The Cross-correlation of KSZ Effect and 21 cm Intensity Mapping with Tidal Reconstruction

We discuss the possibility of studying diffuse baryon distributions with kinematic Sunyaev-Zel'dovich (kSZ) effect by correlating cosmic microwave background (CMB) temperature fluctuations with density fluctuations from 21\,cm intensity mapping (IM). The biggest challenge for the cross-correlation is the loss of large-scale information in IM, due to foregrounds and the zero spacing problem of interferometers. We apply the tidal reconstruction algorithm to restore the lost large-scale modes, which increases the correlation by more than a factor of three. With the predicted foreground level, we expect a $\sim20\,\sigma$ detection of kSZ signal for $0.8\lesssim z\lesssim2.5$ with CHIME and Planck, and a $\sim40\, \sigma$ detection with HIRAX and Planck. The significance can be greatly increased with next-generation facilities of higher spatial resolutions.Comment: 8 pages, 4 figures, submit to PR

Optimized Structured Sparse Sensing Matrices for Compressive Sensing

We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently We design the robust structured sparse sensing matrix through minimizing the distance between the Gram matrix of the equivalent dictionary and the target Gram of matrix holding small mutual coherence. Moreover, a regularization is added to enforce the robustness of the optimized structured sparse sensing matrix to the sparse representation error (SRE) of signals of interests. An alternating minimization algorithm with global sequence convergence is proposed for solving the corresponding optimization problem. Numerical experiments on synthetic data and natural images show that the obtained structured sensing matrix results in a higher signal reconstruction than a random dense sensing matrix.Comment: 2 tables, 10 figure

Ill-posedness for the 2D viscous shallow water equations in the critical Besov spaces

In this paper, we prove that the 2D viscous shallow water equations is ill-posed in the critical Besov spaces \B^{\frac2p-1}_{p,1}(\R^2) with $p>4$. Our proof mainly depends on the method introduced by the paper \cite{C-M-Z4}.Comment:

Unbiased constraints on the clumpiness of universe from standard candles

We perform unbiased tests for the clumpiness of universe by confronting the Zel'dovich-Kantowski-Dyer-Roeder luminosity distance which describes the effect of local inhomogeneities on the propagation of light with the observational one estimated from measurements of standard candles, i.e., type Ia supernovae (SNe Ia) and gamma-ray bursts (GRBs). Methodologically, we first determine the light-curve fitting parameters which account for distance estimation in SNe Ia observations and luminosity/energy relations which are responsible for distance estimation of GRBs in the global fit to reconstruct the Hubble diagrams in the context of a clumpy universe. Subsequently, these Hubble diagrams allow us to achieve unbiased constraints on the matter density parameter $\Omega_m$ as well as clumpiness parameter $\eta$ which quantifies the fraction of homogeneously distributed matter within a given light cone. At 1$\sigma$ confidence level, the constraints are $\Omega_m=0.34\pm0.02$ and $\eta=1.00^{+0.00}_{-0.02}$ from the joint analysis. The results suggest that the universe full of Friedman-Lema\^{i}tre-Robertson-Walker fluid is favored by observations of standard candles with very high statistical significance. On the other hand, they may also indicate that the Zel'dovich-Kantowski-Dyer-Roeder approximation is a sufficient accurate form to describe the effects of local homogeneity in the expanding universe.Comment: 20 pages, 5 figures, and 2 tables. Accepted for publication in Phys. Rev.

Non-Markovian dynamics without using quantum trajectory

Open quantum system interacting with structured environment is important and manifests non- Markovian behavior, which was conventionally studied using quantum trajectory stochastic method. In this paper, by dividing the effects of the environment into two parts, we propose a deterministic method without using quantum trajectory. This method is more efficient and accurate than stochastic method in most Markovian and non-Markovian cases. We also extend this method to the generalized Lindblad master equation.Comment: 4 pages, 2 figure

Nonlinear reconstruction of redshift space distortions

We apply nonlinear reconstruction to the dark matter density field in redshift space and solve for the nonlinear mapping from the initial Lagrangian position to the final redshift space position. The reconstructed anisotropic field inferred from the nonlinear displacement correlates with the linear initial conditions to much smaller scales than the redshift space density field. The number of linear modes in the density field is improved by a factor of 30-40 after reconstruction. We thus expect this reconstruction approach to substantially expand the cosmological information including baryon acoustic oscillations and redshift space distortions for dense low-redshift large scale structure surveys including for example SDSS main sample, DESI BGS, and 21 cm intensity mapping surveys.Comment: 18 pages, 21 figures, published version. The nonlinear reconstruction code is available at https://github.com/ColdThunder/NR-cod

Regularity of powers of edge ideals of vertex-weighted oriented unicyclic graphs

In this paper we provide some exact formulas for the regularity of powers of edge ideals of vertex-weighted oriented cycles and vertex-weighted unicyclic graphs. These formulas are functions of the weight of vertices and the number of edges. We also give some examples to show that these formulas are related to direction selection and the weight of vertices

Projective dimension and regularity of edge ideals of some vertex-weighted oriented mm-partite graphs

In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals associated to three special types of vertex-weighted oriented $m$-partite graphs. These formulas are functions of the weight and number of vertices. We also give some examples to show that these formulas are related to direction selection and the weight of vertices.Comment: arXiv admin note: substantial text overlap with arXiv:1904.03019, arXiv:1904.02305, arXiv:1802.0631

Resistive MHD Modelling of Quasi-Single Helicity State in the KTX Regimes

The potential formation of the quasi-single-helicity (QSH) state in the Keda Torus eXperiment (KTX) is investigated in resistive MHD simulations using the NIMROD code. We focus on the effects of finite resistivity on the mode structure and characteristics of the dominant linear and nonlinear resistive tearing-mode in a finite $\beta$, cylindrical configuration of reversed field pinch model for KTX. In the typical resistive regimes of KTX where Lundquist number $S=5 \times 10^4$, the plasma transitions to a steady QSH state after evolving through an initial transient phase with multiple helicities. The dominant mode of the QSH state develops from the dominant linear tearing mode instability. In lower $\beta$ regime, the QSH state are intermittent and short in duration; in higher $\beta$ regime, the QSH state persists for a longer time and should be more observable in experiment.Comment: The manuscript confirms that the MHD dynamics of RFP quasi-single helical states is based on the resistive-kink tearing modes, shows the spontaneous emergence of a QSH state during the RFP dynamics and studies the effect of a finite pressure on the system. The authors find that higher plasma pressure increases the persistence of QSH state

Projective dimension and regularity of edge ideal of some weighted oriented graphs

In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals associated to vertex weighted rooted forests and oriented cycles. As some consequences, we give some exact formulas for the depth of these ideals.Comment: 11 page