This paper investigates the distributed CONTROLLABILITY of nonlocal Rayleigh beam. The mathematical problem is formulated as an abstract di, erential equation. It is shown that a sequence of eigenfunction of nonlocal Rayleigh beam forms Riesz basis. Based on Riesz basis properties and theory of abstract di, erential equation, it is proved that a vibrating nonlocal Rayleigh beam is approximately controllable under suitable distributed control force while it is not exponentially stable.

Introduction. This fascinating disorder is also known as Sinus Histiocytosis. It is very rare, probably less than 1000 cases reported in the literature. R.D.D affects lymph nodes, although extranodal involvement has been reported such as: Centaral nervous system (CN.S). All of the cases of R.D.D with CN.S involvement without other sites involvement are 11 cases. Methods. The case is a male patient, 26y/o, with a history of head trauma 2 years ago that has been resulted to unconsciousness. He has been referred to a hospital and brain CT scan and brain M.R.I has been done for him. In M.R.I a brain tumor with left orbit and sphenoidal sinus involvement and compression effect on frontal lobe has been seen. A neurosurgeon operated him and the pathological report was Rosai-Dorfman DISEASE. Then he was referred to radiation therapy department.Results. Treatment approach in CN.S involvement cases consists of surgery, radiotherapy and chemotherapy. Discussion. Over all, response has been inferior to those expected with malignant hematopoietic neoplasms.

CONTROLLABILITY is our ability to steer a dynamic system to a desired final state in finite time. A compartmental model is general mathematical modeling used to predict the time evolution of complex systems. We consider a three-dimensional nonlinear system with a transition threshold. It has only one steady state (equilibrium fixed point) which it reachs a long period. Our goal is to drive this system towards the desired stable fixed point at the beginning of the dynamics (finite time). The nonlinear system was investigated as a compartmental model. We used the control strategy of multidimensional dynamical systems and proposed the canonical transformation from which the control function was obtained. In order to show that the fixed points of the system are stable, we used the linear stability method and the Gershgorin circle theorem. By numerically solving the differential equations after control, the system reached the desired fixed points in a finite time. We plotted the state space for different fixed points, and four regions were obtained. We found the points where the control function can steer the system to a stable state in a finite time. We found fixed points that are non-physical.

Introduction: Recent reports have shown that rare fluctuations in cardiac cycles are ‘ forgotten’ quickly in healthy individuals and it is possible to quantify the “ memory length” of a physiological time-series using an inverse statistical approach. Methods: In the present study, we assessed the effect of aging on memory length in cardiac rhythm. Results: There was a longer memory length in cardiac time-series of elderly subjects in comparison with younger adults for both decelerating and accelerating rare fluctuations in cardiac rhythm. Conclusion: The increased memory length of the cardiac time-series in elderly subjects may indicate reduced CONTROLLABILITY of cardiovascular regulatory system.

Right selection of the type and number of driver nodes plays an important role in improving the CONTROLLABILITY and performance of the dynamical networks. In this paper the CONTROLLABILITY and performance of a network has been studied when a new approach for selecting the driver nodes, based on the three main node centrality criteria, has been proposed. For each criterion, the percentage of the least number of driver nodes to achieve the desired performance has been calculated for several network model structures. The results for pure random networks show that for the “betweenness centrality criterion’’ the number of driver nodes is minimal. Similar results hold for Small World networks subject to the fact that for dense, the number of driver nodes increases. It is shown that the “closeness centrality criterion’’ is the proper choice for the State Free networks, especially when the network is dense. Another important result is that in Small World networks, increasing the nearest neighborhood coefficient decreases the number of driver nodes for a desired performance. Similar results hold for Scale Free networks where increasing the heterogeneity coefficient improves the network pinning CONTROLLABILITY.