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We have derived the Wigner equations at global equilibrium with constant vorticity but space-time dependent electromagnetic fields up to second order in semiclassical expansion. We obtain the new second-order contributions to the charge currents and energy-momentum tensor from the varying electromagnetic fields. We also compute the new corrections to the spin polarization pesudo-vector from both contant and varying electromagnetic fields. We also find that the space-time dependent electromagnetic field provides a tighter constraint on the solutions of Wigner functions in global equilibrium compared with constant electromagnetic field., Comment: 20 pages, typos corrected, Sec.VI reorganized

We have investigated the collisional corrections to the spin polarization pseudo-vector, $\delta\mathcal{P}^{\mu}$, using quantum kinetic theory in Chapman-Enskog expansion. We derive the spin Boltzmann equation incorporating M{\o}ller scattering process. We further consider two distinct scenarios using hard thermal loop approximations for simplification. In scenario (I), the vector charge distribution function is treated as off-equilibrium under the validity domain of gradient expansion. Remarkably, the polarization induced by gradients of thermal chemical potential and shear viscous tensors are modified, but $\delta\mathcal{P}_{\textrm{ }}^{\mu}$ in this scenario does not depend on the coupling constant. In scenario (II), the vector charge distribution function is assumed to be in local thermal equilibrium. Then collisional corrections $\delta\mathcal{P}_{\textrm{ }}^{\mu}$ in this scenario are at $\mathcal{O}(\hbar^{2}\partial^{2})$. Additionally, we evaluate the $\delta\mathcal{P}^{\mu}$ using relaxation time approach for comparative analysis. Our results establish the theoretical framework necessary for the future numerical investigations on the interaction corrections to spin polarization., Comment: 32 pages, 1 figure

We have implemented the 3+1 dimensional CLVisc hydrodynamics model with TRENTO-3D initial conditions to investigate the spin polarization of $\Lambda$ hyperons along the beam direction in p+Pb collisions at $\sqrt{s_{NN}} = 8.16$ TeV. Following our previous theoretical framework based on quantum kinetic theory, we consider three different scenarios: $\Lambda$ equilibrium, $s$ quark equilibrium, and iso-thermal equilibrium scenarios. We have computed the second Fourier sine coefficients of spin polarization along the beam direction, denoted as $\left\langle P_{z} \sin 2(\phi_{p} - \Psi_{2}) \right\rangle$, with $\phi_{p} - \Psi_{2}$ being the azimuthal angle relative to the second-order event plane $\Psi_{2}$, as functions of multiplicity, transverse momentum and pseudo-rapidity in the three scenarios. Additionally, we have also computed the spin polarization along the beam direction, $P_{z}$, as a function of the azimuthal angle. We find that the spin polarization induced by thermal vorticity always provides an opposite contribution compared to the shear-induced polarization in p+Pb collisions. The total spin polarization computed by the current hydrodynamic model disagrees with the data measured by LHC-CMS experiments. Our findings imply that other non-flow effects may play a crucial role in p+Pb collisions., Comment: 8 pages, 5 figures and 1 table. A new figure for local polarization as a function of pseudo-rapidity is added. submitted to PRC

We have investigated the late-time asymptotic solutions, attractor, and focusing behavior of minimal causal spin hydrodynamics in Bjorken expansion. Using the method of dominant balance, we derive the late-time asymptotic solutions of the evolution equation for spin density and identify the specific conditions necessary for the spin density to exhibit a power-law decay. We then analyze both the late-time and early-time attractors for the decay rate of spin density. Additionally, we report the focusing behavior in spin hydrodynamics, which has not been found in conventional relativistic hydrodynamics in Bjorken expansion. Our findings suggest that spin density can be treated as a conventional hydrodynamic variable at late times under certain conditions., Comment: 34 pages, 6 figures

In the modern paradigm of multi-agent networks, communication has become one of the main bottlenecks for decentralized optimization, where a large number of agents are involved in minimizing the average of the local cost functions. In this paper, we propose a robust compressed push-pull algorithm (RCPP) that combines gradient tracking with communication compression. In particular, RCPP is robust under a much more general class of compression operators that allow both relative and absolute compression errors, in contrast to the existing works which can handle either one of them or assume convex problems. We show that RCPP enjoys sublinear convergence rate for smooth and possibly nonconvex objective functions over general directed networks. Moreover, under the additional Polyak-{\L}ojasiewicz condition, linear convergence rate can be achieved for RCPP. Numerical examples verify the theoretical findings and demonstrate the efficiency, flexibility, and robustness of the proposed algorithm., Comment: arXiv admin note: substantial text overlap with arXiv:2303.07091

We have investigated light nuclei pair photoproduction in relativistic heavy ion ultraperipheral collisions. As a first attempt, we employ our previously developed quantum electrodynamics model, which incorporates a wave-packet description of initial nuclei, to compute the cross section for proton-antiproton pair photoproduction. The effective vertex for the photon and proton interaction is chosen based on studies of two-photon exchange effects in hadron physics. We present the transverse momentum, invariant mass, and azimuthal angle distributions of proton-antiproton pairs at $\sqrt{s_{NN}}=200$ GeV in Au+Au ultraperipheral collisions. We observe a $\cos(2\phi)$ modulation and an almost negligible $\cos(4\phi)$ modulation in the azimuthal angle distribution. Our studies helps us better understand the matter generated by light., Comment: 6 pages, 3 figures

Human priors play a crucial role in efficiently utilizing data in deep learning. However, with the development of large language models (LLMs), there is an increasing emphasis on scaling both model size and data volume, which often diminishes the importance of human priors in data construction. Influenced by these trends, existing Small Language Models (SLMs) mainly rely on web-scraped large-scale training data, neglecting the proper incorporation of human priors. This oversight limits the training efficiency of language models in resource-constrained settings. In this paper, we propose a principle to leverage human priors for data construction. This principle emphasizes achieving high-performance SLMs by training on a concise dataset that accommodates both semantic diversity and data quality consistency, while avoiding benchmark data leakage. Following this principle, we train an SLM named HARE-1.1B. Extensive experiments on large-scale benchmark datasets demonstrate that HARE-1.1B performs favorably against state-of-the-art SLMs, validating the effectiveness of the proposed principle. Additionally, this provides new insights into efficient language model training in resource-constrained environments from the view of human priors.

We have investigated the $\rho^{0}$ meson photoproduction in ultraperipheral isobaric collisions between $_{44}^{96}\textrm{Ru}+_{44}^{96}\textrm{Ru}$ and $_{40}^{96}\textrm{Zr}+_{40}^{96}\textrm{Zr}$ at $\sqrt{s_{NN}}=200$ GeV, employing the dipole model with the equivalent photon approximation. By implementing the Woods-Saxon distribution to represent the nuclear mass density, which is derived from density functional theory with an inclusion of nuclear deformation effects, we have calculated the transverse momentum $q_{T}$ spectra in isobaric collisions. We observe the characteristic dip behavior in these spectra, indicative of diffraction phenomena in high-energy physics. We notice that the deformation effects cause a nearly linear increase with $q_{T}^{2}$ for $q_{T}^{2}\lesssim0.015$ $\textrm{GeV}^{2}$, aligning with experimental observations. We offer a simple explanation for the observed behavior in these spectra by introducing the effective width of the nuclei in the thickness function. We also extend our discussion on the $\rho^{0}$ meson photoproduction with the targets $^{63}\textrm{Cu}$,$^{197}\textrm{Au}$, and $^{238}\textrm{U}$., Comment: 9 pages, 5 figures

We have applied thermodynamic stability analysis to derive the stability and causality conditions for conventional relativistic viscous hydrodynamics and spin hydrodynamics. We obtain the thermodynamic stability conditions for second-order relativistic hydrodynamics with shear and bulk viscous tensors, finding them identical to those derived from linear mode analysis. We then derive the thermodynamic stability conditions for minimal causal extended second-order spin hydrodynamics in canonical form, both with and without viscous tensors. Without viscous tensors, the constraints from thermodynamic stability exactly match those from linear mode analysis. In the presence of viscous tensors, the thermodynamic stability imposes more stringent constraints than those obtained from linear mode analysis. Our results suggest that conditions derived from thermodynamic stability analysis can guarantee both causality and stability in linear mode analysis., Comment: 30 pages; published version

This paper considers the distributed learning problem where a group of agents cooperatively minimizes the summation of their local cost functions based on peer-to-peer communication. Particularly, we propose a highly efficient algorithm, termed ``B-ary Tree Push-Pull'' (BTPP), that employs two B-ary spanning trees for distributing the information related to the parameters and stochastic gradients across the network. The simple method is efficient in communication since each agent interacts with at most $(B+1)$ neighbors per iteration. More importantly, BTPP achieves linear speedup for smooth nonconvex objective functions with only $\tilde{O}(n)$ transient iterations, significantly outperforming the state-of-the-art results to the best of our knowledge.

In this paper, we introduce an accelerated distributed stochastic gradient method with momentum for solving the distributed optimization problem, where a group of $n$ agents collaboratively minimize the average of the local objective functions over a connected network. The method, termed ``Distributed Stochastic Momentum Tracking (DSMT)'', is a single-loop algorithm that utilizes the momentum tracking technique as well as the Loopless Chebyshev Acceleration (LCA) method. We show that DSMT can asymptotically achieve comparable convergence rates as centralized stochastic gradient descent (SGD) method under a general variance condition regarding the stochastic gradients. Moreover, the number of iterations (transient times) required for DSMT to achieve such rates behaves as $\mathcal{O}(n^{5/3}/(1-\lambda))$ for minimizing general smooth objective functions, and $\mathcal{O}(\sqrt{n/(1-\lambda)})$ under the Polyak-{\L}ojasiewicz (PL) condition. Here, the term $1-\lambda$ denotes the spectral gap of the mixing matrix related to the underlying network topology. Notably, the obtained results do not rely on multiple inter-node communications or stochastic gradient accumulation per iteration, and the transient times are the shortest under the setting to the best of our knowledge., Comment: 32 pages, 5 figures

Polarization has opened a new physics chapter in relativistic heavy-ion collisions. Since the first prediction and experimental observation of global spin polarization, a lot of progress has been made in understanding its features, both at experimental and theoretical level. In this paper, we give an overview on the recent advances in this field. The covered topics include a review of measurements of global and local spin polarization of hyperons and the global spin alignment of vector mesons. We account for the basic theoretical framework to describe spin polarization in a relativistic fluid such as the Quark Gluon Plasma, including statistical quantum field theory and local thermodynamic equilibrium, spin hydrodynamics, relativistic kinetic theory with spin and coalescence models., Comment: RevTeX 4, 41 pages, 12 figures, review article as a book chapter for QGP6

We study the spin alignment of neutral rho mesons in a pion gas using spin kinetic or Boltzmann equations. The $\rho\pi\pi$ coupling is given by the chiral effective theory. The collision terms at the leading and next-to-leading order in spin Boltzmann equations are derived. The evolution of the spin density matrix of the neutral rho meson is simulated with different initial conditions. The numerical results show that the interaction of pions and neutral rho mesons creates very small spin alignment in the central rapidity region if there is no rho meson in the system at the initial time. Such a small spin alignment in the central rapidity region will decay rapidly toward zero in later time. If there are rho mesons with a sizable spin alignment at the initial time the spin alignment will also decrease rapidly. We also considered the effect on $\rho_{00}$ from the elliptic flow of pions in the blast wave model. With vanishing spin alignment at the initial time, the deviation of $\rho_{00}$ from 1/3 is positive but very small., Comment: RevTex 4, 17 pages, 12 figures

We report our recent study on the global and local polarization of $\Lambda$ hyperons in Au+Au collisions at RHIC-BES energies within the (3+1)-dimensional CLVisc hydrodynamics framework. We present our numerical results for the global polarization as the function of collision energies and the local polarization along the beam direction as functions of azimuthal angle in $20-50$% centrality at $\sqrt{s_{NN}}$=7.7 GeV Au+Au collision energy. We have discussed the effects of initial conditions, Spin Hall effect and baryon diffusion., Comment: 4 pages, 3 figures. Contribution to the proceedings of Quark Matter 2023 (Houston, TX, 3-9 Sep. 2023)

We derive the quantum kinetic theory for massive fermions with collision terms and self-energy corrections based on quantum field theory. We adopt an effective power counting scheme with $\hbar$ expansion to obtain the leading-order perturbative solutions of the vector and axial Wigner functions and the corresponding kinetic equations. We observe that both the onshell relation and the structure of Wigner functions, along with the kinetic equations, are modified due to the presence of self-energies and their space-time gradients. We further apply our formalism to investigate the spin polarization phenomena in relativistic heavy ion collisions and derive the modification to the spin polarization spectrum of massive quarks. We find that the gradient of vector self-energy plays a similar role to the background electromagnetic fields, which induces a more dominant contribution than the collisional effects by a naive power counting in the gradient expansion and weak coupling. Our findings could further modify the spin polarization of strange quarks and spin alignment of $\phi$ mesons beyond local thermal equilibrium., Comment: 52 pages, 1 table

Causality and stability are fundamental requirements for the differential equations describing predictable relativistic many-body systems. In this work, we investigate the stability and causality criteria in linear mode analysis. We discuss the updated stability criterion in 3+1 dimensional systems and introduce the improved sufficient criterion for causality. Our findings clearly demonstrate that stability implies causality in linear mode analysis. Furthermore, based on the theorems present in this work, we conclude that if updated stability criterion and improved causality criterion are fulfilled in one inertial frame of reference (IFR), they hold for all IFR., Comment: 6+8 pages, 1 figure; references added, typos corrected

We study the rapidity and azimuthal angle dependences of the global spin alignment $\rho_{00}$ for $\phi$ mesons with respect to the reaction plane in Au+Au collisions at RHIC by the relativistic coalescence model in the spin transport theory. The global spin alignment of $\phi$ mesons arises from local fluctuations of strong force fields whose values are extracted from the STAR's data. The calculated results show that $\rho_{00}<1/3$ at the rapidity $Y=0$, and then it increases with rapidity and becomes $\rho_{00}>1/3$ at $Y=1$. Such a rapidity dependence is dominated by the relative motion of the $\phi$ meson in the bulk matter. We also give prediction for the azimuthal angle dependence of $\rho_{00}$ at different rapidities., Comment: RevTex 4, 5 pages, 4 figures

We perform the linear analysis of causality and stability for a minimal extended spin hydrodynamics up to second order of the gradient expansion. The first order spin hydrodynamics, with a rank-3 spin tensor being antisymmetric for only the last two indices, are proved to be acausal and unstable. We then consider the minimal causal spin hydrodynamics up to second order of the gradient expansion. We derive the necessary causality and stability conditions for this minimal causal spin hydrodynamics. Interestingly, the satisfaction of the stability conditions relies on the equations of state for the spin density and chemical potentials. Moreover, different with the conventional relativistic dissipative hydrodynamics, the stability of the theory seems to be broken at the finite wave-vector when the stability conditions are fulfilled at small and large wave-vector limits. It implies that the behavior in small and large wave-vector limits may be insufficient to determine the stability conditions for spin hydrodynamics in linear mode analysis., Comment: 45 pages, 2 figures, typos corrected, published version

This paper proposes two distributed random reshuffling methods, namely Gradient Tracking with Random Reshuffling (GT-RR) and Exact Diffusion with Random Reshuffling (ED-RR), to solve the distributed optimization problem over a connected network, where a set of agents aim to minimize the average of their local cost functions. Both algorithms invoke random reshuffling (RR) update for each agent, inherit favorable characteristics of RR for minimizing smooth nonconvex objective functions, and improve the performance of previous distributed random reshuffling methods both theoretically and empirically. Specifically, both GT-RR and ED-RR achieve the convergence rate of $O(1/[(1-\lambda)^{1/3}m^{1/3}T^{2/3}])$ in driving the (minimum) expected squared norm of the gradient to zero, where $T$ denotes the number of epochs, $m$ is the sample size for each agent, and $1-\lambda$ represents the spectral gap of the mixing matrix. When the objective functions further satisfy the Polyak-{\L}ojasiewicz (PL) condition, we show GT-RR and ED-RR both achieve $O(1/[(1-\lambda)mT^2])$ convergence rate in terms of the averaged expected differences between the agents' function values and the global minimum value. Notably, both results are comparable to the convergence rates of centralized RR methods (up to constant factors depending on the network topology) and outperform those of previous distributed random reshuffling algorithms. Moreover, we support the theoretical findings with a set of numerical experiments., Comment: 16 pages, 8 figures

With the help of conditioning mechanisms, the state-of-the-art diffusion models have achieved tremendous success in guided image generation, particularly in text-to-image synthesis. To gain a better understanding of the training process and potential risks of text-to-image synthesis, we perform a systematic investigation of backdoor attack on text-to-image diffusion models and propose BadT2I, a general multimodal backdoor attack framework that tampers with image synthesis in diverse semantic levels. Specifically, we perform backdoor attacks on three levels of the vision semantics: Pixel-Backdoor, Object-Backdoor and Style-Backdoor. By utilizing a regularization loss, our methods efficiently inject backdoors into a large-scale text-to-image diffusion model while preserving its utility with benign inputs. We conduct empirical experiments on Stable Diffusion, the widely-used text-to-image diffusion model, demonstrating that the large-scale diffusion model can be easily backdoored within a few fine-tuning steps. We conduct additional experiments to explore the impact of different types of textual triggers, as well as the backdoor persistence during further training, providing insights for the development of backdoor defense methods. Besides, our investigation may contribute to the copyright protection of text-to-image models in the future., Comment: Carmera-ready version. To appear in ACM MM 2023. Code will be released at: https://github.com/sf-zhai/BadT2I

We investigate the hydrodynamic helicity polarization of $\Lambda$ hyperons, defined as the projection of the spin polarization vector along the directions of particle momenta, at RHIC-BES energies by utilizing the relativistic (3+1)D CLVisc hydrodynamics framework with SMASH initial conditions. As opposed to local spin polarization at high energy collisions, our hydrodynamic simulations demonstrate that the helicity polarization induced by the kinetic vorticity dominates over other contributions at intermediate and low collision energies. Our findings provide an opportunity to probe the fine structure of local kinetic vorticity as a function of azimuthal angle at intermediate and low collision energies by mapping our predictions to the future measurements in experiments., Comment: 8 pages, 3 figures

In Wigner function approach with relaxation time approximation, we calculate electric and magnetic conductivities of a fermion system in the strong magnetic field. The linear response has been calculated to the perturbation of electromagnetic fields on the background constant magnetic field. The Wigner function is separated into an equilibrium part in the background magnetic field and an off-equilibrium part induced by perturbative fields. The analytical expression for the equilibrium part and the corresponding equilibrium conditions are given. For the off-equilibrium part, we obtain the kinetic equation at the leading order in $\hbar$ from the master equation of the Wigner function. When perturbative fields only depend on the proper time, the off-equilibrium part can be analytically solved from which the vector and axial vector currents are obtained. We obtain the longitudinal and transverse Ohm conductivities as well as Hall conductivity as the linear response of the vector current to the perturbative electric field. The behaviors of these conductivities as functions of the evolving time, relaxation time, particle mass, and strength of the background magnetic field are investigated both analytically and numerically., Comment: 25 pages, 6 figures

In the modern paradigm of multi-agent networks, communication has become one of the main bottlenecks for decentralized optimization, where a large number of agents are involved in minimizing the average of the local cost functions. In this paper, we propose a robust compressed push-pull algorithm (RCPP) that combines gradient tracking with communication compression. In particular, RCPP is compatible with a much more general class of compression operators that allow both relative and absolute compression errors. We show that RCPP achieves linear convergence rate for smooth objective functions satisfying the Polyak-{\L}ojasiewicz condition over general directed networks. Numerical examples verify the theoretical findings and demonstrate the efficiency, flexibility, and robustness of the proposed algorithm.

This paper proposes a unified diffusion framework (dubbed UniDiffuser) to fit all distributions relevant to a set of multi-modal data in one model. Our key insight is -- learning diffusion models for marginal, conditional, and joint distributions can be unified as predicting the noise in the perturbed data, where the perturbation levels (i.e. timesteps) can be different for different modalities. Inspired by the unified view, UniDiffuser learns all distributions simultaneously with a minimal modification to the original diffusion model -- perturbs data in all modalities instead of a single modality, inputs individual timesteps in different modalities, and predicts the noise of all modalities instead of a single modality. UniDiffuser is parameterized by a transformer for diffusion models to handle input types of different modalities. Implemented on large-scale paired image-text data, UniDiffuser is able to perform image, text, text-to-image, image-to-text, and image-text pair generation by setting proper timesteps without additional overhead. In particular, UniDiffuser is able to produce perceptually realistic samples in all tasks and its quantitative results (e.g., the FID and CLIP score) are not only superior to existing general-purpose models but also comparable to the bespoken models (e.g., Stable Diffusion and DALL-E 2) in representative tasks (e.g., text-to-image generation)., Comment: Accepted to ICML2023

Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. Though numerous algorithms have been proposed and successfully applied to general practical problems, their theoretical guarantees mainly rely on certain boundedness conditions on the stochastic gradients, varying from uniform boundedness to the relaxed growth condition. In addition, how to characterize the data heterogeneity among the agents and its impacts on the algorithmic performance remains challenging. In light of such motivations, we revisit the classical Federated Averaging (FedAvg) algorithm (McMahan et al., 2017) as well as the more recent SCAFFOLD method (Karimireddy et al., 2020) for solving the distributed stochastic optimization problem and establish the convergence results under only a mild variance condition on the stochastic gradients for smooth nonconvex objective functions. Almost sure convergence to a stationary point is also established under the condition. Moreover, we discuss a more informative measurement for data heterogeneity as well as its implications., Comment: 16 pages, 2 figure

In this paper, we consider solving the distributed optimization problem over a multi-agent network under the communication restricted setting. We study a compressed decentralized stochastic gradient method, termed ``compressed exact diffusion with adaptive stepsizes (CEDAS)", and show the method asymptotically achieves comparable convergence rate as centralized { stochastic gradient descent (SGD)} for both smooth strongly convex objective functions and smooth nonconvex objective functions under unbiased compression operators. In particular, to our knowledge, CEDAS enjoys so far the shortest transient time (with respect to the graph specifics) for achieving the convergence rate of centralized SGD, which behaves as $\mathcal{O}(n{C^3}/(1-\lambda_2)^{2})$ under smooth strongly convex objective functions, and $\mathcal{O}(n^3{C^6}/(1-\lambda_2)^4)$ under smooth nonconvex objective functions, where $(1-\lambda_2)$ denotes the spectral gap of the mixing matrix, and $C>0$ is the compression-related parameter. In particular, CEDAS exhibits the shortest transient times when $C < \mathcal{O}(1/(1 - \lambda_2)^2)$, which is common in practice. Numerical experiments further demonstrate the effectiveness of the proposed algorithm., Comment: 16 pages, 8 figures

We have derived the solutions of the relativistic anomalous magnetohydrodynamics with longitudinal Bjorken boost invariance and transverse electromagnetic fields in the presence of temperature or energy density dependent electric conductivity. We consider the equations of states in a high temperature limit or in a high chiral chemical potential limit. We obtain both perturbative analytic solutions up to the order of \hbar and numerical solutions in our configurations of initial electromagnetic fields and Bjorken flow velocity. Our results show that the temperature or energy density dependent electric conductivity plays an important role to the decaying of the energy density and electromagnetic fields. We also implement our results to the splitting of global polarization for \Lambda and \bar{\Lambda} hyperons induced by the magnetic fields. Our results for the splitting of global polarization disagree with the experimental data in low energy collisions, which implies that the contribution from gradient of chemical potential may dominate in the low energy collisions.

We investigate the photoproduction of di-electrons in peripheral collisions of $_{44}^{96}\textrm{Ru}+_{44}^{96}\textrm{Ru}$ and $_{40}^{96}\textrm{Zr}+_{40}^{96}\textrm{Zr}$ at 200 GeV. With the charge and mass density distributions given by the calculation of the density functional theory, we calculate the spectra of transverse momentum, invariant mass and azimuthal angle for di-electrons at 40-80\% centrality. The ratios of these spectra in Ru+Ru collisions over to Zr+Zr collisions are shown to be smaller than $(44/40)^{4}$ (the ratio of $Z^{4}$ for Ru and Zr) at low transverse momentum. The deviation arises from the different mass and charge density distributions in Ru and Zr. So the photoproduction of di-leptons in isobar collisions may provide a new way to probe the nuclear structure., Comment: 17 pages, 6 figures

We propose a decentralized optimization algorithm that preserves the privacy of agents' cost functions without sacrificing accuracy, termed EFPSN. The algorithm adopts Paillier cryptosystem to construct zero-sum functional perturbations. Then, based on the perturbed cost functions, any existing decentralized optimization algorithm can be utilized to obtain the accurate solution. We theoretically prove that EFPSN is (epsilon, delta)-differentially private and can achieve nearly perfect privacy under deliberate parameter settings. Numerical experiments further confirm the effectiveness of the algorithm.

Communication compression techniques are of growing interests for solving the decentralized optimization problem under limited communication, where the global objective is to minimize the average of local cost functions over a multi-agent network using only local computation and peer-to-peer communication. In this paper, we propose a novel compressed gradient tracking algorithm (C-GT) that combines gradient tracking technique with communication compression. In particular, C-GT is compatible with a general class of compression operators that unifies both unbiased and biased compressors. We show that C-GT inherits the advantages of gradient tracking-based algorithms and achieves linear convergence rate for strongly convex and smooth objective functions. Numerical examples complement the theoretical findings and demonstrate the efficiency and flexibility of the proposed algorithm., Comment: To appear in TAC. arXiv admin note: substantial text overlap with arXiv:2103.13748

We investigate the dynamical spin polarization of a massless electron probing an electron plasma in locally thermal equilibrium via the Moller scattering from the quantum kinetic theory. We derive an axial kinetic equation delineating the dynamical spin evolution in the presence of the collision term with quantum corrections up to $\mathcal{O}(\hbar)$ and the leading-logarithmic order in coupling by using the hard-thermal-loop (HTL) approximation, from which we extract the spin-polarization rate induced by the spacetime gradients of the medium. When the electron probe approaches local equilibrium, we further simplify the collision term into a relaxation-time expression. Our kinetic equation may be implemented in the future numerical simulations for dynamical spin polarization., Comment: 28 pages, 1 figure, minor revisions, journal version

We study the lepton pair photoproduction in peripheral heavy-ion collisions based on the formalism in our previous work [Phys. Rev. D 104, 056011 (2021)]. We present the numerical results for the distributions of the transverse momentum, azimuthal angle and invariant mass for $e^{+}e^{-}$ and $\mu^{+}\mu^{-}$ pairs as functions of the impact parameter and other kinematic variables in Au+Au collisions. Our calculation incorporates the information on the transverse momentum and polarization of photons which is essential to describe the experimental data. We observe a broadening effect in the transverse momentum for lepton pairs with and without smear effects. We also observe a significant enhancement in the distribution of $\cos(2\varphi)$ for $\mu^{+}\mu^{-}$ pairs. Our results provide a baseline for future studies of other higher order corrections beyond Born approximation and medium effects in the lepton pair production., Comment: 19 pages, 10 figures

We perform a systematic study on the local and global spin polarization of $\Lambda$ and $\overline{\Lambda}$ hyperons in relativistic heavy-ion collisions at beam energy scan energies via the (3+1)-dimensional CLVisc hydrodynamics model with AMPT and SMASH initial conditions. Following the quantum kinetic theory, we decompose the polarization vector as the parts induced by thermal vorticity, shear tensor and the spin Hall effect (SHE). We find that the polarization induced by SHE and the total polarization strongly depends on the initial conditions. At $7.7$GeV, SHE gives a sizeable contribution and even flips the sign of the local polarization along the beam direction for AMPT initial condition, which is not observed for SMASH initial condition. Meanwhile, the local polarization along the out-of-plane direction induced by SHE with AMPT initial condition does not always increase with decreasing collision energies. Next, we find that the polarization along the beam direction is sensitive to the baryon diffusion coefficient, but the local polarization along the out-of-plane direction is not. Our results for the global polarization of $\Lambda$ and $\overline{\Lambda}$ agree well with the STAR data. Interestingly, the global polarization of $\overline{\Lambda}$ is not always larger than that of $\Lambda$ due to various competing effects. Our findings are helpful for understanding the polarization phenomenon and the detailed structure of quark-gluon plasma in relativistic heavy-ion collisions., Comment: 13 pages, 8 figures

Most methods tackle zero-shot video classification by aligning visual-semantic representations within seen classes, which limits generalization to unseen classes. To enhance model generalizability, this paper presents an end-to-end framework that preserves alignment and uniformity properties for representations on both seen and unseen classes. Specifically, we formulate a supervised contrastive loss to simultaneously align visual-semantic features (i.e., alignment) and encourage the learned features to distribute uniformly (i.e., uniformity). Unlike existing methods that only consider the alignment, we propose uniformity to preserve maximal-info of existing features, which improves the probability that unobserved features fall around observed data. Further, we synthesize features of unseen classes by proposing a class generator that interpolates and extrapolates the features of seen classes. Besides, we introduce two metrics, closeness and dispersion, to quantify the two properties and serve as new measurements of model generalizability. Experiments show that our method significantly outperforms SoTA by relative improvements of 28.1% on UCF101 and 27.0% on HMDB51. Code is available., Comment: CVPR 2022

The Berry phase is analyzed for Weyl and Dirac fermions in a phase space representation of the worldline formalism. Kinetic theories are constructed for both at a classical level. Whereas the Weyl fermion case reduces in dimension, resembling a theory in quantum mechanics, the Dirac fermion case takes on a manifestly Lorentz covariant form. To achieve a classical kinetic theory for the non-Abelian Dirac fermion Berry phase a spinor construction of Barut and Zanghi is utilized. The axial anomaly is also studied at a quantum level. It is found that under an adiabatic approximation, which is necessary for facilitating a classical kinetic theory, the index of the Dirac operator for massless fermions vanishes. Even so, similarities of an axial rotation to an exact non-covariant Berry phase transform are drawn by application of the Fujikawa method to the Barut and Zanghi spinors on the worldline., Comment: 13 pages, 0 figures; version accepted for publication in Physical Review D

We use the method of field decomposition, a technique widely used in relativistic magnetohydrodynamics, to study the small velocity approximation (SVA) of the Lorentz transformation in Maxwell equations for slowly moving media. The "deformed" Maxwell equations derived under the SVA in the lab frame can be put into the conventional form of Maxwell equations in the medium's comoving frame. Our results show that the Lorentz transformation in the SVA up to $O(v/c)$ ($v$ is the speed of the medium and $c$ is the speed of light in vacuum) is essential to derive these equations: the time and charge density must also change when transforming to a different frame even in the SVA, not just the position and current density as in the Galilean transformation. This marks the essential difference of the Lorentz transformation from the Galilean one. We show that the integral forms of Faraday and Ampere equations for slowly moving surfaces are consistent with Maxwell equations. We also present Faraday equation the covariant integral form in which the electromotive force can be defined as a Lorentz scalar independent of the observer's frame. No evidences exist to support an extension or modification of Maxwell equations., Comment: 16 pages, 1 figure, 3 tables. Section VI is added about integral forms of Faraday and Ampere laws for moving surfaces. Part of Section IV and V are rewitten

Many novel quantum phenomena emerge in non-equilibrium relativistic quantum matter under extreme conditions such as strong magnetic fields and rotations. The quantum kinetic theory based on Wigner functions in quantum field theory provides a powerful and effective microscopic description of these quantum phenomena. In this article we review some of recent advances in the quantum kinetic theory and its applications in describing these quantum phenomena., Comment: 114 pages, 3 figures; List of acronyms and symbols are added

We have calculated the directed flow $v_{1}$ and charge-dependent directed flow $\Delta v_{1}$ for pions and protons in Au+Au collisions at $\sqrt{s_{NN}}=200$GeV by solving the coupled Boltzmann-Maxwell equations self-consistently. Our numerical results show that $v_{1}$ for pions and protons are all negative in the positive mid rapidity region and have similar behavior and magnitude. In contrast we find a quite different behavior in $\Delta v_{1}$ for pions and protons. The difference lies in that $\Delta v_{1}$ for protons mainly comes from pressure gradients of the medium, while the dominant contribution to $\Delta v_{1}$ for pions is from electromagnetic fields. Our results indicate that the effect of the electric field will slightly exceed that of the magnetic and lead to a small negative slope of $\Delta v_{1}$ for pions, Comment: 9 pages, 6 figures; accepted by Phys. Rev. Research

We have derived the analytic solutions of dissipative relativistic spin hydrodynamics with Gubser expansion. Following the standard strategy of deriving the solutions in a Gubser flow, we take the Weyl rescaling and obtain the energy-momentum and angular momentum conversation equations in the $dS_{3}\times\mathbb{R}$ space-time. We then derive the analytic solutions of spin density, spin potential and other thermodynamic in $dS_{3}\times\mathbb{R}$ space-time and transform them back into Minkowski space-time $\mathbb{R}^{3,1}$. In the Minkowski space-time, the spin density and spin potential including the information of radial expansion decay as $\sim L^{-2}\tau^{-1}$ and $\sim L^{-2}\tau^{-1/3}$ in large $L$ limit, with $\tau$ being proper time and $L$ being the characteristic length of the system, respectively. Moreover, we observe the non-vanishing spin corrections to the energy density and other dissipative terms in the Belinfante form of dissipative spin hydrodynamics. Our results can also be used as test beds for future simulations of relativistic dissipative spin hydrodynamics., Comment: 28 pages; 1 table and 1 figure are added