For Hawking radiation, treated as a tunneling process, the no-hair theorem of black hole together with the law of energy conservation is utilized to postulate that the tunneling rate only depends on the external quali...For Hawking radiation, treated as a tunneling process, the no-hair theorem of black hole together with the law of energy conservation is utilized to postulate that the tunneling rate only depends on the external qualities(e.g., the mass for the Schwarzschild black hole) and the energy of the radiated particle. This postulate is justified by the WKB approximation for calculating the tunneling probability. Based on this postulate, a general formula for the tunneling probability is derived without referring to the concrete form of black hole metric. This formula implies an intrinsic correlation between the successive processes of the black hole radiation of two or more particles. It also suggests a kind of entropy conservation and thus resolves the puzzle of black hole information loss in some sense.展开更多
This work investigates frequency distributions of strings within a text. The mathematical derivation accounts for variable alphabet size, character probabilities, and string/text lengths, under both the Bernoullian an...This work investigates frequency distributions of strings within a text. The mathematical derivation accounts for variable alphabet size, character probabilities, and string/text lengths, under both the Bernoullian and the Markovian model for string generation. The analysis is limited to the set of nonclumpable strings, that cannot overlap with them selves. Two formulae （exact and approximated） are derived, calculating the frequency distribution of a string of length m found inside a text of length n （with m 〈： n）. The approximated formula has a constant complexity （in contrast to an exponential com plexity of the exact） and makes it applicable to very long texts. The proposed formulae were applied to analyze string frequencies in a portion of the human genome, and to recalculate frequencies of known repeated motif within genes, associated to genetic dis eases. A comparison with stateoftheart methods was provided. The formulae presentedhere can be of use in the statistical evaluation of specific motif frequencies within very long texts （e.g. genes or genomes） and help in characterizing motifs in pathologic conditions.展开更多
基金Supported by National Natural Science Foundation of China and the National Fundamental Research Programs of China under Grant Nos. 10874091 and 2006CB921205
文摘For Hawking radiation, treated as a tunneling process, the no-hair theorem of black hole together with the law of energy conservation is utilized to postulate that the tunneling rate only depends on the external qualities(e.g., the mass for the Schwarzschild black hole) and the energy of the radiated particle. This postulate is justified by the WKB approximation for calculating the tunneling probability. Based on this postulate, a general formula for the tunneling probability is derived without referring to the concrete form of black hole metric. This formula implies an intrinsic correlation between the successive processes of the black hole radiation of two or more particles. It also suggests a kind of entropy conservation and thus resolves the puzzle of black hole information loss in some sense.
文摘This work investigates frequency distributions of strings within a text. The mathematical derivation accounts for variable alphabet size, character probabilities, and string/text lengths, under both the Bernoullian and the Markovian model for string generation. The analysis is limited to the set of nonclumpable strings, that cannot overlap with them selves. Two formulae （exact and approximated） are derived, calculating the frequency distribution of a string of length m found inside a text of length n （with m 〈： n）. The approximated formula has a constant complexity （in contrast to an exponential com plexity of the exact） and makes it applicable to very long texts. The proposed formulae were applied to analyze string frequencies in a portion of the human genome, and to recalculate frequencies of known repeated motif within genes, associated to genetic dis eases. A comparison with stateoftheart methods was provided. The formulae presentedhere can be of use in the statistical evaluation of specific motif frequencies within very long texts （e.g. genes or genomes） and help in characterizing motifs in pathologic conditions.
