Optimal change point detection and localization in sparse dynamic networks

We study the problem of change point localization in dynamic networks models. We assume that we observe a sequence of independent adjacency matrices of the same size, each corresponding to a realization of an unknown inhomogeneous Bernoulli model. The underlying distribution of the adjacency matrices are piecewise constant, and may change over a subset of the time points, called change points. We are concerned with recovering the unknown number and positions of the change points. In our model setting, we allow for all the model parameters to change with the total number of time points, including the network size, the minimal spacing between consecutive change points, the magnitude of the smallest change and the degree of sparsity of the networks. We first identify a region of impossibility in the space of the model parameters such that no change point estimator is provably consistent if the data are generated according to parameters falling in that region. We propose a computationally-simple algorithm for network change point localization, called network binary segmentation, that relies on weighted averages of the adjacency matrices. We show that network binary segmentation is consistent over a range of the model parameters that nearly cover the complement of the impossibility region, thus demonstrating the existence of a phase transition for the problem at hand. Next, we devise a more sophisticated algorithm based on singular value thresholding, called local refinement, that delivers more accurate estimates of the change point locations. Under appropriate conditions, local refinement guarantees a minimax optimal rate for network change point localization while remaining computationally feasible

Univariate Mean Change Point Detection: Penalization, CUSUM and Optimality

The problem of univariate mean change point detection and localization based on a sequence of $n$ independent observations with piecewise constant means has been intensively studied for more than half century, and serves as a blueprint for change point problems in more complex settings. We provide a complete characterization of this classical problem in a general framework in which the upper bound $\sigma^2$ on the noise variance, the minimal spacing $\Delta$ between two consecutive change points and the minimal magnitude $\kappa$ of the changes, are allowed to vary with $n$. We first show that consistent localization of the change points, when the signal-to-noise ratio $\frac{\kappa \sqrt{\Delta}}{\sigma} < \sqrt{\log(n)}$, is impossible. In contrast, when $\frac{\kappa \sqrt{\Delta}}{\sigma}$ diverges with $n$ at the rate of at least $\sqrt{\log(n)}$, we demonstrate that two computationally-efficient change point estimators, one based on the solution to an $\ell_0$-penalized least squares problem and the other on the popular wild binary segmentation algorithm, are both consistent and achieve a localization rate of the order $\frac{\sigma^2}{\kappa^2} \log(n)$. We further show that such rate is minimax optimal, up to a $\log(n)$ term

Repetitive Nanosecond Volume Discharges under Airflows

Atmospheric pressure discharges are widely used in active airflow control, material synthesis, and air treatment. The key to an optimal application performance lies in how to generate stable and diffuse plasma especially in a large volume and in high-speed airflows. This chapter presents the study of repetitive nanosecond volume discharges under high-speed airflows. The volume discharge strongly depends on the airflows, and the corresponding discharge modes vary from filament to diffuse modes with addition of airflows. The role of airflows provides negative effects on discharge currents as well as discharge densities. Moreover, a type of discharge device with upstream and downstream structure is proposed to demonstrate that charged particles produced by the upstream discharge are transported to the downstream zone and play a pre-ionization and enhanced effect to the downstream discharges

Application of an Electric Field to Low-Frequency Oscillation Control in Hall Thrusters

In order to satisfy the national demands for developing a long-life satellite platform, lunar exploration, and deep-space exploitation, Hall thrusters are now considered the preferred candidate for spacecraft propulsion. A Hall thruster is a type of electric propulsion with an annular structure, in which a propellant, usually xenon, is ionized and then accelerated by electrostatic force to create a propulsive thrust. Low-frequency discharge current oscillations, also called breathing mode oscillations in some references, are among the major research topics of Hall thrusters. Low-frequency oscillations in the range of 10–100 kHz might affect the reliability of power processing unit and reduce the efficiency and specific impulse of Hall thrusters. The control of low-frequency oscillations is an essential challenge in the space application of Hall thrusters. It is proved that the electric field is a highly important influence factor for low-frequency oscillations; therefore, application of a dynamic electric field is a practical way to control low-frequency oscillation

Gain Scheduling Control of Nonlinear Shock Motion Based on Equilibrium Manifold Linearization Model

AbstractThe equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analyzes the physical significance of the equilibrium manifold linearization model, and the self-feedback mechanism of shock motion is revealed. This helps to describe the stability and dynamics of shock motion. Based on the model, the paper puts forwards a gain scheduling control method for nonlinear shock motion. Simulation has shown the validity of the control scheme

Long-Life Technology for Space Flight Hall Thrusters

The vastly improved durability of spacecrafts, coupled with the simultaneous continuous development of thrusters for high power output, has created a strong demand for Hall thrusters (HT) with long service lives. However, erosion of the discharge channel walls by high-energy ions is the most impactful and visible process that limits the lifetime of the thruster. This process is very sensitive to the operation mode of the thruster and the corresponding power density. We hereby present the results of our investigation on the factors that limit the lifetime of Hall thrusters, and three proven techniques for improving longevity of use including magnetic shielding (MS), wall-less technology, and aft-magnetic fields with large gradient