P-T phase diagram of a holographic s+p model from Gauss-Bonnet gravity

In this paper, we study the holographic s+p model in 5-dimensional bulk gravity with the Gauss-Bonnet term. We work in the probe limit and give the $\Delta$-T phase diagrams at three different values of the Gauss-Bonnet coefficient to show the effect of the Gauss-Bonnet term. We also construct the P-T phase diagrams for the holographic system using two different definitions of the pressure and compare the results.Comment: 17 pages, 5 figures, we have added new P-T phase diagrams with the pressure defined in boundary stress-energy tenso

Statistical Analysis in Empirical Bayes and in Causal inference

In Part I titled Empirical Bayes Estimation, we discuss the estimation of a heteroscedastic multivariate normal mean in terms of the ensemble risk. We first derive the ensemble minimax properties of various estimators that shrink towards zero through the empirical Bayes method. We then generalize our results to the case where the variances are given as a common unknown but estimable chi-squared random variable scaled by different known factors. We further provide a class of ensemble minimax estimators that shrink towards the common mean. We also make comparison and show differences between results from the heteroscedastic case and those from the homoscedastic model.In Part II titled Causal Inference Analysis, we study the estimation of the causal effect of treatment on survival probability up to a given time point among those subjects who would comply with the assignment to both treatment and control when both administrative censoring and noncompliance occur. In many clinical studies with a survival outcome, administrative censoring occurs when follow-up ends at a pre-specified date and many subjects are still alive. An additional complication in some trials is that there is noncompliance with the assigned treatment. We first discuss the standard instrumental variable method for survival outcomes and parametric maximum likelihood methods, and then develop an efficient plug-in nonparametric empirical maximum likelihood estimation (PNEMLE) approach. The PNEMLE method does not make any assumptions on outcome distributions, and makes use of the mixture structure in the data to gain efficiency over the standard instrumental variable method. Theoretical results of the PNEMLE are derived and the method is illustrated by an analysis of data from a breast cancer screening trial. From our limited mortality analysis with administrative censoring times 10 years into the follow-up, we find a significant benefit of screening is present after 4 years (at the 5% level) and this persists at 10 years follow-up

Split degenerate states and stable p+ip phases from holography

In this paper, we investigate the p+$i$p superfluid phases in the complex vector field holographic p-wave model. We find that in the probe limit, the p+$i$p phase and the p-wave phase are equally stable, hence the p and $i$p orders can be mixed with an arbitrary ratio to form more general p+$\lambda i$p phases, which are also equally stable with the p-wave and p+$i$p phases. As a result, the system possesses a degenerate thermal state in the superfluid region. We further study the case with considering the back reaction on the metric, and find that the degenerate ground states will be separated into p-wave and p+$i$p phases, and the p-wave phase is more stable. Finally, due to the different critical temperature of the zeroth order phase transitions from p-wave and p+$i$p phases to the normal phase, there is a temperature region where the p+$i$p phase exists but the p-wave phase doesn't. In this region we find the stable p+$i$p phase for the first time.Comment: 16 pages, 5 figures; typos correcte

Phase transitions in a holographic s+p model with backreaction

In a previous paper (arXiv:1309.2204, JHEP 1311 (2013) 087), we present a holographic s+p superconductor model with a scalar triplet charged under an SU(2) gauge field in the bulk. We also study the competition and coexistence of the s-wave and p-wave orders in the probe limit. In this work we continue to study the model by considering the full back-reaction The model shows a rich phase structure and various condensate behaviors such as the "n-type" and "u-type" ones, which are also known as reentrant phase transitions in condensed matter physics. The phase transitions to the p-wave phase or s+p coexisting phase become first order in strong back-reaction cases. In these first order phase transitions, the free energy curve always forms a swallow tail shape, in which the unstable s+p solution can also play an important role. The phase diagrams of this model are given in terms of the dimension of the scalar order and the temperature in the cases of eight different values of the back reaction parameter, which show that the region for the s+p coexisting phase is enlarged with a small or medium back reaction parameter, but is reduced in the strong back-reaction cases.Comment: 15 pages(two-column), 9 figure

Observation of Landau level-like quantizations at 77 K along a strained-induced graphene ridge

Recent studies show that the electronic structures of graphene can be modified by strain and it was predicted that strain in graphene can induce peaks in the local density of states (LDOS) mimicking Landau levels (LLs) generated in the presence of a large magnetic field. Here we report scanning tunnelling spectroscopy (STS) observation of nine strain-induced peaks in LDOS at 77 K along a graphene ridge created when the graphene layer was cleaved from a sample of highly oriented pyrolytic graphite (HOPG). The energies of these peaks follow the progression of LLs of massless 'Dirac fermions' (DFs) in a magnetic field of 230 T. The results presented here suggest a possible route to realize zero-field quantum Hall-like effects at 77 K

Ensemble Minimax Estimation for Multivariate Normal Means

This article discusses estimation of a heteroscedastic multivariate normal mean in terms of the ensemble risk. We first derive the ensemble minimaxity properties of various estimators that shrink towards zero. We then generalize our results to the case where the variances are given as a common unknown but estimable chi-squared random variable scaled by different known factors. We further provide a class of ensemble minimax estimators that shrink towards the common mea