This article introduces a systematic study for computational aspects of classical Wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical Wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as a finite coherent sum of classical Wavelet coefficients.

Introduction: A major problem facing the patients with chronic liver diseases is the diagnostic procedure. The conventional diagnostic method depends mainly on needle biopsy which is an invasive method. There are some approaches to develop a reliable noninvasive method of evaluating histological changes in sonograms. The main characteristic used to distinguish between the normal, hepatitis and cirrhosis liver is the texture of liver surface. The problem of defining a set of meaningful features that explores the characteristics of the texture, leads to several methods of determining tissue texture. Some of these methods, which have been developed so far, are based on Wavelet transform. The selection of Wavelet transform type affects the accuracy of determining the texture. In this study, an optimal Wavelet transform called Gabor Wavelet was introduced and three different methods of determining tissue texture were evaluated. These include statistical, dyadic Wavelet transform and Gabor Wavelet transform methods.Materials and Methods: The proposed algorithm was applied to differentiate ultrasonic liver images into two disease states (hepatitis and cirrhosis) and normal liver. In this experiment, 50 liver sample images for each three states which already been proven by needle biopsy were used. These images are taken from a Toshiba Sonolayer SSA250A device using a 3.75 MHz transducer. For each image, a region of interest (ROI) with 75×35 pixels is selected. The ROI is chosen to include only liver tissue without major blood vessel or hepatic duct.The classification method used for this work is "Minimum Distance", where the distance is calculated between feature vectors of test image and reference images. In order to evaluate the diagnostic results, two quantities named "Sensitivity" and "Specificity" were calculated for each method.Results: The obtained results show that Gabor Wavelet has 85% and dyadic Wavelet has 71% sensitivity in the hepatitis liver images. On the other hand, Gabor Wavelet shows 86% sensitivity in the cirrhosis liver images, while dyadic Wavelet has 78%. The specificity of Gabor Wavelet in the hepatitis and cirrhosis liver images is 77% and 79% respectively, while the specificity of dyadic Wavelet is 65% and 72%, respectively. Discussion and Conclusion: Based on this experiment, the Gabor Wavelet is more appropriate than the dyadic Wavelet and statistical based method for the texture classification as it leads to higher classification accuracy, because the dyadic Wavelet loses some middle-band information, while the Gabor Wavelet preserves it. Based on what was observed, the most significant information regarding the texture is mainly located in the middle-frequency bands of Wavelet decomposition. Therefore, using Gabor Wavelet, a more flexible decomposition of the entire frequency band can be achieved leading to a superior differentiation of the texture information.

The paper focuses on detecting, locating and quantifying the damage occurring in three different forms, namely (a) a beam with only a dominant crack, (b) a uniformly degraded beam, and (c) a uniformly degraded beam with a dominant crack. Generalised methodologies have been proposed to solve the three damage cases. Fixed beams have been considered to demonstrate the effectiveness of the generalised method for damage identification. The beam is loaded with a point load. The static deflection has been used as the response to perform continuous Wavelet transform (CWT). The continuous Wavelet transform coefficients are used to compute the Holder exponent and an Intensity factor. The intensity factor is used to relate the damage (crack damage and/or degradation) characteristics to the magnitude of the Wavelet coefficients. The proposed generalised method can be used to solve the damage identification problem for all fixed beams, irrespective of changes in the magnitude of load applied, geometrical and material properties. The effectiveness of the proposed method is demonstrated by validating with several numerical examples available in the literature.

In Cyber Security Analysis, in addition to data and information obtained from machine-based sensors like intrusion detection systems, firewalls and vulnerability scanners (hard data), human observations and conclusions from world's state including problems reported by users and network administrators, and assessments made by security analysts about network security status (soft data), can be used to obtain more accurate and more reliable estimation and decision. Hard and soft data fusion in cyber security analysis has many challenges such as framework design for problem modeling and representation of different types of uncertainty. This paper presents a new model based on ontology for fusion of hard and soft data in cyber security analysis. First, the concepts and problem variables are modeled and then the inference of assets’ security status is made by using a set of rules. Also, for fusion of data and unified modeling of different uncertainties, transferable belief model (TBM) and Dempster-Shafer combination rule are used. Results of applying the proposed model in a sample scenario of cyber security analysis show its operability for hard and soft data fusion. Considering the extensibility of ontology and knowledge base, high flexibility and dynamism are characteristics of the proposed model.

Introduction: The methods of system identification used to estimate the ordinates of Instantaneous Unit Hydrograph (IUH) encounter the presence of noise in the form of oscillation. Noise in the IUH originates from the errors in the rainfall- runoff data and the linear assumptions in unit hydrograph theory. Rao and Delleur (1971) used Fourier transform to estimate IUH. In their work noise is controlled by the moving average technique. The aperiodic and transient signals with short duration (like in an IUH) are signals for which Wavelet transform are particularly useful. Chou and Wang (2002) controlled the noise using a Haar Wavelet with a boxcar-like function. Soman and Ramachandran (2005) showed that for smoothly varying signals a smooth Wavelet function such as Daubechies (1992) Wavelets should be selected. In this paper, the fast Fourier transforms (FFT) are used to estimate the IUH in the presence of noise. Daubechies Wavelets are also applied for noise reduction.