Darwin’s neuroscientist: Gerald M. Edelman, 1929-2014

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Fractional Dynamical Systems

In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential equations describing systems experiencing periodic kicks. Their properties depend on the value of two parameters: the non-linearity parameter, which arises from the corresponding regular dynamical systems; and the memory parameter which is the order of the fractional derivative in the corresponding non-linear fractional differential equations. The examples of the fractional Standard and Logistic maps demonstrate that phase space of non-linear fractional dynamical systems may contain periodic sinks, attracting slow diverging trajectories, attracting accelerator mode trajectories, chaotic attractors, and cascade of bifurcations type trajectories whose properties are different from properties of attractors in regular dynamical systems. The author argues that discovered properties should be evident in the natural (biological, psychological, physical, etc.) and engineering systems with power-law memory.Comment: 6 pages, 4 figure

Opening Address For The Seventh Annual Stein Center Symposium on Contemporary Urban Challenges

This article is a published version of the opening address of Peter Edelman at the Seventh Annual Stein Center Symposium on Contemporary Urban Challenges, which identifies the challenges in lawyering to the poor and proposes approaches for lawyers to reduce poverty. Peter Edelman\u27s speech challenges the private Bar to take on greater responsibility in helping to formulate policy that will work to eradicate the plight of the poor, calls for greater lawyer involvement in policy adaptation and implementation, identifies new roles that lawyers can and should play in helping to build and strengthen community institutions, and maintains that community building needs to become a major focus of lawyering for the poor