Intersective polynomials and the primes

Intersective polynomials are polynomials in $\Z[x]$ having roots every modulus. For example, $P_1(n)=n^2$ and $P_2(n)=n^2-1$ are intersective polynomials, but $P_3(n)=n^2+1$ is not. The purpose of this note is to deduce, using results of Green-Tao \cite{gt-chen} and Lucier \cite{lucier}, that for any intersective polynomial $h$, inside any subset of positive relative density of the primes, we can find distinct primes $p_1, p_2$ such that $p_1-p_2=h(n)$ for some integer $n$. Such a conclusion also holds in the Chen primes (where by a Chen prime we mean a prime number $p$ such that $p+2$ is the product of at most 2 primes)

The seventh visual object tracking VOT2019 challenge results

180The Visual Object Tracking challenge VOT2019 is the seventh annual tracker benchmarking activity organized by the VOT initiative. Results of 81 trackers are presented; many are state-of-the-art trackers published at major computer vision conferences or in journals in the recent years. The evaluation included the standard VOT and other popular methodologies for short-term tracking analysis as well as the standard VOT methodology for long-term tracking analysis. The VOT2019 challenge was composed of five challenges focusing on different tracking domains: (i) VOTST2019 challenge focused on short-term tracking in RGB, (ii) VOT-RT2019 challenge focused on 'real-time' shortterm tracking in RGB, (iii) VOT-LT2019 focused on longterm tracking namely coping with target disappearance and reappearance. Two new challenges have been introduced: (iv) VOT-RGBT2019 challenge focused on short-term tracking in RGB and thermal imagery and (v) VOT-RGBD2019 challenge focused on long-term tracking in RGB and depth imagery. The VOT-ST2019, VOT-RT2019 and VOT-LT2019 datasets were refreshed while new datasets were introduced for VOT-RGBT2019 and VOT-RGBD2019. The VOT toolkit has been updated to support both standard shortterm, long-term tracking and tracking with multi-channel imagery. Performance of the tested trackers typically by far exceeds standard baselines. The source code for most of the trackers is publicly available from the VOT page. The dataset, the evaluation kit and the results are publicly available at the challenge website.openopenKristan M.; Matas J.; Leonardis A.; Felsberg M.; Pflugfelder R.; Kamarainen J.-K.; Zajc L.C.; Drbohlav O.; Lukezic A.; Berg A.; Eldesokey A.; Kapyla J.; Fernandez G.; Gonzalez-Garcia A.; Memarmoghadam A.; Lu A.; He A.; Varfolomieiev A.; Chan A.; Tripathi A.S.; Smeulders A.; Pedasingu B.S.; Chen B.X.; Zhang B.; Baoyuanwu B.; Li B.; He B.; Yan B.; Bai B.; Li B.; Li B.; Kim B.H.; Ma C.; Fang C.; Qian C.; Chen C.; Li C.; Zhang C.; Tsai C.-Y.; Luo C.; Micheloni C.; Zhang C.; Tao D.; Gupta D.; Song D.; Wang D.; Gavves E.; Yi E.; Khan F.S.; Zhang F.; Wang F.; Zhao F.; De Ath G.; Bhat G.; Chen G.; Wang G.; Li G.; Cevikalp H.; Du H.; Zhao H.; Saribas H.; Jung H.M.; Bai H.; Yu H.; Peng H.; Lu H.; Li H.; Li J.; Li J.; Fu J.; Chen J.; Gao J.; Zhao J.; Tang J.; Li J.; Wu J.; Liu J.; Wang J.; Qi J.; Zhang J.; Tsotsos J.K.; Lee J.H.; Van De Weijer J.; Kittler J.; Ha Lee J.; Zhuang J.; Zhang K.; Wang K.; Dai K.; Chen L.; Liu L.; Guo L.; Zhang L.; Wang L.; Wang L.; Zhang L.; Wang L.; Zhou L.; Zheng L.; Rout L.; Van Gool L.; Bertinetto L.; Danelljan M.; Dunnhofer M.; Ni M.; Kim M.Y.; Tang M.; Yang M.-H.; Paluru N.; Martinel N.; Xu P.; Zhang P.; Zheng P.; Zhang P.; Torr P.H.S.; Wang Q.Z.Q.; Guo Q.; Timofte R.; Gorthi R.K.; Everson R.; Han R.; Zhang R.; You S.; Zhao S.-C.; Zhao S.; Li S.; Li S.; Ge S.; Bai S.; Guan S.; Xing T.; Xu T.; Yang T.; Zhang T.; Vojir T.; Feng W.; Hu W.; Wang W.; Tang W.; Zeng W.; Liu W.; Chen X.; Qiu X.; Bai X.; Wu X.-J.; Yang X.; Chen X.; Li X.; Sun X.; Chen X.; Tian X.; Tang X.; Zhu X.-F.; Huang Y.; Chen Y.; Lian Y.; Gu Y.; Liu Y.; Chen Y.; Zhang Y.; Xu Y.; Wang Y.; Li Y.; Zhou Y.; Dong Y.; Xu Y.; Zhang Y.; Li Y.; Luo Z.W.Z.; Zhang Z.; Feng Z.-H.; He Z.; Song Z.; Chen Z.; Zhang Z.; Wu Z.; Xiong Z.; Huang Z.; Teng Z.; Ni Z.Kristan, M.; Matas, J.; Leonardis, A.; Felsberg, M.; Pflugfelder, R.; Kamarainen, J. -K.; Zajc, L. C.; Drbohlav, O.; Lukezic, A.; Berg, A.; Eldesokey, A.; Kapyla, J.; Fernandez, G.; Gonzalez-Garcia, A.; Memarmoghadam, A.; Lu, A.; He, A.; Varfolomieiev, A.; Chan, A.; Tripathi, A. S.; Smeulders, A.; Pedasingu, B. S.; Chen, B. X.; Zhang, B.; Baoyuanwu, B.; Li, B.; He, B.; Yan, B.; Bai, B.; Li, B.; Li, B.; Kim, B. H.; Ma, C.; Fang, C.; Qian, C.; Chen, C.; Li, C.; Zhang, C.; Tsai, C. -Y.; Luo, C.; Micheloni, C.; Zhang, C.; Tao, D.; Gupta, D.; Song, D.; Wang, D.; Gavves, E.; Yi, E.; Khan, F. S.; Zhang, F.; Wang, F.; Zhao, F.; De Ath, G.; Bhat, G.; Chen, G.; Wang, G.; Li, G.; Cevikalp, H.; Du, H.; Zhao, H.; Saribas, H.; Jung, H. M.; Bai, H.; Yu, H.; Peng, H.; Lu, H.; Li, H.; Li, J.; Li, J.; Fu, J.; Chen, J.; Gao, J.; Zhao, J.; Tang, J.; Li, J.; Wu, J.; Liu, J.; Wang, J.; Qi, J.; Zhang, J.; Tsotsos, J. K.; Lee, J. H.; Van De Weijer, J.; Kittler, J.; Ha Lee, J.; Zhuang, J.; Zhang, K.; Wang, K.; Dai, K.; Chen, L.; Liu, L.; Guo, L.; Zhang, L.; Wang, L.; Wang, L.; Zhang, L.; Wang, L.; Zhou, L.; Zheng, L.; Rout, L.; Van Gool, L.; Bertinetto, L.; Danelljan, M.; Dunnhofer, M.; Ni, M.; Kim, M. Y.; Tang, M.; Yang, M. -H.; Paluru, N.; Martinel, N.; Xu, P.; Zhang, P.; Zheng, P.; Zhang, P.; Torr, P. H. S.; Wang, Q. Z. Q.; Guo, Q.; Timofte, R.; Gorthi, R. K.; Everson, R.; Han, R.; Zhang, R.; You, S.; Zhao, S. -C.; Zhao, S.; Li, S.; Li, S.; Ge, S.; Bai, S.; Guan, S.; Xing, T.; Xu, T.; Yang, T.; Zhang, T.; Vojir, T.; Feng, W.; Hu, W.; Wang, W.; Tang, W.; Zeng, W.; Liu, W.; Chen, X.; Qiu, X.; Bai, X.; Wu, X. -J.; Yang, X.; Chen, X.; Li, X.; Sun, X.; Chen, X.; Tian, X.; Tang, X.; Zhu, X. -F.; Huang, Y.; Chen, Y.; Lian, Y.; Gu, Y.; Liu, Y.; Chen, Y.; Zhang, Y.; Xu, Y.; Wang, Y.; Li, Y.; Zhou, Y.; Dong, Y.; Xu, Y.; Zhang, Y.; Li, Y.; Luo, Z. W. Z.; Zhang, Z.; Feng, Z. -H.; He, Z.; Song, Z.; Chen, Z.; Zhang, Z.; Wu, Z.; Xiong, Z.; Huang, Z.; Teng, Z.; Ni, Z

Positivity properties of Jacobi-Stirling numbers and generalized Ramanujan polynomials

Generalizing recent results of Egge and Mongelli, we show that each diagonal sequence of the Jacobi-Stirling numbers \js(n,k;z) and \JS(n,k;z) is a P\'olya frequency sequence if and only if $z\in [-1, 1]$ and study the $z$-total positivity properties of these numbers. Moreover, the polynomial sequences \biggl\{\sum_{k=0}^n\JS(n,k;z)y^k\biggr\}_{n\geq 0}\quad \text{and} \quad \biggl\{\sum_{k=0}^n\js(n,k;z)y^k\biggr\}_{n\geq 0} are proved to be strongly $\{z,y\}$-log-convex. In the same vein, we extend a recent result of Chen et al. about the Ramanujan polynomials to Chapoton's generalized Ramanujan polynomials. Finally, bridging the Ramanujan polynomials and a sequence arising from the Lambert $W$ function, we obtain a neat proof of the unimodality of the latter sequence, which was proved previously by Kalugin and Jeffrey.Comment: 17 pages, 2 tables, the proof of Lemma 3.3 is corrected, final version to appear in Advances in Applied Mathematic