The progress of mini black holes: principles and analytical astronomical observation techniques

Mini-black hole (MBH) is a concept first proposed by Stephen Hawking in the 1970s. Normally, exploring MBHs will enhance the understanding of quantum theory and gravity theory as well as be helpful in predicting the configuration of the early universe. Based on information retrieval, this paper summarizes the progress of MBHs and takes three major aspects: background, models, practical methods for observations, and analysis. Specifically, the descriptive equations are derived, and different models are discussed separately. These results shed light on the prospective development of quantum field theorem, general relativity, and string theory.

Angle domain generalized Radon transform for elastic multi-parameter inverse scattering inversion

Linearized algorithms based on the Born approximation are well-known and popular techniques for quantitative seismic imaging and inversion. However, linearization methods usually suffer from some significant problems, such as computational cost for the required number of iterations, requirement for background models, and uncertain and unstable multi-parameter extraction, which make the methods difficult to implement in practical applications. To avoid these problems, we propose an angle-domain generalized Radon transform (AD-GRT) inversion in 2D elastic isotropic media. This AD-GRT is an approximate transform between the seismic data and an angle-domain model, which acts as a scattering function, and the seismic data can be reconstructed accurately, even when the background models are incorrect. The density and Lam短oduli perturbation parameters can be extracted stably from the inverted angle-domain scattering function. Deconvolution of the source wavelet is taken into account to remove the effect of the wavelet and improve the resolution and accuracy of the inversion results. The derived AD-GRT inversion is non-iterative and is as efficient as the traditional elastic GRT method. The additional dimension of the angle domain has little effect on the computational cost of the AD-GRT, as opposed to other extended-domain inversion/migration methods. Our method also can be used to solve non-linear Born inversion problems using iteration, which can significantly improve their convergence rate. Three numerical examples illustrate that the angle-domain scattering function inversion, data reconstruction, and multi-parameter extraction using the presented AD-GRT inversion are effective.

On the inverse problem of reflection Green’s function seismograms over stratified acoustic media: Estimation of background models

A theory is presented for estimating the background velocity and density of an acoustic stratified medium by iterative least-squares waveform inversion in the frequency-horizontal slowness domain of low-frequency precritical reflection incidence seismograms of time length [Formula: see text]. The initial model is constant. The prerequisites for the method are that the reflection seismograms should be Green’s function seismograms and that the fundamental frequency component [Formula: see text] is present. Then, the gradients of the objective function provide the low-wavenumber trend of the medium. A matrix formulation for the model update is expressed mathematically by the classic seismogram residual, Jacobian, gradient, and Hessian in the Levenberg-Marquardt approximation. The first iteration, which is equal to a constant-parameter migration inversion (CPMI), is thoroughly analyzed, and expressions for band-limited gradients and block Hessians are found. For primary precritical reflection incidence seismograms of infinite bandwidth, it is shown theoretically that the partial gradients in the CPMI model become a reflection strength-weighted sum of shifted discrete sign functions, typical of step or staircase functions, which provide interface locations in Born depth and amplitudes that can be mapped to velocity and density information. For frequency-band-limited primary reflection seismograms, the partial gradients become a reflection strength-weighted sum of wavenumber-band-limited discrete sign functions. When the fundamental frequency component in the seismograms is present, the band-limited discrete sign functions are oscillatory but keep the information of the step function characteristic of the partial gradient. When the fundamental frequency component in the seismograms is absent, the band-limited discrete sign functions keep information of where the steps are located but lose the information of the amplitudes of the steps. The Hessian elements are nonstandard with the Hessian modeled over a broader frequency range than the frequencies of the observed low-frequency seismogram to avoid it becoming close to singular. The main mathematical findings are illustrated by a simple model and seismograms, for which the background models are found after two iterations. For the sake of completeness, the background models are classically used as initial models in a Levenberg-Marquardt least-squares inversion scheme to estimate the layer velocities and densities from broadband seismograms.

Human-like Computer Vision

Statistical machine learning is widely used in image classification and typically 1) requires many images to achieve high accuracy and 2) does not provide support for reasoning below the level of classification. By contrast this paper describes an approach called machine learning approach called Logical Vision (LV) which uses a) background knowledge such as light reflection that can itself be learned and used for resolving visual ambiguities, which cannot be easily modeled using statistical approaches, b) a wider class of background models representing classical 2D shapes such as circles and ellipses, c) primitive-level statistical estimators to handle noise in real images, Our results indicate that in real images the new noise-robust version of LV using a single example (ie one-shot LV) converges to an accuracy at least comparable to thirty-shot statistical machine learner on the prediction of hidden light sources.

A Comparison Study of Explicit and Implicit 3-D Transient Electromagnetic Forward Modeling Schemes on Multi-Resolution Grid

This study compares the efficiency of 3-D transient electromagnetic forward modeling schemes on the multi-resolution grid for various modeling scenarios. We developed time-domain finite-difference modeling based on the explicit scheme earlier. In this work, we additionally implement 3-D transient electromagnetic forward modeling using the backward Euler implicit scheme. The iterative solver is used for solving the system of equations and requires a proper initial guess that has significant effect on the convergence. The standard approach usually employs the solution of a previous time step as an initial guess, which might be too conservative. Instead, we test various initial guesses based on the linear extrapolation or linear combination of the solutions from several previous steps. We build up the implicit scheme forward modeling on the multi-resolution grid, which allows for the adjustment of the horizontal resolution with depth, hence improving the performance of the forward operator. Synthetic examples show the implicit scheme forward modeling using the linearly combined initial guess estimate on the multi-resolution grid additionally reduces the run time compared to the standard initial guess approach. The result of comparison between the implicit scheme developed here with the previously developed explicit scheme shows that the explicit scheme modeling is more efficient for more conductive background models often found in environmental studies. However, the implicit scheme modeling is more suitable for the simulation with highly resistive background models, usually occurring in mineral exploration scenarios. Thus, the inverse problem can be solved using more efficient forward solution depending on the modeling setup and background resistivity.

Joint wave-equation traveltime inversion of diving/direct and reflected waves for the P- and S-wave velocity macromodel building

Full waveform inversion (FWI) suffers from the local minima problem and requires a sufficiently accurate starting model to converge to the correct solution. Wave-equation traveltime inversion (WETI) is an effective tool to retrieve the long-wavelength components of the velocity model. We develop a joint diving/direct and reflected wave WETI (JDRWETI) method to build the P- and S-wave velocity macromodels. We estimate the traveltime shifts of seismic events (diving/direct waves, PP and PS reflections) through the dynamic warping scheme and construct a misfit function using both the time shifts of diving/direct and reflected waves. We derive the adjoint wave equations and the gradients with respect to the background models based on the joint misfit function. We apply the kernel decomposition scheme to extract the kernel of the diving/direct wave and the tomography kernels of PP and PS reflections. For an explosive source, the kernels of diving/direct wave and PP reflections and the kernel of PS reflections are used to compute the P- and S-wave gradients of the background models, respectively. We implement JDRWETI by a two-stage inversion workflow: first invert the P- and S-wave velocity models using the P-wave gradients and then improve the S-wave velocity model using the S-wave gradients. Numerical tests on synthetic and field datasets reveal that the JDRWETI method successfully recovers the long-wavelength components of P- and S-wave velocity models, which can be used for an initial model for the subsequent elastic FWI. Moreover, the proposed JDRWETI method prevails over the existing reflection WETI method and the cascaded diving/direct and reflected wave WETI method, especially when large velocity errors are present in the shallow part of the starting models. The JDRWETI method with the two-stage inversion workflow can give rise to reasonable inversion results even for the model with different P- and S-wave velocity structures.

Mean Shift Fusion Color Histogram Algorithm for Nonrigid Complex Target Tracking in Sports Video

We analyze and study the tracking of nonrigid complex targets of sports video based on mean shift fusion color histogram algorithm. A simple and controllable 3D template generation method based on monocular video sequences is constructed, which is used as a preprocessing stage of dynamic target 3D reconstruction algorithm to achieve the construction of templates for a variety of complex objects, such as human faces and human hands, broadening the use of the reconstruction method. This stage requires video sequences of rigid moving target objects or sets of target images taken from different angles as input. First, the standard rigid body method of Visuals is used to obtain the external camera parameters of the sequence frames as well as the sparse feature point reconstruction data, and the algorithm has high accuracy and robustness. Then, a dense depth map is computed for each input image frame by the Multi-View Stereo algorithm. The depth reconstruction with a too high resolution not only increases the processing time significantly but also generates more noise, so the resolution of the depth map is controlled by parameters. The multiple hypothesis target tracking algorithms are used to track multiple targets, while the chunking feature is used to solve the problem of mutual occlusion and adhesion between targets. After finishing the matching, the target and background models are updated online separately to ensure the validity of the target and background models. Our results of nonrigid complex target tracking by mean shift fusion color histogram algorithm for sports video improve the accuracy by about 8% compared to other studies. The proposed tracking method based on the mean shift algorithm and color histogram algorithm can not only estimate the position of the target effectively but also depict the shape of the target well, which solves the problem that the nonrigid targets in sports video have complicated shapes and are not easy to track. An example is given to demonstrate the effectiveness and adaptiveness of the applied method.