Manifold turnpikes, trims, and symmetries

A Flat Manifold with No Symmetries

where G is a finite group and L is a faithful ZG-lattice of finite rank, i.e., a free Z-module of finite rank on which G acts faithfully. Let X be a flat manifold with fundamental group Γ. The group Aff(X) of affine self-equivalences of X is a Lie group. Its identity component Aff0(X) is a torus whose dimension is the rank of the center of Γ, and Aff(X)/Aff0(X) is isomorphic to Out(Γ), the oute...

Portfolio Turnpikes

Portfolio turnpike theorems show that if preferences at large wealth levels are similar to power utility, then the investment strategy converges to the power utility strategy as the horizon increases. We state and prove two simple and general portfolio turnpike theorems. Unlike existing literature, our main result does not assume independence of returns and depends only on discounting of future...

Graphs, Maneuvers and Turnpikes

The Singular Manifold Method: Darboux Transformations and Nonclassical Symmetries

We present in this paper the singular manifold method (SMM) derived from Painlevé analysis, as a helpful tool to obtain much of the characteristic features of nonlinear partial differential equations. As is well known, it provides in an algorithmic way the Lax pair and the Bäcklund transformation for the PDE under scrutiny. Moreover, the use of singular manifold equations under homographic inva...

Fish 'n' TRIMs

A novel diversified multigene family of tripartite-motif (TRIM) intracellular receptors with putative antiviral activity has been identified in teleost fish and published in BMC Biology. The history of these receptors involves ancient linkage to paralogs of the major histocompatibility complex, and the family has invertebrate precursors.