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The density dependence of nuclear symmetry energy $E_{\rm sym}(\rho)$ remains the most uncertain aspect of the equation of state (EOS) of supradense neutron-rich nucleonic matter. Implications of observational crustal fraction of neutron star (NS) moment of inertia $\Delta I/I$ on the $E_{\rm sym}(\rho)$ are examined in the present work, utilizing an isospin-dependent parameterization of NS EOS. We find that symmetry energy parameters significantly influence the $\Delta I/I$, while the EOS of symmetric nuclear matter has a negligible effect. An increase in the slope $L$ and skewness $J_{\rm sym}$ of symmetry energy results in a larger $\Delta I/I$, whereas an increase in the curvature $K_{\rm sym}$ leads to a reduction in $\Delta I/I$. Additionally, we discuss the imprints of observational $\Delta I/I$ on the symmetry energy for NSs with masses of 1.0 M$_\odot$ or 1.4 M$_\odot$. Our results indicate that the $\Delta I/I$ has the potential to set a lower limit of symmetry energy at densities exceeding $3\rho_0$, particularly when $L$ is constrained to values less than $60$ MeV, thereby enhancing our understanding of supradense NS matter., Comment: Submitted to Chinese Physics C

The strong-field gravity in General Relativity (GR) realized in neutron stars (NSs) renders the Equation of State (EOS) $P(\varepsilon)$ of supradense neutron star (NS) matter to be essentially nonlinear and refines the upper bound for $\phi\equiv P/\varepsilon$ to be much smaller than the Special Relativity (SR) requirement with linear EOSs, where $P$ and $\varepsilon$ are respectively the pressure and energy density of the system considered. Specifically, a tight bound $\phi\lesssim0.374$ is obtained by anatomizing perturbatively the intrinsic structures of the scaled Tolman--Oppenheimer--Volkoff (TOV) equations without using any input nuclear EOS. New insights gained from this novel analysis provide EOS-model independent constraints on properties (e.g., density profiles of the sound speed squared $s^2=\d P/\d\varepsilon$ and trace anomaly $\Delta=1/3-\phi$) of cold supradense matter in NS cores. Using the gravity-matter duality in theories describing NSs, we investigate the impact of gravity on supradense matter EOS in NSs. In particular, we show that the NS mass $M_{\rm{NS}}$, radius $R$ and its compactness $\xi\equiv M_{\rm{NS}}/R$ scale with certain combinations of its central pressure and energy density (encapsulating its central EOS). Thus, observational data on these properties of NSs can straightforwardly constrain NS central EOSs without relying on any specific nuclear EOS-model., Comment: 27 pages with 10 figures. Review Article for the Research Topic "Strong and Weak Interactions in Compact Stars" hosted by Mark Alford, David Blaschke, Ignazio Bombaci, James Lattimer, and Armen Sedrakian in Frontiers in Astronomy and Space Sciences

Diffusion models have emerged as the leading paradigm in generative modeling, excelling in various applications. Despite their success, these models often misalign with human intentions, generating outputs that may not match text prompts or possess desired properties. Inspired by the success of alignment in tuning large language models, recent studies have investigated aligning diffusion models with human expectations and preferences. This work mainly reviews alignment of diffusion models, covering advancements in fundamentals of alignment, alignment techniques of diffusion models, preference benchmarks, and evaluation for diffusion models. Moreover, we discuss key perspectives on current challenges and promising future directions on solving the remaining challenges in alignment of diffusion models. To the best of our knowledge, our work is the first comprehensive review paper for researchers and engineers to comprehend, practice, and research alignment of diffusion models., Comment: 35 pages, 5 figures, 3 tables

We theoretically explore the precise control of a molecular polariton by strongly coupling the lowest three rotational states of a single molecule with a single-mode cavity. We examine two distinct cavity resonance configurations: a fundamental frequency cavity ($\omega_c = 2B$ with the rotational constant $B$) resonating with the lowest two rotational states, and a second harmonic cavity ($\omega_c = 4B$) coupling with the first and second excited rotational states. We propose two control schemes based on the two polariton configurations and derive the corresponding pulse-area theorems to achieve a theoretical maximum orientation of 0.7746, identical to the molecule in the absence of the cavity. The control schemes are analyzed in Carbonyl Sulfide (OCS) molecules in their ground rotational state. Our numerical simulation results demonstrate the theoretical control schemes and analyze the sensitivity of the molecular polariton orientation degree to the control field bandwidth and phases. This work provides a valuable reference for achieving maximum field-free orientation of ultracold three-state molecules in a cavity using analytically designed pulses., Comment: 22 pages, 7 figures

In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture., Comment: There is an error in Theorem 1.6

To more precisely constrain the Equation of State (EOS) of supradense neutron-rich nuclear matter, future high-precision X-ray and gravitational wave observatories are proposed to measure the radii of neutron stars (NSs) with an accuracy better than about 0.1 km. However, it remains unclear what particular aspects (other than the stiffness generally spoken of in the literature) of the EOS and to what precision they will be better constrained. In this work, within a Bayesian framework using a meta-model EOS for NSs, we infer the posterior probability distribution functions (PDFs) of incompressibility $K_{0}$ and skewness $J_{0}$ of symmetric nuclear matter (SNM) as well as the slope $L$, curvature $K_{\rm{sym}}$, and skewness $J_{\rm{sym}}$ characterizing the density dependence of nuclear symmetry energy $E_{\rm{sym}}(\rho)$, respectively, from mean values of NS radii consistent with existing observations and an expected accuracy $\Delta R$ ranging from about 1.0 km to 0.1 km. We found that (1) the $\Delta R$ has little effect on inferring the stiffness of SNM at suprasaturation densities, (2) smaller $\Delta R$ reveals more accurately not only the PDFs but also pairwise correlations among parameters characterizing high-density $E_{\rm{sym}}(\rho)$, (3) a double-peak feature of the PDF($K_{\rm{sym}}$) corresponding to the strong $K_{\rm{sym}}-J_{\rm{sym}}$ and $K_{\rm{sym}}-L$ anti-correlations is revealed when $\Delta R$ is less than about 0.2 km, and the locations of the two peaks are sensitive to the maximum value of $J_{\rm{sym}}$ reflecting the stiffness of $E_{\rm{sym}}(\rho)$ above about 3 times the saturation density $\rho_0$ of SNM, (4) the high-precision radius measurement for canonical NSs is more useful than that for massive ones for constraining the EOS of nucleonic matter around $(2-3)\rho_0$., Comment: 34 pages with additional results, discussions and appendices. Phys. Rev. D in press

Applications of new techniques in machine learning are speeding up progress in research in various fields. In this work, we construct and evaluate a deep neural network (DNN) to be used within a Bayesian statistical framework as a faster and more reliable alternative to the Gaussian Process (GP) emulator of an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model simulator of heavy-ion reactions at intermediate beam energies. We found strong evidence of DNN being able to emulate the IBUU simulator's prediction on the strengths of protons' directed and elliptical flow very efficiently even with small training datasets and with accuracy about ten times higher than the GP. Limitations of our present work and future improvements are also discussed., Comment: Added more results and discussions. Phys. Rev. C in press

Twin stars-two stable neutron stars (NSs) with the same mass but different radii have long been proposed to appear as a consequence of a possible first-order phase transition in NS matter. Within a meta-model for the EOS of hybrid stars, we revisit the viability of twin stars and its dependence on numerous parameters characterizing the EOS of nuclear matter, quark matter, and the phase transition between them. While essentially no experimental constraint exists for the last two, parameters characterizing the EOS of neutron-rich nucleonic matter have been constrained within various ranges by terrestrial experiments and astrophysical observations. Within these ranges, the impact of nuclear EOS on the formation of twin stars is studied. It is found that the symmetry energy of neutron-rich nucleonic matter notably influences the formation of twin stars, particularly through its slope $L$ and curvature $K_{\rm sym}$. Conversely, the EOS of symmetric nuclear matter shows minimal influence on the formation of twin stars, partially owing to its relatively well-constrained parameters., Comment: 9 pages including 7 figures

The trace anomaly $\Delta\equiv 1/3-P/\varepsilon$ quantifies the possibly broken conformal symmetry in supradense matter under pressure $P$ at energy density $\varepsilon$. Perturbative QCD (pQCD) predicts a vanishing $\Delta$ at extremely high energy or baryon densities when the conformal symmetry is realized but its behavior at intermediate densities reachable in neutron stars (NSs) are still very uncertain. The extraction of $\Delta$ from NS observations strongly depends on the employed model for nuclear Equation of State (EOS). Based on the analytical results from perturbatively analyzing the dimensionless Tolman-Oppenheimer-Volkoff (TOV) equations that are further verified numerically by using $10^5$ EOSs generated randomly with a meta-model in a very broad EOS parameter space constrained by terrestrial nuclear experiments and astrophysical observations, here we first show that the compactness $\xi\equiv M_{\rm{NS}}/R$ of a NS with mass $M_{\rm{NS}}$ and radius $R$ scales very accurately with $\Pi_{\rm{c}}\equiv\mathrm{X}/(1+3\mathrm{X}^2+4\mathrm{X})$ where $\mathrm{X}\equiv P_{\rm{c}}/\varepsilon_{\rm{c}}$ is the ratio of pressure over energy density at NS centers. The scaling of NS compactness thus enables one to readily read off the central trace anomaly $\Delta_{\rm{c}}=1/3-\mathrm{X}$ directly from the observational data of either the mass-radius or red-shift measurements. We then demonstrate indeed that the available NS data themselves from recent X-ray and gravitational wave observations can determine model-independently the trace anomaly as a function of energy density in NS cores, providing a stringent test of existing NS models and a clear guidance in a new direction for further understanding the nature and EOS of supradense matter., Comment: 5 pages of main text with 4 pages of supplementary materials

In order to investigate the potential observational signals of different regularization ambiguities in loop quantum cosmological models, we systematically compute and compare the primordial scalar power spectra and the resulting angular power spectra in the standard loop quantum cosmology (LQC) and its Thiemann regularized versions -- modified LQC-I/II (mLQC-I/II), using both the dressed metric and the hybrid approaches. All three loop quantum cosmological models yield a non-singular bounce with a post-bounce physics that converges rapidly in a few Planck seconds. Using Starobinsky potential and the initial conditions for the background dynamics chosen to yield the same inflationary e-foldings, which are fixed to be $65$ in all three LQC models, we require that all three models result in the same scale-invariant regime for the primordial power spectrum with a relative difference of less than one percent. This permits us to explore the differences resulting from the deep Planck regime in the angular power spectrum. For the adiabatic states, our results demonstrate that the angular power spectrum predicted by the hybrid approach has a smaller deviation from the angular power spectrum predicted by the standard $\Lambda$CDM cosmological model at large angles in comparison with the dressed metric approach for all three models. The angular power spectrum predicted by mLQC-I in both the hybrid and the dressed metric approaches shows the smallest deviation from the one predicted by the standard $\Lambda$CDM cosmological model at large angular scales, except for the case of fourth order adiabatic initial states in the hybrid approach. On the contrary, mLQC-II results in the largest deviations for the amplitude of the angular power spectrum at large angles and is most disfavored., Comment: 29 pages, 12 figures. Minor revision to match published version in Phys Rev D

The interplay of three light-matter interaction processes - rotating and counter-rotating interactions and two-photon relaxation of the light field - is a topic of interest in quantum optics and quantum information processing. In this work, we theoretically investigate the three light-matter interaction processes using the anisotropic Rabi model, which accounts for different strengths of rotating and counter-rotating interactions and the unique occurrence of photon escape exclusively in pairs. By numerically solving the Lindblad master equation, we analyze the excitation-relaxation dynamics and derive a non-Hermitian effective Hamiltonian to gain further physical insights. To explore the individual effects of these interactions, we examine three analytically tractable limits of the effective Hamiltonian. Our analysis reveals that the three competitive light-matter interaction processes exhibit sensitivity to parity, leading to intriguing phenomena in both transient and steady states. Particularly interesting dynamical patterns resembling quantum phase transitions emerge when these three interaction terms compete. This work deepens the understanding of ultrastrong light-matter interaction in open quantum systems and offers valuable insights into cavity-based quantum computations., Comment: 13 pages, 8 figures

Thanks to the recent advancement in producing rare isotopes and measuring their masses with unprecedented precision, the updated nuclear masses around the waiting-point nucleus $^{64}$Ge in the rapid-proton capture process have led to a significant revision of the surface gravitational redshift of the neutron star (NS) in GS 1826-24 by re-fitting its X-ray burst light curve ({\it X. Zhou et al., Nature Physics {\bf 19}, 1091 (2023)}) using Modules for Experiments in Stellar Astrophysics (MESA). The resulting NS compactness $\xi$ is between 0.244 and 0.342 at 95\% confidence level and its upper boundary is significantly smaller than the maximum $\xi$ previously known. Incorporating this new data within a comprehensive Bayesian statistical framework, we investigate its impact on the Equation of State (EOS) of supradense neutron-rich matter and the required spin frequency for GW190814's minor $m_2$ with mass $2.59\pm 0.05$M$_{\odot}$ to be a rotationally stable pulsar. We found that the EOS of high-density symmetric nuclear matter (SNM) has to be softened significantly while the symmetry energy at supersaturation densities stiffened compared to our prior knowledge from earlier analyses using data from both astrophysical observations and terrestrial nuclear experiments. In particular, the skewness $J_0$ characterizing the stiffness of high-density SNM decreases significantly, while the slope $L$, curvature $K_{\rm{sym}}$, and skewness $J_{\rm{sym}}$ of nuclear symmetry energy all increase appreciably compared to their fiducial values. We also found that the most probable spin rate for the $m_2$ to be a stable pulsar is very close to its mass-shedding limit once the revised redshift data from GS 1826-24 is considered, making the $m_2$ unlikely the most massive NS observed so far., Comment: Additional results and discussions added. Phys. Rev. D in press

We report on the results of a search for radio pulsars in five supernova remnants (SNRs) with FAST. The observations were made using the 19-beam receiver in the Snapshot mode. The integration time for each pointing is 10 min. We discovered a new pulsar PSR J1845$-$0306 which has a spin period of 983.6 ms and a dispersion measure of 444.6$\pm$2.0 cm$^{-3}$ pc in observations of SNR G29.6+0.1. To judge the association between the pulsar and the SNR, further verification is needed. We also re-detected some known pulsars in the data from SNRs G29.6+0.1 and G29.7$-$0.3. No pulsars were detected in observations of other three SNRs., Comment: 6 pages, 2 figures, 2 tables published in CPL

Directly predicting human epidermal growth factor receptor 2 (HER2) status from widely available hematoxylin and eosin (HE)-stained whole slide images (WSIs) can reduce technical costs and expedite treatment selection. Accurately predicting HER2 requires large collections of multi-site WSIs. Federated learning enables collaborative training of these WSIs without gigabyte-size WSIs transportation and data privacy concerns. However, federated learning encounters challenges in addressing label imbalance in multi-site WSIs from the real world. Moreover, existing WSI classification methods cannot simultaneously exploit local context information and long-range dependencies in the site-end feature representation of federated learning. To address these issues, we present a point transformer with federated learning for multi-site HER2 status prediction from HE-stained WSIs. Our approach incorporates two novel designs. We propose a dynamic label distribution strategy and an auxiliary classifier, which helps to establish a well-initialized model and mitigate label distribution variations across sites. Additionally, we propose a farthest cosine sampling based on cosine distance. It can sample the most distinctive features and capture the long-range dependencies. Extensive experiments and analysis show that our method achieves state-of-the-art performance at four sites with a total of 2687 WSIs. Furthermore, we demonstrate that our model can generalize to two unseen sites with 229 WSIs.

The speed of sound squared (SSS) $s^2$ in massive neutron stars (NSs) characterizes not only the stiffness of supradense neutron-rich matter within but also equivalently properties of the curved geometry due to the strong-field gravity and matter-geometry coupling. A peaked density or radius profile of $s^2$ has been predicted for massive NSs using various NS Equation of State (EOS) models. However, the nature, cause, location and size of the peak in $s^2$ profiles are still very EOS model dependent. In this work, we investigate systematically $s^2$ profiles in massive NSs in a new approach that is independent of the nuclear EOS model and without any presumption about the NS structure and/or composition. In terms of the small quantities (reduced radius, the energy density and pressure scaled by their central values), we perform double-element perturbative expansions in solving perturbatively the scaled Tolman--Oppenheimer--Volkoff (TOV) equations and analyzing $s^2$ profiles from the Newtonian limit to the general relativistic (GR) case. The GR term in the TOV equations plays a twofold role: it compresses NS matter and modifies the pressure/energy density ratio from small values in Newtonian stars showing no $s^2$ peak to large ones for massive NSs possessing a peak in their $s^2$ profiles, and eventually takes away the peak in extremely compact/massive NSs approaching the causality limit. {In particular, the peaked behavior in $s^2$ is expected to emerge near the center of massive NSs like PSR J0740+6620, while a sharp phase transition is unlikely to occur there.} These features revealed from our analyses are universal as they are intrinsic properties of the GR stellar structure equations independent of the still very uncertain EOS of supradense neutron-rich matter in NSs., Comment: Added/revised some discussions. Phys. Rev. D in press

This article aims to study the Lorentz/U(1) gauge symmetry-breaking electrodynamics in the framework of the Standard-Model Extension and analyze the Hamiltonian structure for the theory with a specific dimension $d\leq 4$ of Lorentz breaking operators. For this purpose, we consider a general quadratic action of the modified electrodynamics with Lorentz/gauge-breaking operators and calculate the number of independent components of the operators at different dimensions in gauge invariance and breaking. With this general action, we then analyze how the Lorentz/gauge symmetry-breaking can change the Hamiltonian structure of the theories by considering Lorentz/gauge-breaking operators with dimension $d\leq 4$ as examples. We show that the Lorentz-breaking operators with gauge invariance do not change the classes of the constraints of the theory and the number of the physical degrees of freedom of the standard Maxwell's electrodynamics. When the U(1) gauge symmetry-breaking operators are present, the theories in general lack first-class constraint and have one additional physical degree of freedom, compared to the standard Maxwell's electrodynamics., Comment: 13 pages; v2: version to be published in Chinese Physics C

Modifications to the Mukhanov-Sasaki equation in loop quantum cosmology (LQC) have been phenomenologically explored using polymerization of the connection and related variables in the classical expressions in order to capture the quantum gravity effects in cosmological perturbations which replace the classical big bang by a big bounce. Examples of this strategy include the dressed metric and the hybrid approaches whose inter-relationship at an effective level was demonstrated by the authors recently. In this manuscript, we propose a new family of the effective mass functions in the modified Mukhanov-Sasaki equation of LQC by investigating the polymerization of a particular form of the classical mass function in terms of variable $z_s$($=a\dot \phi/H$) which relates the Mukhanov-Sasaki variable with the comoving curvature perturbation. Using a generalized ansatz motivated by quantum gravity effects in the background dynamics we find alternative effective mass functions which are distinct from those used in the dressed metric and the hybrid approaches with differences originating from the non-commutativity of the evaluation of the Poisson brackets and the polymerization procedures. The new effective mass functions acquire four correction terms in the effective potential whose exact forms are closely tied up with the ansatz used for polymerizing the inverse Hubble rate. In contrast to earlier works, one of these correction terms can in principle produce sizable effects even when the bounce is kinetic dominated. Our investigation opens a new window to explore the phenomenological implications of a large family of effective mass functions in LQC which can potentially lead to significant departures from the dressed metric and the hybrid approaches in the bounce regime., Comment: References added. Version published in PRD

In this paper, we study analytical approximate solutions of the second-order homogeneous differential equations with the existence of only two turning points (but without poles), by using the uniform asymptotic approximation (UAA) method. To be more concrete, we consider the P\"oschl-Teller (PT) potential, for which analytical solutions are known. Depending on the values of the parameters involved in the PT potential, we find that the upper bounds of the errors of the approximate solutions in general are $\lesssim 0.15\% \sim 10\% $, to the first-order approximation of the UAA method. The approximations can be easily extended to high-order, with which the errors are expected to be much smaller. Such obtained analytical solutions can be used to study cosmological perturbations in the framework of quantum cosmology, as well as quasi-normal modes of black holes., Comment: Universe 2023, 9 (11), 471. In Honor of Prof. Jorge Pullin on His 60th Anniversary

Within the TMEP, we present a detailed study of the performance of different transport models in Sn+Sn collisions at $270A$ MeV, and put particular emphasis on the production of pions and $\Delta$ resonances, which have been used as probes of the nuclear symmetry energy. We prescribe a common and rather simple physics model, and follow in detail the results of 4 BUU models and 6 QMD models. The nucleonic evolution of the collision and the nucleonic observables in these codes do not completely converge, but the differences among the codes can be understood as being due to several reasons: the basic differences between BUU and QMD models in the representation of the phase-space distributions, computational differences in the mean-field evaluation, and differences in the adopted strategies for the Pauli blocking in the collision integrals. For pionic observables, we find that a higher maximum density leads to an enhanced pion yield and a reduced $\pi^-/\pi^+$ yield ratio, while a more effective Pauli blocking generally leads to a slightly suppressed pion yield and an enhanced $\pi^-/\pi^+$ yield ratio. We specifically investigate the effect of the Coulomb force, and find that it increases the total $\pi^-/\pi^+$ yield ratio but reduces the ratio at high pion energies, although differences in its implementations do not have a dominating role in the differences among the codes. Taking into account only the results of codes that strictly follow the homework specifications, we find a convergence of the codes in the final charged pion yield ratio to a $1\sigma$ deviation of about $5\%$. However, the uncertainty is expected to be reduced to about $1.6\%$ if the same or similar strategies and ingredients, i.e., an improved Pauli blocking and calculation of the non-linear term in the mean-field potential, are similarly used in all codes., Comment: 39 pages, 17 figures

We perform a combined analytical and numerical investigation to explore how an analytically designed pulse can precisely control the rotational motions of a single-molecular polariton formed by the strong coupling of two low-lying rotational states with a single-mode cavity. To this end, we derive a pulse-area theorem that gives amplitude and phase conditions of the pulses in the frequency domain for driving the polariton from a given initial state to an arbitrary coherent state. The pulse-area theorem is examined for generating the maximum degree of orientation using a pair of pulses. We show that the phase condition can be satisfied by setting the initial phases of the two identically overlapped pulses or by controlling the time delay between pulses for practical applications., Comment: 6 figures

The central speed of sound (SS) measures the stiffness of the Equation of State (EOS) of superdense neutron star (NS) matter. Its variations with density and radial coordinate in NSs in conventional analyses often suffer from uncertainties of the specific nuclear EOSs used. Using the central SS and NS mass/radius scaling obtained from solving perturbatively the scaled Tolman-Oppenheimer-Volkoff (TOV) equations, we study the variations of SS, trace anomaly and several closely related properties of NSs in an EOS-model independent manner. We find that the SS increases with the reduced central pressure $\widehat{P}_{\rm{c}}\equiv P_{\rm{c}}/\varepsilon_{\rm{c}}$ (scaled by the central energy density $\varepsilon_{\rm{c}}$), and the conformal bound for SS tends to break down for NSs with masses higher than about 1.9$M_{\odot}$. The ratio $P/\varepsilon$ is upper bounded as $P/\varepsilon\lesssim0.374$ around the centers of stable NSs. We demonstrate that it is an intrinsic property of strong-field gravity and is more relevant than the perturbative QCD bound on it. While a sharp phase transition at high densities characterized by a sudden vanishing of SS in cores of massive NSs are basically excluded, the probability for a continuous crossover signaled by a peaked radial profile of SS is found to be enhanced as $\widehat{P}_{\rm{c}}$ decreases, implying it likely happens near the centers of massive NSs. Moreover, a new and more stringent causality boundary as $R_{\max}/\rm{km}\gtrsim 4.73M_{\rm{NS}}^{\max}/M_{\odot}+1.14$ for NS M-R curve is found to be excellently consistent with observational data on NS masses and radii. Furthermore, new constraints on the ultimate energy density and pressure allowed in NSs before collapsing into black holes are obtained and compared with earlier predictions in the literature., Comment: Phys. Rev. D (2023) in press

Within an isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we investigate the hard photons emission from neutron-proton bremsstrahlung in reaction system of $^{208}Pb+^{208}Pb$ around Fermi energy. Effects of neutron skins in coordinate ($r$) space and proton skins in momentum ($k$) space on the time evolution, the angular distribution, and the transverse momentum spectra of hard photons with different energies are studied. It is shown that the emission of direct hard photons is sensitive to the neutron skin, which has larger effects for more energetic hard photons. Meanwhile, we find that the proton skins have an important influence on the emission of direct hard photons, and its effect is actually even larger than that of neutron skins. It needs to take the effect of proton skins into account when we determine the size of neutron skins by comparing transport mode predictions of hard photons with the corresponding experiment measurements.

Given the significant advancement in Bayesian inference of nuclear Equation of State (EOS) from gravitational wave and X-ray observations of neutron stars (NSs), especially since GW170817, is there a data-driven and robust empirical formula for the radius $R_{1.4}$ of canonical NSs in terms of the characteristic EOS parameters (features)? What is the single most important but currently poorly known EOS parameter for determining the $R_{1.4}$? We study these questions by extending the traditional Bayesian analysis which normally ends at presenting the marginalized posterior probability distribution functions (PDFs) of individual EOS parameters and their correlations (or sometimes only the Pearson correlation coefficients which are only reliably useful when the variables are linearly correlated while they are actually often not). Using three regression model-building methodologies: bidirectional step-wise feature selection, Least Absolute Shrinkage Selection Operator (LASSO) regression, and neural network regression on a large set of posterior EOSs and the corresponding $R_{1.4}$ values inferred from earlier comprehensive Bayesian analyses of NS observational data, we systematically and rigorously develop the most probable $R_{1.4}$ formulas with varying statistical accuracy and technical complexity. The most important EOS parameters for determining $R_{1.4}$ are found consistently in each of the feature/model selection processes to be (in order of decreasing importance): curvature $K_{sym}$, slope $L$, skewness $J_{sym}$ of nuclear symmetry energy, skewness $J_{0}$, incompressibility $K_{0}$ of symmetric nuclear matter, and the magnitude $E_{sym} (\rho_0)$ of symmetry energy at the saturation density $\rho_0$ of nuclear matter., Comment: Phys. Rev. C (2023) in press

Given an Equation of State (EOS) for neutron star (NS) matter, there is a unique mass-radius sequence characterized by a maximum mass $M_{\rm{NS}}^{\max}$ at radius $R_{\max}$. We first show analytically that the $M_{\rm{NS}}^{\max}$ and $R_{\max}$ scale linearly with two different combinations of NS central pressure $P_{\rm{c}}$ and energy density $\varepsilon_{\rm{c}}$ by dissecting perturbatively the dimensionless Tolman-Oppenheimer-Volkoff (TOV) equations governing NS internal variables. The scaling relations are then verified via 87 widely used and rather diverse phenomenological as well as 17 microscopic NS EOSs with/without considering hadron-quark phase transitions and hyperons by solving numerically the original TOV equations. The EOS of densest NS matter allowed before it collapses into a black hole (BH) is then obtained. Using the universal $M_{\rm{NS}}^{\max}$ and $R_{\max}$ scalings and NICER (Neutron Star Interior Composition Explorer) and XMM-Newton mass-radius observational data for PSR J0740+6620, a very narrow constraining band on the NS central EOS is extracted directly from the data for the first time without using any specific input EOS model., Comment: APJ in press