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We study the chaotic signatures of the geodesic dynamics of a non-spinning test particle in the effective-one-body (EOB) formalism for the inspiral process of spinning binary black holes. We first show that the second order post-Newtonian (2PN) EOB dynamics is non-integrable by demonstrating that the EOB metric does not satisfy the criterion for the existence of Carter constant. We then employ the numerical study to find the plateaus of the rotation curve, which are associated with the existence of Birkhoff islands in the Poincar\'e surface of section, signifying the chaotic dynamics in the system. Our results show the signatures of chaos for the EOB dynamics, especially in the regime of interest for which the Kerr bounds of the component black holes hold. We also find that chaotic behavior is more obvious as the spin parameter $a$ of the deformed EOB background metric increases. Our results can help to uncover the implications of dynamical chaos in gravitational wave astronomy. Finally, we also present some preliminary results due to corrections at 3PN order., Comment: 19 pages, 11 figures. Improvements and references added. Accepted for publication in Phys. Rev. D

We construct a Bayesian inference deep learning machine for parameter estimation of gravitational wave events of binaries of black hole coalescence. The structure of our deep Bayesian machine adopts the conditional variational autoencoder scheme by conditioning on both the gravitational wave strains and the variations of the amplitude spectral density (ASD) of the detector noise. We show that our deep Bayesian machine is capable of yielding posteriors compatible with the ones from the nested sampling method and better than the one without conditioning on the ASD. Our result implies that the process of parameter estimation can be accelerated significantly by deep learning even with large ASD drifting/variation. We also apply our deep Bayesian machine to the LIGO/Virgo O3 events, the result is compatible with the one by the traditional Bayesian inference method for the gravitational wave events with signal-to-noise ratios higher than typical threshold value. We also discuss some possible ways for future improvement., Comment: 12 pages, 18 figures; v2 minor changes; v2 adopt a new ASD model to accommodate large ASD variations, and redo the PE analysis accordingly. Main conclusion remains

We consider the spike mass density profile in a dark halo by self-consistently solving the relativistic Bondi accretion of dark matter onto a non-spining black hole of mass $M$. We assume that the dominant component of the dark matter in the halo is a Standard model gauge-singlet scalar. Its mass $m\simeq 10^{-5}{\rm eV}$ and quartic self-coupling $\lambda\lesssim10^{-19}$ are constrained to be compatible with the properties of galactic dark halos. In the hydrodynamic limit, we find that the accretion rate is bounded from below, $\dot{M}_{\rm min}=96\pi G^2M^2 m^4/\lambda\hbar^3$. Therefore, for $M=10^6~{\rm M}_\odot$ we have $\dot{M}_{\rm min}\simeq1.41\times 10^{-9}~{\rm M}_\odot~{\rm yr}^{-1}$, which is subdominant compared to the Eddington accretion of baryons. The spike density profile $\rho_0(r)$ within the self-gravitating regime cannot be fitted well by a single-power law but a double-power one. Despite that, we can fit $\rho_0(r)$ piecewise and find that $\rho_0(r) \propto r^{-1.20}$ near the sound horizon, $\rho_0(r) \propto r^{-1.00}$ towards the Bondi radius and $\rho_0(r) \propto r^{-1.08}$ for the region in between. This contrasts with more cuspy $\rho_0(r) \propto r^{-1.75}$ for dark matter with Coulomb-like self-interaction., Comment: 20 pages, 2 figures, version accepted for publication in JCAP

Former time-series analyses on the influence of causal relationship between economic growth and military spending may encounter the potential accumulation and neglected variable deviates from accumulating high frequency data generally employed to evaluate business cycles, e.g., monthly macroeconomic and quarterly gross domestic product per capita data, into low frequency data, e.g., yearly military spending data. The mixed frequency vector auto-regressive (MF-VAR) model for solving such temporal aggregation problem in this study, is firstly applied to assess the causal link between economic growth and military spending from the first quarter (Q1) of 1975 to the fourth quarter (Q4) of 2017 in Taiwan. These results via the prediction error variance shows that the MF-VAR model reaches higher explanatory power than the traditional VAR model belonging to single frequency data. Although not only counter-cyclicality but also pro-cyclicality of military spending on economic growth shock in Taiwan is found for the feedback hypothesis via the mixed frequency Granger causality tests, a varying correlation between military spending and economic growth results from the impulse-response analyses via the MF-VAR model. The above-mentioned findings significantly meet the arguable results with respect to former time-series analyses on the business-cycle effect on military spending.

This study investigated the relationship between R&D investments and financial and environmental performance. The direction, size, and significance of various phases of these variables were generated using the bootstrap Fourier quantiles Granger causality test. In our results, a positive relationship between R&D investment and CO2 emission reductions was found at two tails of quantiles. Additionally, we observed a significantly positive relationship between financial performance and CO2 emission reductions at the 0.5 quantile and above. The correlation between R&D investment and financial performance was identified to be positive under the 0.3, 0.4, 0.5 and 0.9 quantiles and negative under the 0.5 and 0.6 quantiles. The changing linkages among R&D investment, environmental performance and financial performance found in this study provide important information for policy makers, aiding in the development of R&D strategies to upgrade financial and environmental performance simultaneously.

We construct few deep generative models of gravitational waveforms based on the semi-supervising scheme of conditional autoencoders and their variational extensions. Once the training is done, we find that our best waveform model can generate the inspiral-merger waveforms of binary black hole coalescence with more than $97\%$ average overlap matched filtering accuracy for the mass ratio between $1$ and $10$. Besides, the generation time of a single waveform takes about one millisecond, which is about $10$ to $100$ times faster than the EOBNR algorithm running on the same computing facility. Moreover, these models can also help to explore the space of waveforms. That is, with mainly the low-mass-ratio training set, the resultant trained model is capable of generating large amount of accurate high-mass-ratio waveforms. This result implies that our generative model can speed up the waveform generation for the low latency search of gravitational wave events. With the improvement of the accuracy in future work, the generative waveform model may also help to speed up the parameter estimation and can assist the numerical relativity in generating the waveforms of higher mass ratio by progressively self-training., Comment: 12 pages, 16 figures; v2 use overlap match to estimate accuracy but key conclusion does not change, emphasis more on autoencoder without variational latent layer; v3 match the published version

It is known that a trained restricted Boltzmann machine (RBM) on the binary Monte Carlo Ising spin configurations, generates a series of iterative reconstructed spin configurations which spontaneously flow and stabilize to the critical point of physical system. Here we construct a variety of neural network (NN) flows using the RBM and (variational) autoencoders, to study the q-state Potts and clock models on the square lattice for q = 2, 3, 4. The NN are trained on Monte Carlo spin configurations at various temperatures. We find that the trained NN flow does develop a stable point that coincides with critical point of the q-state spin models. The behavior of the NN flow is nontrivial and generative, since the training is unsupervised and without any prior knowledge about the critical point and the Hamiltonian of the underlying spin model. Moreover, we find that the convergence of the flow is independent of the types of NNs and spin models, hinting a universal behavior. Our results strengthen the potential applicability of the notion of the NN flow in studying various states of matter and offer additional evidence on the connection with the renormalization group flow.

Motivated by the recent discoveries of compact objects from LIGO/Virgo observations, we study the possibility of identifying some of these objects as compact stars made of dark matter called dark stars, or the mix of dark and nuclear matters called hybrid stars. In particular, in GW190814, a new compact object with 2.6 $M_{\odot}$ is reported. This could be the lightest black hole, the heaviest neutron star, and a dark or hybrid star. In this work, we extend the discussion on the interpretations of the recent LIGO/Virgo events as hybrid stars made of various self-interacting dark matter (SIDM) in the isotropic limit. We pay particular attention to the saddle instability of the hybrid stars which will constrain the possible SIDM models., Comment: 19 pages, 7 figures, for Universe special issue "Neutron Star Astrophysics"; v2: minor revisions, references added, published version

In this study, we use a recently developed Bootstrap ARDL model to examine the influence of longevity (life expectancy after giving birth) and alcohol consumption on economic progression (GDP) in both China and India during the years between 1992 and 2015. Empirical results have shown an extended link across economic development, longevity, and alcohol use in both China and India. The Granger causality test, derived from the Bootstrap ARDL model, demonstrates a unidirectional relationship between economic growth and longevity in China. However, a bidirectional causality exists between longevity and alcohol use in India. Results have important implications for Indian and Chinese governments' public health policies, focused on alcohol consumption reduction specifically, and population health generally.

We examine the weak cosmic censorship conjecture (WCCC) for the extremal charged black hole in possible generalizations of Einstein-Maxwell theory due to the higher order corrections, up to fourth-derivative terms. Our derivation is based on Wald's gedanken experiment to destroy an extremal black hole. We find that, provided the null energy condition for the falling matter, the WCCC is preserved for all possible generalizations. Thus, the WCCC cannot serve as a constraint to the higher order effective theories. We also show that up to first order variations of black hole mass and charge, WCCC is preserved for non-rotating extremal black holes in all $n$-dimensional diffeomorphism-covariant theories of gravity and $U(1)$ gauge field., 22 pages, 2 figures

Background: The stimulus coupon plan is one of the economic relief plans used to boost Taiwan&rsquo, s slumping economy in the aftermath of the COVID-19 pandemic outbreak. In order to obtain prior information to understand whether or not the stimulus coupon plan would effectively revive the economy in advance, the purpose of this study is to learn lessons from Taiwan&rsquo, s consumption voucher scheme initiated during the 2007&ndash, 2009 global financial crisis through evaluating the effect of the consumption voucher scheme on private consumption expenditure. Methods: The smooth time-varying cointegration analysis was applied to estimate the income elasticity of consumption, indicating the individual&rsquo, s reaction to consumption vouchers in terms of private consumption expenditure, and then the multiple structural change model was estimated to identify endogenous regime changes of the income elasticity of consumption. Results: We found that the income elasticity of consumption dramatically decreased after 2007Q1, a period that covered the subprime mortgage crisis in 2007&ndash, 2009 and the time of issuance of the consumption vouchers in 2009. Conclusions: We concluded that Taiwan&rsquo, s consumption voucher scheme might have had either no or little effect on stimulating the economy, so policymakers should be cautioned concerning the potential ineffectiveness of the stimulus coupon plan in the future.

We propose three scenarios for compact hybrid stars composed of nuclear and dark matter. These hybrid stars could provide alternative interpretations to the LIGO/Virgo events GW170817 and GW190425. To demonstrate our proposal, we solve the Tolman-Oppenheimer-Volkoff configurations of hybrid stars by using the SLy4, APR4, and SKb equations of state (EoS) for nuclear matter, and an EoS for a bosonic self interacting dark matter (SIDM) proposed by Colpi et al \cite{Colpi:1986ye}. We then obtain their mass-radius and tidal Love number (TLN)-mass relations, and further examine the possible saddle instability of these compact objects by the generalized Bardeen-Thorne-Meltzer (BTM) criteria. Our results show that the hybrid star scenarios are able to explain GW170817 and GW190425. Some hybrid stars can have compact neutron or mixed cores around 10 km while possessing thick dark matter shells, thus they can be more massive than the maximum mass of the typical neutron stars but are electromagnetically detected with about the same size of neutron stars. Reversely, we also infer the dark matter model from the parameter estimation of GW190425. Our proposed hybrid stars can be further tested by the coming LIGO/Virgo O3 events., 16 pages, 17 figures, 1 table; v2: major revision, nuclear matter EoS SLy4 case included, figures and references added; v3: minor revision, figures replaced, references added; v4: published version, accepted by EPJC

We use a holographic model of quantum chromodynamics to extract the equation of state (EoS) for the cold nuclear matter of moderate baryon density. This model is based on the Sakai-Sugimoto model in the deconfined Witten's geometry with the additional point-like D4-brane instanton configuration as the holographic baryons. Our EoS takes the following doubly-polytropic form: $ \epsilon=2.629 {\cal A}^{-0.192} p^{1.192}+0.131 {\cal A}^{0.544} p^{0.456}$ with $\cal A$ a tunable parameter of order $10^{-1}$, where $\epsilon$ and $p$ are the energy density and pressure, respectively. The sound speed satisfies the causality constraint and breaks the sound barrier. We solve the Tolman-Oppenheimer-Volkoff equations for the compact stars and obtain the reasonable compactness for the proper choices of $\cal A$. Based on these configurations we further calculate the tidal deformability of the single and binary stars. We find our results agree with the inferred values of LIGO/Virgo data analysis for GW170817., Comment: 7 pages, 5 figures; v2: published version

Modern ground-based gravitational wave (GW) detectors require a complex interferometer configuration with multiple coupled optical cavities. Since achieving the resonances of the arm cavities is the most challenging among the lock acquisition processes, the scheme called arm length stabilization (ALS) had been employed for lock acquisition of the arm cavities. We designed a new type of the ALS, which is compatible with the interferometers having long arms like the next generation GW detectors. The features of the new ALS are that the control configuration is simpler than those of previous ones and that it is not necessary to lay optical fibers for the ALS along the kilometer-long arms of the detector. Along with simulations of its noise performance, an experimental test of the new ALS was performed utilizing a single arm cavity of KAGRA. This paper presents the first results of the test where we demonstrated that lock acquisition of the arm cavity was achieved using the new ALS and residual noise was measured to be $8.2\,\mathrm{Hz}$ in units of frequency, which is smaller than the linewidth of the arm cavity and thus low enough to lock the full interferometer of KAGRA in a repeatable and reliable manner., Comment: 21 pages, 8figures

To form optimum firm capital structure strategies to face unanticipated economic events, firm managers should understand the stability of a firm&rsquo, s capital structure. The aim of this research was to study whether the debt ratio is stationary in listed firms on the Dow Jones Industrial Average (DJIA). Two vital capital structure concepts regarding pecking order and trade-off theory are fairly contradictory. Using opposing theoretical contexts, the Sequential Panel Selection Method apparently categorizes which and how many series are stationary processes in the panel. This method was used to test the mean reverting properties of the 25 companies listed on Dow Jones Industrial Average between 2001 and 2017 in this study, which is expected to fill the current gap in the literature. The overall results show that stationary debt ratios exist in 10 of the 25 studied firms, supporting the trade-off theory. Moreover, the 10 firms utilizing trade-off theory are affected by firm size, profitability, growth opportunity, and dividend payout ratio. These results provide vital information for firms to certify strategies to optimize capital structure.

Among the lead-free thermoelectric material, germanium telluride (GeTe) has been extensively investigated due to its high thermoelectric performance (ZT) in mid-temperature; however, high p-type carrier density (∼1021 cm-3) hinder its suitability for higher ZT. In turn, to enhance the thermoelectric performance of the environmentally favorable GeTe, we explored that the Mo doping significantly optimizes the carrier concentration along with uniquely unveiled microcrystalline rods accompanying compact grain boundaries, high-density planar defects, and point defects effectuating all-frequency phonon scattering yields to lower down the thermal conductivity. Furthermore, Sb/Bi co-doping with Mo at the Ge sites predominantly reduces the carrier concentration and thermal conductivity to attain a higher ZT. The co-doping of Bi manifested a more prominent role in achieving the highest ZT of ∼2.3 at 673 K for the sample composition with Ge0.89Mo0.01Bi0.1Te. This study demonstrates an exciting hidden aspect of microstructural modification by forming highly dense microcrystalline rods (MCRs) through Mo and Sb/Bi doping to achieve high-performance in GeTe.

This study revisits coal consumption, CO2 emissions and economic growth nexus for both China and India using a newly developed Bootstrap ARDL model over the period of 1969–2015. Empirical results indicate no long-run relationship among these three variables for both China and India, and Granger causality test based on Bootstrap ARDL model indicates a feedback between coal consumption and economic growth, between economic growth and CO2 emissions and between coal consumption and CO2 emissions in China. However, we find a one-way Granger causality running from coal consumption to economic growth and the feedback hypothesis is confirmed between economic growth and CO2 emissions and between coal consumption and CO2 emissions in India. The coefficients signal that coal consumption is an important factor towards the promotion economic growth in both China and India. For China, higher economic growth reduces CO2 emissions, while for India, it further increases CO2 emissions. Our empirical results have important policy implications for the government conducting effective energy polices to promote economic growth in both China and India.

This study applies asymmetric causality tests, proposed by Hatemi-J (Asymmetric panel causality tests with an application to the impact of fiscal policy on economic performance in Scandinavia, 2011; Empir Econ 43(1):447–456, 2012), to revisit military expenditures-growth nexus for the world top six defense spenders during the period of 1988–2013. Empirical results indicate that the military expenditure-led hypothesis is supported in China and Japan. However, the growth-led hypothesis is supported in four countries, i.e. France, Russia, Saudi Arabia and US. Except for Saudi Arabia, strong economic growth by no means implies automatic expansion of military expenditures. Defense planning in these countries is a matter of matching their limited resources to attain the suitable priorities. The more threats they perceive, the more spend for defense. This evidence provides useful insight into the behavior of other potential defense suppliers.

A test of quantum gravity Quantum mechanics and the general theory of relativity represent two pillars of modern physics, but unification of the two theories remains an open problem. Theories of quantum gravity abound, but they tend to lack an experimental foundation. One such proposed theory, event formalism, predicts that a pair of entangled particles decorrelate as they pass through different regions of the gravitational well of a planetary object. Xu et al. present results of a quantum optical test of this proposal using the quantum satellite Micius. Using entangled photon pairs, one sent to the satellite and the other retained on Earth, they find no evidence for the predicted decorrelation effects. The results may help shed light on the interplay between quantum theory and gravity. Science , this issue p. 132

This study attempts to investigate if suicide is interlinked with unemployment in Mexico by making use of a recently developed Bootstrap ARDL bound test over the years of 1981–2016. To avoid omitting variable bias, we use economic growth rate as a control variable. The empirical results indicate that no co-integration among these three variables and there is a positively bidirectional causality between suicide rate and the unemployment rate. This study will showcase that the economic growth rate negatively affects unemployment rate and unidirectional Granger causality running from economic growth rate to the unemployment rate in Mexico. The findings presented in this study could provide with valuable information for society and health policy makers to formulate the policies on suicide prevention in Mexico.

We consider gedanken experiments to destroy an extremal or near-extremal BTZ black hole by throwing matter into the horizon. These black holes are vacuum solutions to (2+1)-dimensional gravity theories, and are asymptotically $\mathrm{AdS}_3$. Provided the null energy condition for the falling matter, we prove the following---(i) in a Mielke-Baekler model without ghost fields, when torsion is present, an extremal BTZ black hole can be overspun and becomes a naked conical singularity; (ii) in 3-dimensional Einstein gravity and chiral gravity, which both live in torsionless limits of Mielke-Baekler model, an extremal BTZ black hole cannot be overspun; and (iii) in both Einstein gravity and chiral gravity, a near-extremal BTZ black hole cannot be overspun, leaving the weak cosmic censorship preserved. To obtain these results, we follow the analysis of Sorce and Wald on their gedanken experiments to destroy a Kerr-Newman black hole, and calculate the second order corrections to the black hole mass. Furthermore, Wald's type of gedanken experiment provides an operational procedure of proving the third law of black hole mechanics. Through the AdS/CFT correspondence, our results on BTZ black holes also indicate that a third law of thermodynamics holds for the holographic conformal field theories dual to 3-dimensional Einstein gravity and chiral gravity., 26 pages, 4 figures

We investigate the R\'enyi entropy and entanglement entropy of an interval with an arbitrary length in the canonical ensemble, microcanonical ensemble and primary excited states at large energy density in the thermodynamic limit of a two-dimensional large central charge $c$ conformal field theory. As a generalization of the recent work [Phys. Rev. Lett. 122 (2019) 041602], the main purpose of the paper is to see whether one can distinguish these various large energy density states by the R\'enyi entropies of an interval at different size scales, namely, short, medium and long. Collecting earlier results and performing new calculations in order to compare with and fill gaps in the literature, we give a more complete and detailed analysis of the problem. Especially, we find some corrections to the recent results for the holographic R\'enyi entropy of a medium size interval, which enlarge the validity region of the results. Based on the R\'enyi entropies of the three interval scales, we find that R\'enyi entropy cannot distinguish the canonical and microcanonical ensemble states for a short interval, but can do the job for both medium and long intervals. At the leading order of large $c$ the entanglement entropy cannot distinguish the canonical and microcanonical ensemble states for all interval lengths, but the difference of entanglement entropy for a long interval between the two states would appear with $1/c$ corrections. We also discuss R\'enyi entropy and entanglement entropy differences between the thermal states and primary excited state. Overall, our work provides an up-to-date picture of distinguishing different thermal or primary states at various length scales of the subsystem., Comment: V1, 20 pages, 7 figures; V2, 22 pages, 7 figures, minor revision, references added; V3, 22 pages, 5 figures, publised version

We use the Holevo information in a two-dimensional conformal field theory (CFT) with a large central charge $c$ to distinguish microstates from the underlying thermal state. Holographically, the CFT microstates of a thermal state are dual to black hole microstate geometries in three-dimensional anti-de Sitter space. It was found recently that the holographic Holevo information shows plateau behaviors at both short and long interval regions. This indicates that the black hole microstates are indistinguishable from the thermal state by measuring over a small region, and perfectly distinguishable over a region with its size comparable to the whole system. In this letter, we demonstrate that the plateaus are lifted by including the $1/c$ corrections from both the vacuum and non-vacuum conformal families of CFT in either the canonical ensemble or microcanonical ensemble thermal state. Our results imply that the aforementioned indistinguishability and distinguishability of black hole microstate geometries from the underlying black hole are spoiled by higher order Newton constant $G_N$ corrections of quantum gravity., V1, 5+7 pages, 3 figures; V2, discussions on numbers of primary and descendant states refined; V3, 5+7 page, 1+2 figures, references added, published version

In this paper, we apply the K-theory scheme of classifying the topological insulators/superconductors to classify the topological classes of the massive multi-flavor fermions in anti-de Sitter (AdS) space. In the context of AdS/conformal field theory (CFT) correspondence, the multi-flavor fermionic mass matrix is dual to the pattern of operator mixing in the boundary CFT. Thus, our results classify the possible patterns of operator mixings among fermionic operators in the holographic CFT.

Executive pay relative to that of average workers has risen dramatically worldwide. Such a high level of executive pay raises the question of whether a steep rise in executive pay affects firm value. This study examined the relationship between executive pay and firm value. A panel smooth transition regression model is adopted to determine an optimal level of executive pay that maximizes firm value for a sample of 512 Taiwanese-listed firms over the period 2006-2011. The finding is that when the ratio of executive pay to net income after tax exceeds 2.71%, the firm value increases. The results suggest a correlation between large executive ownership (corresponding to high executive pay) and both increased operational efficiencies and firm value. These findings may be useful when contemplating executive compensation policy. Key words: Executive ownership, Firm value, Executive pay, Optimal level.JEL: G30, G32, G35, G38.