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Machine learning (ML) pervades an increasing number of academic disciplines and industries. Its impact is profound, and several fields have been fundamentally altered by it, autonomy and computer vision for example; reliability engineering and safety will undoubtedly follow suit. There is already a large but fragmented literature on ML for reliability and safety applications, and it can be overwhelming to navigate and integrate into a coherent whole. In this work, we facilitate this task by providing a synthesis of, and a roadmap to this ever-expanding analytical landscape and highlighting its major landmarks and pathways. We first provide an overview of the different ML categories and sub-categories or tasks, and we note several of the corresponding models and algorithms. We then look back and review the use of ML in reliability and safety applications. We examine several publications in each category/sub-category, and we include a short discussion on the use of Deep Learning to highlight its growing popularity and distinctive advantages. Finally, we look ahead and outline several promising future opportunities for leveraging ML in service of advancing reliability and safety considerations. Overall, we argue that ML is capable of providing novel insights and opportunities to solve important challenges in reliability and safety applications. It is also capable of teasing out more accurate insights from accident datasets than with traditional analysis tools, and this in turn can lead to better informed decision-making and more effective accident prevention., Comment: 50 pages

The observed rotation curves of low surface brightness (LSB) galaxies play an essential role in studying dark matter, and indicate that there exists a central constant density dark matter core. However, the cosmological N-body simulations of cold dark matter predict an inner cusped halo with a power-law mass density distribution, and can't reproduce a central constant-density core. This phenomenon is called cusp-core problem. When dark matter is quiescent and satisfies the condition for hydrostatic equilibrium, using the equation of state can get the density profile in the static and spherically symmetric space-time. To solve the cusp-core problem, we assume that the equation of state is independent of the scaling transformation. Its lower order approximation for this type of equation of state can naturally lead to a special case, i.e. $p=\zeta\rho+2\epsilon V_{rot}^{2}\rho$, where $p$ and $\rho$ are the pressure and density, $V_{rot}$ is the rotation velocity of galaxy, $\zeta$ and $ \epsilon$ are positive constants. It can obtain a density profile that is similar to the pseudo-isothermal halo model when $\epsilon$ is around $0.15$. To get a more widely used model, let the equation of state include the polytropic model, i.e. $p= \frac{\zeta}{\rho_{0}^{s}}\rho^{1+s}+ 2\epsilon V_{rot}^{2}\rho$, we can get other kinds of density profiles, such as the profile that is nearly same with the Burkert profile, where $s$ and $\rho_{0}$ are positive constants., Comment: 10 pages, 4 figures

A novel dual-function radar communication (DFRC) system is proposed, that achieves high target resolution and high communication rate. It consists of a multiple-input multiple-output (MIMO) radar, where only a small number of antennas are active in each channel use. The probing waveforms are orthogonal frequency division multiplexing (OFDM) type. The OFDM carriers are divided into two groups, one that is used by the active antennas in a shared fashion, and another one, where each subcarrier is assigned to an active antenna in an exclusive fashion (private subcarriers). Target estimation is carried out based on the received and transmitted symbols. The system communicates information via the transmitted OFDM data symbols and the pattern of active antennas in a generalized spatial modulation (GSM) fashion. A multi-antenna communication receiver can identify the indices of active antennas via sparse signal recovery methods. The use of shared subcarriers enables high communication rate. The private subcarriers are used to synthesize a virtual array for high angular resolution, and also for improved estimation on the active antenna indices. The OFDM waveforms allow the communication receiver to easily mitigate the effect of frequency selective fading, while the use of a sparse array at the transmitter reduces the hardware cost of the system. The radar performance of the proposed DFRC system is evaluated via simulations, and bit error rate (BER) results for the communication system are provided.

Recently, Rastall gravity is undergoing a significant surge in popularity. We obtain a power-law total mass-density profile for the inner region (within several effective radius) of early-type galaxies (ETGs) from the space-time structures which are described by the static spherically-symmetric solutions of Rastall gravity under the assumption of perfect fluid matter. We find that in the inner region of ETGs, the Rastall dimensionless parameter $\beta=\kappa\lambda$ determines the mass distribution. We then use 118 galaxy-galaxy strong gravitational lensing systems to constrain the Rastall dimensionless parameter $\beta$. We find that the mean value of $\beta$ for total 118 ETGs is $\beta=0.163\pm0.001$(68\% CL) with a minor intrinsic scatter of $\delta=0.020\pm 0.001$. Our work observationally illustrates the physical meaning of the Rastall dimensionless parameter in galaxy scale. From the Newtonian approximation of Rastall gravity, we also find that an absolute isothermal mass distribution for ETGs is not allowed in the framework of Rastall gravity., Comment: 6 pages, 1 figure. Accepted by MNRAS

The Rastall gravity is a modification of Einstein's general relativity, in which the energy-momentum conservation is not satisfied and depends on the gradient of the Ricci curvature. It is in dispute whether the Rastall gravity is equivalent to the general relativity (GR). In this work, we constrain the theory using the rotation curves of Low Surface Brightness (LSB) spiral galaxies. Through fitting the rotation curves of LSB galaxies, we obtain the parameter $\beta$ of the Rastall gravity. The $\beta$ values of LSB galaxies satisfy Weak Energy Condition (WEC) and Strong Energy Condition(SEC). Combining the $\beta$ values of type Ia supernovae and gravitational lensing of elliptical galaxies on the Rastall gravity, we conclude that the Rastall gravity is equivalent to the general relativity., Comment: 4 pages

We study analytically the shadow cast by the rotating black hole in the perfect fluid dark matter. The apparent shape of the shadow depends upon the black hole spin $a$ and the perfect fluid dark matter intensity parameter $k$ ($k>0$). In general, the shadow is a perfect circle in the non-rotating case ($a=0$) and a deformed one in the rotating case ($a\neq 0$). The deformation gets more and more significant with the increasing $a$, similar to the Schwarzschild and Kerr black holes. In addition, there exists a reflection point $k_0$. When $kk_0$, the size of the shadow increases with the increasing $k$ and the distortion decreases with the increasing $k$. Furthermore, the energy emission rate of the black hole in the perfect fluid dark matter increases with the increasing $k$ and the peak of the emission shifts to higher frequencies. Finally, we propose that to observe the effect of the black hole spin $a$ and the perfect fluid dark matter intensity $k$ on the shadow of the black hole Sgr A$^{*}$ at the center of the Milky Way, highly improved techniques would be necessary for the development of future astronomical instruments., Comment: 9 pages, 3 figures. arXiv admin note: text overlap with arXiv:1806.09415, arXiv:1804.08110

The spectroscopy measurement is one of main pathways for exploring and understanding the nature. Today, it seems that racing artificial intelligence will remould its styles. The algorithms contained in huge neural networks are capable of substituting many of expensive and complex components of spectrum instruments. In this work, we presented a smart machine learning strategy on the measurement of absorbance curves, and also initially verified that an exceedingly-simplified equipment is sufficient to meet the needs for this strategy. Further, with its simplicity, the setup is expected to infiltrate into many scientific areas in versatile forms., Comment: This is the second version. On pages 7 through 8, we have added a new case about the spectral properties of mixtures. Specifically, paragraph 1 on page 8 and Fig.7 is added

Shadows cast by the rotating black hole in perfect fluid matter are studied using analytical method. We consider three kinds of matter with standard equation of state in Cosmology: $-1/3$ (dark matter), 0 (dust) and $1/3$ (radiation). The apparent shape of the shadow depends on the black hole spin $a$ and the perfect fluid matter intensity $k$. We find that the shadow is a perfect circle in the non-rotating case ($a=0$) and a distorted one in the rotating case ($a\neq0$), similar to what is found for other black holes. Interestingly, different kinds of matter have different influence on the black hole shadow. Dark matter has the strongest effect, dust is the next and radiation is the weakest. By applying our result to the black hole Sgr A$^{*}$ at the center of the Milky Way, we find that the angular resolution required to distinguish among different kinds of matter around the black hole is not much higher than the resolution of current astronomical instruments would be able to achieve in the near future. We propose that observing the black hole shadow provides a possibility of identifying the dominant matter near the black hole., Comment: 10 pages, 7 figures, 1 table. arXiv admin note: text overlap with arXiv:1804.08110

We naturally obtain a power-law total mass-density profile for the inner regions (within several effective radius) of early-type galaxies(ETGs) from space-time structures, which are described by the static spherically-symmetric solutions of Einstein equations with the perfect fluid matters. We point out that, in the inner region of an early type galaxy, the average value of the equation of state $\omega$ determines the power-law index $\gamma$ of the total mass-density profile given by \cite{2006ApJ...649..599K}. We then use 119 galaxy-galaxy strong gravitational lensing systems from SLACS, BELLS, BELLS GALLERY and SL2S, to constrain the equation of state $\omega$ for the inner regions of ETGs. We find that the average value of $\omega$ for totally 119 ETGs is $\omega=-0.315\pm0.073$ (68\% CL), which is very close to $-1/3$. If $\omega=-1/3$ is the best value to describe the equation of state of the inner regions of the dark matter in galaxies, the deviation from $-1/3$ could represent the mixture of baryonic matter and dark matter in galaxies., Comment: The basic theory is wrong

We study, for the first time, the shadow of the supermassive black hole Sgr A$^{*}$ at the center of the Milky Way in dark matter halos. For the Cold Dark Matter and Scalar Field Dark Matter models considered in this work, the apparent shape of the shadow depends upon the black hole spin $a$ and the dark matter parameter $k$. We find that both dark matter models influence the shadow in a similar way. The shadow is a perfect circle in the non-rotating case ($a=0$) and a deformed one in the rotating case ($a\neq0$). The size of the shadow increases with increasing $k$ in both non-rotating and rotating cases, while the shadow gets more and more distorted with increasing $a$ in the rotating case. We further investigate the black hole emission rate in both dark matter halos. We find that the emission rate decreases with increasing $k$ and the peak of the emission shifts to lower frequency. Finally, by calculating the angular radius of the shadow, we estimate that the dark matter halo could influence the shadow of Sgr A$^{*}$ at a level of order of magnitude of $10^{-3}$ $\mu$as and $10^{-5}$ $\mu$as, for CDM and SFDM, respectively. Future astronomical instruments with high angular resolution would be able to observe this effect and shed light on the nature of Sgr A$^{*}$. More interestingly, it may be possible to distinguish between CDM and SFDM models given the resolutions required differing by two orders of magnitude from each other., Comment: 12 pages, 7 figures, JCAP accepted

We investigate the discrepancy between the two-dimensional projected lensing mass and the dynam- ical mass for an ensemble of 97 strong gravitational lensing systems discovered by the Sloan Lens ACS (SLACS) Survey, the BOSS Emission-Line Lens Survey (BELLS), and the BELLS for GALaxy-Ly{\alpha} EmitteR sYs- tems (BELLS GALLERY) Survey. We fit the lensing data to obtain the Einstein mass, and use the velocity dispersion of the lensing galaxies provided by the Sloan Digital Sky Survey (SDSS) to get the projected dynamical mass within the Einstein radius by assuming the power-law mass approximation. The discrepancy is found to be obvious and quantified by Bayesian analysis. For the singular isothermal sphere (SIS) mass model, we obtain that the Einstein mass is 20.7% more than the dynamical mass, and the discrepancy increases with the redshift of the lensing galaxies. For more general power-law mass model, the discrepancy still exists within 1{\sigma} credible region. The main reason of the the discrepancy could be mass contamination, including all invisible masses along the line of sight. In addition, the measurement errors and the approximation of the mass models could lead to part of the discrepancy., Comment: 7 pages, 5 figures

For the first time, we obtain the analytical form of black hole space-time metric in dark matter halo for the stationary situation. Using the relation between the rotation velocity (in the equatorial plane) and the spherical symmetric space-time metric coefficient, we obtain the space-time metric for pure dark matter. By considering the dark matter halo in spherical symmetric space-time as part of the energy-momentum tensors in the Einstein field equation, we then obtain the spherical symmetric black hole solutions in dark matter halo. Utilizing Newman-Jains method, we further generalize spherical symmetric black holes to rotational black holes. As examples, we obtain the space-time metric of black holes surrounded by Cold Dark Matter and Scalar Field Dark Matter halos, respectively. Our main results regarding the interaction between black hole and dark matter halo are as follows: (i) For both dark matter models, the density profile always produces "cusp" phenomenon in small scale in the relativity situation; (ii) Dark matter halo makes the black hole horizon to increase but the ergosphere to decrease, while the magnitude is small; (iii) Dark matter does not change the singularity of black holes. These results are useful to study the interaction of black hole and dark matter halo in stationary situation. Particularly, the "cusp" produced in the $0\sim 1$ kpc scale would be observable in the Milky Way. Perspectives on future work regarding the applications of our results in astrophysics are also briefly discussed., Comment: 12 pages, 1 figure

We obtain the Kerr-anti-de-sitter (Kerr-AdS) and Kerr-de-sitter (Kerr-dS) black hole (BH) solutions to the Einstein field equation in the perfect fluid dark matter background using the Newman-Janis method and Mathematica package. We discuss in detail the black hole properties and obtain the following main results: (i) From the horizon equation $g_{rr}=0$, we derive the relation between the perfect fluid dark matter parameter $\alpha$ and the cosmological constant $\Lambda$ when the cosmological horizon $r_{\Lambda}$ exists. For $\Lambda=0$, we find that $\alpha$ is in the range $0<\alpha<2M$ for $\alpha>0$ and $-7.18M<\alpha<0$ for $\alpha<0$. For positive cosmological constant $\Lambda$ (Kerr-AdS BH), $\alpha_{max}$ decreases if $\alpha>0$, and $\alpha_{min}$ increases if $\alpha<0$. For negative cosmological constant $-\Lambda$ (Kerr-dS BH), $\alpha_{max}$ increases if $\alpha>0$ and $\alpha_{min}$ decreases if $\alpha<0$; (ii) An ergosphere exists between the event horizon and the outer static limit surface. The size of the ergosphere evolves oppositely for $\alpha>0$ and $\alpha<0$, while decreasing with the increasing $\mid\alpha\mid$. When there is sufficient dark matter around the black hole, the black hole spacetime changes remarkably; (iii) The singularity of these black holes is the same as that of rotational black holes. In addition, we study the geodesic motion using the Hamilton-Jacobi formalism and find that when $\alpha$ is in the above ranges for $\Lambda=0$, stable orbits exist. Furthermore, the rotational velocity of the black hole in the equatorial plane has different behaviour for different $\alpha$ and the black hole spin $a$. It is asymptotically flat and independent of $\alpha$ if $\alpha>0$ while is asymptotically flat only when $\alpha$ is close to zero if $\alpha<0$., Comment: 22 pages, 4 figures

The Rastall gravity is the modified Einstein general relativity, in which the energy-momentum conservation law is generalized to $T^{\mu\nu}_{~~;\mu}=\lambda R^{,\nu}$. In this work, we derive the Kerr-Newman-AdS (KN-AdS) black hole solutions surrounded by the perfect fluid matter in the Rastall gravity using the Newman-Janis method and Mathematica package. We then discuss the black hole properties surrounded by two kinds of specific perfect fluid matter, the dark energy ($\omega=-2/3$) and the perfect fluid dark matter ($\omega=-1/3$). Firstly, the Rastall parameter $\kappa\lambda$ could be constrained by the weak energy condition and strong energy condition. Secondly, by analyzing the number of roots in the horizon equation, we get the range of the perfect fluid matter intensity $\alpha$, which depends on the black hole mass $M$ and the Rastall parameter $\kappa\lambda$. Thirdly, we study the influence of the perfect fluid dark matter and dark energy on the ergosphere. We find that the perfect fluid dark matter has significant effects on the ergosphere size, while the dark energy has smaller effects. Finally, we find that the perfect fluid matter does not change the singularity of the black hole. Furthermore, we investigate the rotation velocity in the equatorial plane for the KN-AdS black hole with dark energy and perfect fluid dark matter. We propose that the rotation curve diversity in Low Surface Brightness galaxies could be explained in the framework of the Rastall gravity when both the perfect fluid dark matter halo and the baryon disk are taken into account., Comment: 23 pages, 4 figures

Based on Reissner-Nordstrom-anti-de Sitter(RN-AdS) black hole surrounded by perfect fluid dark matter, we study the thermodynamics and phase transition by extending the phase space defined by the charge square $Q^{2}$ and the conjugate quantity $\psi$, where $\psi$ is a function of horizon radius. The first law of thermodynamics and the equation of state are derived in the form $Q^{2}=Q^{2}(T,\psi)$. By investigating the critical behaviour of perfect fluid dark matter around Reissner-Nordstrom-anti-de Sitter black hole, we find that these thermodynamics system are similar to Van der Waals system, and can be explained by mean field theory. We also explore the Ruppeiner thermodynamic geometry feature and their connection with microscopic structure. We find that in extended phase space there existence singularity points of Ruppeiner curvature and it's could explained as phase transitions., Comment: 12 pages, 0 figures

In this work, we investigate the thermodynamic properties of rotational Kiselev black holes (KBH). Specifically, we use the first-order approximation of the event horizon (EH) to calculate thermodynamic properties for general equations of state $\omega$. These thermodynamic properties include areas, entropies, horizon radii, surface gravities, surface temperatures, Komar energies and irreducible masses at the Cauchy horizon (CH) and EH. We study the products of these thermodynamic quantities, we find that these products are determined by the equation of state $\omega$ and strength parameter $\alpha$. In the case of the quintessence matter ($\omega=-2/3$), radiation ($\omega=1/3$) and dust ($\omega=0$), we discuss their properties in detail. We also generalize the Smarr mass formula and Christodoulou-Ruffini mass formula to rotational KBH. Finally we study the phase transition and thermodynamic geometry for rotational KBH with radiation ($\omega=1/3$). Through analysis, we find that this phase transition is a second order phase transition. Furthermore, we also obtain the scalar curvature in the thermodynamic geometry framework, indicating that the radiation matter may change the phase transition condition and properties for Kerr black hole., Comment: 19pages,2figures

Quintessential dark energy with pressure $p$ and density $\rho$ is related by equation of state $p=\omega\rho$ with the state parameter $-1<\omega<-1/3$. The cosmological dark energy influence on black hole spacetime are interesting and important. In this paper, we study the Kerr-Newman-AdS solutions of the Einstein-Maxwell equation in quintessence field around a black hole by Newman-Janis algorithm and complex computations. From the horizon structure equation, we obtain the expression between quintessence parameter $\alpha$ and cosmological constant $\Lambda$ if the black hole exists two cosmological horizon $r_{q}$ and $r_{c}$ when $\omega=-2/3$, the result is different from rotational black hole in quintessence matter situation. Through analysis we find that the black hole charge cannot change the value of $\alpha$. But the black hole spin and cosmological constant are opposite. The black hole spin and cosmological constant make the maximum value of $\alpha$ to become small. The existence of four horizon leads seven types of extremal black holes to constraint the parameter $\alpha$. With the state parameter $\omega$ ranging from $-1$ to $-1/3$, the maximum value of $\alpha$ changes from $\Lambda$ to $1$. When $\omega\rightarrow -1$, the quintessential dark energy likes cosmological constant. The singularity of the black holes is the same with that of Kerr black hole. We also discuss the rotation velocity of the black holes on the equatorial plane for $\omega=-2/3,-1/2$ and $-1/3$. For small value of $\alpha$, the rotation velocity on the equatorial plane is asymptotically flat and it can explain the rotation curves in spiral galaxies., Comment: 17 pages, 5 figures

Based on the Lagrangian of the steady axisymmetric force-free magnetosphere (FFM) equation around Kerr black holes(KBHs), we find that the FFM equation can be rewritten in a new form as $f_{,rr} / (1-\mu^{2}) + f_{,\mu\mu} / \Delta + K(f(r,\mu),r,\mu) = 0$, where $\mu = -\cos\theta$. By coordinate transformation, the form of the above equation can be given by $s_{,yy} + s_{,zz} + D(s(y,z),y,z) = 0$. Based on the form, we prove finally that the Meissner effect is not possessed by a KBH-FFM with the condition where $d\omega/d A_{\phi} \leqslant 0$ and $H_{\phi}(dH_{\phi}/dA_{\phi}) \geqslant 0$, here $A_{\phi}$ is the $\phi$ component of the vector potential $\vec{A}$, $\omega$ is the angular velocity of magnetic fields and ${H_{\phi}}$ corresponds to twice the poloidal electric current.