The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the comparison of the maximum likelihood estimates and the Bayes estimates of two-parameter power function distribution. The Bayes estimates are obtained, using conjugate priors, under five loss functions consist of square error, precautionary, weighted, LINEX and DeGroot loss function. The Gibbs sampling algorithm is proposed to generate samples from posterior distributions and in result the Bayes estimates are computed. The comparison of the maximum likelihood estimates and the Bayes estimates are done through the root mean squared errors. One real-life data set is analyzed to illustrate the evaluation of proposed methods of estimation. Finally, results from the simulation are discussed to assess the performance behavior of the maximum likelihood estimates and the Bayes estimates.

In this study, based on a new quantum integral identity, the authors establish some quantum estimates of Hermite-Hadamard type inequalities for convex functions. These results generalize and improve some known results given in literatures.

Glioma accounts for the highest proportion of primary intracranial malignant tumors. Microenvironment enormously influences the process of glioma progression. Our study is to establish an individualized prognostic nomogram for glioma patients with microenvironment signature. Glioma samples of Chinese Glioma Genome Atlas (CGGA) were grouped by the immune and stromal score based on ESTIMATE algorithm. Microenvironment-related genes (MRGs) in glioma were analyzed by R. To determine the best prognostic correlation genes, univariate and multivariate Cox regression analysis were used to analyze MRGs. Use the selected genes (CHI3L1, SOCS3, SLC47A2, COL3A1, SRPX2 and SERPINA3), we established the prognostic risk score model (microenvironment signature) and validated it. Gene Set Enrichment Analysis (GSEA) showed that the high-risk group was mainly enriched in immune and stromal function KEGG pathways. Finally, the nomogram was constructed and evaluated. The receiver operating characteristic (ROC) curve, Calibration plots and decision curve analysis (DCA) of training and validation set indicated the excellent predictive performance of nomogram. In conclusion, the 6-gene microenvironment signature can not only provide directions for the basic research of glioma, but also can be included as an independent prognostic index in nomogram for individual prediction to guide clinical treatment.

InSAR and associated analytic methods enable relative surface deformation measurements from low Earth orbit with a potential accuracy of centimeters to millimeters. However, assessing the actual accuracy can be quite difficult. The analytic methods are complicated enough that naive analytic error propagation is infeasible, and, in many settings, InSAR practitioners lack sufficient ground truth to assess results. Phase noise due to partial decorrelation from changes in the scattering properties of the ground is a prominent source of accuracy loss. In this paper we present a method to assess the loss of precision due to this component of phase noise. The proposed method consists of generating synthetic data stacks whose statistical properties match those of the actual input SAR data stacks, and then using the synthetic data for an ensemble calculation. The spread of the results of the ensemble calculation indicates the loss of precision. We show examples of the ensemble analysis at a mining operation in South Africa, and demonstrate the ability to estimate the precision of two InSAR deformation retrieval methods on a point-by-point and epoch-by-epoch basis.

Accelerating, exact, explicit and simple solutions of relativistic hydrodynamics allow for a simple and natural description of highly relativistic p+p collisions. These solutions yield a finite rapidity distribution, thus they lead to an advanced estimate of the initial energy density of high energy collisions. We show that such an advanced estimate yields an initial energy density in $\sqrt{s}=7$ and 8 TeV p+p collisions at LHC around or above the critical energy density from lattice QCD, and a corresponding initial temperature above the critical temperature from QCD and the Hagedorn temperature. This suggests that the collision energy of the LHC corresponds to a large enough initial energy density to create a non-hadronic perfect fluid even in pp collisions. %We also show, that several times the %critical energy density may have been reached in high multiplicity events, hinting at a non-hadronic medium created in %high multiplicity $\sqrt{s}=7$ and 8 TeV p+p collisions.

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

The task of determining the distance from one object to another is one of the important tasks solved in robotics systems. Conventional algorithms rely on an iterative process of predicting distance estimates, which results in an increased computational burden. Algorithms used in robotic systems should require minimal time costs, as well as be resistant to the presence of noise. To solve these problems, the paper proposes an algorithm for Kalman combination filtering with a Goldschmidt divisor and a median filter. Software simulation showed an increase in the accuracy of predicting the estimate of the developed algorithm in comparison with the traditional filtering algorithm, as well as an increase in the speed of the algorithm. The results obtained can be effectively applied in various computer vision systems.

Since the electro-hydraulic servo shaking table exists many nonlinear elements, such as, dead zone, friction and blacklash, its acceleration response has higher harmonics which result in acceleration harmonic distortion, when the electro-hydraulic system is excited by sinusoidal signal. For suppressing the harmonic distortion and precisely identify harmonics, a combination of the adaptive linear neural network and least mean M-estimate (ADALINE-LMM), is proposed to identify the amplitude and phase of each harmonic component. Namely, the Hampel’s three-part M-estimator is applied to provide thresholds for detecting and suppressing the error signal. Harmonic generators are used by this harmonic identification scheme to create input vectors and the value of the identified acceleration signal is subtracted from the true value of the system acceleration response to construct the criterion function. The weight vector of the ADALINE is updated iteratively by the LMM algorithm, and the amplitude and phase of each harmonic, even the results of harmonic components, can be computed directly online. The simulation and experiment are performed to validate the performance of the proposed algorithm. According to the experiment result, the above method of harmonic identification possesses great real-time performance and it has not only good convergence performance but also high identification precision.

The main idea of this paper is to investigate the exact solutions and dynamic properties in optical nanofibers, which is modeled by space-time fractional perturbed nonlinear schr\"odinger equation involving Kerr law nonlinearity with conformal fractional derivative. Firstly, by the complex fractional traveling wave transformation, the traveling wave system of the original equation is obtained, then a conserved quantity, namely the Hamiltonian is constructed, and the qualitative analysis of this system is conducted via this quantity by classifying the equilibrium points. Moreover, the prior estimate of the existence of the soliton and periodic solution is established via the bifurcation method. Furthermore, all exact traveling wave solutions are constructed to illustrate our results explicitly by the complete discrimination system for polynomial method.

Nowadays, wearable devices for human health monitoring are increasingly become popular and widely used. Typically, the wearable device is small size and operates with batteries. Therefore, the wearable device acquires bio-signals and transfers to smartphones or personal computers (PC) via WiFi/ Bluetooth for processing data. To reduce power consumption is one of the most important challenges of designing wearable devices. To solve this problem, the proposed signal quality valuation (SQV) method can be select the high-quality signal and reduce the transfer time to other devices. In this paper, the proposed SQV and data compression method rely on real-time PPG signals analysis to retain important information of PPG signal, improve performance and power consumption of PPG devices. Besides, we also proposed Heuristic rules for heart rate (HR) estimation with compression data. The experimental results show that the highest compression ratio (CR) is 387.8 with BIDMC Physionet database (sampling frequencies of 125 Hz) and HR error as 1.43 bpm for averaging absolute error (avAE), the standard deviation absolute error (sdAE as 0.4) and relative error mean (avRE as 0.019). The proposed real-time PPG measurement system (sampling frequency as 100/ 200/ 400 Hz) reduce power consumption and open the new structure for healthcare application systems