In recent years, fractional(-order) differential equations have attracted increasing interests due to their applications in modeling anomalous diffusion, time dependent materials and processes with long range dependence, allometric scaling laws, and complex networks. Although an autonomous system cannot define a dynamical system in the sense of semigroup because of the memory property determined by the fractional derivative, we can still use the Lyapunov exponents to discuss its dynamical evolution. In this paper, we first define the Lyapunov exponents for fractional differential systems then estimate the bound of the corresponding Lyapunov exponents. For linear fractional differential system, the bounds of its Lyapunov exponents are conveniently derived which can be regarded as an example for the theoretical results established in this paper. Numerical example is also included which supports the theoretical analysis.
High-quality traffic flow generation is the core module in building simulators for autonomous driving. However, the majority of available simulators are incapable of replicating traffic patterns that accurately reflect the various features of real-world data while also simulating human-like reactive responses to the tested autopilot driving strategies. Taking one step forward to addressing such a problem, we propose Realistic Interactive TrAffic flow (RITA) as an integrated component of existing driving simulators to provide high-quality traffic flow for the evaluation and optimization of the tested driving strategies. RITA is developed with fidelity, diversity, and controllability in consideration, and consists of two core modules called RITABackend and RITAKit. RITABackend is built to support vehicle-wise control and provide traffic generation models from real-world datasets, while RITAKit is developed with easy-to-use interfaces for controllable traffic generation via RITABackend. We demonstrate RITA's capacity to create diversified and high-fidelity traffic simulations in several highly interactive highway scenarios. The experimental findings demonstrate that our produced RITA traffic flows meet all three design goals, hence enhancing the completeness of driving strategy evaluation. Moreover, we showcase the possibility for further improvement of baseline strategies through online fine-tuning with RITA traffic flows.
Feature extraction and matching of remote sensing images is becoming increasingly important with a wide range of applications. It matches and superimposes images obtained from the same scene at different times, different sensors, and different angles, and maps the optimal to the target image. CNN-based algorithms have shown superior expressiveness compared to traditional methods in almost all fields with image. This paper optimises the network based on SuperPoint by replacing convolution with a depth-separable convolution which has smaller number of parameters, and replacing the conv block with a spindle-type Inverted Residuals block composed of dimension expansion, depth-separable convolution and Dimension reduction. The network depth is fine-tuned to ensure accuracy. The model is trained on the RSSCN7 remote sensing dataset. Compared with other traditional algorithms in a cross-sectional manner with the combination of SuperGlue, the optimized algorithm shows the superior comprehensive performance.
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