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Proton-neutron pairing and like-nucleon pairing are two different facets of atomic nuclear configurations. While like-nucleon pair condensates manifest their superfluidic nature in semi magic nuclei, it is not absolutely clear if there exists a T=0 proton-neutron pair condensate phase in $N=Z$ nuclei. With an explicit formalism of general pair condensates with good particle numbers, we optimize proton-neutron pair condensates for all $N=Z$ nuclei between $^{16}$O and $^{100}$Sn, given shell model effective interactions. As comparison, we also optimize like-nucleon pair condensates for their semi-magic isotones. Shannon entanglement entropy is a measurement of mixing among pair configurations, and can signal intrinsic phase transition. It turns out the like-nucleon pair condensates for semi-magic nuclei have large entropies signaling an entangled phase, but the proton-neutron pair condensates end up not far from a Hartree-Fock solution, with small entropy. With artificial pairing interaction strengths, we show that the general proton-neutron pair condensate can transit from an entangled T=1 phase to an entangled T=0 phase, i.e. pairing phase transition driven by external parameters. In the T=0 limit, the proton-neutron pair condensate optimized for $^{24}$Mg turns out to be a purely P pair condensate with large entanglement entropy, although such cases may occur in cold atom systems, unlikely in atomic nuclei.

Otto's (2001) Wasserstein gradient flow of the exclusive KL divergence functional provides a powerful and mathematically principled perspective for analyzing learning and inference algorithms. In contrast, algorithms for the inclusive KL inference, i.e., minimizing $ \mathrm{KL}(\pi \| \mu) $ with respect to $ \mu $ for some target $ \pi $, are rarely analyzed using tools from mathematical analysis. This paper shows that a general-purpose approximate inclusive KL inference paradigm can be constructed using the theory of gradient flows derived from PDE analysis. We uncover that several existing learning algorithms can be viewed as particular realizations of the inclusive KL inference paradigm. For example, existing sampling algorithms such as Arbel et al. (2019) and Korba et al. (2021) can be viewed in a unified manner as inclusive-KL inference with approximate gradient estimators. Finally, we provide the theoretical foundation for the Wasserstein-Fisher-Rao gradient flows for minimizing the inclusive KL divergence.

The purpose of this paper is to answer a few open questions in the interface of kernel methods and PDE gradient flows. Motivated by recent advances in machine learning, particularly in generative modeling and sampling, we present a rigorous investigation of Fisher-Rao and Wasserstein type gradient flows concerning their gradient structures, flow equations, and their kernel approximations. Specifically, we focus on the Fisher-Rao (also known as Hellinger) geometry and its various kernel-based approximations, developing a principled theoretical framework using tools from PDE gradient flows and optimal transport theory. We also provide a complete characterization of gradient flows in the maximum-mean discrepancy (MMD) space, with connections to existing learning and inference algorithms. Our analysis reveals precise theoretical insights linking Fisher-Rao flows, Stein flows, kernel discrepancies, and nonparametric regression. We then rigorously prove evolutionary $\Gamma$-convergence for kernel-approximated Fisher-Rao flows, providing theoretical guarantees beyond pointwise convergence. Finally, we analyze energy dissipation using the Helmholtz-Rayleigh principle, establishing important connections between classical theory in mechanics and modern machine learning practice. Our results provide a unified theoretical foundation for understanding and analyzing approximations of gradient flows in machine learning applications through a rigorous gradient flow and variational method perspective.

Occlusion-aware decision-making is essential in autonomous driving due to the high uncertainty of various occlusions. Recent occlusion-aware decision-making methods encounter issues such as high computational complexity, scenario scalability challenges, or reliance on limited expert data. Benefiting from automatically generating data by exploration randomization, we uncover that reinforcement learning (RL) may show promise in occlusion-aware decision-making. However, previous occlusion-aware RL faces challenges in expanding to various dynamic and static occlusion scenarios, low learning efficiency, and lack of predictive ability. To address these issues, we introduce Pad-AI, a self-reinforcing framework to learn occlusion-aware decision-making through active perception. Pad-AI utilizes vectorized representation to represent occluded environments efficiently and learns over the semantic motion primitives to focus on high-level active perception exploration. Furthermore, Pad-AI integrates prediction and RL within a unified framework to provide risk-aware learning and security guarantees. Our framework was tested in challenging scenarios under both dynamic and static occlusions and demonstrated efficient and general perception-aware exploration performance to other strong baselines in closed-loop evaluations.

In this paper, we study the single production of doubly charged Higgs $H^{\pm\pm}$ in the type-II seesaw at the high energy muon collider. Compared with the pair production channel $\mu^+\mu^-\to H^{++} H^{--}$, the single production channel $\mu^+\mu^-\to \mu^\mp\ell^\mp H^{\pm\pm}$ in principle could probe the mass region above the threshold $m_{H^{\pm\pm}}>\sqrt{s}/2$. The single production channel depends on the Yukawa coupling $h$, which is related to the neutrino oscillation parameters. We show that the Majorana phases $\phi_1$ and $\phi_2$ have great impact on the individual cross section of the single production. We find that the same sign dilepton signature from $H^{\pm\pm}\to \ell^\pm\ell^\pm$ could probe $m_{H^{\pm\pm}}\lesssim2.6(7.1)$ TeV at the 3 (10) TeV muon collider when the triplet VEV $v_\Delta\lesssim3$ eV., Comment: 19 pages, 11 figures

The (re)analysis of data on the X-ray emitting pulsars PSR J0030+0451 and PSR J0740+6620, as well as new results on PSR J0437-4715, are confronted with the predictions of the equation of state (EoS) models allowing for strong first-order phase transition for the mass-radius ($M$-$R$) diagram. We use models that are based on a covariant density functional (CDF) EoS for nucleonic matter at low densities and a quark matter EoS, parameterized by the speed of sound, at higher densities. To account for the variations in the ellipses for PSR J0030+0451 obtained from different analyses, we examined three scenarios to assess their consistency with our models, focusing particularly on the potential formation of twin stars. We found that in two scenarios, where the ellipses for PSR J0030+0451 and PSR J0437-4715 with masses close to the canonical mass $\sim 1.4\,M_{\odot}$ are significantly separated, our models allow for the presence of twin stars as a natural explanation for potential differences in the radii of these stars., Comment: 10 pages, 4 figures

The $CP$ violation (CPV) in the baryon system has not yet been definitively established. We demonstrate that individual partial-wave CPV in the $\Lambda_b\to p\pi^-,pK^-$ decays can exceed $10\%$, but the destruction between different partial waves results in small net direct CPV as observed in current experiments. There is thus high possibility of identifying CPV in $b$-baryon decays through measurements of partial-wave CPV. The above observation is supported by the first full QCD calculation of two-body hadronic $\Lambda_b$ baryon decays with controllable uncertainties in the perturbative QCD formalism., Comment: 5 pages, 2 figures,4 tables

Properties of fluids flow in granular aggregates are important for the design of pervious infrastructures used to alleviate urban water-logging problems. Here in this work, five groups of aggregates packing with similar average porosities but varying particle sizes were scanned by a high-energy X-ray computed tomography (X-CT) facility. The structures of the packings were reconstructed. Porosities were calculated and compared with those measured by the volume and mass of infilled water in the packing. Then pore networks were extracted and analyzed. Simulations of fluids flow in the packings were performed by using a lattice Boltzmann method (LBM) with BGK (Bhatnagar-Gross-Krook) collision model in the pore-network domain of the packings. Results showed wall effect on the porosity of aggregates packing was significant and the influence increased with the aggregate sizes. In addition, Poisson law and power law can be used to fit the coordination number and coordination volume of the packing's pore network, respectively. Moreover, the mass flow rates of fluids in the aggregates were affected by the porosities. On the two-dimensional slices, the mass flow rate decreased when the slice porosity increased. But for the three-dimensional blocks, the average mass flow rate increased with the volume porosity. And the permeability of the aggregates packing showed correlating change trend with the average pore diameter and fitting parameters of coordination volumes, when the sizes of aggregates changed. Though the limitation of merging interfaces causing fluctuation and discontinuity on micro parameters of fluid flow existed, the methods and results here may provide knowledge and insights for numerical simulations and optimal design of aggregate-based materials., Comment: This article is published on https://doi.org/10.1016/j.compfluid.2023.105787

This paper presents a new gradient flow dissipation geometry over non-negative and probability measures. This is motivated by a principled construction that combines the unbalanced optimal transport and interaction forces modeled by reproducing kernels. Using a precise connection between the Hellinger geometry and the maximum mean discrepancy (MMD), we propose the interaction-force transport (IFT) gradient flows and its spherical variant via an infimal convolution of the Wasserstein and spherical MMD tensors. We then develop a particle-based optimization algorithm based on the JKO-splitting scheme of the mass-preserving spherical IFT gradient flows. Finally, we provide both theoretical global exponential convergence guarantees and improved empirical simulation results for applying the IFT gradient flows to the sampling task of MMD-minimization. Furthermore, we prove that the spherical IFT gradient flow enjoys the best of both worlds by providing the global exponential convergence guarantee for both the MMD and KL energy.

The study of kagome materials has attracted much attention in the past few years due to the presence of many electron-electron interaction-driven phases in a single material.In this work, we report the discovery of intrinsic spin-polarized p-wave superconductivity in the thin-flake kagome material RbV$_3$Sb$_5$. Firstly, when an in-plane magnetic field is swept in opposite directions, we observe a unique form of hysteresis in magnetoresistance which is different from the hysteresis induced by extrinsic mechanisms such as flux-trapping or superheating and supercooling effects. The unconventional hysteresis indicates the emergence of an intrinsic time-reversal symmetry-breaking superconducting phase. Strikingly, at a fixed magnetic field, the finite-resistance state can be quenched to the zero-resistance state by applying a large current. Secondly, at temperatures around 400 mK, the re-entrance of superconductivity occurs during an in-plane field-sweeping process with a fixed sweeping direction. This kind of re-entrance is asymmetric about the zero field axis and observed in all field directions for a fixed current direction, which is different from the re-entrance observed in conventional superconductors. Moreover, the angle-dependent in-plane critical field measurements reveal a two-fold symmetry that deviates from the original, centrosymmetric D$_{6h}$ point group symmetry of the crystal. These findings put very strong constraints on the possible superconducting pairing symmetry of RbV$_3$Sb$_5$. We point out that the pairing symmetry, which is consistent with the crystal symmetry and all the observed novel properties, is a time-reversal symmetry-breaking, p-wave pairing with net spin polarization. Importantly, this p-wave pairing gives rise to a nodal topological superconducting state with Majorana flat bands on the sample edges., Comment: 21 pages, 4 figures

Online construction of open-ended language scenes is crucial for robotic applications, where open-vocabulary interactive scene understanding is required. Recently, neural implicit representation has provided a promising direction for online interactive mapping. However, implementing open-vocabulary scene understanding capability into online neural implicit mapping still faces three challenges: lack of local scene updating ability, blurry spatial hierarchical semantic segmentation and difficulty in maintaining multi-view consistency. To this end, we proposed O2V-mapping, which utilizes voxel-based language and geometric features to create an open-vocabulary field, thus allowing for local updates during online training process. Additionally, we leverage a foundational model for image segmentation to extract language features on object-level entities, achieving clear segmentation boundaries and hierarchical semantic features. For the purpose of preserving consistency in 3D object properties across different viewpoints, we propose a spatial adaptive voxel adjustment mechanism and a multi-view weight selection method. Extensive experiments on open-vocabulary object localization and semantic segmentation demonstrate that O2V-mapping achieves online construction of language scenes while enhancing accuracy, outperforming the previous SOTA method.

By choosing a suitable function space as the dual to the non-negative measure cone, we study in a unified framework a class of functional saddle-point optimization problems, which we term the Mixed Functional Nash Equilibrium (MFNE), that underlies several existing machine learning algorithms, such as implicit generative models, distributionally robust optimization (DRO), and Wasserstein barycenters. We model the saddle-point optimization dynamics as an interacting Fisher-Rao-RKHS gradient flow when the function space is chosen as a reproducing kernel Hilbert space (RKHS). As a discrete time counterpart, we propose a primal-dual kernel mirror prox (KMP) algorithm, which uses a dual step in the RKHS, and a primal entropic mirror prox step. We then provide a unified convergence analysis of KMP in an infinite-dimensional setting for this class of MFNE problems, which establishes a convergence rate of $O(1/N)$ in the deterministic case and $O(1/\sqrt{N})$ in the stochastic case, where $N$ is the iteration counter. As a case study, we apply our analysis to DRO, providing algorithmic guarantees for DRO robustness and convergence., Comment: Accepted to AISTATS 2024

The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in both deterministic and stochastic settings. We conduct extensive convergence analysis and show that by choosing the inexactness tolerances appropriately, the inexact schemes admit an $O(k^{-1})$ convergence rate in terms of the (expected) residue norm. Our results relax the state-of-the-art inexactness conditions employed in the literature while sharing the same competitive convergence properties. We then demonstrate how the proposed methods can be applied for solving two classes of data-driven Wasserstein distributionally robust optimization problems that admit convex-concave min-max optimization reformulations. We highlight its capability of performing inexact computations for distributionally robust learning with stochastic first-order methods., Comment: Correct a typo in the title and update authors' information

Recent astrophysical mass inferences of compact stars HESS J1731-347 and PSR J0952-0607, with extremely small and large masses respectively, as well as the measurement of the neutron skin of Ca in the CREX experiment challenge and constrain the models of dense matter. We examine the concept of hybrid stars - objects containing quark cores surrounded by nucleonic envelopes - as models that account for these new data along with other inferences. We employ a family of 81 nucleonic equations of state (EoSs) with variable skewness and slope of symmetry energy at saturation density and a constant speed-of-sound EoS for quark matter. For each nucleonic EoS, a family of hybrid EoSs is generated by varying the transition density, the energy jump, and the speed of sound. These models are tested against the data from GW170817 and J1731-347, which favor low-density soft EoS and J0592-0607 and J0740+6620, which require high-density stiff EoS. The addition of J0592-0607's mass measurement to the constraints has no significant impact on the parameter space of the admissible EoS, but allows us to explore the potential effect of pulsars more massive than J0740+6620, if such exists. We then examine the occurrence of twin configurations and quantify the ranges of masses and radii that they can possess. It is shown that including J1731-347 data favors EoSs that predict low-mass twins with $M \lesssim 1.3\,M_{\odot}$ that can be realized if the deconfinement transition density is low. If combined with large speed of sound in quark matter such models allow for maximum masses of hybrid stars in $2.0$--$2.6\,M_{\odot}$., Comment: v2: 8 pages, 6 figures, 1 table, expanded data and discussion, matches published version

Neutron stars may experience differential rotation on short, dynamical timescales following extreme astrophysical events like binary neutron star mergers. In this work, the masses and radii of differentially rotating neutron star models are computed. We employ a set of equations of states for dense hypernuclear and $\Delta$-admixed-hypernuclear matter obtained within the framework of CDF theory in the relativistic Hartree-Fock (RHF) approximation. Results are shown for varying meson-$\Delta$ couplings, or equivalently the $\Delta$-potential in nuclear matter. A comparison of our results with those obtained for non-rotating stars shows that the maximum mass difference between differentially rotating and static stars is independent of the underlying particle composition of the star. We further find that the decrease in the radii and increase in the maximum masses of stellar models when $\Delta$-isobars are added to hyperonuclear matter (as initially observed for static and uniformly rotating stars) persist also in the case of differentially rotating neutron stars., Comment: 7 pages, 6 figures

Gauge/gravity duality is used to study properties of the doubly heavy baryon $(\mathrm{QQq})$ at finite rapidity and temperature in the heavy-ion collision. We investigate the impact of rapidity on string breaking and screening of $\mathrm{QQq}$, and compare these effects with the results for $\rm Q\bar{Q}$ in detail. Computations reveal that the string-breaking distances of $\mathrm{QQq}$ and $\rm Q\bar{Q}$ are close in the confined state and the effects of rapidity and temperature on the string breaking are not significant. An interesting result shows that $\mathrm{QQq}$ cannot be found at high enough temperatures and rapidities; however, $\rm Q\bar{Q}$ can exist under any conditions as long as the separation distance is small enough. Besides, the screening distances of $\mathrm{QQq}$ and $\rm Q\bar{Q}$ are also compared at finite rapidity and temperature. Based on the above analysis, we infer that $\rm Q\bar{Q}$ is more stable than $\mathrm{QQq}$ at finite rapidity and temperature.

In this work, we use gauge/gravity duality to study potential energy and string-breaking of triply heavy baryons at finite temperature and chemical potential. Two different possible configurations of triply heavy baryon are considered. The effect of temperature and chemical potential on string-breaking distance is investigated. With increasing temperature/chemical potential, the sting-breaking distance decreases and then increases in symmetric collinear geometry while steadily increasing in equilateral triangle geometry. Our study provides insights into triply heavy baryon configuration and string-breaking behavior.

We generate three families of extended covariant density functionals of nuclear matter that have varying slope of symmetry energy and skewness at nuclear saturation density, but otherwise share the same basic parameters (symmetry energy, compressibility, saturation parameters, etc.) with the standard DDME2, DD2, and MPE functionals. Tables of the parameters of these new density functionals are given, which can be straightforwardly used in DDME2, DD2, and MPE parameterization-based codes. Furthermore, we provide tables of a large number of equations of state (81 for each family) that can be used in astrophysical simulations to assess the impact of variations of not-well-known slope of symmetry energy and skewness of nuclear systems on the astrophysics of compact objects. We also provide tables of computed integral parameters (mass, radius, and tidal deformability) that can be used, e.g., for modeling gravitational waveforms. Finally, for the extended DDME2-based parameterization, we implement a first-order phase transition to quark matter to obtain a family of equations of state that accommodates a phase transition to quark matter. Analogous tables of the equations of state and integral parameters are provided for this case as well., Comment: v2: matches published version. v1: 8 pages, 4 figures, 5 tables

A set of hadronic equations of state derived from covariant density functional theory and constrained by terrestrial experiments, and astrophysical observations, in particular by the NICER experiment inferences is used to explore the universal relations among the global properties of compact stars containing heavy baryons at high densities. We confirm the validity of universal $I$-Love-$Q$ relations connecting the moment of inertia $(I)$, the tidal deformability ($\Lambda$), and the spin-induced quadrupole moment ($Q$) for isolated non-rotating stars. We further confirm the validity of the $I$-$C$-$Q$ relations connecting the moment of inertia, compactness $(C)$, and quadrupole moment for uniformly and slowly rotating stars, and extend the validity of these relations to maximally rotating sequences. We then investigate the relations between integral parameters of maximally rotating and static compact stars. The universalities are shown to persist for equations of state and compositions containing hyperons and $\Delta$ degrees of freedom. When heavy baryons are included, however, the radial profiles of integrands in expressions of global properties exhibit ``bumps", which are not present in the case of nucleonic stars in which case the profiles are smooth. We determine the coefficients entering the universal relations in the case of hyperonic and $\Delta$-resonance containing stars., Comment: 19 pages, 15 figures; matches published version

The recent attempt on mass and radius inference of the central compact object within the supernova remnant HESS J1731-347 suggests for this object an unusually low mass of $M = 0.77^{+0.20}_{-0.17}\,M_{\odot}$ and a small radius of $R = 10.4^{+0.86}_{-0.78}$\,km. We explore the ways such a result can be accommodated within models of dense matter with heavy baryonic degrees of freedom which are constrained by the multi-messenger observations. We find that to do so using only purely nucleonic models, one needs to assume a rather small value of the slope of symmetry energy $L_{\rm sym}$. Once heavy baryons are included higher values of the slope $L_{\rm sym}$ become acceptable at the cost of a slightly reduced maximum mass of static configuration. These two scenarios are distinguished by the particle composition and will undergo different cooling scenarios. In addition, we show that the universalities of the $I$-Love-$Q$ relations for static configurations can be extended to very low masses without loss in their accuracy., Comment: v2: matches published version, 8 pages, 6 figures

In this paper, we employ gauge/gravity duality to investigate the string breaking and melting of doubly-heavy tetraquark that includes two heavy quarks and two light antiquarks in a holographic model at finite temperature. Firstly, we investigate four configurations of $\rm{QQ\bar{q}\bar{q}}$ in the confined phase and consider different separation distances of the heavy quarks at varying temperatures. At high temperature, $\rm{QQ\bar{q}\bar{q}}$ melts at certain distances and the confined quarks are released. As the temperature continues to increase, some configurations of doubly-heavy tetraquark can not exist. Furthermore, we investigate three decay modes of $\rm{QQ\bar{q}\bar{q}}$ and compare the potential energy of $\rm{QQ\bar{q}\bar{q}}$ with that of $\rm{QQq}$ at finite temperature .