Second order cone programming approaches for handling missing and uncertain data

We propose a novel second order cone programming formulation for designing robust classifiers which can handle uncertainty in observations. Similar formulations are also derived for designing regression functions which are robust to uncertainties in the regression setting. The proposed formulations are independent of the underlying distribution, requiring only the existence of second order moments. These formulations are then specialized to the case of missing values in observations for both classification and regression problems. Experiments show that the proposed formulations outperform imputation.

Model-theoretic approach to clustering

The paper deals with a model-theoretic approach to clustering. The approach can be used to generate cluster description based on knowledge alone. Such a process of generating descriptions would be extremely useful in clustering partially specified objects. A natural byproduct of the proposed approach is that missing values of attributes of an object can be estimated with ease in a meaningful fashion. An important feature of the approach is that noisy objects can be detected effectively, leading to the formation of natural groups. The proposed algorithm is applied to a library database consisting of a collection of books.

Characterization and Space-Time Downscaling of the Inundation Extent over the Inner Niger Delta Using GIEMS and MODIS Data

The objective in this work is to develop downscaling methodologies to obtain a long time record of inundation extent at high spatial resolution based on the existing low spatial resolution results of the Global Inundation Extent from Multi-Satellites (GIEMS) dataset. In semiarid regions, high-spatial-resolution a priori information can be provided by visible and infrared observations from the Moderate Resolution Imaging Spectroradiometer (MODIS). The study concentrates on the Inner Niger Delta where MODIS-derived inundation extent has been estimated at a 500-m resolution. The space-time variability is first analyzed using a principal component analysis (PCA). This is particularly effective to understand the inundation variability, interpolate in time, or fill in missing values. Two innovative methods are developed (linear regression and matrix inversion) both based on the PCA representation. These GIEMS downscaling techniques have been calibrated using the 500-m MODIS data. The downscaled fields show the expected space-time behaviors from MODIS. A 20-yr dataset of the inundation extent at 500 m is derived from this analysis for the Inner Niger Delta. The methods are very general and may be applied to many basins and to other variables than inundation, provided enough a priori high-spatial-resolution information is available. The derived high-spatial-resolution dataset will be used in the framework of the Surface Water Ocean Topography (SWOT) mission to develop and test the instrument simulator as well as to select the calibration validation sites (with high space-time inundation variability). In addition, once SWOT observations are available, the downscaled methodology will be calibrated on them in order to downscale the GIEMS datasets and to extend the SWOT benefits back in time to 1993.

Combining data sets of satellite-retrieved products for basin-scale water balance study: 2. Evaluation on the Mississippi Basin and closure correction model

In this study, we applied the integration methodology developed in the companion paper by Aires (2014) by using real satellite observations over the Mississippi Basin. The methodology provides basin-scale estimates of the four water budget components (precipitation P, evapotranspiration E, water storage change Delta S, and runoff R) in a two-step process: the Simple Weighting (SW) integration and a Postprocessing Filtering (PF) that imposes the water budget closure. A comparison with in situ observations of P and E demonstrated that PF improved the estimation of both components. A Closure Correction Model (CCM) has been derived from the integrated product (SW+PF) that allows to correct each observation data set independently, unlike the SW+PF method which requires simultaneous estimates of the four components. The CCM allows to standardize the various data sets for each component and highly decrease the budget residual (P - E - Delta S - R). As a direct application, the CCM was combined with the water budget equation to reconstruct missing values in any component. Results of a Monte Carlo experiment with synthetic gaps demonstrated the good performances of the method, except for the runoff data that has a variability of the same order of magnitude as the budget residual. Similarly, we proposed a reconstruction of Delta S between 1990 and 2002 where no Gravity Recovery and Climate Experiment data are available. Unlike most of the studies dealing with the water budget closure at the basin scale, only satellite observations and in situ runoff measurements are used. Consequently, the integrated data sets are model independent and can be used for model calibration or validation.

Average Overlap for Clustering Incomplete Data using Symmetric Non-Negative Matrix Factorization

Clustering techniques which can handle incomplete data have become increasingly important due to varied applications in marketing research, medical diagnosis and survey data analysis. Existing techniques cope up with missing values either by using data modification/imputation or by partial distance computation, often unreliable depending on the number of features available. In this paper, we propose a novel approach for clustering data with missing values, which performs the task by Symmetric Non-Negative Matrix Factorization (SNMF) of a complete pair-wise similarity matrix, computed from the given incomplete data. To accomplish this, we define a novel similarity measure based on Average Overlap similarity metric which can effectively handle missing values without modification of data. Further, the similarity measure is more reliable than partial distances and inherently possesses the properties required to perform SNMF. The experimental evaluation on real world datasets demonstrates that the proposed approach is efficient, scalable and shows significantly better performance compared to the existing techniques.

Comprehensive evaluation of multisatellite precipitation estimates over India using gridded rainfall data

This study presents a comprehensive evaluation of five widely used multisatellite precipitation estimates (MPEs) against 1 degrees x 1 degrees gridded rain gauge data set as ground truth over India. One decade observations are used to assess the performance of various MPEs (Climate Prediction Center (CPC)-South Asia data set, CPC Morphing Technique (CMORPH), Precipitation Estimation From Remotely Sensed Information Using Artificial Neural Networks, Tropical Rainfall Measuring Mission's Multisatellite Precipitation Analysis (TMPA-3B42), and Global Precipitation Climatology Project). All MPEs have high detection skills of rain with larger probability of detection (POD) and smaller ``missing'' values. However, the detection sensitivity differs from one product (and also one region) to the other. While the CMORPH has the lowest sensitivity of detecting rain, CPC shows highest sensitivity and often overdetects rain, as evidenced by large POD and false alarm ratio and small missing values. All MPEs show higher rain sensitivity over eastern India than western India. These differential sensitivities are found to alter the biases in rain amount differently. All MPEs show similar spatial patterns of seasonal rain bias and root-mean-square error, but their spatial variability across India is complex and pronounced. The MPEs overestimate the rainfall over the dry regions (northwest and southeast India) and severely underestimate over mountainous regions (west coast and northeast India), whereas the bias is relatively small over the core monsoon zone. Higher occurrence of virga rain due to subcloud evaporation and possible missing of small-scale convective events by gauges over the dry regions are the main reasons for the observed overestimation of rain by MPEs. The decomposed components of total bias show that the major part of overestimation is due to false precipitation. The severe underestimation of rain along the west coast is attributed to the predominant occurrence of shallow rain and underestimation of moderate to heavy rain by MPEs. The decomposed components suggest that the missed precipitation and hit bias are the leading error sources for the total bias along the west coast. All evaluation metrics are found to be nearly equal in two contrasting monsoon seasons (southwest and northeast), indicating that the performance of MPEs does not change with the season, at least over southeast India. Among various MPEs, the performance of TMPA is found to be better than others, as it reproduced most of the spatial variability exhibited by the reference.

Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)

Design of high-order filters with restricted component values

The feasibility of realising a high-order LC filter with a small set of different capacitor values, without sacrificing the frequency response specifications, is indicated. This idea could be conveniently adopted in other filter structures also—for example the FDNR transformed filter realisations.

Calorimetric values of composite solid propellants

The calorimetric values of composite solid propellant based on polystyrene, polyphenolformaldehyde, poly(vinyl chloride) and carboxy-terminated polybutadiene were determined using combustion calorimetry in order to assess the uncertainities in their measurements. The dependence of the calorimetric values on various propellant composition was obtained. The stoichiometry of oxidizer and fuel in the propellant for complete combustion obtained experimentally were compared with the theoretical stoichiometry calculated based on the oxidizer decomposition.

Precise Values of the "C Component Vicinal Coupling Constants for Calculating Side-Chain Conformations in Amino Acids

From consideration of 'H-lH vicinal coupling constants and '"G'H long-range coupling constants in a series of amino acid derivatives, the precise values of uC component vicinal coupling constants have been calculated for the three minimum energy staggered rotamers for the C(or)H-C(P)H, side-chains of amino acids.

New method of calculating calorific values from elemental compositions of fossil fuels

A new method of calculating the calorific values of fossil fuels from their chemical composition has been developed, based on the concept that heats of reaction of stoichiometric fuel-oxidizer systems are rectilinearly related with the total oxidizing or reducing valancies of the mixture. The calorific value of fossil fuels has been shown to be directly related to the net reducing valencies of the fuel. The proposed method is simple and compares favourably with the other prominent methods reported in the literature.

Absolute values of instantaneous corrosion rates by faradaic rectification

Doss and Agarwal 1 discovered the "redoxokinetic effect" which is now familiarly known as faradaic rectification. Subsequently, the theory and applications of faradaic rectification due to a single electrode reaction have been developed by several workers 2-5. The theory and application of faradaic rectification in the case of a corrosion cell sustaining mixed electrode reactions on a corroding metal was reported recently 6"7. This led to the development of a new electrochemical method of corrosion rate determination. It was shown that changes in the instantaneous corrosion rates of a metal are readily evaluated by faradaic rectification measurements at the corrosion potential of the metal in a given medium. The aim of the present work is to show that absolute values of instantaneous corrosion rates may also be obtained by the new method under certain conditions. The practical advantages that arise from this development are pointed out.

Temperature dependence of g values in tetragonal ionic Cu++ salts

A temperature dependence has been observed in the spin-Hamiltonian parameters of the Cu++ ion in a tetragonal crystal field and the variation has been interpreted in terms of vibronic effects.

Growth of ionization currents in dry air at high values of E/N

Uniform field steady-state ionization currents were measured in dry air as a function of N at constant E/N (E is the electric field strength and N the gas number density) and constant electrode separation d for 14·13 × 10-16 less-than-or-eq, slant E/N less-than-or-eq, slant 282·5 × 10-16 V cm2. Uniform field sparking potentials were also measured for Nd range 1·24 × 1016 less-than-or-eq, slant Nd less-than-or-eq, slant 245 × 1016 cm-2. The ratio of the Townsend primary ionization coefficient α to N, α/N, was found to depend on E/N only. The secondary coefficients were also evaluated for aluminium and gold-plated electrodes for the above range of E/N. Measurements of the sparking potentials showed that Paschen's law is not obeyed in air at values of Nd near and below the Paschen minimum.