CFT(4) partition functions and the heat kernel on AdS(5)

We consider four-dimensional CFTs which admit a large-N expansion, and whose spectrum contains states whose conformal dimensions do not scale with N. We explicitly reorganise the partition function obtained by exponentiating the one-particle partition function of these states into a heat kernel form for the dual string spectrum on AdS(5). On very general grounds, the heat kernel answer can be expressed in terms of a convolution of the one-particle partition function of the light states in the four-dimensional CFT. (C) 2013 Elsevier B.V. All rights reserved.

Bivariate frequency analysis of floods using a diffusion based kernel density estimator

Recent focus of flood frequency analysis (FFA) studies has been on development of methods to model joint distributions of variables such as peak flow, volume, and duration that characterize a flood event, as comprehensive knowledge of flood event is often necessary in hydrological applications. Diffusion process based adaptive kernel (D-kernel) is suggested in this paper for this purpose. It is data driven, flexible and unlike most kernel density estimators, always yields a bona fide probability density function. It overcomes shortcomings associated with the use of conventional kernel density estimators in FFA, such as boundary leakage problem and normal reference rule. The potential of the D-kernel is demonstrated by application to synthetic samples of various sizes drawn from known unimodal and bimodal populations, and five typical peak flow records from different parts of the world. It is shown to be effective when compared to conventional Gaussian kernel and the best of seven commonly used copulas (Gumbel-Hougaard, Frank, Clayton, Joe, Normal, Plackett, and Student's T) in estimating joint distribution of peak flow characteristics and extrapolating beyond historical maxima. Selection of optimum number of bins is found to be critical in modeling with D-kernel.

Spatially Adaptive Kernel Regression Using Risk Estimation

An important question in kernel regression is one of estimating the order and bandwidth parameters from available noisy data. We propose to solve the problem within a risk estimation framework. Considering an independent and identically distributed (i.i.d.) Gaussian observations model, we use Stein's unbiased risk estimator (SURE) to estimate a weighted mean-square error (MSE) risk, and optimize it with respect to the order and bandwidth parameters. The two parameters are thus spatially adapted in such a manner that noise smoothing and fine structure preservation are simultaneously achieved. On the application side, we consider the problem of image restoration from uniform/non-uniform data, and show that the SURE approach to spatially adaptive kernel regression results in better quality estimation compared with its spatially non-adaptive counterparts. The denoising results obtained are comparable to those obtained using other state-of-the-art techniques, and in some scenarios, superior.

Regional flood frequency analysis using kernel- based fuzzy clustering approach

Regionalization approaches are widely used in water resources engineering to identify hydrologically homogeneous groups of watersheds that are referred to as regions. Pooled information from sites (depicting watersheds) in a region forms the basis to estimate quantiles associated with hydrological extreme events at ungauged/sparsely gauged sites in the region. Conventional regionalization approaches can be effective when watersheds (data points) corresponding to different regions can be separated using straight lines or linear planes in the space of watershed related attributes. In this paper, a kernel-based Fuzzy c-means (KFCM) clustering approach is presented for use in situations where such linear separation of regions cannot be accomplished. The approach uses kernel-based functions to map the data points from the attribute space to a higher-dimensional space where they can be separated into regions by linear planes. A procedure to determine optimal number of regions with the KFCM approach is suggested. Further, formulations to estimate flood quantiles at ungauged sites with the approach are developed. Effectiveness of the approach is demonstrated through Monte-Carlo simulation experiments and a case study on watersheds in United States. Comparison of results with those based on conventional Fuzzy c-means clustering, Region-of-influence approach and a prior study indicate that KFCM approach outperforms the other approaches in forming regions that are closer to being statistically homogeneous and in estimating flood quantiles at ungauged sites. Key Points Kernel-based regionalization approach is presented for flood frequency analysis Kernel procedure to estimate flood quantiles at ungauged sites is developed A set of fuzzy regions is delineated in Ohio, USA

Coconut kernel-derived activated carbon as electrode material for electrical double-layer capacitors

Carbonization of milk-free coconut kernel pulp is carried out at low temperatures. The carbon samples are activated using KOH, and electrical double-layer capacitor (EDLC) properties are studied. Among the several samples prepared, activated carbon prepared at 600 A degrees C has a large surface area (1,200 m(2) g(-1)). There is a decrease in surface area with increasing temperature of preparation. Cyclic voltammetry and galvanostatic charge-discharge studies suggest that activated carbons derived from coconut kernel pulp are appropriate materials for EDLC studies in acidic, alkaline, and non-aqueous electrolytes. Specific capacitance of 173 F g(-1) is obtained in 1 M H2SO4 electrolyte for the activated carbon prepared at 600 A degrees C. The supercapacitor properties of activated carbon sample prepared at 600 A degrees C are superior to the samples prepared at higher temperatures.

Hybrid Working Set Algorithm for SVM Learning With a Kernel Coprocessor on FPGA

Support vector machines (SVM) are a popular class of supervised models in machine learning. The associated compute intensive learning algorithm limits their use in real-time applications. This paper presents a fully scalable architecture of a coprocessor, which can compute multiple rows of the kernel matrix in parallel. Further, we propose an extended variant of the popular decomposition technique, sequential minimal optimization, which we call hybrid working set (HWS) algorithm, to effectively utilize the benefits of cached kernel columns and the parallel computational power of the coprocessor. The coprocessor is implemented on Xilinx Virtex 7 field-programmable gate array-based VC707 board and achieves a speedup of upto 25x for kernel computation over single threaded computation on Intel Core i5. An application speedup of upto 15x over software implementation of LIBSVM and speedup of upto 23x over SVMLight is achieved using the HWS algorithm in unison with the coprocessor. The reduction in the number of iterations and sensitivity of the optimization time to variation in cache size using the HWS algorithm are also shown.

Counting zero kernel pairs over a finite field

Helmke et al. have recently given a formula for the number of reachable pairs of matrices over a finite field. We give a new and elementary proof of the same formula by solving the equivalent problem of determining the number of so called zero kernel pairs over a finite field. We show that the problem is, equivalent to certain other enumeration problems and outline a connection with some recent results of Guo and Yang on the natural density of rectangular unimodular matrices over F-qx]. We also propose a new conjecture on the density of unimodular matrix polynomials. (C) 2016 Elsevier Inc. All rights reserved.