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There is a close relationship between linear codes and $t$-designs. Through their research on a class of narrow-sense BCH codes, Ding and Tang made a breakthrough by presenting the first two infinite families of near MDS codes holding $t$-designs with $t=2$ or 3. In this paper, we present an infinite family of MDS codes over $\mathbb{F}_{2^s}$ and two infinite families of almost MDS codes over $\mathbb{F}_{p^s}$ for any prime $p$, by investigating the parameters of the dual codes of two families of BCH codes. Notably, these almost MDS codes include two infinite families of near MDS codes over $\mathbb{F}_{3^s}$, resolving a conjecture posed by Geng et al. in 2022. Furthermore, we demonstrate that both of these almost AMDS codes and their dual codes hold infinite families of $3$-designs over \(\mathbb{F}_{p^s}\) for any prime $p$. Additionally, we study the subfield subcodes of these families of MDS and near MDS codes, and provide several binary, ternary, and quaternary codes with best known parameters.

Accurately characterizing the true redshift (true-$z$) distribution of a photometric redshift (photo-$z$) sample is critical for cosmological analyses in imaging surveys. Clustering-based techniques, which include clustering-redshift (CZ) and self-calibration (SC) methods--depending on whether external spectroscopic data are used--offer powerful tools for this purpose. In this study, we explore the joint inference of the true-$z$ distribution by combining SC and CZ (denoted as SC+CZ). We derive simple multiplicative update rules to perform the joint inference. By incorporating appropriate error weighting and an additional weighting function, our method shows significant improvement over previous algorithms. We validate our approach using a DES Y3 mock catalog. The true-$z$ distribution estimated through the combined SC+CZ method is generally more accurate than using SC or CZ alone. To account for the different constraining powers of these methods, we assign distinct weights to the SC and CZ contributions. The optimal weights, which minimize the distribution error, depend on the relative constraining strength of the SC and CZ data. Specifically, for a spectroscopic redshift sample that represents 1% of the photo-$z$ sample, the optimal combination reduces the total error by 20% (40%) compared to using CZ (SC) alone, and it keeps the bias in mean redshift [$\Delta \bar{z} / (1 + z) $] at the level of 0.3%. Furthermore, when CZ data is only available in the low-$z$ range and the high-$z$ range relies solely on SC data, SC+CZ enables consistent estimation of the true-$z$ distribution across the entire redshift range. Our findings demonstrate that SC+CZ is an effective tool for constraining the true-$z$ distribution, paving the way for clustering-based methods to be applied at $z\gtrsim 1$., Comment: 17 pages, 13 figures

Intermediate dimensions are a class of new fractal dimensions which provide a spectrum of dimensions interpolating between the Hausdorff and box-counting dimensions. In this paper, we study the intermediate dimensions of Moran sets. Moran sets may be regarded as a generalization of self-similar sets generated by using different class of similar mappings at each level with unfixed translations, and this causes the lack of ergodic properties on Moran set. Therefore, the intermediate dimensions do not necessarily exist, and we calculate the upper and lower intermediate dimensions of Moran sets. In particular, we obtain a simplified intermediate dimension formula for homogeneous Moran sets. Moreover, we study the visualization of the upper intermediate dimensions for some homogeneous Moran sets, and we show that their upper intermediate dimensions are given by Mobius transformations.

We combined data from the Sloan Digital Sky Survey (SDSS) and the Arecibo Legacy Fast ALFA Survey (ALFALFA) to establish the HI mass vs. stellar mass and halo mass scaling relations using an abundance matching method that is free of the Malmquist bias. To enable abundance matching, a cross-match between the SDSS DR7 galaxy group sample and the ALFALFA HI sources provides a catalog of 16,520 HI-galaxy pairs within 14,270 galaxy groups (halos). By applying the observational completeness reductions for both optical and HI observations, we used the remaining 8,180 ALFALFA matched sources to construct the model constraints. Taking into account the dependence of HI mass on both the galaxy and group properties, we establish two sets of scaling relations: one with a combination of stellar mass, $({g-r})$ color and halo mass, and the other with stellar mass, specific star-formation rate ($\rm sSFR$), and halo mass. We demonstrate that our models can reproduce the HI mass component as both a stellar and halo mass. Additional tests showed that the conditional HI mass distributions as a function of the cosmic web type and the satellite fractions were well recovered., Comment: arXiv admin note: text overlap with arXiv:2008.09804

In this paper, we set out to construct a set of reference mock galaxy redshift surveys (MGRSs) for the future Chinese Space-station Survey Telescope (CSST) observation, where subsequent survey selection effects can be added and evaluated. This set of MGRSs is generated using the dark matter subhalos extracted from a high-resolution Jiutian $N$-body simulation of the standard $\Lambda$CDM cosmogony with $\Omega_m=0.3111$, $\Omega_{\Lambda}=0.6889$, and $\sigma_8=0.8102$. The simulation has a boxsize of $1~h^{-1} {\rm Gpc}$, and consists of $6144^3$ particles with mass resolution $3.723 \times 10^{8} h^{-1} M_\odot $. In order to take into account the effect of redshift evolution, we first use all 128 snapshots in the Jiutian simulation to generate a light-cone halo/subhalo catalog. Next, galaxy luminosities are assigned to the main and subhalo populations using the subhalo abundance matching (SHAM) method with the DESI $z$-band luminosity functions at different redshifts. Multi-band photometries, as well as images, are then assigned to each mock galaxy using a 3-dimensional parameter space nearest neighbor sampling of the DESI LS observational galaxies and groups. Finally, the CSST and DESI LS survey geometry and magnitude limit cuts are applied to generate the required MGRSs. As we have checked, this set of MGRSs can generally reproduce the observed galaxy luminosity/mass functions within 0.1 dex for galaxies with $L > 10^8 L_\odot$ (or $M_* > 10^{8.5} M_\odot$) and within 1-$\sigma$ level for galaxies with $L < 10^8L_\odot$ (or $M_* < 10^{8.5} M_\odot$). Together with the CSST slitless spectra and redshifts for our DESI LS seed galaxies that are under construction, we will set out to test various slitless observational selection effects in subsequent probes., Comment: 13 pages, 9 figures, accepted for publication in MNRAS

We use a galaxy sample derived from the DECaLS DR9 to measure the Baryonic Acoustic Oscillations (BAO). The magnitude-limited sample consists of 10.6 million galaxies in an area of 4974 deg$^2$ over the redshift range of [0.6, 1]. A key novelty of this work is that the true redshift distribution of the photo-$z$ sample is derived from the self calibration method, which determines the true redshift distribution using the clustering information of the photometric data alone. Through the angular correlation function in four tomographic bins, we constrain the BAO scale dilation parameter $\alpha$ to be $1.025\pm 0.033 $, consistent with the fiducial Planck cosmology. Alternatively, the ratio between the comoving angular diameter distance and the sound horizon, $D_{\rm M} / r_{\rm s}$ is constrained to be $18.94 \pm 0.61 $ at the effective redshift of 0.749. We corroborate our results with the true redshift distribution obtained from a weighted spectroscopic sample, finding very good agreement. We have conducted a series of tests to demonstrate the robustness of the measurement. Our work demonstrates that the self calibration method can effectively constrain the true redshift distribution in cosmological applications, especially in the context of photometric BAO measurement., Comment: 13 pages, 10 figures, matched to the published version

We report a $\sim5.2\sigma$ detection of the kinetic Sunyaev-Zel'dovich (kSZ) effect in Fourier space, by combining the DESI galaxy groups and the Planck data. We use the density-weighted pairwise kSZ power spectrum as the summary statistic, and the detailed procedure of its measurement is presented in this paper. Meanwhile, we analyze the redshift space group density power spectrum to constrain its bias parameters and photo-z uncertainties. These best-fitted parameters are substituted to a nonlinear kSZ model, and we fit the measured kSZ power spectrum with this model to constrain the group optical depth $\bar{\tau}$. Selected by a varying lower mass threshold $M_{\rm th}$, the galaxy group catalogs with different median masses ($\tilde{M}$) are constructed from the DR9 data of the DESI Legacy Imaging Surveys. $\tilde{M}$ spans a wide range of $\sim10^{13}-10^{14}M_\odot/h$ and the heaviest $\tilde{M}\sim10^{14} M_\odot/h$ is larger than those of most other kSZ detections. When the aperture photometric filter radius $\theta_{\rm AP}$ is set to be $4.2$ arcmin, the $\tilde{M}=1.75\times10^{13}M_\odot/h$ group sample at the median redshift $\tilde{z}=0.64$ has the highest kSZ detection ${\rm S/N}=5.2$. By fitting $\bar{\tau}$s from various samples against their $\tilde{M}$s, we obtain a linear $\log\bar{\tau}-\log \tilde{M}$ relation: $\log\bar{\tau} = \gamma(\log \tilde{M}-14)+\log\beta$, in which $\gamma=0.55\pm0.1$. We also vary the aperture photometric filter radius and measure the $\bar{\tau}$ profiles of group samples, whose constraints on the baryon distribution within and around dark matter halos will be discussed in a companion paper., Comment: 25 pages, 14 figures, ApJS accepted

In this investigation, we leverage the combination of Dark Energy Spectroscopic Instrument Legacy imaging Surveys Data Release 9 (DESI LS DR9), Survey Validation 3 (SV3), and Year 1 (Y1) data sets to estimate the conditional luminosity and stellar mass functions (CLFs & CSMFs) of galaxies across various halo mass bins and redshift ranges. To support our analysis, we utilize a realistic DESI Mock Galaxy Redshift Survey (MGRS) generated from a high-resolution Jiutian simulation. An extended halo-based group finder is applied to both MGRS catalogs and DESI observation. By comparing the r and z-band luminosity functions (LFs) and stellar mass functions (SMFs) derived using both photometric and spectroscopic data, we quantified the impact of photometric redshift (photo-z) errors on the galaxy LFs and SMFs, especially in the low redshift bin at low luminosity/mass end. By conducting prior evaluations of the group finder using MGRS, we successfully obtain a set of CLF and CSMF measurements from observational data. We find that at low redshift the faint end slopes of CLFs and CSMFs below $10^{9}h^{-2}L_{\odot}$ (or $h^{-2}M_{\odot}$) evince a compelling concordance with the subhalo mass functions. After correcting the cosmic variance effect of our local Universe following arXiv:1809.00523, the faint end slopes of the LFs/SMFs turn out to be also in good agreement with the slope of the halo mass function., Comment: 28 pages, 13 figures, Accepted for publication in ApJ

In this paper, the sufficient and necessary condition for the minimum distance of the BCH codes over $\mathbb{F}_q$ with length $q+1$ and designed distance 3 to be 3 and 4 are provided. Let $d$ be the minimum distance of the BCH code $\mathcal{C}_{(q,q+1,3,h)}$. We prove that (1) for any $q$, $d=3$ if and only if $\gcd(2h+1,q+1)>1$; (2) for $q$ odd, $d=4$ if and only if $\gcd(2h+1,q+1)=1$. By combining these conditions with the dimensions of these codes, the parameters of this BCH code are determined completely when $q$ is odd. Moreover, several infinite families of MDS and almost MDS (AMDS) codes are shown. Furthermore, the sufficient conditions for these AMDS codes to be distance-optimal and dimension-optimal locally repairable codes are presented. Based on these conditions, several examples are also given.

The Conditional Colour-Magnitude Distribution (CCMD) is a comprehensive formalism of the colour-magnitude-halo mass relation of galaxies. With joint modelling of a large sample of SDSS galaxies in fine bins of galaxy colour and luminosity, Xu et al. inferred parameters of a CCMD model that well reproduces colour- and luminosity-dependent abundance and clustering of present-day galaxies. In this work, we provide a test and investigation of the CCMD model by studying the colour and luminosity distribution of galaxies in galaxy groups. An apples-to-apples comparison of group galaxies is achieved by applying the same galaxy group finder to identify groups from the CCMD galaxy mocks and from the SDSS data, avoiding any systematic effect of group finding and mass assignment on the comparison. We find an overall nice agreement in the conditional luminosity function (CLF), the conditional colour function (CCF), and the CCMD of galaxies in galaxy groups inferred from CCMD mock and SDSS data. We also discuss the subtle differences revealed by the comparison. In addition, using two external catalogues constructed to only include central galaxies with halo mass measured through weak lensing, we find that their colour-magnitude distribution shows two distinct and orthogonal components, in line with the prediction of the CCMD model. Our results suggest that the CCMD model provides a good description of halo mass dependent galaxy colour and luminosity distribution. The halo and CCMD mock catalogues are made publicly available to facilitate other investigations., Comment: Match with published version. The halo catalogues and CCMD mocks are publicly available at https://www.astro.utah.edu/~zhengzheng/data.html

Alternative to weak lensing measurements through cosmic shear, we present a weak lensing convergence $\hat{\kappa}$ map reconstructed through cosmic magnification effect in DECaLS galaxies of the DESI imaging surveys DR9. This is achieved by linearly weighing $12$ maps of galaxy number overdensity in different magnitude bins of $grz$ photometry bands. The weight is designed to eliminate the mean galaxy deterministic bias, minimize galaxy shot noise while maintaining the lensing convergence signal. We also perform corrections of imaging systematics in the galaxy number overdensity. The $\hat{\kappa}$ map has $8365$ deg$^2$ sky coverage. Given the low number density of DECaLS galaxies, the $\hat{\kappa}$ map is overwhelmed by shot noise and the map quality is difficult to evaluate using the lensing auto-correlation. Alternatively, we measure its cross-correlation with the cosmic shear catalogs of DECaLS galaxies of DESI imaging surveys DR8, which has $8365$ deg$^2$ overlap in sky coverage with the $\hat{\kappa}$ map. We detect a convergence-shear cross-correlation signal with $S/N\simeq 10$. The analysis also shows that the galaxy intrinsic clustering is suppressed by a factor $\mathcal{O}(10^2)$ and the residual galaxy clustering contamination in the $\hat{\kappa}$ map is consistent with zero. Various tests with different galaxy and shear samples, and the Akaike information criterion analysis all support the lensing detection. So is the imaging systematics corrections, which enhance the lensing signal detection by $\sim 30\%$. We discuss various issues for further improvement of the measurements.

We present a tentative constraint on cosmological parameters $\Omega_m$ and $\sigma_8$ from a joint analysis of galaxy clustering and galaxy-galaxy lensing from DESI Legacy Imaging Surveys Data Release 9 (DR9), covering approximately 10000 square degrees and spanning the redshift range of 0.1 to 0.9. To study the dependence of cosmological parameters on lens redshift, we divide lens galaxies into seven approximately volume-limited samples, each with an equal width in photometric redshift. To retrieve the intrinsic projected correlation function $w_{\rm p}(r_{\rm p})$ from the lens samples, we employ a novel method to account for redshift uncertainties. Additionally, we measured the galaxy-galaxy lensing signal $\Delta\Sigma(r_{\rm p})$ for each lens sample, using source galaxies selected from the shear catalog by applying our \texttt{Fourier\_Quad} pipeline to DR9 images. We model these observables within the flat $\Lambda$CDM framework, employing the minimal bias model. To ensure the reliability of the minimal bias model, we apply conservative scale cuts: $r_{\rm p} > 8$ and $12 ~h^{-1}{\rm Mpc}$, for $w_{\rm p}(r_{\rm p})$ and $\Delta\Sigma(r_{\rm p})$, respectively. Our findings suggest a mild tendency that $S_8 \equiv \sigma_8 \sqrt{\Omega_m/0.3} $ increases with lens redshift, although this trend is only marginally significant. When we combine low redshift samples, the value of $S_8$ is determined to be $0.84 \pm 0.02$, consistent with the Planck results but significantly higher than the 3$\times$ 2pt analysis by 2-5$\sigma$. Despite the fact that further refinements in measurements and modeling could improve the accuracy of our results, the consistency with standard values demonstrates the potential of our method for more precise and accurate cosmology in the future., Comment: slightly different with the published version

We explore the feasibility of learning the connection between SDSS galaxies and ELUCID subhaloes with random forest (RF). ELUCID is a constrained $N$-body simulation constructed using the matter density field of SDSS. Based on an SDSS-ELUCID matched catalogue, we build RF models that predict $M_r$ magnitude, colour, stellar mass $M_*$, and specific star formation rate (sSFR) with several subhalo properties. While the RF can predict $M_r$ and $M_*$ with reasonable accuracy, the prediction accuracy of colour and sSFR is low, which could be due to the mismatch between galaxies and subhaloes. To test this, we shuffle the galaxies in subhaloes of narrow mass bins in the local neighbourhood using galaxies of a semi-analytic model (SAM) and the TNG hydrodynamic simulation. We find that the shuffling only slightly reduces the colour prediction accuracy in SAM and TNG, which is still considerably higher than that of the SDSS. This suggests that the true connection between SDSS colour and subhalo properties could be weaker than that in the SAM and TNG without the mismatch effect. We also measure the Pearson correlation coefficient between galaxy properties and the subhalo properties in SDSS, SAM, and TNG. Similar to the RF results, we find that the colour-subhalo correlation in SDSS is lower than both the SAM and TNG. We also show that the galaxy-subhalo correlations depend on subhalo mass in the galaxy formation models. Advanced surveys with more fainter galaxies will provide new insights into the galaxy-subhalo relation in the real Universe., Comment: 14 pages, 9 figures, submitted to MNRAS

The precise estimation of the statistical errors and accurate removal of the systematical errors are the two major challenges for the stage IV cosmic shear surveys. We explore their impact for the China Space-Station Telescope (CSST) with survey area $\sim17,500\deg^2$ up to redshift $\sim4$. We consider statistical error contributed from Gaussian covariance, connected non-Gaussian covariance and super-sample covariance. We find the non-Gaussian covariances, which is dominated by the super-sample covariance, can largely reduce the signal-to-noise of the two-point statistics for CSST, leading to a $\sim1/3$ loss in the figure-of-merit for the matter clustering properties ($\sigma_8-\Omega_m$ plane) and $1/6$ in the dark energy equation-of-state ($w_0-w_a$ plane). We further put requirements of systematics-mitigation on: intrinsic alignment of galaxies, baryonic feedback, shear multiplicative bias, and bias in the redshift distribution, for an unbiased cosmology. The $10^{-2}$ to $10^{-3}$ level requirements emphasize strong needs in related studies, to support future model selections and the associated priors for the nuisance parameters., Comment: accepted by MNRAS

In this paper, we present our solution to the MuSe-Humor sub-challenge of the Multimodal Emotional Challenge (MuSe) 2022. The goal of the MuSe-Humor sub-challenge is to detect humor and calculate AUC from audiovisual recordings of German football Bundesliga press conferences. It is annotated for humor displayed by the coaches. For this sub-challenge, we first build a discriminant model using the transformer module and BiLSTM module, and then propose a hybrid fusion strategy to use the prediction results of each modality to improve the performance of the model. Our experiments demonstrate the effectiveness of our proposed model and hybrid fusion strategy on multimodal fusion, and the AUC of our proposed model on the test set is 0.8972., Comment: 7 pages, 1 figure, to appear in MuSe 2022 (ACM MM2022 co-located workshop)

Calibrating the redshift distributions of photometric galaxy samples is essential in weak lensing studies. The self-calibration method combines angular auto- and cross-correlations between galaxies in multiple photometric redshift (photo-$z$) bins to reconstruct the scattering rates matrix between redshift bins. In this paper, we test a recently proposed self-calibration algorithm using the DECaLS Data Release 9 and investigate to what extent the scattering rates are determined. We first mitigate the spurious angular correlations due to imaging systematics by a machine learning based method. We then improve the algorithm for $\chi^2$ minimization and error estimation. Finally, we solve for the scattering matrices, carry out a series of consistency tests and find reasonable agreements: (1) finer photo-$z$ bins return a high-resolution scattering matrix, and it is broadly consistent with the low-resolution matrix from wider bins; (2) the scattering matrix from the Northern Galactic Cap is almost identical to that from Southern Galactic Cap; (3) the scattering matrices are in reasonable agreement with those constructed from the power spectrum and the weighted spectroscopic subsample. We also evaluate the impact of cosmic magnification. Although it changes little the diagonal elements of the scattering matrix, it affects the off-diagonals significantly. The scattering matrix also shows some dependence on scale cut of input correlations, which may be related to a known numerical degeneracy between certain scattering pairs. This work demonstrates the feasibility of the self-calibration method in real data and provides a practical alternative to calibrate the redshift distributions of photometric samples., Comment: Matched with publish version

In these proceedings, we present the measurements of neutron skin thickness and nuclear deformation using isobar $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV by the STAR detector. The significant deviations from unity of the isobar ratios of elliptic flow $v_{2}$, triangular flow $v_{3}$, mean $p_{\rm T}$ fluctuations $\langle\delta p_{\rm T}^{2}\rangle/\langle p_{\rm T}\rangle^{2}$, and asymmetric cumulant ${\rm ac}_{2}\{3\}$ indicate large differences in their quadrupole and octuple deformations. The significant deviations of the isobar ratios of produced hadron multiplicity $N_{\rm ch}$, mean transverse momentum $\langle p_{\rm T}\rangle$, and net charge number $\Delta Q$ indicate a halo-type neutron skin for the Zr nucleus, much thicker than for the Ru nucleus, consistent with nuclear structure calculations. We discuss how we extract the neutron skin thickness, the symmetry energy slope parameter, and deformation parameters from data., Comment: Presented at Quark Matter 2022, Karkow, Poland, April 4-10, 2022

Based on a large group/cluster catalog recently constructed from the DESI Legacy Imaging Surveys DR9 using an extended halo-based group finder, we measure and model the group-galaxy weak lensing signals for groups/clusters in a few redshift bins within redshift range $0.1 \leqslant z<0.6$. Here, the background shear signals are obtained based on the DECaLS survey shape catalog derived with the \textsc{Fourier\_Quad} method. We divide the lens samples into 5 equispaced redshift bins and 7 mass bins, which allow us to probe the redshift and mass dependence of the lensing signals and hence the resulting halo properties. In addition to these sample selections, we have also checked the signals around different group centers, e.g., brightest central galaxy (BCG), luminosity weighted center and number weighted center. We use a lensing model that includes off-centering to describe the lensing signals we measure for all mass and redshift bins. The results demonstrate that our model predictions for the halo masses, bias and concentrations are stable and self-consistent among different samples for different group centers. Taking advantage of the very large and complete sample of groups/clusters, as well as the reliable estimation of their halo masses, we provide measurements of the cumulative halo mass functions up to redshift $z=0.6$, with a mass precision at $0.03\sim0.09$ dex., Comment: revised version submitted to ApJ

Using the extended halo-based group finder developed by Yang et al. (2021), which is able to deal with galaxies via spectroscopic and photometric redshifts simultaneously, we construct galaxy group and candidate protocluster catalogs in a wide redshift range ($0 < z < 6$) from the joint CFHT Large Area $U$-band Deep Survey (CLAUDS) and Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) deep data set. Based on a selection of 5,607,052 galaxies with $i$-band magnitude $m_{i} < 26$ and a sky coverage of $34.41\ {\rm deg}^2$, we identify a total of 2,232,134 groups, within which 402,947 groups have at least three member galaxies. We have visually checked and discussed the general properties of those richest groups at redshift $z>2.0$. By checking the galaxy number distributions within a $5-7\ h^{-1}\mathrm{Mpc}$ projected separation and a redshift difference $\Delta z \le 0.1$ around those richest groups at redshift $z>2$, we identified a list of 761, 343 and 43 protocluster candidates in the redshift bins $2\leq z<3$, $3\leq z<4$ and $z \geq 4$, respectively. In general, these catalogs of galaxy groups and protocluster candidates will provide useful environmental information in probing galaxy evolution along the cosmic time., Comment: 25 pages, 16 figures, 2 tables, accepted for publication in ApJ

The uncertainty in the photometric redshift estimation is one of the major systematics in weak lensing cosmology. The self-calibration method is able to reduce this systematics without assuming strong priors. We improve the recently proposed self-calibration algorithm to enhance the stability and robustness with the noisy measurement. The improved algorithm is tested on the power spectra measured from the simulated catalogues constructed according to DECaLS DR8 photometric catalogue. For the fiducial analysis with 5 equal-width redshift bins over $0

In a recent study, we developed a method to model the impact of photometric redshift uncertainty on the two-point correlation function (2PCF). In this method, we can obtain both the intrinsic clustering strength and the photometric redshift errors simultaneously by fitting the projected 2PCF with two integration depths along the line-of-sight. Here we apply this method to the DESI Legacy Imaging Surveys Data Release 8 (LS DR8), the largest galaxy sample currently available. We separate galaxies into 20 samples in 8 redshift bins from $z=0.1$ to $z=1.0$, and a few $\rm z$-band absolute magnitude bins, with $M_{\rm z} \le -20$. These galaxies are further separated into red and blue sub-samples according to their $M^{0.5}_{\rm r}-M^{0.5}_{\rm z}$ colors. We measure the projected 2PCFs for all these galaxy (sub-)samples, and fit them using our photometric redshift 2PCF model. We find that the photometric redshift errors are smaller in red sub-samples than the overall population. On the other hand, there might be some systematic photometric redshift errors in the blue sub-samples, so that some of the sub-samples show significantly enhanced 2PCF at large scales. Therefore, focusing only on the red and all (sub-)samples, we find that the biases of galaxies in these (sub-)samples show clear color, redshift and luminosity dependencies, in that red brighter galaxies at higher redshift are more biased than their bluer and low redshift counterparts. Apart from the best fit set of parameters, $\sigma_{z}$ and $b$, from this state-of-the-art photometric redshift survey, we obtain high precision intrinsic clustering measurements for these 40 red and all galaxy (sub-)samples. These measurements on large and small scales hold important information regarding the cosmology and galaxy formation, which will be used in our subsequent probes in this series., Comment: 16 pages, 12 figures, SCPMA in press