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Qing Gao

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Published work

25 published item(s)

preprint2026arXiv

DScheLLM: Enabling Dynamic Scheduling through a Fine-Tuned Dual-System Large language Model

Production scheduling is highly susceptible to dynamic disruptions, such as variations in processing times, machine availability, and unexpected task insertions. Conventional approaches typically rely on event-specific models and explicit analytical formulations, which limits their adaptability and generalization across previously unseen disturbances. To overcome these limitations, this paper proposes DScheLLM, a dynamic scheduling approach that leverages fine-tuned large language models within a dual-system (fast-slow) reasoning architecture to address disturbances of different scales. A unified large language model-based framework is constructed to handle dynamic events, where training datasets for both fast and slow reasoning modes are generated using exact schedules obtained from an operations research solver. The Huawei OpenPangu Embedded-7B model is subsequently fine-tuned under the hybrid reasoning paradigms using LoRA. Experimental evaluations on standard job shop scheduling benchmarks demonstrate that the fast-thinking mode can efficiently generate high-quality schedules and the slow-thinking mode can produce solver-compatible and well-formatted decision inputs. To the best of our knowledge, this work represents one of the earliest studies applying large language models to job shop scheduling in dynamic environments, highlighting their considerable potential for intelligent and adaptive scheduling optimization.

preprint2026arXiv

Triple Spectral Fusion for Sensor-based Human Activity Recognition

The field of sensor-based human activity recognition (HAR) mainly uses posture, motion and context data of Inertial Measurement Units (IMUs) to identify daily activities. Despite the advancements in learning-based methods, it is challenging to perform information fusion from the temporal perspective due to the complexities in fusing heterogeneous sensor data and establishing long-term context correlations. This paper proposes a novel triple spectral fusion framework tailored for HAR. First, we develop an adaptive complementary filtering technique for noise suppression and organize each IMU's sensors into posture and motion modality nodes. Given that IMU nodes form a dynamic heterogeneous graph, we then apply adaptive filtering within the graph Fourier domain to merge both homogeneous and heterogeneous node information. Furthermore, an adaptive wavelet frequency selection approach is implemented to suppress context redundancy and shorten the length of features. This approach enhances both timestamp-based graph aggregation and the correlation of long-term contexts. Our framework uses adaptive filtering in the Fourier, graph Fourier, and wavelet domains, enabling effective multi-sensor fusion and context correlation. Extensive experiments on ten benchmark datasets demonstrate the superior performance of our framework. Project page: https://github.com/crocodilegogogo/TSF-TPAMI2026.

preprint2024arXiv

D3PRefiner: A Diffusion-based Denoise Method for 3D Human Pose Refinement

Three-dimensional (3D) human pose estimation using a monocular camera has gained increasing attention due to its ease of implementation and the abundance of data available from daily life. However, owing to the inherent depth ambiguity in images, the accuracy of existing monocular camera-based 3D pose estimation methods remains unsatisfactory, and the estimated 3D poses usually include much noise. By observing the histogram of this noise, we find each dimension of the noise follows a certain distribution, which indicates the possibility for a neural network to learn the mapping between noisy poses and ground truth poses. In this work, in order to obtain more accurate 3D poses, a Diffusion-based 3D Pose Refiner (D3PRefiner) is proposed to refine the output of any existing 3D pose estimator. We first introduce a conditional multivariate Gaussian distribution to model the distribution of noisy 3D poses, using paired 2D poses and noisy 3D poses as conditions to achieve greater accuracy. Additionally, we leverage the architecture of current diffusion models to convert the distribution of noisy 3D poses into ground truth 3D poses. To evaluate the effectiveness of the proposed method, two state-of-the-art sequence-to-sequence 3D pose estimators are used as basic 3D pose estimation models, and the proposed method is evaluated on different types of 2D poses and different lengths of the input sequence. Experimental results demonstrate the proposed architecture can significantly improve the performance of current sequence-to-sequence 3D pose estimators, with a reduction of at least 10.3% in the mean per joint position error (MPJPE) and at least 11.0% in the Procrustes MPJPE (P-MPJPE).

preprint2022arXiv

Deep Depth Completion from Extremely Sparse Data: A Survey

Depth completion aims at predicting dense pixel-wise depth from an extremely sparse map captured from a depth sensor, e.g., LiDARs. It plays an essential role in various applications such as autonomous driving, 3D reconstruction, augmented reality, and robot navigation. Recent successes on the task have been demonstrated and dominated by deep learning based solutions. In this article, for the first time, we provide a comprehensive literature review that helps readers better grasp the research trends and clearly understand the current advances. We investigate the related studies from the design aspects of network architectures, loss functions, benchmark datasets, and learning strategies with a proposal of a novel taxonomy that categorizes existing methods. Besides, we present a quantitative comparison of model performance on three widely used benchmarks, including indoor and outdoor datasets. Finally, we discuss the challenges of prior works and provide readers with some insights for future research directions.

preprint2022arXiv

Primordial black holes and secondary gravitational waves from natural inflation

The production of primordial black hole (PBH) dark matter (DM) and the generation of scalar induced secondary gravitational waves by using the enhancement mechanism with a peak function in the non-canonical kinetic term in natural inflation is discussed. We show explicitly that the power spectrum for the primordial curvature perturbation can be enhanced at $10^{12}$ Mpc$^{-1}$, $10^{8}$ Mpc$^{-1}$ and $10^{5}$ Mpc$^{-1}$ by adjusting the model parameters. With the enhanced primordial curvature perturbations, we show the production of PBH DM with peak masses around $10^{-13}\ M_{\odot}$, the Earth's mass and the stellar mass, and the generation of scalar induced gravitational waves (SIGWs) with peak frequencies around mHz, $10^{-6}$ Hz and nHz, respectively. The PBHs with the mass scale $10^{-13}\ M_{\odot}$ can make up almost all the DM and the associated SIGWs is testable by spaced based gravitational wave observatory.

preprint2022arXiv

Robust optimization for quantum reinforcement learning control using partial observations

The current quantum reinforcement learning control models often assume that the quantum states are known a priori for control optimization. However, full observation of quantum state is experimentally infeasible due to the exponential scaling of the number of required quantum measurements on the number of qubits. In this paper, we investigate a robust reinforcement learning method using partial observations to overcome this difficulty. This control scheme is compatible with near-term quantum devices, where the noise is prevalent and predetermining the dynamics of quantum state is practically impossible. We show that this simplified control scheme can achieve similar or even better performance when compared to the conventional methods relying on full observation. We demonstrate the effectiveness of this scheme on examples of quantum state control and quantum approximate optimization algorithm. It has been shown that high-fidelity state control can be achieved even if the noise amplitude is at the same level as the control amplitude. Besides, an acceptable level of optimization accuracy can be achieved for QAOA with noisy control Hamiltonian. This robust control optimization model can be trained to compensate the uncertainties in practical quantum computing.

preprint2021arXiv

Design and Control of a Highly Redundant Rigid-Flexible Coupling Robot to Assist the COVID-19 Oropharyngeal-Swab Sampling

The outbreak of novel coronavirus pneumonia (COVID-19) has caused mortality and morbidity worldwide. Oropharyngeal-swab (OP-swab) sampling is widely used for the diagnosis of COVID-19 in the world. To avoid the clinical staff from being affected by the virus, we developed a 9-degree-of-freedom (DOF) rigid-flexible coupling (RFC) robot to assist the COVID-19 OP-swab sampling. This robot is composed of a visual system, UR5 robot arm, micro-pneumatic actuator and force-sensing system. The robot is expected to reduce risk and free up the clinical staff from the long-term repetitive sampling work. Compared with a rigid sampling robot, the developed force-sensing RFC robot can facilitate OP-swab sampling procedures in a safer and softer way. In addition, a varying-parameter zeroing neural network-based optimization method is also proposed for motion planning of the 9-DOF redundant manipulator. The developed robot system is validated by OP-swab sampling on both oral cavity phantoms and volunteers.

preprint2020arXiv

Fault-tolerant Coherent H-infinity Control for Linear Quantum Systems

Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this paper is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance and H-infinity disturbance attenuation performance. This paper first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault tolerant H-infinity control problem to the dissipation properties and the solutions of Riccati differential equations, an H-infinity controller for the quantum system is then designed by solving a set of linear matrix inequalities (LMIs). In particular, an algorithm is employed to introduce additional noises and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. For real applications of the developed fault-tolerant control strategy, we present a linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values. It is demonstrated that a quantum H-infinity controller can be designed and implemented using some basic optical components to achieve the desired control goal.

preprint2020arXiv

Full analytical formulas for frequency response of space-based gravitational wave detectors

The discovery of gravitational waves, which are ripples of space-time itself, opened a new window to test general relativity, because it predicts that there are only plus and cross polarizations for gravitational waves. For alternative theories of gravity, there may be up to six polarizations. The measurement of the polarization is one of the major scientific goals for future gravitational wave detectors. To evaluate the capability of the detector, we need to use the frequency dependent response functions averaged over the source direction and polarization angle. We derive the full analytical formulas of the averaged response functions for all six possible polarizations and present their asymptotic behaviors based on these analytical formulas. Compared with the numerical simulation, the full analytical formulas are more efficient and valid for any equal-arm interferometric gravitational wave detector without optical cavities in the arms and for a time-delay-interferometry Michelson combination.

preprint2020arXiv

KIC 12268220: A $δ$ Scuti Pulsating Star and an Active Protohelium White Dwarf in an Eclipsing Binary System

We present a photometric, spectroscopic, asteroseismic, and evolutionary analysis of the Algol-type eclipsing binary KIC 12268220. We find the O'Connell effect and anticorrelated eclipse timing variations in the Kepler light curve, revealing the presence of large starspots. Radial velocities and atmospheric parameters are obtained from ground-based spectroscopic observations. Combined with the radial velocity measurements and Gaia-derived total luminosity, our light-curve modeling yields the solution of the physical parameters for both the primary and secondary components. We find 14 independent frequencies arising from the $δ$ Scuti primary, and the observed frequencies agree with the frequency range of unstable modes from nonadiabatic calculations. Based on the conclusion from previous literature, we run a grid of models to study the evolution process of our system. The evolutionary tracks of our model suggest that the low-mass ($\sim 0.23\,M_\odot$) evolved secondary shows a similar evolutionary state to the R CMa-type system, which might evolve to an EL CVn system.

preprint2020arXiv

Primordial black holes and secondary gravitational waves from k/G inflation

The possibility that in the mass range around $10^{-12}\ M_\odot$ most of dark matter constitutes of primordial black holes (PBHs) is a very interesting topic. To produce PBHs with this mass, the primordial scalar power spectrum needs to be enhanced to the order of 0.01 at the scale $k\sim 10^{12}\ \text{Mpc}^{-1}$. The enhanced power spectrum also produces large secondary gravitational waves at the mHz band. A phenomenological delta function power spectrum is usually used to discuss the production of PBHs and secondary gravitational waves. Based on G and k inflations, we propose a new mechanism to enhance the power spectrum at small scales by introducing a non-canonical kinetic term $[1-2G(ϕ)]X$ with the function $G(ϕ)$ having a peak. Away from the peak, $G(ϕ)$ is negligible and we recover the usual slow-roll inflation which is constrained by the cosmic microwave background anisotrpy observations. Around the peak, the slow-roll inflation transiently turns to ultra slow-roll inflation. The enhancement of the power spectrum can be obtained with generic potentials, and there is no need to fine tune the parameters in $G(ϕ)$. The energy spectrum $Ω_{GW}(f)$ of secondary gravitational waves have the characteristic power law behaviour $Ω_{GW}(f)\sim f^{n}$ and is testable by pulsar timing array and space based gravitational wave detectors.

preprint2020arXiv

The TianQin project: current progress on science and technology

TianQin is a planned space-based gravitational wave (GW) observatory consisting of three earth orbiting satellites with an orbital radius of about $10^5~{\rm km}$. The satellites will form a equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4}~{\rm Hz}$ and $1~{\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe or exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new generation $17~{\rm cm}$ single-body hollow corner-cube retro-reflector which has been launched with the QueQiao satellite on 21 May 2018; a new laser ranging station equipped with a $1.2~{\rm m}$ telescope has been constructed and the station has successfully ranged to all the five retro-reflectors on the Moon; and the TianQin-1 experimental satellite has been launched on 20 December 2019 and the first round result shows that the satellite has exceeded all of its mission requirements.

preprint2016arXiv

Alignment and measurement of the magnetic field for the BESIII muon counter

Based on cosmic ray events without a magnetic field taken with the BESIII detector during the summer shutdown of BEPCII in 2012 and di-muon events from a data sample taken at center-of-mass energy of 3.686 GeV in 2009, we compare the coordinates of hits registered in the BESIII muon counter with the expected interaction point extrapolated from reconstructed tracks from the inner tracking system in the absence of a magnetic field. By minimizing the difference, we align the muon counter with the inner tracking system. Moreover, the strength of the magnetic field in the muon counter is measured for the first time with di-muon events from data taken at a center-of-mass energy of 3.686~GeV. After the alignment and the magnetic field strength measurement, the offsets in the reconstructed hit positions for muon tracks are reduced, which improves the muon identification. The alignment and magnetic field strength measurement have been adopted in the latest version of the BESIII offline software system. This addition to the software reduces the systematic uncertainty for the physics analysis in cases where the muon counter information is used.

preprint2016arXiv

The Distance Measurement of NGC 1313 With Cepheids

We present the detection of Cepheids in the barred spiral galaxy NGC 1313, using the Wide Field and Planetary Camera 2 on the Hubble Space Telescpoe. Twenty B (F450W) and V (F555W) epochs of observations spanning over three weeks were obtained, on which the profile-fitting photometry of all stars in the monitored field was performed using the package HSTphot. A sample of 26 variable stars have been identified to be Cepheids, with periods between 3 and 14 days. Based on the derived period-luminosity relations in B and V bands, we obtain an extinction-corrected distance modulus of mu = 28.32 +- 0.08 (random) +- 0.06 (systematic), employing the Large Magellanic Cloud as the distance zero point calibrator. The above moduli correspond to a distance of 4.61 +- 0.17 (random) +- 0.13 (systematic) Mpc, consistent with previous measurements reported in the literature with uncertainties. In addition, the reddening to NGC 1313 is found to be small.

preprint2016arXiv

The reconstruction of inflationary potentials

The observational data on the anisotropy of the cosmic microwave background constraints the scalar spectral tilt $n_s$ and the tensor to scalar ratio $r$ which depend on the first and second derivatives of the inflaton potential. The information can be used to reconstruct the inflaton potential in the polynomial form up to some orders. However, for some classes of potentials, $n_s$ and $r$ behave as $n_s(N)$ and $r(N)$ universally in terms of the number of e-folds $N$. The universal behaviour of $n_s(N)$ can be used to reconstruct a class of inflaton potentials. By parametrizing one of the parameters $n_s(N)$, $ε(N)$ and $ϕ(N)$, and fitting the parameters in the models to the observational data, we obtain the constraints on the parameters and reconstruct the classes of the inflationary models which include the chaotic inflation, T-model, hilltop inflation, s-dual inflation, natural inflation and $R^2$ inflation.

preprint2016arXiv

Time-Variable Aluminum Absorption in the Polar AR Ursae Majoris, and an Updated Estimate for the Mass of the White Dwarf

We present spectra of the extreme polar AR Ursae Majoris (AR UMa) which display a clear Al I absorption doublet, alongside spectra taken less than a year earlier in which that feature is not present. Re-examination of earlier SDSS spectra indicates that the Al I absorption doublet was also present $\approx$8 years before our first non-detection. We conclude that this absorbing material is unlikely to be on the surface of either the white dwarf (WD) or the donor star. We suggest that this Al I absorption feature arises in circumstellar material, perhaps produced by the evaporation of asteroids as they approach the hot WD. The presence of any remaining reservoir of rocky material in AR UMa might help to constrain the prior evolution of this unusual binary system. We also apply spectral decomposition to find the stellar parameters of the M dwarf companion, and attempt to dynamically measure the mass of the WD in AR UMa by considering both the radial velocity curves of the H$_β$ emission line and the Na I absorption line. Thereby we infer a mass range for the WD in AR UMa of 0.91 $M_{\odot}$ $<$ $M_{\mathrm{WD}}$ $<$ 1.24 $M_{\odot}$.

preprint2016arXiv

White-Light Flares on Close Binaries Observed with Kepler

Based on Kepler data, we present the results of a search for white-light flares on 1049 close binaries. We identify 234 flare binaries, on which 6818 flares are detected. We compare the flare-binary fraction in different binary morphologies ("detachedness"). The result shows that the fractions in over-contact and ellipsoidal binaries are approximately 10-20 percent lower than those in detached and semi-detached systems. We calculate the binary flares activity level (AL) of all the flare binaries, and discuss its variations along the orbital period (P_orb) and rotation period (P_rot, calculated for only detached binaries). We find that AL increases with decreasing P_orb or P_rot up to the critical values at P_orb near 3 days or P_rot near 1.5 days, thereafter, the AL starts decreasing no matter how fast the stars rotate. We examine the flaring rate as a function of orbital phase in 2 eclipsing binaries on which a large number of flares are detected. It appears that there is no correlation between flaring rate and orbital phase in these 2 binaries. In contrast, when we examine the function with 203 flares on 20 non-eclipse ellipsoidal binaries, bimodal distribution of amplitude weighted flare numbers shows up at orbital phase 0.25 and 0.75. Such variation could be larger than what is expected from the cross-section modification.

preprint2015arXiv

Modified Lyth bound and implications of BICEP2 results

To reconcile the BICEP2 measurement on the tensor-to-scalar ratio $r$ with Planck constraint, a large negative running of scalar spectral index $n_s$ is needed. So the inflationary observable such as $n_s$ should be expanded at least to the second-order slow-roll parameters for single-field inflationary models. The large value of $r$ and the Lyth bound indicate that it is impossible to obtain the sub-Planckian excursion for the inflaton. However, we derive an absolutely minimal bound $Δϕ/M_{\rm Pl}>\sqrt{r/2}$ on the inflaton excursion for single-field inflationary models, which can be applied to non-slow-roll inflationary models as well. This bound excludes the possibility of the small-field inflation with $Δϕ<0.1 M_{\rm Pl}$ if the BICEP2 result on $r$ stands and it opens the window of sub-Planckian excursion with $Δϕ<M_{\rm Pl}$ even if $r$ is as large as $0.1$. To get the sub-Planckian excursion with $Δϕ<0.1 M_{\rm Pl}$, our modified bound requires $r<0.02$. Using a fifth-order polynomial potential as an explicit example, we show that it not only agrees with the observational results, but also violates the Lyth bound.

preprint2015arXiv

The Phase-space analysis of scalar fields with non-minimally derivative coupling

We perform a dynamical analysis for the exponential scalar field with non-minimally derivative coupling. For the quintessence case, the stable fixed points are the same with and without the non-minimally derivative coupling. For the phantom case, the attractor with dark energy domination exists for the minimal coupling only. For the non-minimally derivative coupling without the standard canonical kinetic term, only the de-Sitter attractor exists, and the dark matter solution is unstable.

preprint2014arXiv

On the effect of the degeneracy between w_0 and w_a

The dynamics of scalar fields as dark energy is well approximated by some general relations between the equation of state parameter $w(z)$ and the fraction energy density $Ω_ϕ$. Based on the approximation, for slowly-rolling scalar fields, we derived the analytical expressions of $w(z)$ which reduce to the popular Chevallier-Polarski-Linder parametrization with explicit degeneracy relation between $w_0$ and $w_a$. The models approximate the dynamics of scalar fields well and help eliminate the degeneracies among $w_a$, $w_0$ and $Ω_{m0}$. With the explicit degeneracy relations, we test their effects on the constraints of cosmological parameters. We find that: (1) The analytical relations between $w_0$ and $w_a$ for the two models are consistent with observational data; (2) The degeneracies have little effect on $Ω_{m0}$; (3) The $1σ$ error of $w_0$ was reduced about 30% with the degeneracy relations.

preprint2014arXiv

The challenge for single field inflation with BICEP2 result

The detection of B-mode power spectrum by the BICEP2 collaboration constrains the tensor-to-scalar ratio $r=0.20^{+0.07}_{-0.05}$ for the lensed-$Λ$CDM model. The consistency of this big value with the {\em Planck} results requires a large running of the spectral index. The large values of the tensor-to-scalar ratio and the running of the spectral index put a challenge to single field inflation. For the chaotic inflation, the larger the value of the tensor-to-scalar ratio is, the smaller the value of the running of the spectral index is. For the natural inflation, the absolute value of the running of the spectral index has an upper limit.

preprint2014arXiv

The Simple Single Field Inflation Models and the Running of Spectral Index

The BICEP2 experiment confirms the existence of primordial gravitational wave with the tensor-to-scalar ratio $r=0$ ruled out at $7σ$ level. The consistency of this large value of $r$ with the {\em Planck} data requires a large negative running $n'_s$ of the scalar spectral index. Herein we propose two types of the single field inflation models with simple potentials to study the possibility of the consistency of the models with the BICEP2 and {\em Planck} observations. One type of model suggested herein is realized in the supergravity model building. These models fail to provide the needed $n'_s$ even though both can fit the tensor-to-scalar ratio and spectral index.

preprint2014arXiv

The tension on the cosmological parameters from different observational data

Planck measurements of the cosmic microwave background power spectra find a lower value of the Hubble constant $H_0$ and a higher value of the fractional matter energy density $Ω_{m0}$ for the concordance $Λ$CDM model, and these results are in tension with other measurements. The {\em Planck} group argued that the tension came either from some sources of unknown systematic errors in some astrophysical measurements or the wrong $Λ$CDM model applied in fitting the data. We studied the reason for the tension on $H_0$ from different measurements by considering two dynamical dark energy models. We found that there is no tension between different data, the constraint on $H_0$ is almost unchanged for different dark energy models and the tension with the local measurements remains when the error bar on $H_0$ is tightened to be around 1. We argue that the tension on $H_0$ is not caused by the fitting model.

preprint2013arXiv

Constraints on thawing scalar field models from fundamental constants

We consider a dark energy model with a relation between the equation of state parameter $w$ and the energy density parameter $Ω_ϕ$ derived from thawing scalar field models. Assuming the variation of the fine structure constant is caused by dark energy, we use the observational data of the variation of the fine structure constant to constrain the current value of $w_0$ and $Ω_{ϕ0}$ for the dark energy model. At the $1σ$ level, the observational data excluded some areas around $w_0=-1$, which explains the positive detection of the variation of the fine structure constant at the $1σ$ level, but $Λ$CDM model is consistent with the data at the $2σ$ level.

preprint2013arXiv

The effect of different observational data on the constraints of cosmological parameters

The constraints on the $Λ$CDM model from type Ia supernova (SNe Ia) data alone and BAO data alone are similar, so it is worthwhile to compare their constraints on the property of dark energy. We apply the SNLS3 compilation of 472 SNe Ia data, the baryon acoustic oscillation measurement of distance, the cosmic microwave background radiation data from the WMAP7, and the Hubble parameter data to study the effect of their different combinations on the fittings of cosmological parameters in the modified holographic dark energy model and the Chevallier-Polarski-Linder model. Neither BAO nor WMAP7 data alone give good constraint on the equation of state parameter of dark energy, but both WMAP7 data and BAO data help SNe Ia data break the degeneracies among the model parameters, hence tighten the constraint on the variation of equation of state parameter $w_a$, and WMAP7 data do the job a little better. Although BAO and WMAP7 data provide reasonably good constraints on $Ω_m$ and $Ω_k$, they are not able to constrain the dynamics of dark energy. On the other hand, SNe Ia data do not provide good constraints on $Ω_m$ and $Ω_k$, but they provide good constraint on the dynamics of dark energy, especially the variation of the equation of state parameter of dark energy, so we need to combine SNe Ia with BAO and WMAP7 data to probe the property of dark energy. The addition of $H(z)$ data helps better constrain the geometry of the Universe $Ω_k$ and the property of dark energy. For the SNLS SNe Ia data, the nuisance parameters $α$ and $β$ are consistent for all different combinations of the above data, and their impacts on the fittings of cosmological parameters are minimal. By fitting the data to different models, $Λ$CDM model is still consistent with all the observational data.