Abstract Let G be a group and A set equipped with collection of finitary operations. We study cellular automata $$\tau :{A^G} \to {A^G}$$ that preserve the operations induced componentwise from . show τ is an endomorphism if only its local function homomorphism. When entropic (i.e. all are homomorphisms), we establish EndCA( G;A ), consisting such endomorphic automata, isomorphic to direct limi...

A linear complementarity problem (LCP) is formulated for the price of American options under the Bates model which combines the Heston stochastic volatility model and the Merton jump-diffusion model. A finite difference discretization is described for the partial derivatives and a simple quadrature is used for the integral term due to jumps. A componentwise splitting method is generalized for t...

We introduce CLS, for continuous local search, a class of polynomial-time checkable total functions that lies at the intersection of PPAD and PLS, and captures a particularly benign kind of local optimization in which the domain is continuous, as opposed to combinatorial, and the functions involved are continuous. We show that this class contains several well known intriguing problems which wer...

We present a straightforward way to use temporal decorrelation as preprocessing in linear and post-nonlinear independent component analysis (ICA) with higher order statistics (HOS). Contrary to the separation methods using second order statistics (SOS), the proposed method can be applied when the sources have similar temporal structure. The main idea is that componentwise decorrelation increase...

We present normwise and componentwise perturbation bounds for the hyperbolic QR factorization by using a new approach. The explicit expressions of mixed and componentwise condition numbers for the hyperbolic QR factorization are derived.

We present a new control design method which guarantees any prespecified componentwise ultimate bound on the state of multiple-input systems with matched perturbations. The method is based on eigenstructure assignment by state feedback and utilises a componentwise bound computation procedure recently proposed by the authors. This procedure exploits both the system and perturbation structures by...

A new data science tool named wavelet-based gradient boosting is proposed and tested. The approach is special case of componentwise linear least squares gradient boosting, and involves wavelet functions of the original predictors.Wavelet-based gradient boosting takes advantages of the approximate 1 penalization induced by gradient boosting to give appropriate penalized additive fits. The method...

We present a new control design method for perturbed multiple-input systems, which guarantees any desired componentwise ultimate bound on the system state. The method involves eigenvalue/eigenvector assignment by state feedback and utilises a componentwise bound computation procedure. This procedure directly takes into account both the system and perturbation structures by performing componentw...