Finite elements for symmetric and traceless tensors in three dimensions

We construct a family of finite element sub-complexes of the conformal complex on tetrahedral meshes. This complex includes vector fields and symmetric and traceless tensor fields, interlinked through the conformal Killing operator, the linearized Cotton-York operator, and the divergence operator, respectively. This leads to discrete versions of transverse traceless (TT) tensors and York splits in general relativity. We provide bubble complexes and investigate supersmoothness to facilitate the construction. We show the exactness of the finite element complex on contractible domains.Comment: 44 pages, 1 figur

Suboptimal Safety-Critical Control for Continuous Systems Using Prediction-Correction Online Optimization

This paper investigates the control barrier function (CBF) based safety-critical control for continuous nonlinear control affine systems using more efficient online algorithms by the time-varying optimization method. The idea of the algorithms is that when quadratic programming (QP) or other convex optimization algorithms needed in the CBF-based method is not computation affordable, the alternative suboptimal feasible solutions can be obtained more economically. By using the barrier-based interior point method, the constrained CBF-QP problems are transformed into unconstrained ones with suboptimal solutions tracked by two continuous descent-based algorithms. Considering the lag effect of tracking and exploiting the system information, the prediction method is added to the algorithms, which achieves exponential convergence to the time-varying suboptimal solutions. The convergence and robustness of the designed methods as well as the safety criteria of the algorithms are studied theoretically. The effectiveness is illustrated by simulations on the anti-swing and obstacle avoidance tasks

TND-NAS: Towards Non-differentiable Objectives in Progressive Differentiable NAS Framework

Differentiable architecture search has gradually become the mainstream research topic in the field of Neural Architecture Search (NAS) for its capability to improve efficiency compared with the early NAS (EA-based, RL-based) methods. Recent differentiable NAS also aims at further improving search efficiency, reducing the GPU-memory consumption, and addressing the "depth gap" issue. However, these methods are no longer capable of tackling the non-differentiable objectives, let alone multi-objectives, e.g., performance, robustness, efficiency, and other metrics. We propose an end-to-end architecture search framework towards non-differentiable objectives, TND-NAS, with the merits of the high efficiency in differentiable NAS framework and the compatibility among non-differentiable metrics in Multi-objective NAS (MNAS). Under differentiable NAS framework, with the continuous relaxation of the search space, TND-NAS has the architecture parameters ($\alpha$) been optimized in discrete space, while resorting to the search policy of progressively shrinking the supernetwork by $\alpha$. Our representative experiment takes two objectives (Parameters, Accuracy) as an example, we achieve a series of high-performance compact architectures on CIFAR10 (1.09M/3.3%, 2.4M/2.95%, 9.57M/2.54%) and CIFAR100 (2.46M/18.3%, 5.46/16.73%, 12.88/15.20%) datasets. Favorably, under real-world scenarios (resource-constrained, platform-specialized), the Pareto-optimal solutions can be conveniently reached by TND-NAS

Communication security of autonomous ground vehicles based on networked control systems: The optimized LMI approach

The paper presents a study of networked control systems (NCSs) that are subjected to periodic denial-of-service (DoS) attacks of varying intensity. The use of appropriate Lyapunov–Krasovskii functionals (LKFs) help to reduce the constraints of the basic conditions and lower the conservatism of the criteria. An optimization problem with constraints is formulated to select the trigger threshold, which is solved using the gradient descent algorithm (GDA) to improve resource utilization. An intelligent secure event-triggered controller (ISETC) is designed to ensure the safe operation of the system under DoS attacks. The approach is validated through experiments with an autonomous ground vehicle (AGV) system based on the Simulink platform. The proposed method offers the potential for developing effective defense mechanisms against DoS attacks in NCSs

Late Neo-Proterozoic Tectono-Sedimentary Evolution of the Tarim Block, NW China

The study of the late Neo-Proterozoic tectono-sedimentary evolution of the Tarim Basin is a key to unravel the tectonic setting, the intracontinental rift formation mechanism, and the sedimentary filling processes of this basin. Since in the Tarim Basin, the late Neo-Proterozoic to early Cambrian sedimentary successions were preserved, this basin represents an excellent site in order to study the Precambrian geology. Based on the outcrop data collected in the peripheral areas of the Tarim Basin, coupled with the intra-basinal drill sites and seismic data previously published, the late Neo-proterozoic tectono-sedimentary evolution of the Tarim Basin has been investigated. These data show that there were two individual blocks before the Cryogenian Period, namely, the north Tarim Block and the south Tarim Block. In the early Neo-Proterozoic (ca. 800 Ma), the amalgamation of two blocks resulted in the formation of the unified basement. During the late Neo-Proterozoic, the Tarim Block was in an extensional setting as a result of the Rodinia supercontinent breakup and then evolved into an intracontinental rift basin. The tectono-sedimentary evolution of the basin may be divided into three stages: the rifting stage (780–700 Ma), the rifting to depression transitional stage (660–600 Ma), and the post-rift depression stage (580–540 Ma). In the rifting stage, intracontinental rifts (i.e., the Awati Rift, the North Manjar Rift, and the South Manjar Rift) were formed, in which coarse-grained clastic sediments were deposited, generally accompanied by a massive volcanic activity due to an intensive stretching. In the rifting-depression transitional stage and in the post-rift depression stage, the paleogeography was characterized by uplifts to the south and depressions to the north. Three types of depositional association (i.e., clastic depositional association, clastic-carbonate mixed depositional association, and carbonate depositional association) were formed. The distribution of the lower Cambrian source rock was genetically related to the tectono-sedimentary evolution during the late Neo-Proterozoic. The lower Cambrian source rock was a stable deposit in the northern Tarim Basin, where the late Ediacaran carbonate was deposited, thinning out toward the central uplift. It was distributed throughout the entire Mangar region in the east and may be missing in the Magaiti and the southwestern Tarim Basin

Mixed-Delay-Dependent Augmented Functional for Synchronization of Uncertain Neutral-Type Neural Networks with Sampled-Data Control

In this paper, the synchronization problem of uncertain neutral-type neural networks (NTNNs) with sampled-data control is investigated. First, a mixed-delay-dependent augmented Lyapunov--Krasovskii functional (LKF) is proposed, which not only considers the interaction between transmission delay and communication delay, but also takes the interconnected relationship between neutral delay and transmission delay into consideration. Then, a two-sided looped functional is also involved in the LKF, which effectively utilizes the information on the intervals [tk, t], [tk − τ, t − τ], [t, tk+ 1), [t − τ, tk+ 1 − τ). Furthermore, based on the suitable LKF and a free-matrix-based integral  inequality, two synchronization criteria via a sampled-data controller considering communication delay are derived in forms of linear matrix inequalities (LMIs). Finally, three numerical examples are carried out to confirm the validity of the proposed criteria

Mixed-Delay-Dependent Augmented Functional for Synchronization of Uncertain Neutral-Type Neural Networks with Sampled-Data Control

In this paper, the synchronization problem of uncertain neutral-type neural networks (NTNNs) with sampled-data control is investigated. First, a mixed-delay-dependent augmented Lyapunov–Krasovskii functional (LKF) is proposed, which not only considers the interaction between transmission delay and communication delay, but also takes the interconnected relationship between neutral delay and transmission delay into consideration. Then, a two-sided looped functional is also involved in the LKF, which effectively utilizes the information on the intervals [tk,t], [tk−τ,t−τ],[t,tk+1),[t−τ,tk+1−τ). Furthermore, based on the suitable LKF and a free-matrix-based integral inequality, two synchronization criteria via a sampled-data controller considering communication delay are derived in forms of linear matrix inequalities (LMIs). Finally, three numerical examples are carried out to confirm the validity of the proposed criteria

New Delay-Dependent Exponential Stability Criteria for Neural Networks with Mixed Time-Varying Delays

This study is concerned with the problem of new delay-dependent exponential stability criteria for neural networks (NNs) with mixed time-varying delays via introducing a novel integral inequality approach. Specifically, first, by taking fully the relationship between the terms in the Leibniz-Newton formula into account, several improved delay-dependent exponential stability criteria are obtained in terms of linear matrix inequalities (LMIs). Second, together with some effective mathematical techniques and a convex optimization approach, less conservative conditions are derived by constructing an appropriate Lyapunov-Krasovskii functional (LKF). Third, the proposed methods include the least numbers of decision variables while keeping the validity of the obtained results. Finally, three numerical examples with simulations are presented to illustrate the validity and advantages of the theoretical results

Complex Dynamical Sampling Mechanism for the Random Pulse Circulation Model and Its Application

The fast multi-pulse spectrum is a spectrum acquisition method that obtains an average pulse amplitude in a dynamic window, which improves the energy resolution by sharpening peaks in the acquired spectra, but produces the counting loss. Owing to the counting loss problem, a counting rate multiplication method based on uniform sampling, also called the pulse circulation method, is presented in this paper. Based on the theory of mathematical statistics and uniform sampling, this method adopted a dynamic sample pool to update the pulse amplitude sample in real time. Random numbers from the uniform distribution were sampled from the sample pool, and the sampled results were stored in the random pulse circulator so that the pulse amplitude information used for spectrum generation was uniformly expanded. In the experiment section, the obtained spectrum was analyzed to verify the multiplication effect of the pulse circulation method on the counting rate and the compensation effect of the fast multi-pulse spectrum algorithm on the counting rate loss. The results indicated that the characteristic peaks of each element in the X-ray spectrogram obtained by the pulse circulation method could realize counting rate multiplication uniformly, and the multiplication ratio of every element was approximately equal. This is of great significance for obtaining an accurate X-ray fluorescence spectrum