Method for obtaining high-resolution velocity spectrum based on weighted similarity

Seismic wave velocity is one of the most important processing parameters of seismic data,which also determines the accuracy of imaging.The conventional method of velocity analysis involves scanning through a series of equal intervals of velocity,producing the velocity spectrum by superposing energy or similarity coefficients.In this method,however,the sensitivity of the semblance spectrum to change of velocity is weak,so the resolution is poor.In this paper,to solve the above deficiencies of conventional velocity analysis,a method for obtaining a high-resolution velocity spectrum based on weighted similarity is proposed.By introducing two weighting functions,the resolution of the similarity spectrum in time and velocity is improved.Numerical examples and real seismic data indicate that the proposed method provides a velocity spectrum with higher resolution than conventional methods and can separate cross reflectors which are aliased in conventional semblance spectrums;at the same time,the method shows good noise-resistibility.

Einstein’s Dark Energy via Similarity Equivalence, ‘tHooft Dimensional Regularization and Lie Symmetry Groups

Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv2 leads to Einstein’s celebrated maximal energy equation E = mc2 and how in turn this can be dissected into the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) of the cosmos where m is the mass;v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.

The Similarity Transformation of Regularizing Functionals and Simularity Property of Their Fourier Transformations

Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.

Research and Implementation of Text Similarity System Based on Power Spectrum Analysis

The paper proposed the research and implement of text similarity system based on power spectrum analysis. It is not difficult to imagine that the signals of brain are closely linked with writing process. So we build text modeling and set pulse signal function to get the power spectrum of the text. The specific detail is getting power spectrum from economic field to build spectral library, and then using the method of power spectrum matching algorithm to judge whether the test text belonged to the economic field. The method made text similarity system finish the function of text intelligent classification efficiently and accurately.

THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS

A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..

Measuring System Regularity Using Fuzzy Similarity-based Approximate Entropy

Approximate entropy (ApEn), a measure quantifying regularity and complexity, is believed to be an effective analyzing method of diverse settings that include both deterministic chaotic and stochastic processes, particularly operative in the analysis of physiological signals that involve relatively small amount of data. However, the similarity definition of vectors based on Heaviside function, of which the boundary is discontinuous and hard, may cause some problems in the validity and accuracy of ApEn. To overcome these problems, a modified ApEn based on fuzzy similarity (mApEn) was proposed. The performance on the MIX stochastic model, as well as those on the Logistic map and the Hennon map with noise, shows that the fuzzy similarity-based ApEn gets more satisfying results than the standard ApEn when characterizing systems with different regularities.

Modeling of 3D-structure for regular fragments of low similarity unknown structure proteins

Because it is hard to search similar structure for low similarity unknown structure proteins directly from the Protein Data Bank （PDB） database, 3D-structure is modeled in this paper for secondary structure regular fragments （α-Helices, β-Strands） of such proteins by the protein secondary structure prediction software, the Basic Local Alignment Search Tool （BLAST） and the side chain construction software SCWRL3. First, the protein secondary structure prediction software is adopted to extract secondary structure fragments from the unknown structure proteins. Then, regular fragments are regulated by BLAST based on comparative modeling, providing main chain configurations. Finally, SCWRL3 is applied to assemble side chains for regular fragments, so that 3D-structure of regular fragments of low similarity unknown structure protein is obtained. Regular fragments of several neurotoxins are used for test. Simulation results show that the prediction errors are less than 0.06nm for regular fragments less than 10 amino acids, implying the simpleness and effectiveness of the proposed method.

Study on algorithms of low SNR inversion of T_2 spectrum in NMR

The method of regularization factor selection determines stability and accuracy of the regularization method. A formula of regularization factor was proposed by analyzing the relationship between the improved SVD and regularization method. The improved SVD algorithm and regularization method could adapt to low SNR. The regularization method is better than the improved SVD in the case that SNR is below 30 and the improved SVD is better than the regularization method when SNR is higher than 30. The regularization method with the regularization factor proposed in this paper can be better applied into low SNR （5〈SNR） NMR logging. The numerical simulations and real NMR data process results indicated that the improved SVD algorithm and regularization method could adapt to the low signal to noise ratio and reduce the amount of computation greatly. These algorithms can be applied in NMR logging.

Classification of hyperspectral remote sensing images using frequency spectrum similarity

An algorithm of hyperspectral remote sensing images classification is proposed based on the frequency spectrum of spectral signature.The spectral signature of each pixel in the hyperspectral image is taken as a discrete signal,and the frequency spectrum is obtained using discrete Fourier transform.The discrepancy of frequency spectrum between ground objects' spectral signatures is visible,thus the difference between frequency spectra of reference and target spectral signature is used to measure the spectral similarity.Canberra distance is introduced to increase the contribution from higher frequency components.Then,the number of harmonics involved in the proposed algorithm is determined after analyzing the frequency spectrum energy cumulative distribution function of ground object.In order to evaluate the performance of the proposed algorithm,two hyperspectral remote sensing images are adopted as experimental data.The proposed algorithm is compared with spectral angle mapper (SAM),spectral information divergence (SID) and Euclidean distance (ED) using the product accuracy,user accuracy,overall accuracy,average accuracy and Kappa coefficient.The results show that the proposed algorithm can be applied to hyperspectral image classification effectively.

Rapid analysis of piperazine ferulate tablets by optic-fiber sensing technology and the similarity of ultraviolet spectra

A rapid analysis method of piperazine ferulate tablets by optic-fiber sensing technology with UV-vis absorption spectrum was established. Qualitative and quantitative data were obtained and compared by maximum and minimum wavelength, absorbance and contrast spectra. Similarity method was used to identify authenticity of drugs. The difference of contents measured by this method and UV determination method in China Pharmacopoeia showed no statistical significance (P40.05), while the similarity can be used as a parameter to identify the authenticity of drugs.

SEMI-SUPERVISED RADIO TRANSMITTER CLASSIFICATION BASED ON ELASTIC SPARSITY REGULARIZED SVM

Non-collaborative radio transmitter recognition is a significant but challenging issue, since it is hard or costly to obtain labeled training data samples. In order to make effective use of the unlabeled samples which can be obtained much easier, a novel semi-supervised classification method named Elastic Sparsity Regularized Support Vector Machine (ESRSVM) is proposed for radio transmitter classification. ESRSVM first constructs an elastic-net graph over data samples to capture the robust and natural discriminating information and then incorporate the information into the manifold learning framework by an elastic sparsity regularization term. Experimental results on 10 GMSK modulated Automatic Identification System radios and 15 FM walkie-talkie radios show that ESRSVM achieves obviously better performance than KNN and SVM, which use only labeled samples for classification, and also outperforms semi-supervised classifier LapSVM based on manifold regularization.

Similarity measurement of Chinese medicine ingredients for cold-hot nature identification

Objective:Nature theory of Chinese medicine (CM) is the core basic theory of Traditional Chinese Medicine (TCM), in which cold-hot nature is the focus of research. Studies have found that CM ingredients are the material basis for the production of medicine natures. Therefore, it is speculated that CMs with similar composition of substances should have similar medicinal nature. Modern work studies cold-hot medicine of CMs with chemical fingerprinting technology because the chemical fingerprint data of CM can reflect the whole composition of CM ingredients. Methods:To verify the hypothesis above, in this work, we study quantifying the similarity of CM ingredients to fingerprint similarity, and explore the relationship between the composition of CMs and cold-hot nature. Firstly, we utilize ultraviolet (UV) spectrum technology to analyze 61 CMs, which have clear cold-hot nature (including 30 ‘cold’ CMs and 31 ‘hot’ CMs). Secondly, with the constructed fingerprint database of CMs, a distance metric learning algorithm is studied to metric the similarity of UV fingerprints. Finally, a retrieval scheme is proposed to build a predictive identification model to identify cold-hot nature of CMs. Results:By means of numerous experiment analyses, ultraviolet spectrum data of petroleum ether solvent can better represent CMs to distinguish between cold and hot natures. Comparing with existing classical models, the proposed identification scheme has better predictive performance. Conclusion:The experimental results prove our inference that CMs with similar composition of substances should have similar medicinal nature. The proposed prediction model is proved to be effective and feasible.

A Comparative Study of Behavior of Multi-Storied Regular and Irregular Buildings under Static and Dynamic Loading

One of the major challenges of constructing any high rise building for civil engineers is to make it earthquake resistant. This resistance largely depends on the building’s shape and structural system. A comparative study has been done in this paper about the seismic behavior and response of buildings having a regular plan and plan irregularity (re-entrant corners). The 5 building models considered in this study are 15 stories each, the same area and identical weight. Among the 5 building models, 2 are with a regular plan (square, rectangle) and the other 3 building models are with plan irregularity (re-entrant corners). All of them are modeled using ETABS 2015 program for Dhaka, Bangladesh (seismic zone 2). Static loads, wind loads and seismic loads are considered for each model and dynamic response under Bangladesh National Building Code (BNBC) 2006 response spectrum has been meticulously analyzed. A comparison for story displacement, base shear, story drift and time period has been established and explored for dynamic response spectrum among the models. The results show that buildings with irregularity have a greater value of time period, drift and displacement and hereby are more susceptible to damage during an earthquake or disaster.

A Note on the Prime Spectrums of Character Rings of Finite Groups

Let G be a finite group with order g and S be a subring of the algebraic number field which contains the integral extension over Z generated by a g-th primitive root co of unity, and R（G） be the character ring of G. The prime spectrum of the commutative ring S×Z R（G） iv denoted by Spec（S×Z R（G）） and set π={p｜p is a rational prime number such that p^-1 S}. We prove that when G is a regroup, a π＇-group, or a finite Abelian group, the number of the connetted components of Spec（ S×Z R （G） ） coincides with the number of the π-regular classes in G,

Similarity law of fluctuating pressure spectrum beneath hydraulic jump

Similarity law is the conversion rule between model and prototype, on which a lot of research works have been done, with no agreement reached referring to the similarity law of fluctuating pressure fre- quency spectrum. Experimental data of peak frequency and dominant frequency range of fluctuating pressure spectrum beneath hydraulic jump obtained from serial models of scales 1:1, 1:2 and 1:5 are compared. As a result, similarity law of fluctuating pressure spectrum in the strongly rolling area agrees with the gravity law. As peak frequency and dominant frequencies of fluctuating pressures in hydraulic jump, toe and tail are rather low, and the similarity is often misunderstood to be λf = 1. However, the normalized spectrums of fluctuating pressures show that the similarity nearly agrees with the gravity law.

Von Neumann Regularity and Quadratic Conorms in JB^＊-triples and C^＊-algebras

We revise the notion of von Neumann regularity in JB^＊-triples by finding a new characterisation in terms of the range of the quadratic operator Q（a）. We introduce the quadratic conorm of an element a in a JB^＊-triple as the minimum reduced modulus of the mapping Q（a）. It is shown that the quadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrum of a. It is established that a contractive bijection between JBW^＊-triples is a triple isomorphism if, and only if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalized inverse are discussed. Some applications to C^＊-algebras and von Neumann algebras are also studied.

An extended similarity in channel turbulence

In this paper, Liutex similarity is extended and revised in channel turbulence. Liutex similarity is free from viscous dissipation, relaxing the very high Reynolds number assumption of K41. Liutex similarity hypothesis in 2-D channel turbulence is first proposed and estimated, which denotes that the statistical properties of Liutex field are uniquely and universally determined by the scale l, Liutex vortex number density n(A) with each area A and mean dissipation rate of square of Liutex magnitude ηL. The Liutex spectrum is EL (k) ∼ C[n(A)1/2ηL]1/3k−5/3 in the inertial range where energy spectrum exhibits double cascades. The scaling behaviors of Liutex spectrum in 2-D are independent of Reynolds number. Liutex structure functions are defined as Liutexp (l) ≡ 〈[δR∥(l)]p〉 which are in dependent of scales. It is found that Liutexp (l) ∼ C′(ηL)p/3l0 by dimensional analysis.

Application of regularization technique in image super-resolution algorithm via sparse representation

To make use of the prior knowledge of the image more effectively and restore more details of the edges and structures, a novel sparse coding objective function is proposed by applying the principle of the non-local similarity and manifold learning on the basis of super-resolution algorithm via sparse representation. Firstly, the non-local similarity regularization term is constructed by using the similar image patches to preserve the edge information. Then, the manifold learning regularization term is constructed by utilizing the locally linear embedding approach to enhance the structural information. The experimental results validate that the proposed algorithm has a significant improvement compared with several super-resolution algorithms in terms of the subjective visual effect and objective evaluation indices.

Multifractal Decomposition of Statistically Self-Similar Sets

Let K be a statistically self-similar set defined by Graf.In this paper,we construct a random measure ρ which is supported by K and study the multifractal decomposition for K with p. Under such a decomposition,we obtain the expression of the spectrum function f(α).

ASYMPTOTIC SIMILARITY OF INFINITE-DIMENSIONAL LINEAR SYSTEMS AND APPLICATIONS TO STABILITY

In this note a generalization of the concept of similarity called asymptotic similarity for infinite-dimensional linear systems is introduced. We show that this asymptotic similarity preserves the spectrum and the exponential growth bound.