We describe a new method of computing functions of highly non-normal matrices, by using the concept of approximate diagonalization. We formulate a conjecture about its efficiency, and provide both theoretical and numerical evidence in support of the conjecture. We apply the method to compute arbitrary real powers of highly non-normal matrices. 1. Introduction. Let A be a non-normal n × n matrix...

We develop and implement a semi-numerical method for computing high order Taylor approximations of the unstable manifold at a hyperbolic fixed point of a compact infinite dimensional analytic map. Even though the method involves several layers of truncation our goal is to obtain a representation of the invariant manifold which is accurate in a large region about the fixed point. In order to ins...

Method We retrospectively reviewed medical records of 398 consecutive patients who underwent isolated elective OPCAB with intention-to-treat base from July 2005 to March 2015. 365 patients underwent successful OPCAB, whereas 24 patients were converted to EBS-CAB due to hemodynamic instability. The early and late clinical outcomes were analyzed and then propensity matched analysis was performed ...

Combustion is the source of eighty percent of the energy produced in the world: it is therefore a topic of major interest in the present context of global warming and decreasing fuel resources. Simulating combustors and especially instability mechanisms in these systems has become a central issue in the combustion community in the last ten years. This can be achieved only on massively parallel ...

In this work we develop a method for computing mathematically rigorous enclosures of some one dimensional manifolds of heteroclinic orbits for nonlinear maps. Our method exploits a rigorous curve following argument build on high order Taylor approximation of the local stable/unstable manifolds. The curve following argument is a uniform interval Newton method applied on short line segments. The ...

Evolvability by means of simple sequence repeat (SSR) instability is a feature under the constant influence of opposing selective pressures to expand and compress the repeat tract and is mechanistically influenced by factors that affect genetic instability. In addition to direct selection for protein expression and structural integrity, other factors that influence tract length evolution were s...