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How do update rules affect the dynamical and steady state properties of a flock? In this study, we have explored the active Ising spins (s = +-1) in one dimension, where spin updates its orientation according to the Metropolis algorithm (based on the neighbors) via two different update rules. (i) Parallel, and (ii) Random-sequential. We explore the effect of Parallel and Random-sequential updates on the dynamical properties of flocks in one dimension. Due to the inherent asynchronous nature of the Random-sequential update, the directional switching of the flock is increased compared to the Parallel one. The nature of phase transition is affected by the difference in the updating mechanism: discontinuous for Parallel and continuous for Random-sequential updates., Comment: 7 pages, 6 figures. arXiv admin note: text overlap with arXiv:1704.04041

The primary objective of this work is to obtain some sufficient conditions so that normalized Gauss hypergeometric function satisfies exponential starlikeness and convexity in the unit disk. Moreover, conditions on parameter of this function has been derived for being Janowski convexity and starlikeness with the help of differential subordination. Results established in this work are presumably new and their significance is illustrated by several consequences.

Current practice in parameter space exploration in euclidean space is dominated by randomized sampling or design of experiment methods. The biggest issue with these methods is not keeping track of what part of parameter space has been explored and what has not. In this context, we utilize the geometric learning of explored data space using modern machine learning methods to keep track of already explored regions and samples from the regions that are unexplored. For this purpose, we use a modified version of a robust random-cut forest along with other heuristic-based approaches. We demonstrate our method and its progression in two-dimensional Euclidean space but it can be extended to any dimension since the underlying method is generic.