Interlacing Log-concavity of the Boros-Moll Polynomials

We introduce the notion of interlacing log-concavity of a polynomial sequence $\{P_m(x)\}_{m\geq 0}$, where $P_m(x)$ is a polynomial of degree m with positive coefficients $a_{i}(m)$. This sequence of polynomials is said to be interlacing log-concave if the ratios of consecutive coefficients of $P_m(x)$ interlace the ratios of consecutive coefficients of $P_{m+1}(x)$ for any $m\geq 0$. Interlacing log-concavity is stronger than the log-concavity. We show that the Boros-Moll polynomials are interlacing log-concave. Furthermore we give a sufficient condition for interlacing log-concavity which implies that some classical combinatorial polynomials are interlacing log-concave.Comment: 10 page

The effects of dog management on Echinococcus spp. prevalence in villages on the eastern Tibetan Plateau, China

Background The pastoral area of the eastern Tibetan plateau is a very important human echinococcosis endemic region. Domestic dogs are the main definitive host for the transmission of Echinococcus granulosus sensu lato (s.1.) and E. multilocularis to humans. To control the infection risks, a national-level canine echinococcosis prevention and control program has been implemented since 2015 in Shiqu County, Sichuan, China, The objective of this investigation was to evaluate its effect on Echinococcus spp. prevalence in dogs. Methods We surveyed 69 households with 84 owned dogs, for dog keeping information in the villages of Rizha and Eduoma. A total of 105 dog fecal samples, consisting of 75 from owned dogs and 30 unknown dog fecal samples were collected between 2015 and 2017 to determine Echinococcus spp. prevalence using copro-PCR. Eight variables based on household surveys were included into a logistic regression model for significantly relevant factors to canine echinococcosis prevalence in dogs. Results The overall Echinococcus spp. copro-DNA prevalence decreased significantly in dogs from 51.2% (2015) to 20.0% (2017) in Rizha, and insignificantly from 11.5% (2016) to 4.3% (2017) in Eduoma. Echinococcus multilocularis was the most prevalent species continually detected during the entire research period, while E. granulosus was rare and not detected in 2017. Echinococcus shiquicus prevalence was as high as E. multilocularis , although only detected in 2015 in Rizha. Unleashed dog feces were mainly collected in Rizha Village in 2015. Although 93.2% of owned dogs were leashed, and the monthly praziquantel dosing rate reached 97%, E. multilocularis infection could still be detected in 11.1% of owned dogs in 2017. Monthly deworming, leashing dogs 24h per day, and the avoidance of dogs feeding on livestock viscera are significant measures to prevent canine echinococcosis infection in owned dogs. Conclusion Carrying out a canine echinococcosis prevention and control program can significantly decrease the Echinococcus prevalence. The potential contact between leashed dogs and wild small mammals is still a risk to re-infect owned dogs. This study shows that the long term application of regular dog dosing in the vast remote echinococcosis endemic areas of west China is still challenging

Geometric phases induced in auxiliary qubits by many-body systems near its critical points

The geometric phase induced in an auxiliary qubit by a many-body system is calculated and discussed. Two kinds of coupling between the auxiliary qubit and the many-body system are considered, which lead to dephasing and dissipation in the qubit, respectively. As an example, we consider the XY spin-chain dephasingly couple to a qubit, the geometric phase induced in the qubit is presented and discussed. The results show that the geometric phase might be used to signal the critical points of the many-body system, and it tends to zero with the parameters of the many-body system going away from the critical points