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Xin Zhang

Publications and source records attributed to Xin Zhang.

At least 1,207 records · Page 67Linked to original sources
arXiv2014

Quantifying the impact of future Sandage-Loeb test data on dark energy constraints

The Sandage-Loeb (SL) test is a unique method to probe dark energy in the "redshift desert" of $2\lesssim z\lesssim 5$, and thus it provides an important supplement to the other dark energy probes. Therefore, it is of great importance to quantify how the future SL test data impact on the dark energy constraints. To avoid the potential inconsistency in data, we use the best-fitting model based on the other geometric measurements as the fiducial model to produce 30 mock SL test data. The 10-yr, 20-yr, and 30-yr observations of SL test are analyzed and compared in detail. We show that compared to the current combined data of type Ia supernovae, baryon acoustic oscillation, cosmic microwave background, and Hubble constant, the 30-yr observation of SL test could improve the constraint on $Ω_m$ by about $80%$ and the constraint on $w$ by about $25%$. Furthermore, the SL test can also improve the measurement of the possible direct interaction between dark energy and dark matter. We show that the SL test 30-yr data could improve the constraint on $γ$ by about $30%$ and $10%$ for the $Q=γHρ_c$ and $Q=γHρ_{de}$ models, respectively.

astro-ph.CO↗
arXiv2014

Optimal investment-reinsurance policy under a long-term perspective

In this paper, we assume an insure is allowed to purchase proportional reinsurance and can invest his or her wealth into the financial market where a savings account, stocks and bonds are available. Different from classical optimal investment and reinsurance problem, this paper studies the insurer's long-term investment decision. Under this setting, our model consider the interest risk and the inflation risk. Specifically, we suppose the interest rate follows a stochastic process, while price index is described by a classical model. By solving Hamilton-Jacobi-Bellman equation, the closed-form expression of the optimal policy is obtained. Further, we prove the corresponding verification theorem without the usual Lipschitz condition. In the end, numerical examples are made to illustrate the difference of the optimal polices under Ho-lee model and Vasicek model.

q-fin.MF↗
arXiv2014

Optimal Hybrid Dividend Strategy Under The Markovian Regime-Switching Economy

In this paper, we consider the optimal dividend problem for a company. We describe the surplus process of the company by a diffusion model with regime switching. The aim of the company is to choose a dividend policy to maximize the expected total discounted payments until ruin. In this article, we consider a hybrid dividend strategy, that is, the company is allowed to conduct continuous dividend strategy as well as impulsive dividend strategy. In addition, we consider the change of economy, which is characterized by a markovian regime-switching, and under the setting of two regimes, we solve the problem and obtain the analytical solution for the value function.

q-fin.MF↗
arXiv2014

Tilt of primordial gravitational wave spectrum in a universe with sterile neutrinos

In this work, we constrain the spectral index $n_t$ of the primordial gravitational wave power spectrum in a universe with sterile neutrinos by using the Planck temperature data, the WMAP 9-year polarization data, the baryon acoustic oscillation data, and the BICEP2 data. We call this model the $Λ$CDM+$r$+$ν_s$+$n_t$ model. The additional massive sterile neutrino species can significantly relieve the tension between the Planck and BICEP2 data, and thus can reduce the possible effects of this tension on the fit results of $n_t$. To constrain the parameters of sterile neutrino, we also utilize the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck CMB lensing data, and the cosmic shear data. We find that due to the fact that the BICEP2 data are most sensitive to the multipole $\ell\sim150$ corresponding to $k\sim0.01$ Mpc$^{-1}$, there exists a strong anticorrelation between $n_t$ and $r_{0.002}$ in the BICEP2 data, and this further results in a strongly blue-tilt spectrum. However, a slightly red-tilt tensor power spectrum is also allowed by the BICEP2 data in the region with larger value of $r_{0.002}$. By using the full data sets, we obtain $m_{ν,{\rm{sterile}}}^{\rm{eff}}=0.48^{+0.11}_{-0.13}$ eV, $N_{\rm{eff}}=3.73^{+0.34}_{-0.37}$, and $n_t=0.96^{+0.48}_{-0.63}$ for the $Λ$CDM+$r$+$ν_s$+$n_t$ model.

astro-ph.CO↗
arXiv2014

The edge chromatic number of outer-1-planar graphs

A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once. In this paper, we completely determine the edge chromatic number of outer 1-planar graphs.

math.CO↗
arXiv2014

Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields

The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are derived for the second eigenvalue problem associated with spin degrees of freedom. It is found that the second eigenvalue problem can be transformed to that of the transfer matrix of the inhomogeneous XXX spin chain, which allows us to obtain the spectrum of the Hamiltonian and the associated Bethe ansatz equations by the off-diagonal Bethe ansatz method.

math-ph↗
arXiv2014

Dark radiation from a unified dark fluid model

We present a unified dark fluid model to describe the possible evolutionary behavior of $ΔN_\mathrm{eff}$ in dark radiation. This model can be viewed as an interacting model for the dark sectors, in which dark matter interacts with dark radiation. We show that the evolution of $ΔN_\mathrm{eff}$ can be nicely explained without some drawbacks, such as the blowup of $ΔN_\mathrm{eff}$ and the non-vanishing interaction at the late time.

astro-ph.CO↗
arXiv2014

Large-scale stable interacting dark energy model: Cosmological perturbations and observational constraints

Dark energy might interact with cold dark matter in a direct, nongravitational way. However, the usual interacting dark energy models (with constant $w$) suffer from some catastrophic difficulties. For example, the $Q\proptoρ_{\rm c}$ model leads to an early-time large-scale instability, and the $Q\proptoρ_{\rm de}$ model gives rise to the future unphysical result for cold dark matter density (in the case of a positive coupling). In order to overcome these fatal flaws, we propose in this paper an interacting dark energy model (with constant $w$) in which the interaction term is carefully designed to realize that $Q\proptoρ_{\rm de}$ at the early times and $Q\proptoρ_{\rm c}$ in the future, simultaneously solving the early-time superhorizon instability and future unphysical $ρ_{\rm c}$ problems. The concrete form of the interaction term in this model is $Q=3βH \frac{ρ_{\rm{de}}ρ_{\rm{c}}}{ρ_{\rm{de}}+ρ_{\rm{c}}}$, where $β$ is the dimensionless coupling constant. We show that this model is actually equivalent to the decomposed new generalized Chaplygin gas (NGCG) model, with the relation $β=-αw$. We calculate the cosmological perturbations in this model in a gauge-invariant way and show that the cosmological perturbations are stable during the whole expansion history provided that $β>0$. Furthermore, we use the Planck data in conjunction with other astrophysical data to place stringent constraints on this model (with eight parameters), and we find that indeed $β>0$ is supported by the joint constraint at more than 1$σ$ level. The excellent theoretical features and the support from observations all indicate that the decomposed NGCG model deserves more attention and further investigation.

astro-ph.CO↗
arXiv2014

A Stochastic Maximum Principle for Processes Driven by G-Brownian Motion and Applications to Finance

In this paper, we consider the stochastic optimal control problems under model risk caused by uncertain volatilities. To have a mathematical consistent framework we use the notion of G-expectation and its corresponding G-Brwonian motion introduced by Peng(2007). Based on the theory of stochastic differential equations on a sublinear expectation space $(Ω,\mathcal{H},\hat{\mathbb{E}})$, we prove a stochastic maximum principle for controlled processes driven by G-Brownian motion. Then we obtain the maximum condition in terms of the $\mathcal{H}$-function plus some convexity conditions constitute sufficient conditions for optimality. Finally, we solve a portfolio optimization problem with ambiguous volatility as an explicitly illustrated example of the main result.

math.OC↗
arXiv2014

Algorithms for envelope estimation

Envelopes were recently proposed as methods for reducing estimative variation in multivariate linear regression. Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable one-dimensional (1D) algorithm for estimating an envelope in general. We reveal an important structural property of envelopes that facilitates our algorithm, and we prove both Fisher consistency and root-n-consistency of the algorithm.

stat.ME↗
arXiv2014

Equitable list point arboricity of graphs

A graph $G$ is list point $k$-arborable if, whenever we are given a $k$-list assignment $L(v)$ of colors for each vertex $v\in V(G)$, we can choose a color $c(v)\in L(v)$ for each vertex $v$ so that each color class induces an acyclic subgraph of $G$, and is equitable list point $k$-arborable if $G$ is list point $k$-arborable and each color appears on at most $\lceil |V(G)|/k\rceil$ vertices of $G$. In this paper, we conjecture that every graph $G$ is equitable list point $k$-arborable for every $k\geq \lceil(Δ(G)+1)/2\rceil$ and settle this for complete graphs, 2-degenerate graphs, 3-degenerate claw-free graphs with maximum degree at least 4, and planar graphs with maximum degree at least 8.

math.CO↗
arXiv2014

Equitable vertex arboricity of planar graphs

Let $G_1$ be a planar graph such that all cycles of length at most 4 are independent and let $G_2$ be a planar graph without 3-cycles and adjacent 4-cycles. It is proved that the set of vertices of $G_1$ and $G_2$ can be equitably partitioned into $t$ subsets for every $t\geq 3$ so that each subset induces a forest. These results partially confirm a conjecture of Wu, Zhang and Li.

math.CO↗
arXiv2014

Exploring the evolution of color-luminosity parameter $β$ and its effects on parameter estimation

It has been found in previous studies that, for the Supernova Legacy Survey three-year (SNLS3) data, there is strong evidence for the redshift-evolution of color-luminosity parameter $β$. In this paper, using three simplest dark energy models ($Λ$CDM, $w$CDM, and CPL), we further explore the evolution of $β$ and its effects on parameter estimation. In addition to the SNLS3 data, we also take into account the Planck distance priors data, as well as the latest galaxy clustering (GC) data extracted from SDSS DR7 and BOSS. We find that, for all the models, adding a parameter of $β$ can reduce $χ^2_{min}$ by $\sim$ 36, indicating that $β_1 = 0$ is ruled out at 6$σ$ confidence levels. In other words, $β$ deviates from a constant at 6$σ$ confidence levels. This conclusion is insensitive to the dark energy models considered, showing the importance of considering the evolution of $β$ in the cosmology-fits. Furthermore, it is found that varying $β$ can significantly change the fitting results of various cosmological parameters: using the SNLS3 data alone, varying $β$ yields a larger $Ω_m$ for the $Λ$CDM model; using the SNLS3+CMB+GC data, varying $β$ yields a larger $Ω_m$ and a smaller $h$ for all the models. Moreover, we find that these results are much closer to those given by the CMB+GC data, compared to the cases of treating $β$ as a constant. This indicates that considering the evolution of $β$ is very helpful for reducing the tension between supernova and other cosmological observations.

astro-ph.CO↗
arXiv2014

Regular and exceptional spectra of the two-qubit quantum Rabi model

Two-qubit system is the foundation of constructing the universal quantum gate. We have studied the two-qubit Rabi model for the general case and its generalizations with dipole, XXX and XYZ Heisenberg qubit-qubit interactions, which are commonly used in quantum computation. Their solutions are presented analytically with eigenstates can be obtained in terms of extended coherent states or Fock states and applied to the construction of the ultrafast two-qubit quantum gate in circuit QED and quantum state storage and transfer. Some novel kinds of quasi-exact solutions are found for specific sets of parameters, causing level crossings within the same parity subspace, which do not appear in the regular spectrum, indicating its non-integrability. These eigenstates are very interesting for quantum computing and single photon experiments because they are formed by just a few Fock states, and in some cases, with at most one photon. They are also easy to prepare, since they exist for all qubit-photon coupling values with constant eigenenergy and the qubit energy splittings can be fine tuned in the experiment in contrast to the coupling.

quant-ph↗
arXiv2014

Revisiting the interacting model of new agegraphic dark energy

In this paper, a new version of the interacting model of new agegraphic dark energy (INADE) is proposed and analyzed in detail. The interaction between dark energy and dark matter is reconsidered. The interaction term $Q=bH_0ρ_{\rm de}^αρ_{\rm dm}^{1-α}$ is adopted, which abandons the Hubble expansion rate $H$ and involves both $ρ_{\rm de}$ and $ρ_{\rm dm}$. Moreover, the new initial condition for the agegraphic dark energy is used, which solves the problem of accommodating baryon matter and radiation in the model. The solution of the model can be given using an iterative algorithm. A concrete example for the calculation of the model is given. Furthermore, the model is constrained by using the combined Planck data (Planck+BAO+SNIa+$H_0$) and the combined WMAP-9 data (WMAP+BAO+SNIa+$H_0$). Three typical cases are considered: (A) $Q=bH_0ρ_{\rm de}$, (B) $Q=bH_0\sqrt{ρ_{\rm de}ρ_{\rm dm}}$, and (C) $Q=bH_0ρ_{\rm dm}$, which correspond to $α=1$, 1/2, and 0, respectively. The departures of the models from the $Λ$CDM model are measured by the $Δ$BIC and $Δ$AIC values. It is shown that the INADE model is better than the NADE model in the fit, and the INADE(A) model is the best in fitting data among the three cases.

astro-ph.CO↗
arXiv2014

The ultra-low-frequency shear modes of 2-4 layer graphenes observed in their scroll structures at edges

The in-plane shear modes between neighbor-layers of 2-4 layer graphenes (LGs) and the corresponding graphene scrolls rolled up by 2-4LGs were investigated by Raman scattering. In contrast to that just one shear mode was observed in 3-4LGs, all the shear modes of 3-4LGs were observed in 3-4 layer scrolls (LSs), whose frequencies agree well with the theoretical predication by both a force-constant model and a linear chain model. In comparison to the broad width (about 12cm$^{-1}$) for the G band in graphite, all the shear modes exhibit an intrinsic line width of about 1.0 cm$^{-1}$. The local electronic structures dependent on the local staking configurations enhance the intensity of the shear modes in corresponding 2-4LSs zones, which makes it possible to observe all the shear modes. It provides a direct evidence that how the band structures of FLGs can be sensitive to local staking configurations. This result can be extended to n layer graphene (n > 4) for the understanding of the basic phonon properties of multi-layer graphenes. This observation of all-scale shear modes can be foreseen in other 2D materials with similar scroll structures.

cond-mat.mtrl-sci↗
arXiv2013

On r-equitable chromatic threshold of Kronecker products of complete graphs

A graph $G$ is $r$-equitably $k$-colorable if its vertex set can be partitioned into $k$ independent sets, any two of which differ in size by at most $r$. The $r$-equitable chromatic threshold of a graph $G$, denoted by $χ_{r=}^*(G)$, is the minimum $k$ such that $G$ is $r$-equitably $k'$-colorable for all $k'\ge k$. Let $G\times H$ denote the Kronecker product of graphs $G$ and $H$. In this paper, we completely determine the exact value of $χ_{r=}^*(K_m\times K_n)$ for general $m,n$ and $r$. As a consequence, we show that for $r\ge 2$, if $n\ge \frac{1}{r-1}(m+r)(m+2r-1)$ then $K_m\times K_n$ and its spanning supergraph $K_{m(n)}$ have the same $r$-equitable colorability, and in particular $χ_{r=}^*(K_m\times K_n)=χ_{r=}^*(K_{m(n)})$, where $K_{m(n)}$ is the complete $m$-partite graph with $n$ vertices in each part.

math.CO↗