An Efficient Dynamic Programming Algorithm for the Generalized LCS Problem with Multiple Substring Exclusion Constrains

In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusion constrains. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constrains $P=\{P_1,...,P_d\}$ of total length $r$, the problem is to find a common subsequence $Z$ of $X$ and $Y$ excluding each of constrain string in $P$ as a substring and the length of $Z$ is maximized. The problem was declared to be NP-hard\cite{1}, but we finally found that this is not true. A new dynamic programming solution for this problem is presented in this paper. The correctness of the new algorithm is proved. The time complexity of our algorithm is $O(nmr)$.Comment: arXiv admin note: substantial text overlap with arXiv:1301.718

A note on the largest number of red nodes in red-black trees

In this paper, we are interested in the number of red nodes in red-black trees. We first present an $O(n^2\log n)$ time dynamic programming solution for computing $r(n)$, the largest number of red internal nodes in a red-black tree on $n$ keys. Then the algorithm is improved to some $O(\log n)$ time recursive and nonrecursive algorithms. Based on these improved algorithms we finally find a closed-form solution of $r(n)$

Complete Solutions for a Combinatorial Puzzle in Linear Time

In this paper we study a single player game consisting of $n$ black checkers and $m$ white checkers, called shifting the checkers. We have proved that the minimum number of steps needed to play the game for general $n$ and $m$ is $nm + n + m$. We have also presented an optimal algorithm to generate an optimal move sequence of the game consisting of $n$ black checkers and $m$ white checkers, and finally, we present an explicit solution for the general game

Effect of lighting schedule, intensity, and colour on reproductive performance of rabbit does

[EN] In order to establish a lighting regime suitable for rabbit farms in East China, the effects of lighting schedule, intensity and colour on the reproductive performance of rabbit does were evaluated by three experiments, respectively. In experiment 1, does were exposed to different lighting schedules: 16L:8D-continuous, 16L:8D-18d (6 d before artificial insemination (AI) to 12 d post-AI), 16L:8D-6d (6 d before AI to the day of AI) and 12L:12D-continuous. In experiment 2, does were exposed to different light intensities: 40 lx, 60 lx, 80 lx and 120 lx. In experiment 3, does were exposed to different light colours: white, yellow, blue and red. For all experiments, conception rate, kindling rate and pre-weaning mortality were calculated; litter size at birth, litter weight at birth, litter size at weaning, litter weight at weaning and individual kit weight at weaning were recorded. Results showed that none of the reproductive parameters of does were affected by the application of 16L:8D-18d lighting schedule compared with the continuous 16L:8D group(P>0.05). Moreover, rabbits does exposed to 80 lx light performed as well as those under 120 lx light in conception rate, kindling rate, litter size (total and alive) at birth and litter weight at birth (P>0.05). Furthermore, the exposures of 60 lx and 80 lx light were beneficial for litter weight at weaning. In addition, red light had a positive effect, as it led to a larger litter size and litter weight at weaning and lower pre-weaning mortality than white light (P<0.05). In summary, a 16L:8D photoperiod with 80 lx red light from 6 d before AI to 12 d post-AI is recommended for use in breeding of rabbit does according to our results.We would like to thank the support of Earmarked Fund for Modern Agro-Industry Technology Research System (CARS-44).Wu, Y.; Zhao, A.; Qin, Y. (2021). Effect of lighting schedule, intensity, and colour on reproductive performance of rabbit does. World Rabbit Science. 29(1):59-64. https://doi.org/10.4995/wrs.2021.14623OJS5964291Abdo M., Haddad S., Emam M. 2017. Development of the New Zealand White Rabbit eye: I. pre- and postnatal development of eye tunics. Anat Histol Embryol., 46: 423-430. https://doi.org/10.1111/ahe.12284Gerencsér Zs., Matics Zs., Nagy I., Szendrő Zs. 2011. Effect of light color and reproductive rhythm on rabbit doe performance. World Rabbit Sci., 19: 161-170. https://doi.org/10.4995/wrs.2011.827Gidenne T., Fortun-Lamothe L. 2002. Feeding strategy for young rabbits around weaning: a review of digestive capacity and nutritional needs. Anim. Sci., 75: 169-184. https://doi.org/10.1017/S1357729800052942Hoy St. 2012. German regulations and guidelines on rabbit housing. In Proc.: 10th World Rabbit Congress, 3-6 September, 2012. Sharm-El Sheikh, Egypt. 1: 999-1003.Li Y., Zhang J., Xu Y., Han Y., Jiang B., Huang L., Zhu H., Xu Y., Yang W., Qin C. 2016. The histopathological investigation of red and blue light emitting diode on treating skin wounds in Japanese big-ear white rabbit. PLoS One, 11: e0157898. https://doi.org/10.1371/journal.pone.0157898.Maertens L., Luzi F. 1995. Effect of diluents and storage time of rabbit semen on the fertility of does reared under two different lighting schedules. World Rabbit Sci., 3: 57-61. https://doi.org/10.4995/wrs.1995.237Matics Zs., Gerencsér Zs., Radnai I., Kasza R., Szendrő Zs. 2016. Effect of light intensities on reproductive performance, nursing behaviour and preference of rabbit does. World Rabbit Sci., 24: 139-144. https://doi.org/10.4995/wrs.2016.4112Mattaraia V.G.M., Bianospino E., Fernandes S., Vasconcelos J.L.M., Moura A.S.A.M.T. 2005. Reproductive responses of rabbit does to a supplemental lighting program. Livest. Prod. Sci., 94: 179-184. https://doi.org/10.1016/j.livprodsci.2004.10.012Mousa-Balabel T.M., Mohamed R.A. 2011. Effect of different photoperiods and melatonin treatment on rabbit reproductive performance. Vet Q., 31: 165-171. https://doi.org/10.1080/01652176.2011.642533Nuboer J. F.W. 1985. A comparative view on color vision. Neth. J. Zool., 36: 344-380. https://doi.org/10.1163/002829686X00126Reyne Y., Prud'hon M., Angerian J. 1978. Influence d'une réduction de la durée d'éclairement du lapin en engraissement. In Proc.: 2émes Journ. Rech. Cunicole, Comm. No 7.Salehpour F., Mahmoudi J., Kamari F., Sadigh-Eteghad S., Rasta S.H., Hamblin M.R. 2018. Brain photobiomodulation therapy: a narrative review. Mol. Neurobiol., 55: 6601-6636. https://doi.org/10.1007/s12035-017-0852-4Shi H.J., Song H.B., Zhao Q.Y., Tao C.X., Liu M., Zhu Q.Q. 2018. Efficacy and safety of combined high-dose interferon and red light therapy for the treatment of human papillomavirus and associated vaginitis and cervicitis: A prospective and randomized clinical study. Medicine (Baltimore), 97: e12398. https://doi.org/10.1097/MD.0000000000012398Szendrő Zs., Gerencsér Zs., McNitt J.I., Matics Zs. 2016. Effect of lighting on rabbits and its role in rabbit production: A review. Livest. Sci., 183: 12-18. https://doi.org/10.1016/j.livsci.2015.11.012Theau-Clement M., Malpaux B., Lamothe E., Milcent N., Juin H., Bodin L. 2008. Influence of photoperiod on the sexual behaviour of non-lactating rabbit does: preliminary results. In Proc.: 9th World Rabbit Congress, 10-13 June, 2008. Verona, Italy. 1: 465-469.Uzcategui M.E., Johnston N.P. 1992. The effect of 10, 12 and 14 hour continuous and intermittent photoperiods on the reproductive performance of female rabbits. In Proc.: 5th World Rabbit Congress, 25-30 July, 1992. Corvallis, USA. 1: 553-559

Using fractional order method to generalize strengthening generating operator buffer operator and weakening buffer operator

Traditional integer order buffer operator is extended to fractional order buffer operator, the corresponding relationship between the weakening buffer operator and the strengthening buffer operator is revealed. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also realize tiny adjustment of buffer effect. The effectiveness of GM(1,1) with the fractional order buffer operator is validated by six cases