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This memoir is concerned with quantitative unique continuation estimates for equations involving a “sum of squares” operator The first result is the tunneling estimate The main result is a stability estimate for solutions to the hypoelliptic wave equation We then prove the approximate controllability of the hypoelliptic heat equation We also explain how the analyticity assumption can be relaxed, and a boundary Most results turn out to be optimal on a family of Grushin-type operators. The main proof relies on the general strategy to produce quantitative unique continuation estimates, developed by the authors in Laurent-Léautaud (2019).

This paper deals with the observability, controllability, and command and control strategy in the Botnet Defense System (BDS) that disinfects malicious botnets with white-hat botnets. The BDS defends an IoT system built over the Internet. The Internet is characterized by openness, but not all nodes are observable and controllable. We incorporated the concept of observability and controllability into the BDS design and theoretically clarified that the BDS can enhance its observability and controllability by utilizing its white-hat botnets. In addition, we proposed a Withdrawal strategy as a basic strategy to command and control white-hat botnets. Then, we modeled the BDS, adopted the Withdrawal strategy with agent-oriented Petri net PN2 and confirmed the effect through the simulation of the model. The result shows that even if considering observability and controllability, the BDS wiped out the malicious bots and reduced the white-hat bots to less than 1% as long as the white-hat worms were sufficiently infectious.

In this paper, we consider the inhomogeneous and anisotropic elastic wave equation on bounded domain. We prove the internal observability, controllability and stabilization of the elastic wave equation under a suitable condition of inhomogeneous and anisotropic medias. The main methods are multiplier methods and compactness-uniqueness arguments.

Testing is a critical aspect of integrated circuit (IC) design, aimed at ensuring thorough evaluation of all nodes within the designs netlist to identify potential defects. The effectiveness of design for testability (DFT) relies on assessing the observability and controllability of each node within the architecture. These attributes form the foundation of DFT, enabling optimal test coverage (TC) with minimal test time (TT). The rigor of design testing is directly linked to the number of patterns used, with crucial parameters, such as multi-voltage conditions, temperature variations, and comprehensive testing methodologies playing key roles during the process. This methodology integrates techniques, such as scan insertion (SI), automatic test pattern generation (ATPG), embedded deterministic testing, and pattern simulation. The primary goal is to compress and minimize test data volume (TDV) and TT. ATPG plays a pivotal role in this approach by generating patterns tailored to meet compression requirements. Simulation validates the effectiveness of these patterns in reducing TT. The application of this methodology leads to significant improvements in testing efficiency. This study effectively determines the optimal multi-voltage and temperature parameters for IC testing. By leveraging automatic pattern generation and compression techniques, it achieves a substantial reduction in both test data and TT. The findings emphasize the importance of adhering to the DFT principles of observability and controllability to maximize TC. The proposed methodology demonstrates clear improvements in TDV and TT efficiency, contributing not only to the field of IC manufacturing but also emphasizing the value of a systematic and comprehensive approach to DFT in enhancing the reliability and performance of ICs.

This paper deals with the study of controllability and observability of fuzzy fractional descriptor dynamical system in terms of granular differentiability. The granular fuzzy solution for granular descriptor fractional dynamical system (GrDFDS) is obtained by using the Mittag–Leffler function and granular Laplace transform and the solution is represented in terms of the state transfer matrix. The controllability and observability of GrDFDS is analysed with the help of theorems using the controllability Gramian matrix and observability Gramian matrix. In order to illustrate the efficacy of our findings, we hereby give the controllability analysis of an engineering problem pertaining to the compatibility of a descriptor fractional electric circuit. The graph visually represents the outcome, indicating that the granular descriptor dynamical system of the electric circuit can be effectively controlled, leading to the successful transition of its state from the granular initial to the final state.

In this paper, necessary and sufficient conditions for zeroing of the transfer matrices of descriptor continuous-time and discrete-time linear systems are established. The conditions are illustrated by simple numerical examples of the descriptor continuous-time and discrete-time linear systems. Also some remarks on the systems with delays in control are given.

Decision making for water resource planning is often related to social, economic and environmental factors. There are various methods for making decisions about water resource planning alternatives and measures with various shortcomings. A comprehensive entropy weight observability-controllability risk analysis approach is presented in this study. Computing methods for entropy weight (EW) and subjective weight (SW) are put forward based on information entropy theory and experimental psychology principles, respectively. Comprehensive weight (CW) consisting of EW and SW is determined. The values of observability-controllability risk (Roc) and gain by comparison (Gbc) are obtained based on the CWs. The quantitative analysis of alternatives and measures is achieved based on Roc and Gbc. A case study on selection of water resource planning alternatives and measures in the Yellow River Basin, China, was performed. Results demonstrate that the approach presented in this study can achieve optimal decision-making results.

By modeling the brain as a network, the challenge of abating seizure can be recast as a problem of network control. In the premise of bringing network under control, the minimum number of nodes prerequisite for controlling seizures are thus a natural aim of interest, which is still an outstanding issue. Here, we use the network structural control theory to guide the selection for the optimal control nodes with the aim of fully abating seizures. Firstly, we construct the dynamical complex network of pathological seizure by estimating the synchronicity and directionality of information flows over time between EEG signals from 10 patients with focal epilepsy. Then, based on the controllability and observability principles of complex systems, the minimum key nodes which are effective to fully control the network seizure behaviors are obtained. Results show that the calculated control nodes are distinct with the focus zones from clinic report. This suggests that the full control of epileptic network may not only related to the focus zone, the other non-focus nodes could also play important roles. This finding is validated by using the spatiotemporal neural network model connected with our modeled dynamical adjacent matrix. It successfully reproduces the original EEG signals which can be effectively abated by applying pulse stimulation on the identified key nodes or resecting them, while the partial effects can be obtained when functioning onto the clinically identified focus zones of 60% patients. Interestingly, for another 30% patients lesser nodes than clinic reports are need to fully control seizures. In addition, our work facilitates to identify the evolution paths of information flows, so the non-clinic focus zones identified through controllability principle can be supposed to be the potential seizure foci. In sum, our work propose a general methodology or strategy for seizures focus localizations that could comprehensively consider the time-evolving information flow and the analysis of controllability mechanisms driven by the real seizures data, as well as the computational validation. This may promote to develop the canonical computational framework with the core intent of providing support for clinical treatment decisions.