The dynamics of a zooplankton–fish system in aquatic habitats

Diel vertical migration is a common movement pattern of zooplankton in marine and freshwater habitats. In this paper, we use a temporally periodic reaction–diffusion–advection system to describe the dynamics of zooplankton and fish in aquatic habitats. Zooplankton live in both the surface water and the deep water, while fish only live in the surface water. Zooplankton undertake diel vertical migration to avoid predation by fish during the day and to consume sufficient food in the surface water during the night. We establish the persistence theory for both species as well as the existence of a time-periodic positive solution to investigate how zooplankton manage to maintain a balance with their predators via vertical migration. Numerical simulations discover the effects of migration strategy, advection rates, domain boundary conditions, as well as spatially varying growth rates, on persistence of the system.     

On pattern avoiding flattened set partitions

Let Π = B_1/B_2/… /B_k be any set partition of[n]= {1,2,...,n} satisfying that entries are increasing in each block and blocks are arranged in increasing order of their first entries.Then Callan defined the flattened Π to be the permutation of[n]obtained by erasing the divers between its blocks,and Callan also enumerated the number of set partitions of[n]whose flattening avoids a single3-letter pattern.Mansour posed the question of counting set partitions of[n]whose flattening avoids a pattern of length 4.In this paper,we present the number of set partitions of[n]whose flattening avoids one of the patterns:1234,1243,1324,1342,1423,1432,3142 and 4132.     

Pattern avoidance in “flattened” partitions

To flatten a set partition (with apologies to Mathematica^®) means to form a permutation by erasing the dividers between its blocks. Of course, the result depends on how the blocks are listed. For the usual listing—increasing entries in each block and blocks arranged in increasing order of their first entries—we count the partitions of [n] whose flattening avoids a single 3-letter pattern. Five counting sequences arise: a null sequence, the powers of 2, the Fibonacci numbers, the Catalan numbers, and the binomial transform of the Catalan numbers.     

Optimal Cooperative Collision Avoidance Strategy for Coplanar Encounter: Merz’s Solution Revisited

Analytic solutions for optimal collision avoidance strategies are of great importance when setting and validating air traffic rules and as a benchmark when validating automated proximity management and collision avoidance systems. Such a solution for optimal air collision avoidance strategies for a coplanar cooperative encounter between two identical aircraft (or ships) was first presented by Merz (Proc. Joint Automatic Control Conf., Pap. 15-3:449–454, 1973; Navigation 20(2):144–152, 1973). Unfortunately, Merz provided only a very brief indicative justification for his solution. This paper presents a rigorous analysis of the problem. New results include a characterization of a complete set of extremals, justification for optimal strategies and an analysis of the properties of the regions of different optimal strategies. A simple, practical and sufficiently accurate closed form approximation for dispersal curves that partition the plane of initial positions into the regions of different optimal strategies is also presented. We thank the anonymous referees and our colleagues Drs. R.S. Anderssen and R. Jarrett for helpful comments and suggestions.     

Pattern avoidance in binary trees

This paper considers the enumeration of trees avoiding a contiguous pattern. We provide an algorithm for computing the generating function that counts n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting mechanism, we study the analogue of Wilf equivalence in which two tree patterns are equivalent if the respective n-leaf trees that avoid them are equinumerous. We investigate the equivalence classes combinatorially. Toward establishing bijective proofs of tree pattern equivalence, we develop a general method of restructuring trees that conjecturally succeeds to produce an explicit bijection for each pair of equivalent tree patterns.     

Descent distribution on Catalan words avoiding a pattern of length at most three

Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We study the distribution of descents on the sets of Catalan words avoiding a pattern of length at most three: for each such a pattern $p$ we provide a bivariate generating function where the coefficient of $x^n{y}^k$ in its series expansion is the number of length $n$$p$-avoiding Catalan words with $k$ descents. As a byproduct, we enumerate the set of Catalan words avoiding $p$, and we provide the popularity of descents on this set.     

Cannabidiol Attenuates MK-801-Induced Cognitive Symptoms of Schizophrenia in the Passive Avoidance Test in Mice

Schizophrenia is a chronic mental disorder that disturbs feelings and behavior. The symptoms of schizophrenia fall into three categories: positive, negative, and cognitive. Cognitive symptoms are characterized by memory loss or attentional deficits, and are especially difficult to treat. Thus, there is intense research into the development of new treatments for schizophrenia-related responses. One of the possible strategies is connected with cannabidiol (CBD), a cannabinoid compound. This research focuses on the role of CBD in different stages of memory (acquisition, consolidation, retrieval) connected with fear conditioning in the passive avoidance (PA) learning task in mice, as well as in the memory impairment typical of cognitive symptoms of schizophrenia. Memory impairment was provoked by an acute injection of the N-methyl-D-aspartate (NMDA) receptor antagonist MK-801 (animal model of schizophrenia). Our results revealed that an acute injection of CBD (30 mg/kg; intraperitoneally (i.p.) improved all phases of long-term fear memory in the PA test in mice. Moreover, the acute injection of non-effective doses of CBD (1 or 5 mg/kg; i.p.) attenuated the memory impairment provoked by MK-801 (0.6 mg/kg; i.p.) in the consolidation and retrieval stages of fear memory, but not in the acquisition of memory. The present findings confirm that CBD has a positive influence on memory and learning processes in mice, and reveals that this cannabinoid compound is able to attenuate memory impairment connected with hypofunction of glutamate transmission in a murine model of schizophrenia.     

配置柔顺机构空间机器人双臂捕获卫星操作力学模拟及基于神经网络的全阶滑模避撞柔顺控制

讨论了空间机器人双臂捕获卫星操作过程避免关节冲击破坏的避撞柔顺控制问题. 为此在关节电机与机械臂之间设计了一种旋转 型串联弹性执行器(rotatory series elastic actuator, RSEA)--柔顺机构,其作用在于:(1) 通过其内置弹簧的拉伸或压缩变形来吸收捕获操作过程中被捕获卫星对空间机器人关节产生的冲击能量;(2) 可以利用合理设计的与之配合的避撞柔顺控制策略来保证关节冲击力矩受限在安全范围. 首先,利用第二类Lagrange方程分别建 立了捕获操作前含柔顺机构双臂空间机器人的开环分系统动力学模型与目标卫星的分系统动力学模型;之后,基于系统动量 守恒关系、闭链系统位置与速度几何约束关系,获得了捕获操作后空间机器人与被捕获卫星闭链混合体系统综合动力学方程; 最后,基于RBF神经网络提出了一种捕获操作后两者混合体系统镇定运动的全阶终端滑模避撞柔顺控制方案. 所提方案结合柔 顺机构在有效吸收、缓冲被捕获卫星冲击能量的同时,还在冲击能量过大时适时开、关空间机器人关节驱动器,以避免关节驱 动器过载、破坏;此外,还通过最小权值范数法分配了机械臂各关节力矩,以保证双臂协调操作. Lyapunov稳定性理论证明了 系统的全局稳定性,系统计算机数值仿真也验证了上述避撞柔顺控制策略的有效性.      

Transfer effects on communication and collision avoidance behavior from playing a three-dimensional auditory game based on a virtual auditory display

Transfer effects on two everyday auditory skills from playing an auditory game using a virtual auditory display (VAD) were investigated using two groups of 20 normally sighted participants. Representative auditory skills of blindfolded participants were pre-tested using communication and collision avoidance tasks. They performed the tasks two weeks later. Participants in a training group played the VAD-based game on seven days (30 min/day) during the two weeks: control group participants did not. Playing the VAD-based game significantly increased face-contacts in the communication task and significantly improved participants’ collision avoidance. No significant differences were found between the groups’ subjective ratings of the rated tension levels during the communication task or between rated levels for the collision threat. Performance revealed transfer effects of playing the VAD-based game on communication behaviors in social interaction and on avoidance of approaching objects: VAD-based games are effective training tools for auditory skills used in daily life.