Symbolic Trajectory Evaluation (STE) is a powerful technique for model checking. It is based on 3-valued symbolic simulation, using 0,1 and X (”unknown”). The X value is used to abstract away parts of the circuit. The abstraction is derived from the user’s specification. Currently the process of abstraction and refinement in STE is performed manually. This paper presents an automatic refinement...

Symbolic trajectory evaluation (STE) is a model checking technique that has been successfully used to verify industrial designs. Existing implementations of STE, however, reason at the level of bits, allowing signals to take values in {0, 1, X}. This limits the amount of abstraction that can be achieved, and presents inherent limitations toion that can be achieved, and presents inherent limitat...

This paper presents biped walking control using a library of optimal trajectories. The biped walking control problem is formulated as an optimal control problem. We take advantage of a parametric trajectory optimization method to find the periodic steady-state trajectory in regular walking. Then we use Differential Dynamic Programming (DDP) to generate a library of optimal trajectories and loca...

Existing moving object’s trajectory prediction algorithms suffer from the data sparsity problem, which affects the accuracy of the trajectory prediction. Aiming to the problem, we present an Entropy-based Sparse Trajectories Prediction method enhanced by Matrix Factorization (ESTP-MF). Firstly, we do trajectory synthesis based on trajectory entropy and put synthesized trajectories into the traj...

In recent years, longitudinal data have become increasingly relevant in many applications, heightening interest in selecting the best longitudinal model to analyze them. Too often traditional practices rather than substantive theory guide the specific longitudinal model selected for the analysis. This opens the possibility that alternative models might better correspond to the data. In this reg...

We have previously proposed a trajectory model which is based on a mixture density network (MDN) trained with target variables augmented with dynamic features together with an algorithm for estimating maximum likelihood trajectories which respects the constraints between those features. In this paper, we have extended that model to allow diagonal covariance matrices and multiple mixture compone...

We provide a method to determine the motion of a classical massive particle in a background geometry of 2-dimensional gravity theories, for which the Birkhoff theorem holds. In particular, we get the particle trajectory in a continuous class of 2-dimensional dilaton gravity theories that includes the Callan-Giddings-HarveyStrominger (CGHS) model, the Jackiw-Teitelboim (JT) model, and the d-dime...

The equal division of tropical cyclone (TC) trajectory method, the mass moment of the TC trajectory method, and the mixed regression model method are clustering algorithms that use space and shape information from complete TC trajectories. In this article, these three clustering algorithms were applied in a TC trajectory clustering analysis to identify the TCs that affected the South China Sea ...

In this paper a closing lemma for C1 nonsingular endomorphisms equivariant under free actions of finite-groups is proved. Hence a recurrent trajectory, as well as all of its symmetric conjugates, of a C1 nonsingular endomorphism equivariant under a free action of a finite group can be closed up simultaneously by an arbitrarily small C1 equivariant perturbation.