The present study sets out to integrate the performance-based seismic design approach with the connection topology optimization method. Performance-based connection topology optimization concept aims to simultaneously optimize the size of members and the type of connections with respect to the framework of performance-based seismic design. This new optimization concept is carried out for unbrac...

In this paper we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using thes...

We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a connection between the considered problem and a stopping problem of an associated continuous diffusion process and demonstrate how this connection may be appl...

We show the link between U(1) lattice gauge theories and the off-equilibrium thermodynamics of a large class of nonlinear oscillators networks. The coupling between the oscillators plays the role of a gauge field, or connection, on the network. The thermodynamical forces that drive energy flows are expressed in terms of the curvature of the connection, analogous to a geometric phase. The model,...

A nonlinear data assimilation technique is applied to determine and track effective connections between ensembles of cultured spinal cord neurons measured with multielectrode arrays. The method is statistical, depending only on confidence intervals, and requiring no form of arbitrary thresholding. In addition, the method updates connection strengths sequentially, enabling real-time tracking of ...

An extension of quantum mechanics to a generalized Nambu dynamics leads to a new version of nonlinear quantum mechanics. The time evolution of states is given in here by a triple bracket generalization of the Liouville-von Neumann equation, where one of the generators is an average energy, and the other is a measure of entropy. A nonlinear evolution can occur only for mixed states, and for syst...