arXiv subjects

Xiaolin Luo

Publications and source records attributed to Xiaolin Luo.

At least 19 recordsLinked to original sources

arXiv2026

Deep Least Squares Monte Carlo methods for the valuation of variable annuities with guarantees

In general, the pricing of variable annuities with guarantees can be done by solving the corresponding optimal stochastic control problem if the contract withdrawal strategy is assumed to be optimal. This is typically solved as a dynamic programming problem using deterministic grid methods, which become computationally infeasible for more than a few state variables. In such situations, one needs to rely on simulation methods. The least-squares Monte Carlo (LSMC) method has become a popular simulation method for solving optimal stochastic control problems in quantitative finance over the last decades. In principle, the LSMC, originally developed for pricing Bermudan options, cannot be used directly for pricing variable annuities without simplifying assumptions because the underlying state variables are affected by the control decisions. This paper presents modifications of the LSMC algorithm that makes the pricing of general variable annuities feasible. For numerical illustrations, the pricing of variable annuities with guaranteed minimum withdrawal benefit under optimal withdrawal strategies is obtained with and without stochastic interest rates, using either polynomial regression or neural network regression in the LSMC algorithm. We found that the classical polynomial LSMC can give very accurate prices, at the cost of manual feature engineering, and with a standard deviation of the estimator that increases greatly when interest rates are made stochastic. By contrast, neural network LSMC gives slightly less accurate prices, requires more training time, but does not require manual feature engineering, and making interest rates stochastic makes no visible difference to its accuracy, suggesting a more stable and robust pricing performance of deep LSMC for higher-dimensional pricing problems.

q-fin.PR↗

arXiv2025

AI-Driven Reconstruction of Large-Scale Structure from Combined Photometric and Spectroscopic Surveys

Galaxy surveys are crucial for studying large-scale structure (LSS) and cosmology, yet they face limitations--imaging surveys provide extensive sky coverage but suffer from photo-$z$ uncertainties, while spectroscopic surveys yield precise redshifts but are sample-limited. To take advantage of both photo-$z$ and spec-$z$ data while eliminating photo-$z$ errors, we propose a deep learning framework based on a dual UNet architecture that integrates these two datasets at the field level to reconstruct the 3D photo-$z$ density field. We train the network on mock samples representative of stage-IV spectroscopic surveys, utilizing CosmicGrowth simulations with a $z=0.59$ snapshot containing $2048^3$ particles in a $(1200~h^{-1}\rm Mpc)^3$ volume. Several metrics, including correlation coefficient, MAE, MSE, PSNR, and SSIM, validate the model's accuracy. Moreover, the reconstructed power spectrum closely matches the ground truth at small scales ($k \gtrsim 0.06~h/\rm Mpc$) within the $1σ$ confidence level, while the UNet model significantly improves the estimation of photo-$z$ power spectrum multipoles. This study demonstrates the potential of deep learning to enhance LSS reconstruction by using both spectroscopic and photometric data.

astro-ph.IM↗

arXiv2025

A New Wavelet Scattering Transform-Based Statistic for Cosmological Analysis of Large-Scale Structure

Large-scale structure (LSS) analysis in galaxy surveys is a powerful cosmological probe but is limited by tracer bias, which can obscure underlying information and weaken parameter constraints. Existing methods either model bias or restrict analyses to low-density regions, yet their sensitivity to bias remains poorly understood. We propose a novel method based on the wavelet scattering transform (WST) to distinguish LSS across cosmological models while mitigating tracer bias. Central to our approach are the WST $m$-mode ratios, $R^{\rm wst}$, a new statistical measure, and a high-density apodization preprocessing that smoothly rescales extreme values. We use a reduced chi-square to assess the cosmological parameter constraints and find that $R^{\rm wst}$, in the scale range $j \in [3,7]$, achieves $\chi^2_{\nu, \rm cos} \approx 6$ for cosmology while maintaining $\chi^2_{\nu, \rm bias} \sim 1$--a regime unattained by other statistics. $R^{\rm wst}$ thus provides robust cosmological sensitivity with effective bias mitigation for future surveys.

astro-ph.CO↗

arXiv2025

Restoring Missing Modes of 21cm Intensity Mapping with Deep Learning: Impact on BAO Reconstruction

In 21cm intensity mapping of the large-scale structure (LSS), regions in Fourier space could be compromised by foreground contamination. In interferometric observations, this contamination, known as the foreground wedge, is exacerbated by the chromatic response of antennas, leading to substantial data loss. Meanwhile, the baryonic acoustic oscillation (BAO) reconstruction, which operates in configuration space to "linearize" the BAO signature, offers improved constraints on the sound horizon scale. However, missing modes within these contaminated regions can negatively impact the BAO reconstruction algorithm. To address this challenge, we employ the deep learning model U-Net to recover the lost modes before applying the BAO reconstruction algorithm. Despite hardware limitations, such as GPU memory, our results demonstrate that the AI-restored 21cm temperature map achieves a high correlation with the original signal, with a correlation ratio of approximately $0.9$ at $k \sim 1 h/Mpc$. Furthermore, subsequent BAO reconstruction indicates that the AI restoration has minimal impact on the performance of the `linearized' BAO signal, proving the effectiveness of the machine learning approach to mitigate the impact of foreground contamination. Interestingly, we demonstrate that the AI model trained on coarser fields can be effectively applied to finer fields, achieving even higher correlation. This success is likely attributable to the scale-invariance properties of non-linear mode coupling in large-scale structure and the hierarchical structure of the U-Net architecture.

astro-ph.CO↗

arXiv2025

Photometric Objects Around Cosmic Webs (PAC). VII. Disentangling Mass and Environment Quenching with the Aid of Galaxy-halo Connection in Simulations

Star formation quenching in galaxies is a critical process in galaxy formation. It is widely believed that the quenching process is dominated by the mass of galaxies and/or their environment. In Paper V, we addressed the challenge to disentangle the effects of mass and environment by employing the PAC method, which combines spectroscopic and deep photometric surveys. This approach enabled us to measure the excess surface density of blue and red galaxies around massive central galaxies down to $10^{9.0}M_{\odot}$. However, it is not straightforward to completely separate the two effects. To address this issue, in this paper, we derive the average quenched fraction of central (isolated) galaxies, $\bar{f}_{\mathrm{q}}^{\mathrm{cen}}(M_{*})$, by combining the 3D quenched fraction distribution $f^{\mathrm{sat}}_{\mathrm{q}}(r; M_{*,\mathrm{cen}}, M_{*,\mathrm{sat}})$, reconstructed from the $\bar{n}_2w_{\mathrm{p}}(r_{\mathrm{p}})$ measurements, with the stellar mass-halo mass relation in N-body simulations from Paper IV, and the observed total quenched fraction, $\bar{f}_{\mathrm{q}}^{\mathrm{all}}(M_{*})$. Using $f^{\mathrm{sat}}_{\mathrm{q}}(r;M_{*,\mathrm{cen}},M_{*,\mathrm{sat}})$, $\bar{f}_{\mathrm{q}}^{\mathrm{cen}}(M_{*})$, and the galaxy-halo connection, we assign a quenched probability to each (sub)halo in the simulation, enabling a comprehensive study of galaxy quenching. We find that the mass-quenched fraction increases from 0.3 to 0.87 across the stellar mass range $[10^{9.5}, 10^{11.0}]M_{\odot}$, while the environmental quenched fraction decreases from 0.17 to 0.03. The mass effect dominates galaxy quenching across the entire stellar mass range we studied. Moreover, more massive host halos are more effective at quenching their satellite galaxies, while satellite stellar mass has minimal influence on environmental quenching.

astro-ph.GA↗

arXiv2025

Photometric Objects Around Cosmic Webs (PAC) Delineated in a Spectroscopic Survey. VIII. Revisiting the Lensing is Low Effect

The issue of over-predicting the galaxy-galaxy lensing (GGL) signal using conventional galaxy-halo connection models has become well-known as the ``Lensing is Low'' problem, which has been extensively investigated using the Baryon Oscillation Spectroscopic Survey (BOSS) galaxy samples. This issue is also tightly related to the so-called $S_8$ tension. By applying our Photometric objects Around Cosmic webs (PAC) method to the BOSS survey and the DESI deep photometric survey, we obtained hundreds of cross-correlation measurements to establish an accurate galaxy-halo connection for BOSS galaxies through the halo abundance matching technique (Paper IV). With this galaxy-halo connection, we show in this work that the predicted GGL signals for BOSS galaxies both in the Planck and WMAP Universes actually agree very well with the GGL measurements. We find the best-fitting value $S_8 = 0.8294 \pm 0.0110$, $0.8073 \pm 0.0372$ and $0.8189 \pm 0.0440$ for the CMASS samples with the source galaxies from HSC, DES and KiDS image surveys, respectively. Our work indicates that accurate modeling of the lens population is so critical to interpret the GGL observation. For the scale of $r_p < 0.6\,h^{-1}\rm{Mpc}$, our GGL prediction for LOWZ samples are also in good agreement with the observations of HSC and DES. However, the GGL observation of KiDS is much lower on the small scale. Our results indicate that no significant baryon feedback is needed to suppress the small scale clustering unless the the GGL observation of KiDS on the small scale will be confirmed.

astro-ph.CO↗

arXiv2024

Accurate Measurement of the Lensing Magnification by BOSS CMASS Galaxies and Its Implications for Cosmology and Dark Matter

Magnification serves as an independent and complementary gravitational lensing measurement to shear. We develop a novel method to achieve an accurate and robust magnification measurement around BOSS CMASS galaxies across physical scales of $0.016h^{-1}{\rm Mpc} < r_{\rm p} < 10h^{-1}{\rm Mpc}$. We first measure the excess total flux density $δM$ of the source galaxies in deep DECaLS photometric catalog that are lensed by CMASS galaxies. We convert $δM$ to magnification $μ$ by establishing the $δμ-δM$ relation using a deeper photometric sample. By comparing magnification measurements in three optical bands ($grz$), we constrain the dust attenuation curve and its radial distribution, discovering a steep attenuation curve in the circumgalactic medium of CMASS galaxies. We further compare dust-corrected magnification measurements to model predictions from high-resolution dark matter-only (DMO) simulations in WMAP and Planck cosmologies, as well as the hydrodynamic simulation \texttt{TNG300-1}, using precise galaxy-halo connections from the Photometric objects Around Cosmic webs method and the accurate ray-tracing algorithm \texttt{P3MLens}. For $r_{\rm p} > 70h^{-1}$ kpc, our magnification measurements are in good agreement with both WMAP and Planck cosmologies, resulting in an estimation of the matter fluctuation amplitude of $S_8=0.816\pm0.024$. However, at $r_{\rm p} < 70h^{-1}$ kpc, we observe an excess magnification signal, which is higher than the DMO model in Planck cosmology at $2.8σ$ and would be exacerbated if significant baryon feedback is included. Implications of the potential small scale discrepancy for the nature of dark matter and for the processes governing galaxy formation are discussed.

astro-ph.CO↗

arXiv2024

PAC.V. The Roles of Mass and Environment in the Quenching of Galaxies

The roles that mass and environment play in the galaxy quenching are still under debate. Leveraging the Photometric objects Around Cosmic webs (PAC) method, we analyze the excess surface distribution $\bar{n}_2w_{\rm{p}}(r_{\rm{p}})$ of photometric galaxies in different color (rest-frame $u-r$) within the stellar mass range of $10^{9.0}M_{\odot}\sim10^{11.0}M_{\odot}$ around spectroscopic massive central galaxies ($10^{10.9}\sim10^{11.7}M_{\odot}$) at the redshift interval $0<z_s<0.7$, utilizing data from the Hyper SuprimeCam Subaru Strategic Program and the spectroscopic samples of Slogan Digital Sky Survey (i.e. Main, LOWZ and CMASS samples). We find that both mass and environment quenching contribute to the evolution of companion galaxies. To isolate the environment effect, we quantify the quenched fraction excess (QFE) of companion galaxies encircling massive central galaxies within $0.01h^{-1}{\rm{Mpc}}<r_{\rm{p}}<20h^{-1}\rm{Mpc}$, representing the surplus quenched fraction relative to the average. We find that the high density halo environment affects the star formation quenching up to about three times of the virial radius, and this effect becomes stronger at lower redshift. We also find that even after being scaled by the virial radius, the environment quenching efficiency is higher for more massive halos or for companion galaxies of higher stellar mass, though the trends are quite weak. We present a fitting formula that comprehensively captures the QFE across central and companion stellar mass bins, halo-centric distance bins, and redshift bins, offering a valuable tool for constraining galaxy formation models. Furthermore, we have made a quantitative comparison with Illustris-TNG that underscores some important differences, particularly in the excessive quenching of low-mass companion galaxies ($<10^{9.5}M_{\odot}$) by TNG.

astro-ph.GA↗

arXiv2023

The DESI One-Percent Survey: A concise model for galactic conformity of ELGs

Galactic conformity is the phenomenon in which a galaxy of a certain physical property is correlated with its neighbors of the same property, implying a possible causal relationship. The observed auto correlations of emission line galaxies (ELGs) from the highly complete DESI One-Percent survey exhibit a strong clustering signal on small scales, providing clear evidence for the conformity effect of ELGs. Building upon the original subhalo abundance matching (SHAM) method developed by Gao et al. (2022, 2023), we propose a concise conformity model to improve the ELG-halo connection. In this model, the number of satellite ELGs is boosted by a factor of $\sim 5$ in the halos whose central galaxies are ELGs. We show that the mean ELG satellite number in such central halos is still smaller than 1, and the model does not significantly increase the overall satellite fraction. With this model, we can well recover the ELG auto correlations to the smallest scales explored with the current data (i.e. $r_{\mathrm{p}} > 0.03$ $\mathrm{Mpc}\,h^{-1}$ in real space and at $s > 0.3$ $\mathrm{Mpc}\,h^{-1}$ in redshift space), while the cross correlations between luminous red galaxies (LRGs) and ELGs are nearly unchanged. Although our SHAM model has only 8 parameters, we further verify that it can accurately describe the ELG clustering in the entire redshift range from $z = 0.8$ to $1.6$. We therefore expect that this method can be used to generate high-quality ELG lightcone mocks for DESI.

astro-ph.GA↗

arXiv2023

Fast generation of mock galaxy catalogues with COLA

We investigate the feasibility of using COmoving Lagrangian Acceleration (COLA) technique to efficiently generate galaxy mock catalogues that can accurately reproduce the statistical properties of observed galaxies. Our proposed scheme combines the subhalo abundance matching (SHAM) procedure with COLA simulations, utilizing only three free parameters: the scatter magnitude ($σ_{\rm scat}$) in SHAM, the initial redshift ($z_{\rm init}$) of the COLA simulation, and the time stride ($da$) used by COLA. In this proof-of-concept study, we focus on a subset of BOSS CMASS NGC galaxies within the redshift range $z\in [0.45, 0.55]$. We perform $\mathtt{GADGET}$ simulation and low-resolution COLA simulations with various combinations of $(z_{\rm init}, da)$, each using $1024^{3}$ particles in an $800~h^{-1}{\rm Mpc}$ box. By minimizing the difference between COLA mock and CMASS NGC galaxies for the monopole of the two-point correlation function (2PCF), we obtain the optimal $σ_{\rm scat}$. We have found that by setting $z_{\rm init}=29$ and $da=1/30$, we achieve a good agreement between COLA mock and CMASS NGC galaxies within the range of 4 to $20~h^{-1}{\rm Mpc}$, with a computational cost two orders of magnitude lower than that of the N-body code. Moreover, a detailed verification is performed by comparing various statistical properties, such as anisotropic 2PCF, three-point clustering, and power spectrum multipoles, which shows similar performance between GADGET mock and COLA mock catalogues with the CMASS NGC galaxies. Furthermore, we assess the robustness of the COLA mock catalogues across different cosmological models, demonstrating consistent results in the resulting 2PCFs. Our findings suggest that COLA simulations are a promising tool for efficiently generating mock catalogues for emulators and machine learning analyses in exploring the large-scale structure of the Universe.

astro-ph.CO↗

arXiv2022

On the Kinematic Morphology around Halos

In this paper, we report an interesting kinematic phenomenon around the halos' edge related to the splashback radius. After the shell-crossing, cosmic flow exhibits various rotational morphologies via stream-mixing. Vorticity is generated in a particular way that coincides with the large-scale structure. Notably, one specific flow morphology, which is spiraling inward and compressing in the third direction, concentrates around halos. A detailed examination that reveals a sharp change in the logarithmic derivative of its volume fraction, coincides with the location of the splashback radius defined as the outermost caustic structure. Such a feature encodes valuable phase space information and provides a new perspective on understanding the dynamical evolution of halos. As a volume-weighted quantity, the profile of flow morphology is purely kinematic. And unlike other related studies, the rotational flow morphologies capture the anisotropic phase structure in the multi-stream region.

astro-ph.CO↗

arXiv2022

Cosmological constraints from the density gradient weighted correlation function

The mark weighted correlation function (MCF) $W(s,μ)$ is a computationally efficient statistical measure which can probe clustering information beyond that of the conventional 2-point statistics. In this work, we extend the traditional mark weighted statistics by using powers of the density field gradient $|\nabla ρ/ρ|^α$ as the weight, and use the angular dependence of the scale-averaged MCFs to constrain cosmological parameters. The analysis shows that the gradient based weighting scheme is statistically more powerful than the density based weighting scheme, while combining the two schemes together is more powerful than separately using either of them. Utilising the density weighted or the gradient weighted MCFs with $α=0.5,\ 1$, we can strengthen the constraint on $Ω_m$ by factors of 2 or 4, respectively, compared with the standard 2-point correlation function, while simultaneously using the MCFs of the two weighting schemes together can be $1.25$ times more statistically powerful than using the gradient weighting scheme alone. The mark weighted statistics may play an important role in cosmological analysis of future large-scale surveys. Many issues, including the possibility of using other types of weights, the influence of the bias on this statistics, as well as the usage of MCFs in the tomographic Alcock-Paczynski method, are worth further investigations.

astro-ph.CO↗

arXiv2021

Reconciling low and high redshift GRB luminosity correlations

The correlation between the peak spectra energy ($E_p$) and the equivalent isotropic energy ($E_{\rm iso}$) of long gamma-ray bursts (GRBs), the so-called Amati relation, is often used to constrain the high-redshift Hubble diagram. Assuming Lambda cold dark matter ($Λ$CDM) cosmology, Wang et al. found a $\gtrsim 3σ$ tension in the data-calibrated Amati coefficients between low- and high-redshift GRB samples. To reduce the impact of fiducial cosmology, we use the Parameterization based on cosmic Age (PAge), an almost model-independent framework to trace the cosmological expansion history. We find that the low- and high-redshift tension in Amati coefficients stays almost the same for the broad class of models covered by PAge, indicating that the cosmological assumption is not the dominant driver of the redshift evolution of GRB luminosity correlation. Next, we analyze the selection effect due to flux limits in observations. We find Amati relation evolves much more significantly across energy scales of $E_{\rm iso}$. We debias the GRB data by selectively discarding samples to match low-$z$ and high-$z$ $E_{\rm iso}$ distributions. After debiasing, the Amati coefficients agree well between low-$z$ and high-$z$ data groups, whereas the evidence of $E_{\rm iso}$-dependence of Amati relation remains to be strong. Thus, the redshift evolution of GRB luminosity correlation can be fully interpreted as a selection bias, and does not imply cosmological evolution of GRBs.

astro-ph.CO↗

arXiv2020

Reaffirming the Cosmic Acceleration without Supernova and CMB

Recent discussions about supernova magnitude evolution have raised doubts about the robustness of the late-universe acceleration. In a previous letter, Huang did a null test of the cosmic acceleration by using a Parameterization based on the cosmic Age (PAge), which covers a broad class of cosmological models including the standard $Λ$ cold dark matter model and its many extensions. In this work, we continue to explore the cosmic expansion history with the PAge approximation. Using baryon acoustic oscillations ({\it without} a CMB prior on the acoustic scale), gravitational strong lens time delay, and passively evolving early galaxies as cosmic chronometers, we obtain $\gtrsim 4σ$ detections of cosmic acceleration for both flat and nonflat PAge universes. In the nonflat case, we find a $\gtrsim 3σ$ tension between the spatial curvatures derived from baryon acoustic oscillations and strong lens time delay. Implications and possible systematics are discussed.

astro-ph.CO↗

arXiv2019

Exploring the Latest Pantheon SNIa Dataset by Using Three Kinds of Statistics Techniques

In this work, we explore the cosmological consequences of the latest Type Ia supernova (SN Ia) data-set, Pantheon, by adopting the $wCDM$ model. The Pantheon data-set is the largest SN Ia samples till now, which contains 1048 supernovae on the redshift range $0 < z < 2.3$. Here we take into account three kinds of SN Ia statistics techniques, including: 1. magnitude statistics (MS), which is the traditional SN Ia statistics technique; 2. flux statistics (FS), which bases on the flux-averaging (FA) method; 3. improved flux statistics (IFS), which combines the advantages of MS and FS. It should be mentioned that, The IFS technique need to scan the $(z_{cut},Δz)$ parameters plane, where $z_{cut}$ and $Δz$ are redshift cut-off and redshift interval of FA, respectively. The results are shown as follows. (1) Using SN data-set only, the best FA recipe for IFS is $(z_{cut},Δz)=(0.1,0.08)$; (2) Comparing to the old SN data-set, JLA, adopting Pantheon data-set can reduce the $2σ$ error bars of equation of state $w$ by 38\%, 47\% and 53\% for MS, FS and IFS, respectively; (3) FS gives closer results to other observations, such as Baryon acoustic oscillations and Cosmic microwave background; (4) Compared with FS and IFS, MS more favors a Universe that will end in a "big rip".

astro-ph.CO↗

arXiv2019

Can Non-standard Recombination Resolve the Hubble Tension?

The inconsistent Hubble constant values derived from cosmic microwave background (CMB) observations and from local distance-ladder measurements may suggest new physics beyond the standard $Λ$CDM paradigm. It has been found in earlier works that, at least phenomenologically, non-standard recombination histories can reduce the $\gtrsim 4σ$ Hubble tension to $\sim 2σ$. Following this path, we vary physical and phenomenological parameters in RECFAST, the standard code to compute ionization history of the universe, to explore possible physics beyond standard recombination. We find that the CMB constraint on the Hubble constant is sensitive to the Hydrogen ionization energy and $2s \rightarrow 1s$ two-photon decay rate, both of which are atomic constants, and is insensitive to other details of recombination. Thus, the Hubble tension is very robust against perturbations of recombination history, unless exotic physics modifies the atomic constants during the recombination epoch.

astro-ph.CO↗

arXiv2019

Cosmological constraints from the redshift dependence of the Alcock-Paczynski effect: Fourier space analysis

The tomographic Alcock-Paczynski (AP) method utilizes the redshift evolution of the AP distortion to place constraints on cosmological parameters. It has proved to be a robust method that can separate the AP signature from the redshift space distortion (RSD) effect, and deliver powerful cosmological constraints using the $\lesssim 40h^{-1}\ \rm Mpc$ clustering region. In previous works, the tomographic AP method was performed via the anisotropic 2-point correlation function statistic. In this work we consider the feasibility of conducting the analysis in the Fourier domain and examine the pros and cons of this approach. We use the integrated galaxy power spectrum (PS) as a function of direction, $\hat P_{Δk}(μ)$, to quantify the magnitude of anisotropy in the large-scale structure clustering, and use its redshift variation to do the AP test. The method is tested on the large, high resolution Big-MultiDark Planck (BigMD) simulation at redshifts $z=0-1$, using the underlying true cosmology $Ω_m=0.3071,\ w=-1$. Testing the redshift evolution of $\hat P_{Δk}(μ)$ in the true cosmology and cosmologies deviating from the truth with $δΩ_m=0.1,\ δw=0.3$, we find that the redshift evolution of the AP distortion overwhelms the effects created by the RSD by a factor of $\sim1.7-3.6$. We test the method in the range of $k\in(0.2,1.8)\ h\ \rm Mpc^{-1}$, and find that it works well throughout the entire regime. We tune the halo mass within the range $2\times 10^{13}$ to $10^{14}\ M_{\odot}$, and find that the change of halo bias results in $\lesssim 5 \%$ change in $\hat P_{Δk}(μ)$, which is less significant compared with the cosmological effect. Our work shows that it is feasible to conduct the tomographic AP analysis in the Fourier space.

astro-ph.CO↗

arXiv2019

Non-parametric dark energy reconstruction using the tomographic Alcock-Paczynski test

The tomographic Alcock-Paczynski (AP) method can result in tight cosmological constraints by using small and intermediate clustering scales of the large scale structure (LSS) of the galaxy distribution. By focusing on the redshift dependence, the AP distortion can be distinguished from the distortions produced by the redshift space distortions (RSD). In this work, we combine the tomographic AP method with other recent observational datasets of SNIa+BAO+CMB+$H_0$ to reconstruct the dark energy equation-of-state $w$ in a non-parametric form. The result favors a dynamical DE at $z\lesssim1$, and shows a mild deviation ($\lesssim2σ$) from $w=-1$ at $z=0.5-0.7$. We find the addition of the AP method improves the low redshift ($z\lesssim0.7$) constraint by $\sim50\%$.

astro-ph.CO↗