Refining One Theorem For The Romanovsky Distribution

The paper considered a refinement of the theorem for a negative-hypergeometric distribution( the Romanovsky distribution), i.e., convergence over variation of the Romanovsky distribution by Erlang distributions. The theorem is proved by the direct asymptotic method.

On the verge of life: Distribution of nucleotide sequences in viral RNAs

The aim of the study is to analyze viruses using parameters obtained from distributions of nucleotide sequences in the viral RNA. Seeking for the input data homogeneity, we analyze single-stranded RNA viruses only. Two approaches are used to obtain the nucleotide sequences; In the first one, chunks of equal length (four nucleotides) are considered. In the second approach, the whole RNA genome is divided into parts by adenine or the most frequent nucleotide as a "space''. Rank--frequency distributions are studied in both cases. The defined nucleotide sequences are signs comparable to a certain extent to syllables or words as seen from the nature of their rank--frequency distributions. Within the first approach, the P\'olya and the negative hypergeometric distribution yield the best fit. For the distributions obtained within the second approach, we have calculated a set of parameters, including entropy, mean sequence length, and its dispersion. The calculated parameters became the basis for the classification of viruses. We observed that proximity of viruses on planes spanned on various pairs of parameters corresponds to related species. In certain cases, such a proximity is observed for unrelated species as well calling thus for the expansion of the set of parameters used in the classification. We also observed that the fourth most frequent nucleotide sequences obtained within the second approach are of different nature in case of human coronaviruses (different nucleotides for MERS, SARS-CoV, and SARS-CoV-2 versus identical nucleotides for four other coronaviruses). We expect that our findings will be useful as a supplementary tool in the classification of diseases caused by RNA viruses with respect to severity and contagiousness.

Order-Preserving and Efficient One-to-Many Search on Encrypted Data

Order-preserving encryption (OPE) is an useful tool in cloud computing as it allows untrustworthy server to execute range query or exact keyword search directly on the ciphertexts. It only requires sub-linear time in the data size while the queries are occurred. This advantage is very suitable in the cloud where the data volume is huge. However, the order-preserving encryption is deterministic and it leaks the plaintexts’ order and its distribution. In this paper, we propose an one-to-many OPE by taking into account the security and the efficiency. For a given plaintext, the encryption algorithm firstly determines the corresponding ciphertext gap by performing binary search on ciphertext space and plaintext space at the same time. An exact sample algorithm for negative hypergeometric distribution is used to fix the size of the gap. Lastly a value in the gap is randomly chosen as the mapping of the given plaintext. It is proven that our scheme is more secure than deterministic OPE with realizing efficient search. In particular, a practical and exact sampling algorithm for the negative hypergeometric distribution (NHGD) is first proposed.