Quantum gravity effects on spectroscopy of Kerr-Newman black hole in gravity’s rainbow

Quantum gravity effects on spectroscopy for the charged rotating gravity’s rainbow are investigated. By utilizing an action invariant obtained from particles tunneling through the event horizon, the entropy and area spectrum for the modified Kerr-Newman black hole are derived. The equally spaced entropy spectrum characteristic of Bekenstein’s original derivation is recovered. And, the entropy spectrum is independent of the energy of the test particles, although the gravity’s rainbow itself is the energy dependent. Such, the quantum gravity effects of gravity’s rainbow has no influence on the entropy spectrum. On the other hand, due to the spacetime quantum effects, the obtained area spectrum is different from the original Bekenstein spectrum. It is not equidistant and has the dependence on the horizon area. And that, by analyzing the area spectrum from a specific rainbow functions, a minimum area with Planck scale is derived for the event horizon. At this, the area quantum is zero and the black hole radiation stops. Thus, the black hole remnant for the gravity’s rainbow is obtained from the area quantization. In addition, the entropy for the modified Kerr-Newman black hole is calculated and the quantum correction to the area law is obtained and discussed.

A new method to study genome mutations using the information entropy

We report a non-clinical, mathematical method of studying genetic sequences based on the information theory. Our method involves calculating the information entropy spectrum of genomes by splitting them into windows containing a fixed number of nucleotides. The information entropy value of each window is computed using the m-block information entropy formula. We show that the information entropy spectrum of genomes contains sufficient information to allow detection of genetic mutations, as well as possibly predicting future ones. Our study indicates that the best m-block size is 2 and the optimal window size should contain more than 9, and less than 33 nucleotides. In order to implement the proposed technique, we created specialized software, which is freely available. Here we report the successful test of this method on the reference RNA sequence of the SARS-CoV-2 virus collected in Wuhan, Dec. 2019 (MN908947) and one of its randomly selected variants from Taiwan, Feb. 2020 (MT370518), displaying 7 mutations.

Boundary entropy spectra as finite subsums

In this paper, we provide a concrete construction of Furstenberg entropy values of [Formula: see text]-boundaries of the group [Formula: see text] by choosing an appropriate random walk [Formula: see text]. We show that the boundary entropy spectrum can be realized as the subsum-set for any given finite sequence of positive numbers.