• A Joint Delay-and-Sum and Fourier Beamforming Method for High Frame Rate Ultrasound Imaging
  • Abstract Frame rate is an important metric for ultrasound imaging systems, and high frame rates (HFR) benefit moving-target imaging. One common way to obtain HFR imaging is to transmit a plane wave. Delay-and-sum (DAS) beamformer is a conventional beamforming algorithm, which is simple and has been widely implemented in clinical application. Fourier beamforming is an alternative method for HFR imaging and has high levels of imaging efficiency, imaging speed, and good temporal dynamic characteristics. Nevertheless, the resolution and contrast performance of HFR imaging based on DAS or Fourier beamforming are insufficient due to the single plane wave transmission. To address this… More
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  • Automatic Sleep Staging Algorithm Based on Random Forest and Hidden Markov Model
  • Abstract In the field of medical informatics, sleep staging is a challenging and timeconsuming task undertaken by sleep experts. According to the new standard of the American Academy of Sleep Medicine (AASM), the stages of sleep are divided into wakefulness (W), rapid eye movement (REM) and non-rapid eye movement (NREM) which includes three sleep stages (N1, N2 and N3) that describe the depth of sleep. This study aims to establish an automatic sleep staging algorithm based on the improved weighted random forest (WRF) and Hidden Markov Model (HMM) using only the features extracted from double-channel EEG signals. The WRF classification model… More
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  • Fractional Analysis of Viscous Fluid Flow with Heat and Mass Transfer Over a Flexible Rotating Disk
  • Abstract An unsteady viscous fluid flow with Dufour and Soret effect, which results in heat and mass transfer due to upward and downward motion of flexible rotating disk, has been studied. The upward or downward motion of non rotating disk results in two dimensional flow, while the vertical action and rotation of the disk results in three dimensional flow. By using an appropriate transformation the governing equations are transformed into the system of ordinary differential equations. The system of ordinary differential equations is further converted into first order differential equation by selecting suitable variables. Then, we generalize the model by using… More
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  • On Caputo-Type Cable Equation: Analysis and Computation
  • Abstract In this paper, a special case of nonlinear time fractional cable equation is studied. For the equation defined on a bounded domain, the existence, uniqueness, and regularity of the solution are firstly studied. Furthermore, it is numerically studied via the weighted and shifted Grünwald difference (WSGD) methods/the local discontinuous Galerkin (LDG) finite element methods. The derived numerical scheme has been proved to be stable and convergent with order O(∆t2 + hk+1), where ∆t, h, k are the time stepsize, the spatial stepsize, and the degree of piecewise polynomials, respectively. Finally, a numerical experiment is presented to verify the theoretical analysis. More
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  • Modelling of Energy Storage Photonic Medium by WavelengthBased Multivariable Second-Order Differential Equation
  • Abstract Wavelength-dependent mathematical modelling of the differential energy change of a photon has been performed inside a proposed hypothetical optical medium. The existence of this medium demands certain mathematical constraints, which have been derived in detail. Using reverse modelling, a medium satisfying the derived conditions is proven to store energy as the photon propagates from the entry to exit point. A single photon with a given intensity is considered in the analysis and hypothesized to possess a definite non-zero probability of maintaining its energy and velocity functions analytic inside the proposed optical medium, despite scattering, absorption, fluorescence, heat generation, and other… More
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  • A Comprehensive Model for Structural Non-Probabilistic Reliability and the Key Algorithms
  • Abstract It is very difficult to know the exact boundaries of the variable domain for problems with small sample size, and the traditional convex set model is no longer applicable. In view of this, a novel reliability model was proposed on the basis of the fuzzy convex set (FCS) model. This new reliability model can account for different relations between the structural failure region and variable domain. Key computational algorithms were studied in detail. First, the optimization strategy for robust reliability is improved. Second, Monte Carlo algorithms (i.e., uniform sampling method) for hyper-ellipsoidal convex sets were studied in detail, and errors… More
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