Directed Network as a Chaotic Piece-Wise Linear One-Dimensional Map and Its Large-Deviation Properties

Rigorous Verification of Poincaré Map Generated by a Continuous Piece-Wise Linear Vector Field and Its Application

This paper provides algorithms in order to solve an interval implicit function of the Poincaré map generated by a continuous piecewise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MAT LAB and INT LAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear...

One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures.

Trajectory piece-wise quasi-linear approximation of large non-linear dynamic systems

In this work we extend the trajectory piece-wise linear (TPWL) approximation of large, non-linear and input-affine dynamical systems to non-linear systems with non-linear input operators. The new technique is called the trajectory piece-wise quasi-linear (TPWQ) approximation. We explain the motivation for this technique in light of previously reported under-performance of the TPWL method and sh...

On a Fast Piece-Wise Linear Hough Transform PLHT and its Application

Replacing the Hough calculation of the trigonomeric functions, sine and cos0,by the piece-wise linear Hough function(PLH), the basic cost for the sine , cose and the multiplications is removed. The PLH function is directly introduced from the usual Hough function. The PLH function inherits the basic properties of the usual Hough function from the view point to extract the line patterns from the...

Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks

We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function. Such networks are often used in deep learning and have been shown to be hard to verify for modern satisfiability modulo theory (SMT) and integer linear programming (ILP) solvers. The starting point of our approach is the addition of a global linear approxi...