We consider piecewise-deterministic Markov processes such as the Bouncy Particle sampler, on target densities with polynomial tails. Using direct drift condition methods, we provide bounds order of processes’ convergence rate to stationary, both one-dimensional and high-dimensional state spaces, in total variation distance f-norm.

Abstract During locomotion, humans sometimes entrain (i.e. synchronize) their steps to external oscillations: e.g. swaying bridges, tandem walking, bouncy harnesses, vibrating treadmills, exoskeletons. Previous studies have discussed the role of nonlinear oscillators (e.g. central pattern generators) in facilitating entrainment. However, energetics such interactions are unknown. Given substanti...

We establish $L^2$-exponential convergence rate for three popular piecewise deterministic Markov processes sampling: the randomized Hamiltonian Monte Carlo method, zigzag process, and bouncy particle sampler. Our analysis is based on a variational framework hypocoercivity, which combines Poincar\'{e}-type inequality in time-augmented state space standard $L^2$ energy estimate. provides explicit...

When designing objects, designers attempt to communicate the purpose and meaning of that object users using various factors such as visual appearance (aesthetic), practical interaction elements (product semantics) meanings beyond product (semiotics). This study sought confirm previous deductively-developed soma-semiotic framework, whose was understand ultimately predict emotional impact differe...

BouncyCastle is an open source Crypto provider written in Java which supplies classes for Elliptic Curve Cryptography (ECC). We have found a flaw in the class ECPoint resulting from an unhappy interaction of elementary algorithms. We show how to exploit this flaw to a real world attack, e.g., on the encryption scheme ECIES. BouncyCastle has since fixed this flaw (version 1.x 133 and higher) but...