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Yi Xie

Yi Xie appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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astro-ph.HEgr-qcastro-ph.SRComputer Visionmath.GTMachine Learningeess.ASquant-phSoundArtificial Intelligenceastro-ph.EPastro-ph.GAComputation and LanguageCryptography and Securityastro-ph.IMcond-mat.mtrl-sciHardware Architecturemath.DGMultiagent Systemsphysics.atom-phphysics.chem-phSocial and Information Networks

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Published work

49 published item(s)

preprint2026arXiv

TeamTR: Trust-Region Fine-Tuning for Multi-Agent LLM Coordination

Multi-agent LLM systems have shown promise for complex reasoning, yet recent evaluations reveal they often underperform single-model baselines. We identify a structural failure mode in sequential fine-tuning of shared-context teams: updating one agent shifts the team's context distribution, and when subsequent updates are evaluated on cached rollouts, this mismatch compounds. We formalize this as the compounding occupancy shift and prove that stale-occupancy evaluation incurs a penalty that scales quadratically with the number of agents. In contrast, intermediate-occupancy evaluation reduces this to linear scaling. We propose TeamTR, a trust-region framework that resamples trajectories after each component update and enforces per-agent divergence control, yielding rigorous per-update and per-stage improvement lower bounds. Experiments show that TeamTR outperforms single-agent and sequential baselines with 7.1% on average, mitigates coordination regressions, and supports plug-and-play component replacement. Code is available at https://github.com/Yydc/TeamTR.

0 citations0 reviewsNo code linkedOpen access
preprint2024arXiv

SAME: Sample Reconstruction against Model Extraction Attacks

While deep learning models have shown significant performance across various domains, their deployment needs extensive resources and advanced computing infrastructure. As a solution, Machine Learning as a Service (MLaaS) has emerged, lowering the barriers for users to release or productize their deep learning models. However, previous studies have highlighted potential privacy and security concerns associated with MLaaS, and one primary threat is model extraction attacks. To address this, there are many defense solutions but they suffer from unrealistic assumptions and generalization issues, making them less practical for reliable protection. Driven by these limitations, we introduce a novel defense mechanism, SAME, based on the concept of sample reconstruction. This strategy imposes minimal prerequisites on the defender's capabilities, eliminating the need for auxiliary Out-of-Distribution (OOD) datasets, user query history, white-box model access, and additional intervention during model training. It is compatible with existing active defense methods. Our extensive experiments corroborate the superior efficacy of SAME over state-of-the-art solutions. Our code is available at https://github.com/xythink/SAME.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

GiT: Graph Interactive Transformer for Vehicle Re-identification

Transformers are more and more popular in computer vision, which treat an image as a sequence of patches and learn robust global features from the sequence. However, pure transformers are not entirely suitable for vehicle re-identification because vehicle re-identification requires both robust global features and discriminative local features. For that, a graph interactive transformer (GiT) is proposed in this paper. In the macro view, a list of GiT blocks are stacked to build a vehicle re-identification model, in where graphs are to extract discriminative local features within patches and transformers are to extract robust global features among patches. In the micro view, graphs and transformers are in an interactive status, bringing effective cooperation between local and global features. Specifically, one current graph is embedded after the former level's graph and transformer, while the current transform is embedded after the current graph and the former level's transformer. In addition to the interaction between graphs and transforms, the graph is a newly-designed local correction graph, which learns discriminative local features within a patch by exploring nodes' relationships. Extensive experiments on three large-scale vehicle re-identification datasets demonstrate that our GiT method is superior to state-of-the-art vehicle re-identification approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

CHIP: CHannel Independence-based Pruning for Compact Neural Networks

Filter pruning has been widely used for neural network compression because of its enabled practical acceleration. To date, most of the existing filter pruning works explore the importance of filters via using intra-channel information. In this paper, starting from an inter-channel perspective, we propose to perform efficient filter pruning using Channel Independence, a metric that measures the correlations among different feature maps. The less independent feature map is interpreted as containing less useful information$/$knowledge, and hence its corresponding filter can be pruned without affecting model capacity. We systematically investigate the quantification metric, measuring scheme and sensitiveness$/$reliability of channel independence in the context of filter pruning. Our evaluation results for different models on various datasets show the superior performance of our approach. Notably, on CIFAR-10 dataset our solution can bring $0.90\%$ and $0.94\%$ accuracy increase over baseline ResNet-56 and ResNet-110 models, respectively, and meanwhile the model size and FLOPs are reduced by $42.8\%$ and $47.4\%$ (for ResNet-56) and $48.3\%$ and $52.1\%$ (for ResNet-110), respectively. On ImageNet dataset, our approach can achieve $40.8\%$ and $44.8\%$ storage and computation reductions, respectively, with $0.15\%$ accuracy increase over the baseline ResNet-50 model. The code is available at https://github.com/Eclipsess/CHIP_NeurIPS2021.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Compute Cost Amortized Transformer for Streaming ASR

We present a streaming, Transformer-based end-to-end automatic speech recognition (ASR) architecture which achieves efficient neural inference through compute cost amortization. Our architecture creates sparse computation pathways dynamically at inference time, resulting in selective use of compute resources throughout decoding, enabling significant reductions in compute with minimal impact on accuracy. The fully differentiable architecture is trained end-to-end with an accompanying lightweight arbitrator mechanism operating at the frame-level to make dynamic decisions on each input while a tunable loss function is used to regularize the overall level of compute against predictive performance. We report empirical results from experiments using the compute amortized Transformer-Transducer (T-T) model conducted on LibriSpeech data. Our best model can achieve a 60% compute cost reduction with only a 3% relative word error rate (WER) increase.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Instanton homology and knot detection on thickened surfaces

Suppose $Σ$ is a compact oriented surface (possibly with boundary) that has genus zero, and L is a link in the interior of $(-1,1)\timesΣ$. We prove that the Asaeda-Przytycki-Sikora (APS) homology of L has rank 2 if and only if L is isotopic to an embedded knot in $\{0\}\timesΣ$. As a consequence, the APS homology detects the unknot in $(-1,1)\timesΣ$. This is the first detection result for generalized Khovanov homology that is valid on an infinite family of manifolds, and it partially solves a conjecture in arxiv:2005.12863. Our proof is different from the previous detection results obtained by instanton homology because in this case, the second page of Kronheimer-Mrowka's spectral sequence is not isomorphic to the APS homology. We also characterize all links in product manifolds that have minimal sutured instanton homology, which may be of independent interest.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Interfacial Charge-transfer Excitonic Insulator in a Two-dimensional Organic-inorganic Superlattice

Excitonic insulators are long-sought-after quantum materials predicted to spontaneously open a gap by the Bose condensation of bound electron-hole pairs, namely, excitons, in their ground state. Since the theoretical conjecture, extensive efforts have been devoted to pursuing excitonic insulator platforms for exploring macroscopic quantum phenomena in real materials. Reliable evidences of excitonic character have been obtained in layered chalcogenides as promising candidates. However, owing to the interference of intrinsic lattice instabilities, it is still debatable whether those features, such as charge density wave and gap opening, are primarily driven by the excitonic effect or by the lattice transition. Herein, we develop a novel charge-transfer excitonic insulator in organic-inorganic superlattice interfaces, which serves as an ideal platform to decouple the excitonic effect from the lattice effect. In this system, we observe the narrow gap opening and the formation of a charge density wave without periodic lattice distortion, providing visualized evidence of exciton condensation occurring in thermal equilibrium. Our findings identify spontaneous interfacial charge transfer as a new strategy for developing novel excitonic insulators and investigating their correlated many-body physics.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Investigation of the Effect of Quantum Measurement on Parity-Time Symmetry

Symmetry, including the parity-time ($\mathcal{PT}$)-symmetry, is a striking topic, widely discussed and employed in many fields. It is well-known that quantum measurement can destroy or disturb quantum systems. However, can and how does quantum measurement destroy the symmetry of the measured system? To answer the pertinent question, we establish the correlation between the quantum measurement and Floquet $\mathcal{PT}$-symmetry and investigate for the first time how the measurement frequency and measurement strength affect the $\mathcal{PT}$-symmetry of the measured system using the $^{40}\mathrm{Ca}^{+}$ ion. It is already shown that the measurement at high frequencies would break the $\mathcal{PT}$ symmetry. Notably, even for an inadequately fast measurement frequency, if the measurement strength is sufficiently strong, the $\mathcal{PT}$ symmetry breaking can occur. The current work can enhance our knowledge of quantum measurement and symmetry and may inspire further research on the effect of quantum measurement on symmetry.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Revisiting the Evidence for an Intermediate-mass Black Hole in the Center of NGC 6624 with Simulations

The acceleration of LMXB 4U 1820-30 that derived from its orbital-period derivative $\dot P_{\rm b}$ was supposed to be the evidence for an Intermediate-mass Black Hole (IMBH) in the Galactic globular cluster (GC) NGC 6624. However, we find that the anomalous $\dot P_{\rm b}$ is mainly due to the gravitational wave emission, rather than the acceleration in cluster potential. Using the standard structure models of GCs, we simulate acceleration distributions for pulsars in the central region of the cluster. By fitting the acceleration of J1823-3021A with the simulated distribution profiles (maximum values), it is suggested that an IMBH with mass $M\gtrsim 950^{+550}_{-350}~M_{\odot}$ may reside in the cluster center. We further show that the second period derivative $\ddot P$ of J1823-3021A is probably due to the gravitational perturbation of a nearby star.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

RIBAC: Towards Robust and Imperceptible Backdoor Attack against Compact DNN

Recently backdoor attack has become an emerging threat to the security of deep neural network (DNN) models. To date, most of the existing studies focus on backdoor attack against the uncompressed model; while the vulnerability of compressed DNNs, which are widely used in the practical applications, is little exploited yet. In this paper, we propose to study and develop Robust and Imperceptible Backdoor Attack against Compact DNN models (RIBAC). By performing systematic analysis and exploration on the important design knobs, we propose a framework that can learn the proper trigger patterns, model parameters and pruning masks in an efficient way. Thereby achieving high trigger stealthiness, high attack success rate and high model efficiency simultaneously. Extensive evaluations across different datasets, including the test against the state-of-the-art defense mechanisms, demonstrate the high robustness, stealthiness and model efficiency of RIBAC. Code is available at https://github.com/huyvnphan/ECCV2022-RIBAC

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Self-Testing of a Single Quantum System: Theory and Experiment

Certifying individual quantum devices with minimal assumptions is crucial for the development of quantum technologies. Here, we investigate how to leverage single-system contextuality to realize self-testing. We develop a robust self-testing protocol based on the simplest contextuality witness for the simplest contextual quantum system, the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements (to an ideal configuration) as a function of the value of the witness under a pragmatic assumption on the measurements we call the KCBS orthogonality condition. We apply the method in an experiment with randomly chosen measurements on a single trapped $^{40}{\rm Ca}^+$ and near-perfect detection efficiency. The observed statistics allow us to self-test the system and provide the first experimental demonstration of quantum self-testing of a single system. Further, we quantify and report that deviations from our assumptions are minimal, an aspect previously overlooked by contextuality experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Enabling Fast and Universal Audio Adversarial Attack Using Generative Model

Recently, the vulnerability of DNN-based audio systems to adversarial attacks has obtained the increasing attention. However, the existing audio adversarial attacks allow the adversary to possess the entire user's audio input as well as granting sufficient time budget to generate the adversarial perturbations. These idealized assumptions, however, makes the existing audio adversarial attacks mostly impossible to be launched in a timely fashion in practice (e.g., playing unnoticeable adversarial perturbations along with user's streaming input). To overcome these limitations, in this paper we propose fast audio adversarial perturbation generator (FAPG), which uses generative model to generate adversarial perturbations for the audio input in a single forward pass, thereby drastically improving the perturbation generation speed. Built on the top of FAPG, we further propose universal audio adversarial perturbation generator (UAPG), a scheme crafting universal adversarial perturbation that can be imposed on arbitrary benign audio input to cause misclassification. Extensive experiments show that our proposed FAPG can achieve up to 167X speedup over the state-of-the-art audio adversarial attack methods. Also our proposed UAPG can generate universal adversarial perturbation that achieves much better attack performance than the state-of-the-art solutions.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Probing Dark Contents in Globular Clusters With Timing Effects of Pulsar Acceleration

We investigate pulsar timing residuals due to the coupling effect of the pulsar transverse acceleration and the R$\rm{\ddot{o}}$mer delay. The effect is relatively small and usually negligible. Only for pulsars in globular clusters, it is possibly important. The maximum residual amplitude, which is from the pulsar near the surface of the core of the cluster, is about tens nanoseconds, and may hardly be identified for most of the globular clusters currently. However, an intermediate-mass black hole in the centre of a cluster can increase apparently the timing residual magnitudes. Particularly for the pulsars in the innermost core region, their residual magnitudes may be significant. The high-magnitude residuals, which above critical lines of each cluster, are strong evidences for the presence of a black hole or dark remnants of comparable total mass in the centre of the cluster. We also explored the timing effects of line-of-sight accelerations for the pulsars. The distribution of measured line-of-sight accelerations are simulated with a Monte Carlo method. A two-dimensional Kolmogorov-Smirnov tests are performed to reexamine the consistency of distributions of the simulated and reported data for various values of parameters of the clusters. It is shown that the structure parameters of Terzan 5 can be well constrained by comparing the distribution of measured line-of-sight accelerations with the distributions from Monte Carlo simulations. We provide that the cluster has an upper limit on the central black hole/dark remnant mass of $ \sim 6000 M_{\odot} $.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Estimation of the Laser Frequency Nosie Spectrum by Continuous Dynamical Decoupling

Decoherence induced by the laser frequency noise is one of the most important obstacles in the quantum information processing. In order to suppress this decoherence, the noise power spectral density needs to be accurately characterized. In particular, the noise spectrum measurement based on the coherence characteristics of qubits would be a meaningful and still challenging method. Here, we theoretically analyze and experimentally obtain the spectrum of laser frequency noise based on the continuous dynamical decoupling technique. We first estimate the mixture-noise (including laser and magnetic noises) spectrum up to $(2π)$530 kHz by monitoring the transverse relaxation from an initial state $+X$, followed by a gradient descent data process protocol. Then the contribution from the laser noise is extracted by enconding the qubits on different Zeeman sublevels. We also investigate two sufficiently strong noise components by making an analogy between these noises and driving lasers whose linewidth assumed to be negligible. This method is verified experimentally and finally helps to characterize the noise.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

ISTD-GCN: Iterative Spatial-Temporal Diffusion Graph Convolutional Network for Traffic Speed Forecasting

Most of the existing algorithms for traffic speed forecasting split spatial features and temporal features to independent modules, and then associate information from both dimensions. However, features from spatial and temporal dimensions influence mutually, separated extractions isolate such dependencies, and might lead to inaccurate results. In this paper, we incorporate the perspective of information diffusion to model spatial features and temporal features synchronously. Intuitively, vertices not only diffuse information to the neighborhood but also to the subsequent state along with the temporal dimension. Therefore, we can model such heterogeneous spatial-temporal structures as a homogeneous process of diffusion. On this basis, we propose an Iterative Spatial-Temporal Diffusion Graph Convolutional Network (ISTD-GCN) to extract spatial and temporal features synchronously, thus dependencies between both dimensions can be better modeled. Experiments on two traffic datasets illustrate that our ISTD-GCN outperforms 10 baselines in traffic speed forecasting tasks. The source code is available at https://github.com/Anonymous.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

PERMDNN: Efficient Compressed DNN Architecture with Permuted Diagonal Matrices

Deep neural network (DNN) has emerged as the most important and popular artificial intelligent (AI) technique. The growth of model size poses a key energy efficiency challenge for the underlying computing platform. Thus, model compression becomes a crucial problem. However, the current approaches are limited by various drawbacks. Specifically, network sparsification approach suffers from irregularity, heuristic nature and large indexing overhead. On the other hand, the recent structured matrix-based approach (i.e., CirCNN) is limited by the relatively complex arithmetic computation (i.e., FFT), less flexible compression ratio, and its inability to fully utilize input sparsity. To address these drawbacks, this paper proposes PermDNN, a novel approach to generate and execute hardware-friendly structured sparse DNN models using permuted diagonal matrices. Compared with unstructured sparsification approach, PermDNN eliminates the drawbacks of indexing overhead, non-heuristic compression effects and time-consuming retraining. Compared with circulant structure-imposing approach, PermDNN enjoys the benefits of higher reduction in computational complexity, flexible compression ratio, simple arithmetic computation and full utilization of input sparsity. We propose PermDNN architecture, a multi-processing element (PE) fully-connected (FC) layer-targeted computing engine. The entire architecture is highly scalable and flexible, and hence it can support the needs of different applications with different model configurations. We implement a 32-PE design using CMOS 28nm technology. Compared with EIE, PermDNN achieves 3.3x~4.8x higher throughout, 5.9x~8.5x better area efficiency and 2.8x~4.0x better energy efficiency on different workloads. Compared with CirCNN, PermDNN achieves 11.51x higher throughput and 3.89x better energy efficiency.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Real-time, Universal, and Robust Adversarial Attacks Against Speaker Recognition Systems

As the popularity of voice user interface (VUI) exploded in recent years, speaker recognition system has emerged as an important medium of identifying a speaker in many security-required applications and services. In this paper, we propose the first real-time, universal, and robust adversarial attack against the state-of-the-art deep neural network (DNN) based speaker recognition system. Through adding an audio-agnostic universal perturbation on arbitrary enrolled speaker's voice input, the DNN-based speaker recognition system would identify the speaker as any target (i.e., adversary-desired) speaker label. In addition, we improve the robustness of our attack by modeling the sound distortions caused by the physical over-the-air propagation through estimating room impulse response (RIR). Experiment using a public dataset of 109 English speakers demonstrates the effectiveness and robustness of our proposed attack with a high attack success rate of over 90%. The attack launching time also achieves a 100X speedup over contemporary non-universal attacks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The Timing Residual Patterns Due to Pulsar Acceleration

The form of timing residuals due to errors in pulsar spin period $P$ and its derivative $\dot{P}$, in positions, as well as in proper motions, have been well presented for decades in the literature. However, the residual patterns due to errors in the pulsar acceleration have not been reported previously, while a pulsar in the galaxy or a globular cluster (GC) will be unavoidably accelerated. The coupling effect of the pulsar transverse acceleration and the R$\rm{\ddot{o}}$mer delay on timing residuals are simulated in this work. The results show that the residual due to the effect can be identified by the oscillation envelopes of the residuals. It is also shown that the amplitude of the residual due to the effect is usually relatively small, however, it may probably be observable for pulsars distributing in the vicinity of the core of a nearby GC.

0 citations0 reviewsNo code linkedOpen access
preprint2018arXiv

Sutured Manifolds and Polynomial Invariants from Higher Rank Bundles

For each integer $N\geq 2$, Mariño and Moore defined generalized Donaldson invariants by the methods of quantum field theory, and made predictions about the values of these invariants. Subsequently, Kronheimer gave a rigorous definition of generalized Donaldson invariants using the moduli spaces of anti-self-dual connections on hermitian vector bundles of rank $N$. In this paper, Mariño and Moore's predictions are confirmed for simply connected elliptic surfaces without multiple fibers and certain surfaces of general type in the case that $N=3$. The primary motivation is to study 3-manifold instanton Floer homologies which are defined by higher rank bundles. In particular, the computation of the generalized Donaldson invariants are exploited to define a Floer homology theory for sutured 3-manifolds.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Influence of the Ion Coordination Number on Cation Exchange Reactions with Copper Telluride Nanocrystals

Cu2-xTe nanocubes were used as starting seeds to access metal telluride nanocrystals by cation exchanges at room temperature. The coordination number of the entering cations was found to play an important role in dictating the reaction pathways. The exchanges with tetrahedrally coordinated cations (i.e. with coordination number 4), such as Cd2+ or Hg2+, yielded monocrystalline CdTe or HgTe nanocrystals with Cu2-xTe/CdTe or Cu2-xTe/HgTe Janus-like heterostructures as intermediates. The formation of Janus-like architectures was attributed to the high diffusion rate of the relatively small tetrahedrally coordinated cations, which could rapidly diffuse in the Cu2-xTe NCs and nucleate the CdTe (or HgTe) phase in a preferred region of the host structure. Also, with both Cd2+ and Hg2+ ions the exchange led to wurtzite CdTe and HgTe phases rather than the more stable zinc-blende ones, indicating that the anion framework of the starting Cu2- xTe particles could be more easily deformed to match the anion framework of the metastable wurtzite structures. As hexagonal HgTe had never been reported to date, this represents another case of metastable new phases that can only be accessed by cation exchange. On the other hand, the exchanges involving octahedrally coordinated ions (i.e. with coordination number 6), such as Pb2+ or Sn2+, yielded rock-salt polycrystalline PbTe or SnTe nanocrystals with Cu2-xTe@PbTe or Cu2-xTe@SnTe core@shell architectures at the early stages of the exchange process. In this case, the octahedrally coordinated ions are probably too large to diffuse easily through the Cu2-xTe structure: their limited diffusion rate restricts their initial reaction to the surface of the nanocrystals, where cation exchange is initiated unselectively, leading to core@shell architectures.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Strong field gravitational lensing by a charged Galileon black hole

Strong field gravitational lensings are dramatically disparate from those in the weak field by representing relativistic images due to light winds one to infinity loops around a lens before escaping. We study such a lensing caused by a charged Galileon black hole, which is expected to have possibility to evade no-hair theorem. We calculate the angular separations and time delays between different relativistic images of the charged Galileon black hole. All these observables can potentially be used to discriminate a charged Galileon black hole from others. We estimate the magnitudes of these observables for the closest supermassive black hole Sgr A*. The strong field lensing observables of the charged Galileon black hole can be close to those of a tidal Reissner-Nordström black hole or those of a Reissner-Nordström black hole. It will be helpful to distinguish these black holes if we can separate the outermost relativistic images and determine their angular separation, brightness difference and time delay, although it requires techniques beyond the current limit.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Strong gravitational field time delay for photons coupled to Weyl tensor in a Schwarzschild black hole

We analyse strong gravitational field time delay for photons coupled to the Weyl tensor in a Schwarzschild black hole. By making use of the method of strong deflection limit, we find that these time delays between relativistic images are significantly affected by polarization directions of such a coupling. A practical problem about determination of the polarization direction by observations is investigated. It is found that if the first and second relativistic images can be resolved, the measurement of time delay can more effectively improve detectability of the polarization direction.

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preprint2016arXiv

Understanding the residual patterns of timing solutions of radio pulsars with a model of magnetic field oscillation

We explain some phenomena existing generally in the timing residuals: amplitude and sign of the second derivative of a pulsar's spin-frequency ($\ddotν$), some sophisticated residual patterns, which also change with the time span of data segments. The sample is taken from Hobbs et al.\,(2010), in which the pulsar's spin-frequency and its first derivative have been subtracted from the timing solution fitting. We first classify the timing residual patterns into different types based on the sign of $\ddotν$. Then we use the magnetic field oscillation model developed in our group \citep{zhang12a} to fit successfully the different kinds of timing residuals with the Markov Chain Monte Carlo method. Finally, we simulate the spin evolution over 20 years for a pulsar with typical parameters and analyze the data with the conventional timing solution fitting. By choosing different segments of the simulated data, we find that most of the observed residual patterns can be reproduced successfully. This is the first time that the observed residual patterns are fitted by a model and reproduced by simulations with very few parameters. From the distribution of the different residual patterns in the $P-\dot P$ diagram, we argue that (1) a single magnetic field oscillation mode exists commonly in all pulsars throughout their lifetimes; (2) there may be a transition period over the lifetimes of pulsars, in which multiple magnetic field oscillation modes exist.

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preprint2015arXiv

Improved upper bounds on Kaluza-Klein gravity with current Solar System experiments and observations

As an extension of previous works on classical tests of Kaluza-Klein (KK) gravity and as an attempt to find more stringent constraints on this theory, its effects on physical experiments and astronomical observations conducted in the Solar System are studied. We investigate the gravitational time delay at inferior conjunction caused by KK gravity, and use new Solar System ephemerides and the observation of \textit{Cassini} to strengthen constraints on KK gravity by up to two orders of magnitude. These improved upper bounds mean that the fifth-dimensional space in the soliton case is a very flat extra dimension in the Solar System, even in the vicinity of the Sun.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Modeling the evolution and distribution of the frequency's second derivative and the braking index of pulsar spin

We model the evolution of the spin frequency's second derivative $\ddotν$ and the braking index $n$ of radio pulsars with simulations within the phenomenological model of their surface magnetic field evolution, which contains a long-term power-law decay modulated by short-term oscillations. For the pulsar PSR B0329+54, a model with three oscillation components can reproduce its $\ddotν$ variation. We show that the "averaged" $n$ is different from the instantaneous $n$, and its oscillation magnitude decreases abruptly as the time span increases, due to the "averaging" effect. The simulated timing residuals agree with the main features of the reported data. Our model predicts that the averaged $\ddotν$ of PSR B0329+54 will start to decrease rapidly with newer data beyond those used in Hobbs et al.. We further perform Monte Carlo simulations for the distribution of the reported data in $|\ddotν|$ and $|n|$ versus characteristic age $τ_{\rm c}$ diagrams. It is found that the magnetic field oscillation model with decay index $α=0$ can reproduce the distributions quite well. Compared with magnetic field decay due to the ambipolar diffusion ($α=0.5$) and the Hall cascade ($α=1.0$), the model with no long term decay ($α=0$) is clearly preferred for old pulsars by the p-values of the two-dimensional Kolmogorov-Smirnov test.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Astronomical relativistic reference systems with multipolar expansion: the global one

With rapid development of techniques for astronomical observations, the precision of measurements has been significantly increasing. Theories of astronomical relativistic reference systems, which are the foundation for processing and interpreting these data now and in the future, may require extensions to satisfy the needs of these trends. Besides building a framework compatible with alternative theories of gravity and the pursuit of higher order post-Newtonian approximation, it will also be necessary to make the first order post-Newtonian multipole moments of celestial bodies be explicitly expressed in the astronomical relativistic reference systems. This will bring some convenience into modeling the observations and experiments and make it easier to distinguish different contributions in measurements. As the first step, the global solar system reference system is multipolarly expanded and the post-Newtonian mass and spin moments are shown explicitly in the metric which describes the coordinates of the system. The full expression of the global metric is given.

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preprint2014arXiv

Interpreting the Spin-down Evolutions of Isolated Neutron Stars with Hall Effects

The observed long-term spin-down evolution of isolated radio pulsars cannot be explained by the standard magnetic dipole radiation with a constant braking torque. However, how and why the torque varies still remains controversial, which is a major issue in understanding neutron stars. Many pulsars have been observed with significant long-term changes of their spin-down rates modulated by quasi-periodic oscillations. Applying the phenomenological model of pulsar timing noise we developed recently to the observed precise pulsar timing data of isolated neutron stars, here we show that the observed long-term evolutions of their spin-down rates and quasi-periodic modulations can be explained by Hall effects in their crusts. Therefore the evolution of their crustal magnetic fields, rather than that in their cores, dominates the observed long term spin-down evolution of these young pulsars. Understanding of the nature of pulsar timing noise not only reveals the interior physics of neutron stars, but also allows physical modeling of pulsar spin-down and thus improves the sensitivity of gravitational wave detections with pulsars.

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preprint2014arXiv

On the (im)possibility of testing new physics in exoplanets using transit timing variations: deviation from inverse-square law of gravity

Ground-based and space-borne observatories studying exoplanetary transits now and in the future will considerably increase the number of known exoplanets and the precision of the measured times of transit minima. Variations in the transit times can not only be used to infer the presence of additional planets, but might also provide opportunities for testing new physics in the places beyond the Solar system. In this work, we take deviation from the inverse-square law of gravity as an example, focus on the fifth-force-like Yukawa-type correction to the Newtonian gravitational force which parameterizes this deviation, investigate its effects on the secular transit timing variations and analyze their observability in exoplanetary systems. It is found that the most optimistic values of Yukawa-type secular transit timing variations are at the level of $\sim 0.1$ seconds per year. Those values unfortunately appear only in rarely unique cases and, most importantly, they are still at least two orders of magnitude below the current capabilities of observations. Such a deviation from the inverse-square law of gravity is likely too small to detect for the foreseeable future. Meanwhile, systematic uncertainties, such as the presence of additional and unknown planets, will likely be exceptionally difficult to remove from a signal that should be seen.

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preprint2014arXiv

Rotational Behaviors and Magnetic Field Evolution of Radio Pulsars

The observed long-term spin-down evolution of isolated radio pulsars cannot be explained by the standard magnetic dipole radiation with a constant braking torque. However how and why the torque varies still remains controversial, which is an outstanding problem in our understanding of neutron stars. We have constructed a phenomenological model of the evolution of surface magnetic fields of pulsars, which contains a long-term decay modulated by short-term oscillations; a pulsar's spin is thus modified by its magnetic field evolution. The predictions of this model agree with the precisely measured spin evolutions of several individual pulsars; the derived parameters suggest that the Hall drift and Hall waves in the NS crusts are probably responsible for the long-term change and short-term quasi-periodical oscillations, respectively. Many statistical properties of the timing noise of pulsars can be well re-produced with this model, including correlations and the distributions of the observed braking indices of the pulsars, which span over a range of more than 100 millions. We have also presented a phenomenological model for the recovery processes of classical and slow glitches, which can successfully model the observed slow and classical glitch events without biases.

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preprint2013arXiv

$f(T)$ gravity: effects on astronomical observation and Solar System experiments and upper-bounds

As an extension of a previous work in which perihelion advances are considered only and as an attempt to find more stringent constraints on its parameters, we investigate effects on astronomical observation and experiments conducted in the Solar System due to the $f(T)$ gravity which contains a quadratic correction of $αT^2$ ($α$ is a model parameter) and the cosmological constant $Λ$. Using a spherical solution describing the Sun's gravitational field, the resulting secular evolution of planetary orbital motions, light deflection, gravitational time delay and frequency shift are calculated up to the leading contribution. Among them, we find qualitatively that the light deflection holds a unique bound on $α$, without dependence on $Λ$, and the time delay experiments during inferior conjunction impose a clean constraint on $Λ$, regardless of $α$. Based on observation and experiments, especially the supplementary advances in the perihelia provided by the INPOP10a ephemeris, we obtain the upper-bounds quantitatively: $|α| \le 1.2 \times 10^{2}$ m${}^2$ and $ |Λ| \le 1.8 \times 10^{-43}$ m${}^{-2}$, at least 10 times tighter than the previous result.

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preprint2013arXiv

Aberration in proper motions for stars in our Galaxy

Accelerations of both the solar system barycenter (SSB) and stars in the Milky Way cause a systematic observational effect on the stellar proper motions, which was first studied in the early 1990s and developed by J. Kovalevsky (aberration in proper motions, 2003, A&A, 404, 743). This paper intends to extend that work and aims to estimate the magnitude and significance of the aberration in proper motions of stars, especially in the region near the Galactic center. We adopt two models for the Galactic rotation curve to evaluate the aberrational effect on the Galactic plane. Based on the theoretical developments, we show that the effect of aberration in proper motions depends on the galactocentric distance of stars; it is dominated by the acceleration of stars in the central region of the Galaxy. Within 200 pc from the Galactic center, the systematic proper motion can reach an amplitude larger than 1000 uas/yr by applying a flat rotation curve. With a more realistic rotation curve which is linearly rising in the core region of the Galaxy, the aberrational proper motions are limited up to about 150 uas/yr. Then we investigate the applicability of the theoretical expressions concerning the aberrational proper motions, especially for those stars with short period orbits. If the orbital period of stars is only a fraction of the light time from the star to the SSB, the expression proposed by Kovalevsky is not appropriate. With a more suitable formulation, we found that the aberration has no effect on the determination of the stellar orbits on the celestial sphere. The aberrational effect under consideration is small but not negligible with high-accurate astrometry in the future, particularly in constructing the Gaia celestial reference system realized by Galactic stars.

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preprint2013arXiv

Modeling the Evolution and Distribution of the Frequency's Second Derivative and Braking Index of Pulsar Spin with Simulations

We model the evolution of spin frequency's second derivative $\ddotν$ and braking index $n$ of radio pulsars with simulations within the phenomenological model of their surface magnetic field evolution, which contains a long-term decay modulated by short-term oscillations. For the pulsar PSR B0329+54, the model can reproduce the main characteristics of its $\ddotν$ variation with oscillation periods, predicts another $\sim 50$ yr oscillation component and another recent swing of the sign of $\ddotν$. We show that the "averaged" $n$ is different from the instantaneous $n$, and its oscillation magnitude decreases abruptly as the time span increases, due to the "averaging" effect. The simulation predicted timing residuals agree with the main features of the reported data. We further perform Monte Carlo simulations for the distribution of the reported data in $|\ddotν|$ versus characteristic age $τ_{\rm c}$ diagram. The model with a power law index $α=0.5$ can reproduce the slope of the linear fit to pulsars' distributions in the diagrams of $\log|\ddotν|-\logτ_{\rm c}$ and $\log|n|-\logτ_{\rm c}$, but the oscillations are responsible for the almost equal number of positive and negative values of $\ddotν$, in agreement with our previous analytical studies; an oscillation period of about several decades is also preferred. However the range of the oscillation amplitudes is $-11.4\lesssim\log f\lesssim-10.2$, slightly lager than the analytical prediction, $\log f\simeq-11.85$, because the "averaging" effect was not included previously.

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preprint2013arXiv

On the Relaxation Behaviors of Slow and Classical Glitches: Observational Biases and Their Opposite Recovery Trends

We study the pulsar timing properties and the data analysis methods during glitch recoveries. In some cases one first fits the time-of-arrivals (TOAs) to obtain the "time-averaged" frequency $ν$ and its first derivative $\dotν$, and then fits models to them. However, our simulations show that $ν$ and $\dotν$ obtained this way are systematically biased, unless the time intervals between the nearby data points of TOAs are smaller than about $10^4$ s, which is much shorter than typical observation intervals. Alternatively, glitch parameters can be obtained by fitting the phases directly with relatively smaller biases; but the initial recovery timescale is usually chosen by eyes, which may introduce a strong bias. We also construct a phenomenological model by assuming a pulsar's spin-down law of $\dotνν^{-3} =-H_0 G(t)$ with $G(t)=1+κe^{-t/τ}$ for a glitch recovery, where $H_0$ is a constant and $κ$ and $τ$ are the glitch parameters to be found. This model can reproduce the observed data of slow glitches from B1822--09 and a giant classical glitch of B2334+61, with $κ<0$ or $κ>0$, respectively. We then use this model to simulate TOA data and test several fitting procedures for a glitch recovery. The best procedure is: 1) use a very high order polynomial (e.g. to 50th order) to precisely describe the phase; 2) then obtain $ν(t)$ and $\dotν(t)$ from the polynomial; and 3) the glitch parameters are obtained from $ν(t)$ or $\dotν(t)$. Finally, the uncertainty in the starting time $t_0$ of a classical glitch causes uncertainties to some glitch parameters, but less so to a slow glitch and $t_0$ of which can be determined from data.

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preprint2013arXiv

Spacecraft Doppler tracking with possible violations of LLI and LPI: a theoretical modeling

Currently two-way and three-way spacecraft Doppler tracking techniques are widely used and playing important roles in control and navigation for deep space missions. Starting from one-way Doppler model, we extend the models of two-way and three-way Doppler by making them include possible violations of the local Lorentz invariance (LLI) and the local position invariance (LPI) in order to test the Einstein equivalence principle which is the cornerstone of general relativity and all other metric theories of gravity. After taking the finite speed of light into account, which is so-called light-time solution (LTS), we have these models depending on the time of reception of the signal only for practical convenience. We find that possible violations of LLI and LPI can not affect two-way Doppler under linear approximation of LTS although this approximation is sufficiently good for most cases in the solar system. We also show that, in three-way Doppler, possible violations of LLI and LPI associate with two stations only, which suggests that it is better to set the stations at places with significant differences in velocities and gravitational potentials to obtain high level of sensitivity for tests.

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preprint2013arXiv

Yukawa effects on the clock onboard a drag-free satellite

The Yukawa correction to the Newtonian gravitational force is accepted as a parameterization of deviations from the inverse-square law of gravity which might be caused by new physics beyond the standard model of particles and the general theory of relativity. We investigate these effects on the clock onboard a drag-free satellite: dynamics of the satellite and influence on the time transfer link. We find the Yukawa signal in the time transfer is much harder to detect with current state of clocks than those effects on the dynamics, especially the secular change of periastron, by laser ranging in the case of an artificial Earth satellite carrying a frequency standard with an orbit of $a=10^7$\,m and $e=0.01$.

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preprint2012arXiv

2PN Light Propagation in the Scalar-Tensor Theory: an $N$-Point-Masses Case

Within the framework of the scalar-tensor theory (STT), its second post-Newtonian (2PN) approximation is obtained with Chandrasekhar's approach. By focusing on an $N$-point-masses system as the first step, we reduce the metric to its 2PN form for light propagation. Unlike previous works, at 2PN order, we abandon the hierarchized hypothesis and do not assume two parametrized post-Newtonian (PPN) parameters $γ$ and $β$ to be unity. We find that although there exist $γ$ and $β$ in the 2PN metric, only $γ$ appears in the 2PN equations of light. As a simple example for applications, a gauge-invariant angle between the directions of two incoming photons for a differential measurement is investigated after the light trajectory is solved in a static and spherically symmetric spacetime. It shows the deviation from the general relativity (GR) $δθ_{\mathrm{STT}}$ does \emph{not} depend on $β$ even at 2PN level in this circumstance, which is consistent with previous results. A more complicated application is light deflection in a 2-point-masses system. We consider a case that the light propagation time is much less than the time scale of its orbital motion and thus treat it as a static system. The 2-body effect at 2PN level originating from relaxing the hierarchized hypothesis is calculated. Our analysis shows the 2PN 2-body effect in the Solar System is one order of magnitude less than future $\sim 1$ nas experiments, while this effect could be comparable with 1PN component of $δθ_{\mathrm{STT}}$ in a binary system with two Sun-like stars and separation by $\sim 0.1$ AU if an experiment would be able to measure $γ-1$ down to $\sim 10^{-6}$.

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preprint2012arXiv

Modeling pulsar time noise with long term power law decay modulated by short term oscillations of the magnetic fields of neutron stars

We model the evolution of the magnetic fields of neutron stars as consisting of a long term power-law decay modulated by short term small amplitude oscillations. Our model predictions on the timing noise $\ddotν$ of neutron stars agree well with the observed statistical properties and correlations of normal radio pulsars. Fitting the model predictions to the observed data, we found that their initial parameter implies their initial surface magnetic dipole magnetic field strength ~ 5E14 G at ~0.4 year old and that the oscillations have amplitude between E-8 to E-5 and period on the order of years. For individual pulsars our model can effectively reduce their timing residuals, thus offering the potential of more sensitive detections of gravitational waves with pulsar timing arrays. Finally our model can also re-produce their observed correlation and oscillations of the second derivative of spin frequency, as well as the "slow glitch" phenomenon.

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preprint2012arXiv

Progenitors of Magnetars and Hyperaccreting Magnetized Disks

We propose that a magnetar could be formed during the core collapse of massive stars or coalescence of two normal neutron stars, through collecting and inheriting the magnetic fields magnified by hyperaccreting disk. After the magnetar is born, its dipole magnetic fields in turn have a major influence on the following accretion. The decay of its toroidal field can fuel the persistent X-ray luminosity of either an SGR or AXP; however the decay of only the poloidal field is insufficient to do so.

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preprint2012arXiv

Testing Lorentz violation with binary pulsars: constraints on standard model extension

Under the standard model extension (SME) framework, Lorentz invariance is tested in five binary pulsars: PSR J0737-3039, PSR B1534+12, PSR J1756-2251, PSR B1913+16 and PSR B2127+11C. By analyzing the advance of periastron, we obtain the constraints on a dimensionless combination of SME parameters that is sensitive to timing observations. The results imply no evidence for the break of Lorentz invariance at $10^{-10}$ level, one order of magnitude larger than previous estimation.

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preprint2012arXiv

Testing Models of Magnetic Field Evolution of Neutron Stars with the Statistical Properties of Their Spin Evolutions

We test models for the evolution of neutron star (NS) magnetic fields (B). Our model for the evolution of the NS spin is taken from an analysis of pulsar timing noise presented by Hobbs et al. (2010). We first test the standard model of a pulsar's magnetosphere in which B does not change with time and magnetic dipole radiation is assumed to dominate the pulsar's spin-down. We find this model fails to predict both the magnitudes and signs of the second derivatives of the spin frequencies ($\ddotν$). We then construct a phenomenological model of the evolution of $B$, which contains a long term decay (LTD) modulated by short term oscillations (STO); a pulsar's spin is thus modified by its B-evolution. We find that an exponential LTD is not favored by the observed statistical properties of $\ddotν$ for young pulsars and fails to explain the fact that $\ddotν$ is negative for roughly half of the old pulsars. A simple power-law LTD can explain all the observed statistical properties of $\ddotν$. Finally we discuss some physical implications of our results to models of the B-decay of NSs and suggest reliable determination of the true ages of many young NSs is needed, in order to constrain further the physical mechanisms of their B-decay. Our model can be further tested with the measured evolutions of $\dotν$ and $\ddotν$ for an individual pulsar; the decay index, oscillation amplitude and period can also be determined this way for the pulsar.

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preprint2012arXiv

Why do the braking indices of pulsars span a range of more than 100 millions?

Here we report that the observed braking indices of the 366 pulsars in the sample of Hobbs et al. range from about $-10^8$ to about $+10^8$ and are significantly correlated with their characteristic ages. Using the model of magnetic field evolution we developed previously based on the same data, we derived an analytical expression for the braking index, which agrees with all the observed statistical properties of the braking indices of the pulsars in the sample of Hobbs et al. Our model is, however, incompatible with the previous interpretation that magnetic field growth is responsible for the small values of braking indices ($<3$) observed for "baby" pulsars with characteristic ages of less than $2\times 10^3$ yr. We find that the "instantaneous" braking index of a pulsar may be different from the "averaged" braking index obtained from fitting the data over a certain time span. The close match between our model-predicted "instantaneous" braking indices and the observed "averaged" braking indices suggests that the time spans used previously are usually smaller than or comparable to their magnetic field oscillation periods. Our model can be tested with the existing data, by calculating the braking index as a function of the time span for each pulsar. In doing so, one can obtain for each pulsar all the parameters in our magnetic field evolution model, and may be able to improve the sensitivity of using pulsars to detect gravitational waves.

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preprint2011arXiv

Magnetic Field Decay Makes Neutron Stars Look Older Than They Are

It is commonly accepted that a neutron star is produced, when a massive star exhausts its nuclear fuel and ends its life in a core-collapse supernova explosion. This scenario is confirmed by the detection of pulsars, which are believed to be rapidly spinning neutron stars, in the central regions of many supernova remnants. Neutron stars and their associated supernova remnants should therefore have the same ages. As expected, the age of the Crab Pulsar, the first to be connected with a supernova remnant (the Crab Nebula), can be inferred from its current spin period and its derivative and indeed has about the same age of the supernova remnant, that was produced from a historically recorded supernova explosion in 1054. However most neutron stars appear to be much older than the ages of their associated supernova remnants, a puzzle not yet understood. Another puzzle is that so far no convincing evidence has been found in favor of magnetic field decay in neutron stars, that is predicted in most models of neutron stars. Here we show convincing evidence of magnetic field decay in some young neutron stars, and that the magnetic field decay can alter their spinning behaviors significantly such that these neutron stars appear much older than they really are.

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preprint2011arXiv

Power-law Magnetic Field Decay and Constant Core Temperatures of Magnetars, Normal and Millisecond Pulsars

The observed correlations, between the characteristic ages and dipole surface magnetic field strengths of all pulsars, can be well explained by magnetic field decay with core temperatures of $~2\times10^{8}$ K, $\sim2\times10^{7}$ K, and $\sim10^{5}$ K, for magnetars, normal radio pulsars, and millisecond pulsars, respectively; assuming that their characteristic ages are about two orders of magnitude larger than their true ages, the required core temperatures may be reduced by about a factor of 10. The magnetic decay follows a power-law and is dominated by the solenoidal component of the ambipolar diffusion mode. In this model, all NSs are assumed to have the same initial magnetic field strength, but different core temperature which do not change as the magnetic field decays. This suggests that the key distinguishing property between magnetars and normal pulsars is that magnetars were born much hotter than normal pulsars, and thus have much longer magnetic field decay time scales, resulting in higher surface magnetic field strength even with the same ages of normal pulsars. The above conclusion agrees well with the observed correlations between the surface temperatures of magnetars and other young NSs, which do not agree with the cooling dominated evolution of neutron stars. This suggests a possible scenario that heating, perhaps due to magnetic field decay, balances neutron star cooling for observed pulsars.

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preprint2010arXiv

Resurvey of order and chaos in spinning compact binaries

This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or initial condition cannot be found in general. Chaos does not depend only on the mass ratio, and the maximal spins do not necessarily bring the strongest effect of chaos. Additionally, chaos does not always become drastic when the initial spin vectors are nearly perpendicular to the orbital plane, and the alignment of spins cannot trigger chaos by itself.

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preprint2010arXiv

Revisit on "Ruling out chaos in compact binary systems"

Full general relativity requires that chaos indicators should be invariant in various spacetime coordinate systems for a given relativistic dynamical problem. On the basis of this point, we calculate the invariant Lyapunov exponents (LEs) for one of the spinning compact binaries in the conservative second post-Newtonian (2PN) Lagrangian formulation without the dissipative effects of gravitational radiation, using the two-nearby-orbits method with projection operations and with coordinate time as an independent variable. It is found that the actual source leading to zero LEs in one paper [J. D. Schnittman and F. A. Rasio, Phys. Rev. Lett. 87, 121101 (2001)] but to positive LEs in the other [N. J. Cornish and J. Levin, Phys. Rev. Lett. 89, 179001 (2002)] does not mainly depend on rescaling, but is due to two slightly different treatments of the LEs. It takes much more CPU time to obtain the stabilizing limit values as reliable values of LEs for the former than to get the slopes (equal to LEs) of the fit lines for the latter. Due to coalescence of some of the black holes, the LEs from the former are not an adaptive indicator of chaos for comparable mass compact binaries. In this case, the invariant fast Lyapunov indicator (FLI) of two-nearby orbits, as a very sensitive tool to distinguish chaos from order, is worth recommending. As a result, we do again find chaos in the 2PN approximation through different ratios of FLIs varying with time. Chaos cannot indeed be ruled out in real binaries.

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preprint2010arXiv

Symplectic structure of post-Newtonian Hamiltonian for spinning compact binaries

The phase space of a Hamiltonian system is symplectic. However, the post-Newtonian Hamiltonian formulation of spinning compact binaries in existing publications does not have this property, when position, momentum and spin variables $[X, P, S_1, S_2]$ compose its phase space. This may give a convenient application of perturbation theory to the derivation of the post-Newtonian formulation, but also makes classic theories of a symplectic Hamiltonian system be a serious obstacle in application, especially in diagnosing integrability and nonintegrability from a dynamical system theory perspective. To completely understand the dynamical characteristic of the integrability or nonintegrability for the binary system, we construct a set of conjugate spin variables and reexpress the spin Hamiltonian part so as to make the complete Hamiltonian formulation symplectic. As a result, it is directly shown with the least number of independent isolating integrals that a conservative Hamiltonian compact binary system with both one spin and the pure orbital part to any post-Newtonian order is typically integrable and not chaotic. And conservative binary system consisting of two spins restricted to the leading order spin-orbit interaction and the pure orbital part at all post-Newtonian orders is also integrable, independently on the mass ratio. For all other various spinning cases, the onset of chaos is possible.

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