A Two-Stage Estimator for Change Point in the Mean of Panel Data

In this paper, a two-stage consistency estimator for change point in the mean of panel data is given. Firstly, a single sequence is extracted, and the initial estimator and confidence interval of the change point are given by the least square method. Based on the confidence interval, a random interval containing change point with probability tending to 1 is constructed. Secondly, using all panel data falling into the random interval, the final estimator of change point is obtained by least square estimation. The asymptotic distribution is established. Simulation results show that our method can not only ensure the estimation accuracy but also greatly reduce time complexity.

Analog-to-Information Conversion with Random Interval Integration

A novel method of analog-to-information conversion—the random interval integration—is proposed and studied in this paper. This method is intended primarily for compressed sensing of aperiodic or quasiperiodic signals acquired by commonly used sensors such as ECG, environmental, and other sensors, the output of which can be modeled by multi-harmonic signals. The main idea of the method is based on input signal integration by a randomly resettable integrator before the AD conversion. The integrator’s reset is controlled by a random sequence generator. The signal reconstruction employs a commonly used algorithm based on the minimalization of a distance norm between the original measurement vector and vector calculated from the reconstructed signal. The signal reconstruction is performed by solving an overdetermined problem, which is considered a state-of-the-art approach. The notable advantage of random interval integration is simple hardware implementation with commonly used components. The performance of the proposed method was evaluated using ECG signals from the MIT-BIH database, multi-sine, and own database of environmental test signals. The proposed method performance is compared to commonly used analog-to-information conversion methods: random sampling, random demodulation, and random modulation pre-integration. A comparison of the mentioned methods is performed by simulation in LabVIEW software. The achieved results suggest that the random interval integration outperforms other single-channel architectures. In certain situations, it can reach the performance of a much-more complex, but commonly used random modulation pre-integrator.

Rhythmic Accessibility to Sequential Working Memory in a Theta Phase-Dependent Manner

Working memory is active short-term memory storage that is easily accessible and underlies various activities, such as maintaining phone numbers in mind for a short period [1,2]. There is accumulating theoretical and physiological evidence that memorized items are represented rhythmically by neural oscillation in the theta range (4-7 Hz) [3,4]. However, the impact of this process on human behavior is yet to be examined. Here we show that simply memorizing sequential information affects a behavioral index (i.e., reaction time, RT) in a rhythmic manner. In the main experiment (Experiment 1), we measured RTs to a visual probe that appeared at one of two sequentially memorized locations after a random interval. Consequently, RTs to the first and second probes each fluctuated in the theta range as a function of the random interval, and the phases of the two theta fluctuations were not in phase or anti-phase, but shifted by approximately 270 degree. Interestingly, the 270 degree phase difference corresponded to the rhythm of "phase coding", where sequential information is represented on the specific phase of theta oscillation [5-7]. These relationships were not observed in tasks simply requiring attention (Experiment 2) or memorization (Experiment 3) of spatial locations without sequential order. In conclusion, the current results demonstrate that our behavior fluctuates when recalling memorized sequential items in the theta-range, suggesting that accessibility to sequential working memory is rhythmic rather than stable, possibly reflecting theta-phase coding.

Representations of hermite processes using local time of intersecting stationary stable regenerative sets

Hermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

Effects of random interval parameters on spur gear vibration

Gear driving devices are commonly used in mechanical transmission systems. Due to the inevitable random errors in manufacturing, installation, and operation, the dynamics of a gear transmission system will fluctuate randomly. To reveal the dynamic characteristics, an interval parameters dynamic model of a single-stage spur gear pair is established, in which the uncertainties of displacement excitation, load excitation, and stiffness excitation are included, and their formulations are derived in detail by using interval mathematics. The established interval parameters dynamic model is solved by combining the Chebyshev inclusion function method and the Runge–Kutta method. Finally, the influence of the random interval parameters of meshing stiffness, input torque, and transmission error as well as backlash on the vibration velocity interval and transmission reliability of the gear transmission system are studied. The analysis results show that the three types of excitations have different effects on the dynamic characteristics. To be specific, the effects of uncertain parameters on the dynamic characteristics can be ordered as meshing stiffness, input torque, backlash, and transmission error in sequence from the strongest to the weakest. The present study may serve as a sound theoretical basis and can provide references for the design and vibration control of spur gear transmission systems.