The study of the critical dynamics in complex systems is always interesting yet challenging. Here, we choose financial markets as an example of a complex system, and do comparative analyses of two stock markets-the S&P 500 (USA) and Nikkei 225 (JPN). Our analyses are based on the evolution of crosscorrelation structure patterns of short-time epochs for a 32 year period . We identify 'market states' as clusters of similar correlation structures, which occur more frequently than by pure chance (randomness). The dynamical transitions between the correlation structures reflect the evolution of the market states. Power mapping method from the random matrix theory is used to suppress the noise on correlation patterns, and an adaptation of the intra-cluster distance method is used to obtain the 'optimum' number of market states. We find that the S&P 500 is characterized by four market states and Nikkei 225 by five. We further analyze the co-occurrence of paired market states; the probability of remaining in the same state is much higher than the transition to a different state. The transitions to other states mainly occur among the immediately adjacent states, with a few rare intermittent transitions to the remote states. The state adjacent to the critical state (market crash) may serve as an indicator or a 'precursor' for the critical state and this novel method of identifying the long-term precursors may be helpful for constructing the early warning system in financial markets, as well as in other complex systems.

Diffusion with stochastic resetting has recently emerged as a powerful modeling tool with a myriad of potential applications. Here, we study local time in this model, covering situations of free and biased diffusion with, and without, the presence of an absorbing boundary. Given a Brownian trajectory that evolved for t units of time, the local time is simply defined as the total time the trajectory spent in a small vicinity of its initial position. However, as Brownian trajectories are stochastic -the local time itself is a random variable which fluctuates round and about its mean value. In the past, the statistics of these fluctuations has been quantified in detail; but not in the presence of resetting which biases the particle to spend more time near its starting point. Here, we extend past results to include the possibility of stochastic resetting with, and without, the presence of an absorbing boundary and/or drift. We obtain exact results for the moments and distribution of the local time and these reveal that its statistics usually admits a simple form in the long-time limit. And yet, while fluctuations in the absence of stochastic resetting are typically non-Gaussian -resetting gives rise to Gaussian fluctuations. The analytical findings presented herein are in excellent agreement with numerical simulations. arXiv:1902.00907v2 [cond-mat.stat-mech] 5 Jun 2019 2

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This paper focuses upon cross-border acquisitions. A three-way comparison is made between the post-takeover performance of UK acquirers of domestic UK, US, and Continental European targets between 1991 and 1996. This study examines if UK firms acquiring large takeover targets experience cumulative abnormal returns significantly different from zero up to two years after the acquisition. This study finds that UK firms acquiring large takeover targets experience negative cumulative abnormal returns over the period examined, at various significance levels. Furthermore, the study finds that the post-takeover performance of UK firms acquiring UK targets is superior to that of UK firms acquiring US targets. In turn, the performance of UK firms acquiring US targets is better than that of UK firms acquiring Continental European targets. If this trend continues, the consequences for institutional investors and pension funds, which respond to a major takeover by increasing their holdings in the acquirer, could be serious. The shares they are buying are the very companies we show to be underperforming. And the particularly poor performance of UK companies acquiring in Europe suggests that this anomaly may become even more significant as European cross-border activity gathers pace.