A New Family of Multistep Methods with Improved Phase Lag Characteristics for the Integration of Orbital Problems

In this work we introduce a new family of ten-step linear multistep methods for the integration of orbital problems. The new methods are constructed by adopting a new methodology which improves the phase lag characteristics by vanishing both the phase lag function and its first derivatives at a specific frequency. The efficiency of the new family of methods is proved via error analysis and numerical applications.Comment: 21 pages, 3 figures, 1 tabl

Synchronization in Complex Systems Following the Decision Based Queuing Process: The Rhythmic Applause as a Test Case

Living communities can be considered as complex systems, thus a fertile ground for studies related to their statistics and dynamics. In this study we revisit the case of the rhythmic applause by utilizing the model proposed by V\'azquez et al. [A. V\'azquez et al., Phys. Rev. E 73, 036127 (2006)] augmented with two contradicted {\it driving forces}, namely: {\it Individuality} and {\it Companionship}. To that extend, after performing computer simulations with a large number of oscillators we propose an explanation on the following open questions (a) why synchronization occurs suddenly, and b) why synchronization is observed when the clapping period ($T_c$) is $1.5 \cdot T_s < T_c < 2.0 \cdot T_s$ ($T_s$ is the mean self period of the spectators) and is lost after a time. Moreover, based on the model, a weak preferential attachment principle is proposed which can produce complex networks obeying power law in the distribution of number edges per node with exponent greater than 3.Comment: 16 pages, 5 figure

Changing memories by interference: the effect of emotional dimensions in reconsolidation of episodic memories

Episodes with an emotional component preoccupy memory formation and this advantage facilitates their preservation and mitigates the impact of interfering episodes. The present study examined the relation of the emotional dimensions of original and interfering episodes to the memory outcome, using a reconsolidation paradigm. In a between-subjects design, 102 healthy young adults were presented with an emotional or neutral image and learned either an emotional or neutral story, respectively (day 1). On day 2, experimental groups were presented with an image of the opposite emotionality, reactivated the original story, and learned a story of the opposite emotionality. On day 3, experimental and control groups were tested for their memory on target and filler clues of the original story and rated both stories for arousal and valence. Overall, there was evidence of interference on the long-term retention of target clues only for the neutral story (i.e. when the interfering story was emotional), and of filler clues for both types of stories. Moreover, individual target clue retention rates correlated with the arousal ratings for both the original neutral story and the interfering emotional story, while they were not related to arousal ratings for the original emotional story or the interfering neutral one

The Use of Phase Lag and Amplification Error Derivatives for the Construction of a Modified Runge-Kutta-Nyström Method

A new modified Runge-Kutta-Nyström method of fourth algebraic order is developed. The new modified RKN method is based on the fitting of the coefficients, due to the nullification not only of the phase lag and of the amplification error, but also of their derivatives. Numerical results indicate that the new modified method is much more efficient than other methods derived for solving numerically the Schrödinger equation