Joint PP and PS AVO inversion based on Bayes theorem

Based on the Aki-Richards approximate equations for reflection coefficients and Bayes theorem, we developed an inversion method to estimate P- and S-wave velocity contrasts and density contrast from combined PP and PS data. This method assumes that the parameters satisfy a normal distribution and introduces the covariance matrix to describe the degree of correlation between the parameters and thus to improve the inversion stability. Then, we suppose that the parameter sequence is subject to the Cauchy distribution and employs another matrix Q to describe the parameter sequence sparseness to improve the inversion result resolution. Tests on both synthetic and real multi-component data prove that this method is valid, efficient, more stable, and more accurate compared to methods using PP data only.

Bayes Theorem Based Virtual Machine Scheduling for Optimal Energy Consumption

This paper proposes an algorithm for scheduling Virtual Machines(VM)with energy saving strategies in the physical servers of cloud data centers.Energy saving strategy along with a solution for productive resource utilizationfor VM deployment in cloud data centers is modeled by a combination of“VirtualMachine Scheduling using Bayes Theorem”algorithm(VMSBT)and Virtual Machine Migration(VMMIG)algorithm.It is shown that the overall data center’sconsumption of energy is minimized with a combination of VMSBT algorithmand Virtual Machine Migration(VMMIG)algorithm.Virtual machine migrationbetween the active physical servers in the data center is carried out at periodicalintervals as and when a physical server is identified to be under-utilized.In VMscheduling,the optimal data centers are clustered using Bayes Theorem and VMsare scheduled to appropriate data center using the selection policy that identifiesthe cluster with lesser energy consumption.Clustering using Bayes rule minimizesthe number of server choices for the selection policy.Application of Bayestheorem in clustering has enabled the proposed VMSBT algorithm to schedule thevirtual machines on to the physical server with minimal execution time.The proposedalgorithm is compared with other energy aware VM allocations algorithmsviz.“Ant-Colony”optimization-based(ACO)allocation scheme and“min-min”scheduling algorithm.The experimental simulation results prove that the proposedcombination of‘VMSBT’and‘VMMIG’algorithm outperforms othertwo strategies and is highly effective in scheduling VMs with reduced energy consumptionby utilizing the existing resources productively and by minimizing thenumber of active servers at any given point of time.

Effective and Efficient Feature Selection for Large-scale Data Using Bayes' Theorem

This paper proposes one method of feature selection by using Bayes＇ theorem. The purpose of the proposed method is to reduce the computational complexity and increase the classification accuracy of the selected feature subsets. The dependence between two attributes （binary） is determined based on the probabilities of their joint values that contribute to positive and negative classification decisions. If opposing sets of attribute values do not lead to opposing classification decisions （zero probability）, then the two attributes are considered independent of each other, otherwise dependent, and one of them can be removed and thus the number of attributes is reduced. The process must be repeated on all combinations of attributes. The paper also evaluates the approach by comparing it with existing feature selection algorithms over 8 datasets from University of California, Irvine （UCI） machine learning databases. The proposed method shows better results in terms of number of selected features, classification accuracy, and running time than most existing algorithms.

Optimization of Well Position and Sampling Frequency for Groundwater Monitoring and Inverse Identification of Contamination Source Conditions Using Bayes’Theorem

Coupling Bayes’Theorem with a two-dimensional(2D)groundwater solute advection-diffusion transport equation allows an inverse model to be established to identify a set of contamination source parameters including source intensity(M),release location(0 X,0 Y)and release time(0 T),based on monitoring well data.To address the issues of insufficient monitoring wells or weak correlation between monitoring data and model parameters,a monitoring well design optimization approach was developed based on the Bayesian formula and information entropy.To demonstrate how the model works,an exemplar problem with an instantaneous release of a contaminant in a confined groundwater aquifer was employed.The information entropy of the model parameters posterior distribution was used as a criterion to evaluate the monitoring data quantity index.The optimal monitoring well position and monitoring frequency were solved by the two-step Monte Carlo method and differential evolution algorithm given a known well monitoring locations and monitoring events.Based on the optimized monitoring well position and sampling frequency,the contamination source was identified by an improved Metropolis algorithm using the Latin hypercube sampling approach.The case study results show that the following parameters were obtained:1)the optimal monitoring well position(D)is at(445,200);and 2)the optimal monitoring frequency(Δt)is 7,providing that the monitoring events is set as 5 times.Employing the optimized monitoring well position and frequency,the mean errors of inverse modeling results in source parameters(M,X0,Y0,T0)were 9.20%,0.25%,0.0061%,and 0.33%,respectively.The optimized monitoring well position and sampling frequency canIt was also learnt that the improved Metropolis-Hastings algorithm(a Markov chain Monte Carlo method)can make the inverse modeling result independent of the initial sampling points and achieves an overall optimization,which significantly improved the accuracy and numerical stability of the inverse modeling results.

State Estimation for Sound and Vibration Emitted from a Machine Based on Sound Measurement Under Existenceof Background Noise

Many studies on the diagnosis for machines have become important recently because of increased use of various complex industrial systems.The correlation information between sound and vibration is very important for machine diagnosis.Usually,vibration pickups are attached directly to the machine in order to measure vibration data.However,in some cases,the sensors can not be attached directly on highly precise devices.In this study,a method to estimate the fluctuation of sound and vibration is proposed based on the measurement data of sound emitted from the machine under existence of background noise.The effectiveness of the proposed theory is experimentally confirmed by applying it to the observed data emitted from a rotational machine driven by an electric motor.

Innovation Research on Fingerprint and DNA Identifications

In this study,two models for fingerprint and DNA identifications are constructed based on modern technologies,while offering significant advances over prior models.Our models have high credibility,obtaining relatively accurate results under different circumstances.Under different assumptions,this model tests the probability of the validity in the statement that human fingerprints are unique to be 93.94%.In other words,the percentage of misidentification is 6.06%.This model is a robust fingerprint identification method that can tolerate highly nonlinear deformations.The model is tested on the basis of a self-built database,proving that the model has high credibility,and convincing results are obtained from sensitivity analysis.In order to estimate the odds of misidentification by DNA evidence,we emphasized on two factors that might contribute to misidentification:random match probability and the probability arising from laboratory errors.Then,a model is developed using Bayes’theorem to reveal the inherent relationship between them,which carries some reference value.The probability of matching by DNA evidence is estimated based on the changes in the significant level.Finally,the probabilities of misidentification by both fingerprint evidence and DNA evidence are compared using numerous data.We found that the probability of the former is 6.06%and that of the latter is smaller than 4.0 x 10^(−10).Therefore,it can be concluded that DNA identification is far better than that of fingerprint identification.

Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.

Modelling the probability of erroneous negative lymph node staging in patients with colon cancer

Background:Patients in who with insufficient number of analysed lymph nodes(LNs)are more likely to receive an incorrect LN staging.The ability to calculate the overall probability of undiagnosed LN involvement errors in these patients could be very useful for approximating the real patient prognosis and for giving possible indications for adjuvant treatments.The objective of this work was to establish the predictive capacity and prognostic discriminative ability of the final error probability(FEP)among patients with colon cancer and with a potentially incorrectly-staged LN-negative disease.Methods:This was a retrospective multicentric population study carried out between January 2004 and December 2007.We used a mathematical model based on Bayes’theorem to calculate the probability of LN involvement given a FEP test result.Cumulative sum graphs were used to calculate risk groups and the survival rates were calculated,by month,using the Kaplan-Meier method.Results:A total of 548 patients were analysed and classified into three risk groups according to their FEP score:low-risk(FEP<2%),intermediate-risk(FEP 2%-15%),and high-risk(FEP>15%).Patients with LN involvement had the lowest overall survival rate when compared to the three risk groups.This difference was statistically significant for the low-and intermediate-risk groups(P=0.002 and P=0.004,respectively),but high-risk group presented similar survival curves to pN+group(P=0.505).In terms of disease-free survival,the high-risk group presented similar curves to the intermediate-risk group until approximately 60 months’follow-up(P=0.906).After 80 months’follow-up,the curve of high-risk group coincided with that of the pN+group(P=0.172).Finally,we summarized the FEP according to the number of analysed LNs and accompanied by a contour plot which represents its calculation graphically.Conclusions:The application of Bayes’theorem in the calculation of FEP is useful to delimit risk subgroups from among patients without LN involvement.