Control Of Nonh=holonomic Systems

Many real-world electrical and mechanical systems have velocity-dependent constraints in their dynamic models. For example, car-like robots, unmanned aerial vehicles, autonomous underwater vehicles and hopping robots, etc. Most of these systems can be transformed into a chained form, which is considered as a canonical form of these nonholonomic systems. Hence, study of chained systems ensure their wide applicability. This thesis studied the problem of continuous feed-back control of the chained systems while pursuing inverse optimality and exponential convergence rates, as well as the feed-back stabilization problem under input saturation constraints. These studies are based on global singularity-free state transformations and controls are synthesized from resulting linear systems. Then, the application of optimal motion planning and dynamic tracking control of nonholonomic autonomous underwater vehicles is considered. The obtained trajectories satisfy the boundary conditions and the vehicles\u27 kinematic model, hence it is smooth and feasible. A collision avoidance criteria is set up to handle the dynamic environments. The resulting controls are in closed forms and suitable for real-time implementations. Further, dynamic tracking controls are developed through the Lyapunov second method and back-stepping technique based on a NPS AUV II model. In what follows, the application of cooperative surveillance and formation control of a group of nonholonomic robots is investigated. A designing scheme is proposed to achieves a rigid formation along a circular trajectory or any arbitrary trajectories. The controllers are decentralized and are able to avoid internal and external collisions. Computer simulations are provided to verify the effectiveness of these designs

Traveling Waves of Modified Leslie-Gower Predator-prey Systems

The spreading phenomena in modified Leslie-Gower reaction-diffusion predator-prey systems are the topic of this paper. We mainly study the existence of two different types of traveling waves. Be specific, with the aid of the upper and lower solutions method, we establish the existence of traveling wave connecting the prey-present state and the coexistence state or the prey-present state and the prey-free state by constructing different and appropriate Lyapunov functions. Moreover, for traveling wave connecting the prey-present state and the prey-free state, we gain more monotonicity information on wave profile based on the asymptotic behavior at negative infinite. Finally, our results are applied to modified Leslie-Gower system with Holling II type or Lotka-Volterra type, and then a novel Lyapunov function is constructed for the latter, which further enhances our results. Meanwhile, some numerical simulations are carried to support our results

A sufficient condition on successful invasion by the predator

In this paper, we provide a sufficient condition on successful invasion by the predator. Specially, we obtain the persistence of traveling wave solutions of predator-prey system, in which the predator can survive without the predation of the prey. This proof heavily depends on comparison principle of scalar monostable equation, the rescaling method and phase-plane analysis

Traveling Wave in a Ratio-dependent Holling-Tanner System with Nonlocal Diffusion and Strong Allee Effect

In this paper, a ratio-dependent Holling-Tanner system with nonlocal diffusion is taken into account, where the prey is subject to a strong Allee effect. To be special, by applying Schauder's fixed point theorem and iterative technique, we provide a general theory on the existence of traveling waves for such system. Then appropriate upper and lower solutions and a novel sequence, similar to squeeze method, are constructed to demonstrate the existence of traveling waves for c>c*. Moreover, the existence of traveling wave for c=c* is also established by spreading speed theory and comparison principle. Finally, the nonexistence of traveling waves for c<c* is investigated, and the minimal wave speed then is determined

A Novel Genetic Variant in Long Non-coding RNA Gene NEXN-AS1 is Associated with Risk of Lung Cancer

Lung cancer etiology is multifactorial, and growing evidence has indicated that long non-coding RNAs (lncRNAs) are important players in lung carcinogenesis. We performed a large-scale meta-analysis of690,564 SNPs in 15,531 autosomal lncRNAs by using datasets from six previously published genome-wideassociation studies (GWASs) from the Transdisciplinary Research in Cancer of the Lung (TRICL) consortiumin populations of European ancestry. Previously unreported significant SNPs (P value \u3c 1 × 10−7) were further validated in two additional independent lung cancer GWAS datasets from Harvard University anddeCODE. In the final meta-analysis of all eight GWAS datasets with 17,153 cases and 239,337 controls, a novel risk SNP rs114020893 in the lncRNA NEXN-AS1 region at 1p31.1 remained statistically significant(odds ratio = 1.17; 95% confidence interval = 1.11–1.24; P = 8.31 × 10−9). In further in silico analysis,rs114020893 was predicted to change the secondary structure of the lncRNA. Our finding indicates that SNP rs114020893 of NEXN-AS1 at 1p31.1 may contribute to lung cancer susceptibility

Swing surfaces and holographic entanglement beyond AdS/CFT

We propose a holographic entanglement entropy prescription for general states and regions in two models of holography beyond AdS/CFT known as flat$_3$/BMSFT and (W)AdS$_3$/WCFT. Flat$_3$/BMSFT is a candidate of holography for asymptotically flat three-dimensional spacetimes, while (W)AdS$_3$/WCFT is relevant in the study of black holes in the real world. In particular, the boundary theories are examples of quantum field theories that feature an infinite dimensional symmetry group but break Lorentz invariance. Our holographic entanglement entropy proposal is given by the area of a swing surface that consists of ropes, which are null geodesics emanating from the entangling surface at the boundary, and a bench, which is a spacelike geodesic connecting the ropes. The proposal is supported by an extension of the Lewkowycz-Maldacena argument, reproduces previous results based on the Rindler method, and satisfies the first law of entanglement entropy.Comment: 45 pages, 4 figures; v2: corrected typos and added comments on strong subadditivity, matches published versio

Beam Squint Assisted User Localization in Near-Field Integrated Sensing and Communications Systems

Integrated sensing and communication (ISAC) has been regarded as a key technology for 6G wireless communications, in which large-scale multiple input and multiple output (MIMO) array with higher and wider frequency bands will be adopted. However, recent studies show that the beam squint phenomenon can not be ignored in wideband MIMO system, which generally deteriorates the communications performance. In this paper, we find that with the aid of true-time-delay lines (TTDs), the range and trajectory of the beam squint in near-field communications systems can be freely controlled, and hence it is possible to reversely utilize the beam squint for user localization. We derive the trajectory equation for near-field beam squint points and design a way to control such trajectory. With the proposed design, beamforming from different subcarriers would purposely point to different angles and different distances, such that users from different positions would receive the maximum power at different subcarriers. Hence, one can simply localize multiple users from the beam squint effect in frequency domain, and thus reduce the beam sweeping overhead as compared to the conventional time domain beam search based approach. Furthermore, we utilize the phase difference of the maximum power subcarriers received by the user at different frequencies in several times beam sweeping to obtain a more accurate distance estimation result, ultimately realizing high accuracy and low beam sweeping overhead user localization. Simulation results demonstrate the effectiveness of the proposed schemes.Comment: This paper has been accepted by IEEE Transactions on Wireless Communications (TWC) on 18 September 202

Modular Hamiltonians in flat holography and (W)AdS/WCFT

We study several aspects of holographic entanglement in two models known as flat$_3$/BMSFT and (W)AdS$_3$/WCFT. These are two examples of holography beyond AdS/CFT where the the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS$_3$ or AdS$_3$ backgrounds with Dirichlet-Neumann boundary conditions. In particular, we derive the modular Hamiltonian for single intervals in both BMSFTs and WCFTs and find the holographic duals in the bulk using the covariant formulation of gravitational charges. We also extend the first law of entanglement entropy to these models of non-AdS holography and discuss the bound on "modular chaos" introduced recently in the context of the AdS/CFT correspondence.Comment: 46 pages, 3 figures; v2: corrected typos, matches published versio