Bogdan I. Epureanu

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An intriguing and unexpected result for students learning numerical analysis is that Newton's method, applied to the simple polynomial z 3 − 1 = 0 in the complex plane, leads to intricately interwoven basins of attraction of the roots. As an example of an interesting open question that may help to stimulate student interest in numerical analysis, we(More)
Motor proteins are biological enzymes that convert chemical energy to mechanical work in cells. Kinesin-1 is a motor protein that transports vesicles along microtubules and is widely believed to be responsible for anterograde transport of synaptic vesicles in neurons. Advances in single-molecule techniques have shown that single kinesin motors are capable(More)
Kinesins are nano-sized biological motors which walk by repeating a mechanochemical cycle. A single kinesin molecule is able to transport its cargo about 1 μm in the absence of external loads. However, kinesins perform much longer range transport in cells by working collectively. This long range of transport by a team of kinesins is surprising because the(More)
A damage detection method is developed for nonlinear systems using model updating. The method uses a nonlinear discrete model of the system and the form of the nonlinearities to create an augmented linear model of the system. A modal analysis technique that uses forcing that is known but not prescribed is then used to solve for the modal properties of the(More)
Renewal-reward processes are used to provide a framework for the mathematical description of single-molecule bead-motor assays for processive motor proteins. The formulation provides a more powerful, general approach to the fluctuation analysis of bead-motor assays begun by Svoboda et al. (Proc. Natl. Acad. Sci. USA 91(25):11782, 1994). Fluctuation analysis(More)
In neurons, several intracellular cargoes are transported by motor proteins (kinesins) which walk on microtubules (MTs). However, kinesins can possibly unbind from the MTs before they reach their destinations. The unbound kinesins randomly diffuse in neurons until they bind to MTs. Then, they walk again along the MTs to continue their tasks. Kinesins repeat(More)
Kinesins are molecular motors which walk along microtubules by moving their heads to different binding sites. The motion of kinesin is realized by a conformational change in the structure of the kinesin molecule and by a diffusion of one of its two heads. In this study, a novel model is developed to account for the 2D diffusion of kinesin heads to several(More)