We investigate two important properties of M-estimator, namely, robustness and tractability, in linear regression setting, when the observations are contaminated by some arbitrary outliers. Specifically, robustness means the statistical property that the estimator should always be close to the underlying true parameters {\em regardless of the distribution of the outliers}, and tractability indicates the computational property that the estimator can be computed efficiently, even if the objective function of the M-estimator is {\em non-convex}. In this article, by learning the landscape of the empirical risk, we show that under mild conditions, many M-estimators enjoy nice robustness and tractability properties simultaneously, when the percentage of outliers is small. We further extend our analysis to the high-dimensional setting, where the number of parameters is greater than the number of samples, $p \gg n$, and prove that when the proportion of outliers is small, the penalized M-estimators with {\em $L_1$} penalty will enjoy robustness and tractability simultaneously. Our research provides an analytic approach to see the effects of outliers and tuning parameters on the robustness and tractability for some families of M-estimators. Simulation and case study are presented to illustrate the usefulness of our theoretical results for M-estimators under Welsch's exponential squared loss.
Abstract Zinc ion batteries (ZIBs) exhibit significant promise in the next generation of grid‐scale energy storage systems owing to their safety, relatively high volumetric energy density, and low production cost. Despite substantial advancements in ZIBs, a comprehensive evaluation of critical parameters impacting their practical energy density ( E practical ) and calendar life is lacking. Hence, we suggest using formulation‐based study as a scientific tool to accurately calculate the cell‐level energy density and predict the cycling life of ZIBs. By combining all key battery parameters, such as the capacity ratio of negative to positive electrode (N/P), into one formula, we assess their impact on E practical . When all parameters are optimized, we urge to achieve the theoretical capacity for a high E practical . Furthermore, we propose a formulation that correlates the N/P and Coulombic efficiency of ZIBs for predicting their calendar life. Finally, we offer a comprehensive overview of current advancements in ZIBs, covering cathode and anode, along with practical evaluations. This Minireview outlines specific goals, suggests future research directions, and sketches prospects for designing efficient and high‐performing ZIBs. It aims at bridging the gap from academia to industry for grid‐scale energy storage.
Robust change point detection for large-scale data streams has many real-world applications in industrial quality control, signal detection, and biosurveillance. Unfortunately, it is highly nontrivial to develop efficient schemes due to three challenges: (1) the unknown sparse subset of affected data streams, (2) the unexpected outliers, and (3) computational scalability for real-time monitoring and detection. In this article, we develop a family of efficient real-time robust detection schemes for monitoring large-scale independent data streams. For each data stream, we propose to construct a new local robust detection statistic called the Lα-CUSUM (cumulative sum) statistic that can reduce the effect of outliers by using the Box-Cox transformation of the likelihood function. Then the global scheme will raise an alarm based upon the sum of the shrinkage transformation of these local Lα-CUSUM statistics to filter out unaffected data streams. In addition, we propose a new concept called false alarm breakdown point to measure the robustness of online monitoring schemes and propose a worst-case detection efficiency score to measure the detection efficiency when the data contain outliers. We then characterize the breakdown point and the efficiency score of our proposed schemes. Asymptotic analysis and numerical simulations are conducted to illustrate the robustness and efficiency of our proposed schemes.
The problem of quickest change detection in anonymous heterogeneous sensor networks is studied. The sensors are clustered into $K$ groups, and different groups follow different data generating distributions. At some unknown time, an event occurs in the network and changes the data generating distribution of the sensors. The goal is to detect the change as quickly as possible, subject to false alarm constraints. The anonymous setting is studied, where at each time step, the fusion center receives unordered samples without knowing which sensor each sample comes from, and thus does not know its exact distribution. In [1], an optimal algorithm was provided, which however is not computational efficient for large networks. In this paper, a computationally efficient test is proposed and a novel theoretical characterization of its false alarm rate is further developed.
Abstract Zinc metal battery (ZMB) is promising as the next generation of energy storage system, but challenges relating to dendrites and corrosion of the zinc anode are restricting its practical application. Here, to stabilize Zn anode, we report a controlled electrolytic method for a monolithic solid‐electrolyte interphase (SEI) via a high dipole moment solvent dimethyl methylphosphonate (DMMP). The DMMP‐based electrolytes can generate a homogeneous and robust phosphate SEI (Zn 3 (PO 4 ) 2 and ZnP 2 O 6 ). Benefiting from the protecting impact of this in situ monolithic SEI, the zinc electrode exhibits long‐term cycling of 4700 h and a high Coulombic efficiency 99.89 % in Zn|Zn and Zn|Cu cell, respectively. The full V 2 O 5 |Zn battery with DMMP‐H 2 O hybrid electrolyte exhibits a high capacity retention of 82.2 % following 4000 cycles under 5 A g −1 . The first success in constructing the monolithic phosphate SEI will open a new avenue in electrolyte design for highly reversible and stable Zn metal anodes.
A new formula for caculating the locking-time of 3 rd Order Charge-Pump PLL is presented. The locking-time is shown to depend on parameters of the loop in the formula. Its validity is verified by the behavior model. So the formula is very adapt to the systematic design and early verification of 3 rd Order CPPLL.
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