Strong gravitational lensing in a rotating Kaluza-Klein black hole with squashed horizons

We have investigated the strong gravitational lensing in a rotating squashed Kaluza-Klein (KK) black hole spacetime. Our result show that the strong gravitational lensings in the rotating squashed KK black hole spacetime have some distinct behaviors from those in the backgrounds of the four-dimensional Kerr black hole and of the squashed KK G\"{o}del black hole. In the rotating squashed KK black hole spacetime, the marginally circular photon radius $\rho_{ps}$, the coefficient $\bar{a}$, $\bar{b}$, the deflection angle $\alpha(\theta)$ in the $\phi$ direction and the corresponding observational variables are independent of whether the photon goes with or against the rotation of the background, which is different with those in the usual four-dimensional Kerr black hole spacetime. Moreover, we also find that with the increase of the scale of extra dimension $\rho_0$, the marginally circular photon radius $\rho_{ps}$ and the angular position of the relativistic images $\theta_\infty$ first decreases and then increases in the rotating squashed KK black hole for fixed rotation parameter $b$, but in the squashed KK G\"{o}del black hole they increase for the smaller global rotation parameter $j$ and decrease for the larger one. In the extremely squashed case $\rho_0=0$, the coefficient $\bar{a}$ in the rotating squashed KK black hole increases monotonously with the rotation parameter, but in the squashed KK G\"{o}del black hole it is a constant and independent of the global rotation of the G\"{o}del Universe.Comment: 20 pages; 7 figures. Accepted for publication in JHEP. arXiv admin note: substantial text overlap with arXiv:1102.008

Functional linear regression that's interpretable

Regression models to relate a scalar $Y$ to a functional predictor $X(t)$ are becoming increasingly common. Work in this area has concentrated on estimating a coefficient function, $\beta(t)$, with $Y$ related to $X(t)$ through $\int\beta(t)X(t) dt$. Regions where $\beta(t)\ne0$ correspond to places where there is a relationship between $X(t)$ and $Y$. Alternatively, points where $\beta(t)=0$ indicate no relationship. Hence, for interpretation purposes, it is desirable for a regression procedure to be capable of producing estimates of $\beta(t)$ that are exactly zero over regions with no apparent relationship and have simple structures over the remaining regions. Unfortunately, most fitting procedures result in an estimate for $\beta(t)$ that is rarely exactly zero and has unnatural wiggles making the curve hard to interpret. In this article we introduce a new approach which uses variable selection ideas, applied to various derivatives of $\beta(t)$, to produce estimates that are both interpretable, flexible and accurate. We call our method "Functional Linear Regression That's Interpretable" (FLiRTI) and demonstrate it on simulated and real-world data sets. In addition, non-asymptotic theoretical bounds on the estimation error are presented. The bounds provide strong theoretical motivation for our approach.Comment: Published in at http://dx.doi.org/10.1214/08-AOS641 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Non-local matching of adjectival modifiers in Mandarin stacked relative clauses

Bhatt (2002) argues for a head-raising analysis (HRA) of relative clauses based on the interpretation of certain adjectival modifiers on the head. This paper evaluates Bhatt’s argument in the configurations of stacked relative clauses (SRCs) in Mandarin and argues that the internal interpretation of adjectival modifiers on the head is not a sufficient argument for HRA. We show that adjectival modifiers on the external head of SRCs can receive an internal interpretation when reconstruction is not possible. We propose that the internal reading can instead be derived by non-local matching between the adjectival modifier and its internal representation

Efficiency of Top-Down Parsing of Recursive Adjunction for Tree Adjoining Grammar

CKY-type parser and Earley-type parser are two widely-used parsing algorithms for Tree Adjoining Grammar (TAG). In contrast, a standard top-down parser is not efficient since the looping problem occurs during both the left and right recursion of standard TAG derivation. Roark (2001) combines the top-down parser for CFG with a beam search, showing that the probabilistic top-down parser yields a perplexity improvement over previous results. In this paper, we define the stochastic tree adjoining grammar and apply the probabilistic top-down parser for CFG to TAG. Comparing the parsing efficiency of the standard and alternative TAG derivation of the recursive adjunction, we find that the alternative derivation is more efficient since it avoids the looping problem of the right recursion, increasing the parsing efficiency of our top-down parser