Injection locking of optomechanical oscillators via acoustic waves

Injection locking is a powerful technique for synchronization of oscillator networks and controlling the phase and frequency of individual oscillators using similar or other types of oscillators. Here, we present the first demonstration of injection locking of a radiation-pressure driven optomechanical oscillator (OMO) via acoustic waves. As opposed to previously reported techniques (based on pump modulation or direct application of a modulated electrostatic force), injection locking of OMO via acoustic waves does not require optical power modulation or physical contact with the OMO and it can easily be implemented on various platforms. Using this approach we have locked the phase and frequency of two distinct modes of a microtoroidal silica OMO to a piezoelectric transducer (PZT). We have characterized the behavior of the injection locked OMO with three acoustic excitation configurations and showed that even without proper acoustic impedance matching the OMO can be locked to the PZT and tuned over 17 kHz with only -30 dBm of RF power fed to the PZT. The high efficiency, simplicity and scalability of the proposed approach paves the road toward a new class of photonic systems that rely on synchronization of several OMOs to a single or multiple RF oscillators with applications in optical communication, metrology and sensing. Beyond its practical applications, injection locking via acoustic waves can be used in fundamental studies in quantum optomechanics where thermal and optical isolation of the OMO are critical

Business Leaders’ Strategies for Addressing Employee Turnover and Promoting Stability

One of the major issues that business leaders face are high rates of employee turnover. From 2013 to 2017, the annual total separation rate increased by 38.1 to 43.0 across all industries (Bureau of Labor Statistics, 2018). This demonstrates that employee turnover is increasing over time in the United States. Turnover is problematic because it forces business leaders and managers to replace reliable and trained employees with new employees, which is a timeconsuming process that is often quite costly. Out of all industries that deal with employee turnover, the hospitality industry is known for having one of the highest employee turnover rates across all industries (Kavanaugh, 2018). This is evidenced by the fact that the United States Bureau of Labor Statistics reported that the turnover rate for restaurants and accommodations was 73% in 2016 (McNamara, 2018). The high rate of employee turnover within this industry is explained by a few factors. For one, seasonality leads to a higher turnover rate because many part-time employees are hired as seasonal workers during summer months, and these workers are often younger students who leave their restaurant positions to return to school in August and September (Navarra, 2018). The turnover rate may also be broken down by position, as roles involving performing counter service or working as the cashier had a turnover rate of 36%, which is much higher than the bar staff turnover rate of 25% or the managerial turnover rate of 23% (Navarra, 2018). Turnover is not something that is inherently inevitable to this industry however, and business leaders within the hospitality industry focus on implementing viable strategies to reduce turnover to a more manageable rate

Randomized Algorithms for Tracking Distributed Count, Frequencies, and Ranks

We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the {\em count-tracking} problem, where there are $k$ players, each holding a counter $n_i$ that gets incremented over time, and the goal is to track an \eps-approximation of their sum $n=\sum_i n_i$ continuously at all times, using minimum communication. While the deterministic communication complexity of the problem is \Theta(k/\eps \cdot \log N), where $N$ is the final value of $n$ when the tracking finishes, we show that with randomization, the communication cost can be reduced to \Theta(\sqrt{k}/\eps \cdot \log N). Our algorithm is simple and uses only O(1) space at each player, while the lower bound holds even assuming each player has infinite computing power. Then, we extend our techniques to two related distributed tracking problems: {\em frequency-tracking} and {\em rank-tracking}, and obtain similar improvements over previous deterministic algorithms. Both problems are of central importance in large data monitoring and analysis, and have been extensively studied in the literature.Comment: 19 pages, 1 figur