Testing the Distance-Duality Relation with a Combination of Cosmological Distance Observations

In this paper, we propose an accurate test of the distance-duality (DD) relation, $\eta=D_{L}(z)(1+z)^{-2}/D_{A}(z)=1$ (where $D_{L}$ and $D_{A}$ are the luminosity distances and angular diameter distances, respectively), with a combination of cosmological observational data of Type Ia Supernave (SNe Ia) from Union2 set and the galaxy cluster sample under an assumption of spherical model. In order to avoid bias brought by redshift incoincidence between observational data and to consider redshift error bars of both clusters and SNe Ia in analysis, we carefully choose the SNe Ia points which have the minimum acceptable redshift difference of the galaxy cluster sample ($|\Delta z|_{\rm min} =\sigma_{z, \rm SN}+\sigma_{z, \rm cluster}$). By assuming $\eta$ a constant and functions of the redshift parameterized by six different expressions, we find that there exists no conceivable evidence for variations in the DD relation concerning with observational data, since it is well satisfied within $1\sigma$ confidence level for most cases. Further considering different values of $\Delta z$ in constraining, we also find that the choosing of $\Delta z$ may play an important role in this model-independent test of the distance-duality relation for the spherical sample of galaxy clusters.Comment: 9 pages, 4 figures, 1 table. accepted for publication in Res. Astron. Astrophy

A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem

We propose a monotone approximation scheme for a class of fully nonlinear PDEs called G-equations. Such equations arise often in the characterization of G-distributed random variables in a sublinear expectation space. The proposed scheme is constructed recursively based on a piecewise constant approximation of the viscosity solution to the G-equation. We establish the convergence of the scheme and determine the convergence rate with an explicit error bound, using the comparison principles for both the scheme and the equation together with a mollification procedure. The first application is obtaining the convergence rate of Peng's robust central limit theorem with an explicit bound of Berry-Esseen type. The second application is an approximation scheme with its convergence rate for the Black-Scholes-Barenblatt equation.Comment: 31 page

An approximation scheme for semilinear parabolic PDEs with convex and coercive Hamiltonians

We propose an approximation scheme for a class of semilinear parabolic equations that are convex and coercive in their gradients. Such equations arise often in pricing and portfolio management in incomplete markets and, more broadly, are directly connected to the representation of solutions to backward stochastic differential equations. The proposed scheme is based on splitting the equation in two parts, the first corresponding to a linear parabolic equation and the second to a Hamilton-Jacobi equation. The solutions of these two equations are approximated using, respectively, the Feynman-Kac and the Hopf-Lax formulae. We establish the convergence of the scheme and determine the convergence rate, combining Krylov's shaking coefficients technique and Barles-Jakobsen's optimal switching approximation.Comment: 24 page

Testing the phenomenological interacting dark energy with observational H(z)H(z) data

In order to test the possible interaction between dark energy and dark matter, we investigate observational constraints on a phenomenological scenario, in which the ratio between the dark energy and matter densities is proportional to the power law case of the scale factor, $r\equiv (\rho_X/\rho_m)\propto a^{\xi}$. By using the Markov chain Monte Carlo method, we constrain the phenomenological interacting dark energy model with the newly revised $H(z)$ data, as well as the cosmic microwave background (CMB) observation from the 7-year Wilkinson Microwave Anisotropy Probe (WMAP7) results, the baryonic acoustic oscillation (BAO) observation from the spectroscopic Sloan Digital Sky Survey (SDSS) data release 7 (DR7) galaxy sample and the type Ia supernovae (SNe Ia) from Union2 set. The best-fit values of the model parameters are $\Omega_{m0}=0.27_{-0.02}^{+0.02}(1\sigma)_{-0.03}^{+0.04}(2\sigma)$, $\xi=3.15_{-0.50}^{+0.48}(1\sigma)_{-0.71}^{+0.72}(2\sigma)$, and $w_X=-1.05_{-0.14}^{+0.15}(1\sigma)_{-0.21}^{+0.21}(2\sigma)$, which are more stringent than previous results. These results show that the standard $\Lambda$CDM model without any interaction remains a good fit to the recent observational data; however, the interaction that the energy transferring from dark matter to dark energy is slightly favored over the interaction from dark energy to dark matter. It is also shown that the $H(z)$ data can give more stringent constraints on the phenomenological interacting scenario when combined to CMB and BAO observations, and the confidence regions of $H(z)$+BAO+CMB, SNe+BAO+CMB, and $H(z)$+SNe+BAO+CMB combinations are consistent with each other.Comment: 6 pages, 4 figures, 1 table. MNRAS in pres

Towards transcriptome-wide studies of mRNA translation in tissues from cancer patients

Gene expression consists of multiple strictly regulated steps, including transcription, RNA modification, splicing, messenger RNA (mRNA) transport, mRNA degradation, mRNA translation and protein degradation. mRNA translation, the most energy consuming step, plays a critical role in gene expression via global and selective control of protein synthesis. Translation is a complex process that is commonly divided into initiation, elongation and termination. Among these, translation initiation is widely acknowledged as the rate-limiting step for mRNA translation. The mammalian/mechanistic target of rapamycin (mTOR) pathway, as one important regulator of translation initiation, delivers vital signaling by phosphorylating eIF4E binding proteins (4E-BPs) thereby facilitating eIF4F complex formation which participates in eukaryotic cap dependent translation. Increased mTOR activity and dysregulation of translation have been observed in many diseases, such as cancer as well as immune and metabolic disorders. Sequence and structure features of the mRNA, the translational apparatus and trans-acting proteins facilitate or restrict translation regulation of an mRNA. Moreover, these factors can potentially alter the translational efficiency of an mRNA thereby impacting protein levels without changes in mRNA levels. Accordingly, a well-established technique to study translatomes, polysome profiling, separates efficiently translated mRNA from total mRNA into multiple fractions based on the number of ribosomes bound on the mRNA. Extraction of these fractions is a time consuming and laborious process, which makes polysome profiling inconvenient for large experiments or samples with low RNA amounts. Until now, these shortcomings have prevented assessments of translatomes in patient tissue samples. This thesis introduces an optimized non-linear sucrose gradient which consistently enriches the efficiently translated mRNA in merely one or two fractions, thus reducing sample handling 5-10 fold and saving time in the lab 10-20 fold. When combined with smart-seq2 RNA sequencing, translatomes can be obtained from samples with low amount of RNA and small bio-banked tissues. mRNA yields and translatomes acquired from the optimized gradients resemble those obtained from the standard linear gradients. Thus, this optimized polysome-profiling technique expands the usage of the methodology to small tissue samples and primary cells in large study designs. Insulin sensitive mRNA translation has been observed in cancer cells derived from insulin insensitive organs, for instance breast. It is largely unknown that if this insulin sensitivity resembles that of cells from insulin sensitive organs or if cancer cells tailor a novel program. To this end, this thesis explored insulin’s effect on metabolomes and translatomes in human primary myotubes, human mammary epithelial cells immortalized with human telomerase (HMEC/hTERT) and the MCF7 breast cancer cells. The data indicates that MCF7 cells have developed pathological responses to insulin induction that differ from those observed in cells from insulin sensitive or insensitive organs. The exploration of mechanisms concealed behind this discrepancy would disclose a potential strategy for cancer treatment through annulment of cancer specific effects of insulin. The role of mRNA translation during treatments with experimental anti-cancer drugs or those used in the clinic is largely unknown. We examined the effect on translation of one such experimental drug called “Reactivation of p53 and induction of tumor cell apoptosis” (RITA). The α subunit of eukaryotic initiation factor 2 (eIF2α) is a key regulator of translation initiation. We found eIF2α to be phosphorylated during RITA treatment and to be involved in RITA induced apoptosis and repression of mRNA translation. This activity of RITA is independent of TP53 and mTOR pathway. The inhibition of eIF2α phosphorylation counteracts the impact of RITA on apoptosis and clonogenicity. Another aspect of this thesis explored regulation of translation in immune cells. Short post- infusion persistence restricts treatment of hematological malignancies via adoptive infusion of stimulated natural killer (NK) cells. Interleukin-15 (IL-15) was demonstrated to hold stronger ability than IL-2 to maintain antitumor functions of NK cells after cytokine deprivation. To explore the mechanism underlying these differences, a transcriptome wide study through polysome-profiling technique was applied. Further, the role of mTOR pathway in this superiority of IL-15 was also investigated. Coupled with clinical outcome of patients with B-cell lymphoma, IL-15 but not IL-2 is argued to be implemented in adoptive NK cell cancer therapy. In conclusion, in order to facilitate studies of the translatome for samples with low amount of RNA and small bio-banked tissues, the optimized non-linear gradient was designed. Its performance in aforementioned samples for large experiment set and general applicability was verified to be satisfying. The study on cancer specific effects of insulin unraveled the prospect to selectively target insulin/IGF1 dependent effects on metabolomes and/or translatomes for cancer therapy. As two important pathways regulating translation initiation, the effect of mTOR in immune cell functions and eIF2α in RITA induced apoptosis were unveiled and explored

Depth Extraction from a Single Image and Its Application

In this chapter, a method for the generation of depth map was presented. To generate the depth map from an image, the proposed approach involves application of a sequence of blurring and deblurring operations on a point to determine the depth of the point. The proposed method makes no assumptions with regard to the properties of the scene in resolving depth ambiguity in complex images. Since applications involving depth map manipulation can be achieved by obtaining all-in-focus images through a deblurring operation and then blurring the obtained images, we have presented methods to derive all-in-focus images from our depth maps. Furthermore, 2D to 3D conversion can also be achieved from the estimated depth map. Some demonstrations show the performance and applications of the estimated depth map in this chapter