Motion Planning of Vehicles for Crash Mitigation in Emergency Driving Scenarios

Motion planning in dynamic environment is crucial to the automated driving safety. In extremely emergency scenarios with unavoidable collisions, especially those with complex impact patterns, the potential crash risk should be well considered in motion planning. This paper proposes a motion planning algorithm for unavoidable collisions, which directly embeds a generalized crash severity index model to vehicle-to-vehicle collisions of multiple impact patterns. Firstly, the clothoid curve is used to sample the vehicle trajectory before collision, and a two-degree-of-freedom model is adopted to predict the vehicle poses corresponding to each sample path. Then, the crash severity index model is to estimate the potential crash severity of all sample paths. To improve the inferring time efficiency, a neural network is constructed and deployed to approximate the nonlinear severity model. Finally, the crash-severity-optimal trajectory is tracked through model predictive control method. Results show that by combining the braking and steering interventions for better crash severity reduction, the proposed strategy can achieve better mitigation effects than commonly-used collision-avoidance strategies. The deployment of real car experiment and sensitivity analysis demonstrate that the planning algorithm can guarantee real-time and reliably safe performances.

Motion Planning of Vehicles for Crash Mitigation in Emergency Driving Scenarios

Motion planning in dynamic environment is crucial to the automated driving safety. In extremely emergency scenarios with unavoidable collisions, especially those with complex impact patterns, the potential crash risk should be well considered in motion planning. This paper proposes a motion planning algorithm for unavoidable collisions, which directly embeds a generalized crash severity index model to vehicle-to-vehicle collisions of multiple impact patterns. Firstly, the clothoid curve is used to sample the vehicle trajectory before collision, and a two-degree-of-freedom model is adopted to predict the vehicle poses corresponding to each sample path. Then, the crash severity index model is to estimate the potential crash severity of all sample paths. To improve the inferring time efficiency, a neural network is constructed and deployed to approximate the nonlinear severity model. Finally, the crash-severity-optimal trajectory is tracked through model predictive control method. Results show that by combining the braking and steering interventions for better crash severity reduction, the proposed strategy can achieve better mitigation effects than commonly-used collision-avoidance strategies. The deployment of real car experiment and sensitivity analysis demonstrate that the planning algorithm can guarantee real-time and reliably safe performances.

Unbiased Simulation of Rare Events in Continuous Time

For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and $$\varepsilon$$ ε -strong simulation of diffusions, which can be used to almost surely constrain sample paths to a given tolerance, suggests one way to do this. We specify how such algorithms can be combined with the classical multilevel splitting method for rare event simulation. This provides unbiased estimations of the probability in question. We discuss the practical feasibility of the algorithm with reference to existing $$\varepsilon$$ ε -strong methods and provide proof-of-concept numerical examples.

Path Aggregation Model for Attributed Network Embedding with a Smart Random Walk

Network embedding has attracted a surge of attention recently. In this field, how to preserve high-order proximity has long been a difficult task. Graph convolutional network (GCN) and random walk-based approaches can preserve high-order proximity to a certain extent. However, they partially concentrate on the aggregation process and sampling process respectively. Path aggregation methods combine the merits of GCN and random walk, and thus can preserve more high-order information and achieve better performance. However, path aggregation framework has not been applied in attributed network embedding yet. In this paper, we propose a path aggregation model for attributed network embedding, with two main contributions. First, we claim that there always exists implicit edge weight in networks, and design a tweaked random walk algorithm to sample paths accordingly. Second, we propose a path aggregation framework dealing with both nodes and attributes. Extensive experimental results show that our proposal outperforms the cutting-edge baselines on downstream tasks, such as node clustering, node classification, and link prediction.

A Special Study of the Mixed Weighted Fractional Brownian Motion

In this work, we present the analysis of a mixed weighted fractional Brownian motion, defined by ηt:=Bt+ξt, where B is a Brownian motion and ξ is an independent weighted fractional Brownian motion. We also consider the parameter estimation problem for the drift parameter θ>0 in the mixed weighted fractional Ornstein–Uhlenbeck model of the form X0=0;Xt=θXtdt+dηt. Moreover, a simulation is given of sample paths of the mixed weighted fractional Ornstein–Uhlenbeck process.

Uncertain Independent Increment Processes are Contour Processes

Uncertain processes are used to model dynamic indeterminate systems associated with human uncertainty, and uncertain independent increment processes are a type of uncertain processes with independent uncertain increments. This paper mainly verifies a basic property about the sample paths of uncertain independent increment processes, which states that uncertain independent increment processes defined on a continuous uncertainty space are contour processes, a type of uncertain processes with a spectrum of sample paths as the skeletons. Based on this property, the extreme values and the time integral of an uncertain independent increment process are investigated, and their inverse uncertainty distributions are obtained.

A Rigorous Proof of Fundamental Theorem of Uncertain Calculus

This paper revises the definition of the general Liu process via requiring its drift and diffusion to be sample-continuous. Then it is verified that almost all sample paths of the general Liu process are locally Lipschitz continuous. At last, a rigorous proof of fundamental theorem of uncertain calculus is given.

Parameter estimation of the stochastic model for oral cancer in response to thymoquinone (TQ) as anticancer therapeutics

Oral Cancer is considered as one of the common problems of global public health and despite the progress in advanced research, the mortality rate has not been improved significantly in the last few decades. A natural product such as Thymoquinone, black seeds (TQ), is an active component of Nigella sativa or black cumin elicits cytotoxic effects on various oral cancer cell lines. A wide range of studies have been concluded that the TQ has two different anti-neoplastic actions that might trigger apoptosis, have the capacity to induce cell death in oral cancer cells. In the presence of TQ, oral cancer has been proved experimentally shows the decelerating trend of the growth. This article models the decelerating of the oral cancer growth by using a linear stochastic differential equation (SDEs). The Markov Chain Monte Carlo (MCMC) method used to estimate model parameters for 100, 500,1000 and 2000 simulations. The best set of kinetic parameters are identified. It can be seen that for 1000 simulations of the sample paths, the model fitted well the data, hence indicating a good fit. However, if the number of simulation is incerasing up to 2000, the parameter obtained shows instablity of the solution. This is due to the high numbers of noise generated, may influenced the stability of the solution.

Stochastic reaction–diffusion equations on networks

We consider stochastic reaction–diffusion equations on a finite network represented by a finite graph. On each edge in the graph, a multiplicative cylindrical Gaussian noise-driven reaction–diffusion equation is given supplemented by a dynamic Kirchhoff-type law perturbed by multiplicative scalar Gaussian noise in the vertices. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. We utilize the semigroup approach for stochastic evolution equations in Banach spaces to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph. In order to do so, we generalize existing results on abstract stochastic reaction–diffusion equations in Banach spaces.

Sample paths of white noise in spaces with dominating mixed smoothness

The sample paths of white noise are proved to be elements of certain Besov spaces with dominating mixed smoothness. Unlike in isotropic spaces, here the regularity does not get worse with increasing space dimension. Consequently, white noise is actually much smoother than the known sharp regularity results in isotropic spaces suggest. An application of our techniques yields new results for the regularity of solutions of Poisson and heat equation on the half space with boundary noise. The main novelty is the flexible treatment of the interplay between the singularity at the boundary and the smoothness in tangential, normal and time direction.