Inspired by a broader perspective viewing intelligent system dynamics in terms of the geometry of ”cognitive spaces,” we conduct a preliminary investigation of the application of information-geometry based learning to ECAN (Economic Attention Networks), the component of the integrative OpenCog AGI system concerned with attention allocation and credit assignment. We generalize Amari’s ”natural g...

The explosion of biological data resulting from genomic and proteomic research has created a pressing need for data analysis techniques that work effectively on a large scale. An area of particular interest is the organization and visualization of large families of protein sequences. An increasingly popular approach is to embed the sequences into a low-dimensional Euclidean space in a way that ...

“Nonlinear control systems” is a subject that deals with the analysis and the design of nonlinear control systems, i.e., the analysis and the design of control system that contains at least one nonlinear component [1]. The classic methods used in the study of the linear systems, particularly the frequency analysis, are not applicable to nonlinear systems [2]. Thus, different approaches are requ...

We describe some recent work on certain nonlinear elliptic equations from geometry. These include the problem of prescribing scalar curvature on (n), the Yamabe problem on manifolds with boundary, and the best Sobolev inequality on Riemannian manifolds.

This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau’s special setting) and its applications to general relativity with a special focus on the distributional description of impulsive gravitational waves.

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to co...

In this work a new approach to stability analysis is applied to nonlinear oscillators. Based on the use of local metrics properties of curvature and torsion resulting from Differential Geometry and while considering trajectory curves as plane or space curves, these properties directly provide their slow manifold analytical equation and its stable and unstable parts. Van der Pol and Colpitts mod...