Age Problem in Lemaitre-Tolman-Bondi Void Models

As is well known, one can explain the current cosmic acceleration by considering an inhomogeneous and/or anisotropic universe (which violates the cosmological principle), without invoking dark energy or modified gravity. The well-known one of this kind of models is the so-called Lema\^{\i}tre-Tolman-Bondi (LTB) void model, in which the universe is spherically symmetric and radially inhomogeneous, and we are living in a locally underdense void centered nearby our location. In the present work, we test various LTB void models with some old high redshift objects (OHROs). Obviously, the universe cannot be younger than its constituents. We find that an unusually large $r_0$ (characterizing the size of the void) is required to accommodate these OHROs in LTB void models. There is a serious tension between this unusually large $r_0$ and the much smaller $r_0$ inferred from other observations (e.g. SNIa, CMB and so on). However, if we instead consider the lowest limit 1.7\,Gyr for the quasar APM 08279+5255 at redshift $z=3.91$, this tension could be greatly alleviated.Comment: 17 pages, 9 figures, revtex4; v2: discussions added, Phys. Lett. B in press; v3: published versio

Complexity growth rates for AdS black holes in massive gravity and f(R)f(R) gravity

The "complexity = action" duality states that the quantum complexity is equal to the action of the stationary AdS black holes within the Wheeler-DeWitt patch at late time approximation. We compute the action growth rates of the neutral and charged black holes in massive gravity and the neutral, charged and Kerr-Newman black holes in $f(R)$ gravity to test this conjecture. Besides, we investigate the effects of the massive graviton terms, higher derivative terms and the topology of the black hole horizon on the complexity growth rate.Comment: 11 pages, no figur

Predicting the Vitality of Stores Along the Street Based on Business Type Sequence via Recurrent Neural Network

The rational planning of store types and locations to maximize street vitality is essential in real estate planning. Traditional business planning relies heavily on the subjective experience of developers. Currently, developers have access to low-resolution urban data to support their decision making, and researchers have done much image-based machine learning research from the scale of urban texture. However, there is still a lack of research on the functional layout with shop-level accuracy. This paper uses a sequence-based neural network (RNN) to explore the relationship between the sequence of store types along a street and its commercial vitality. Currently, the use of RNNs in the architectural and urban fields is very rare. We use customer review data of 80streets from O2O platforms to represent the store vitality degree. In the machine learning model, the input is the sequence of store types on the street, and the output is the corresponding sequence of business vitality indexes. After training and evaluation, the model was shown to have acceptable accuracy. We further combined this evaluation model with a genetic algorithm to develop a business planning optimization tool to maximize the overall street business value, thus guiding real estate business planning at a high resolution