 K equivalent two-input NANDs with 180-ps typical gate delays. The underlying technology is a 0.8-μm, four-level-metal, single-poly CMOS process, with a 0.45-μm nominal effective channel length and 180-ps typical gate delay. Both standard-cell and gate-array circuit libraries are provided, including fixed and growable memory macros. Key new system features are described in the areas of high-level design and synthesis, delay calculation and timing analysis, timing guidance to physical design, physical design, clock construction, and test generation. Early processing results are reported for several test chips, including a 9.7-mm 2-million-transistor chip and a 14.5-mm 300 K-equivalent-gate chip     

Numerical convergence and interpretation of the fuzzy c-shellsclustering algorithm

R. N. Dave's (1990) version of fuzzy c-shells is an iterative clustering algorithm which requires the application of Newton's method or a similar general optimization technique at each half step in any sequence of iterates for minimizing the associated objective function. An important computational question concerns the accuracy of the solution required at each half step within the overall iteration. The general convergence theory for grouped coordination minimization is applied to this question to show that numerically exact solution of the half-step subproblems in Dave's algorithm is not necessary. One iteration of Newton's method in each coordinate minimization half step yields a sequence obtained using the fuzzy c-shells algorithm with numerically exact coordinate minimization at each half step. It is shown that fuzzy c-shells generates hyperspherical prototypes to the clusters it finds for certain special cases of the measure of dissimilarity used.     

A parametric model for fusing heterogeneous fuzzy data

Presented is a model that integrates three data types (numbers, intervals, and linguistic assessments). Data of these three types come from a variety of sensors. One objective of sensor-fusion models is to provide a common framework for data integration, processing, and interpretation. That is what our model does. We use a small set of artificial data to illustrate how problems as diverse as feature analysis, clustering, cluster validity, and prototype classifier design can all be formulated and attacked with standard methods once the data are converted to the generalized coordinates of our model. The effects of reparameterization on computational outputs are discussed. Numerical examples illustrate that the proposed model affords a natural way to approach problems which involve mixed data types     

Generalized fuzzy c-means clustering strategies using Lpnorm distances

Fuzzy c-means (FCM) is a useful clustering technique. Modifications of FCM using L₁ norm distances increase robustness to outliers. Object and relational data versions of FCM clustering are defined for the more general case where the L_p norm (p⩾1) or semi-norm (00 in order to facilitate the empirical examination of the object data models. Both object and relational approaches are included in a numerical study     

Role of epidemiologic studies in evaluating the carcinogenicity of chromium compounds

Epidemiologic and animal studies have identified intermediately-soluble chromates as human carcinogens. Epidemiologic studies also provide moderately strong evidence to conclude that chromates do not cause cancer at sites other than the respiratory tract. This information, combined with the evidence from animal studies and in vitro experiments, has led to the conclusion that chromates do not present a carcinogenic risk from ingestion. Unfortunately, epidemiologic studies have not provided definitive answers to other questions: (i) does trivalent chromium present a cancer risk?; (ii) is there a threshold for carcinogenic effects?; and (iii) what is the appropriate model for predicting cancer risk? Mechanistic research with supporting evidence from animal studies has provided the most useful information to answer these questions. Working hypotheses are: (i) trivalent chromium is not a carcinogen; (ii) there are probably substantial differences in carcinogenic potency between chromates, with the water-soluble compounds having lower potency than intermediately-soluble compounds; (iii) only respiratory tract cancers are caused by exposure to chromates, and ingestion and chromates does not constitute a carcinogenic risk; (iv) there is probably a threshold for carcinogenic effects from chromium due to detoxification mechanisms and lack of bioavailability of low doses; and (v) currently used models for quantitative risk assessment (e.g. the low dose linearized multi-stage model) are inappropriate to predict low dose cancer risks from exposure to chromates.