For a domain $G$ in the one-point compactification $\overline{\mathbb{R}}^n = \mathbb{R}^n \cup \{ \infty\}$ of $\mathbb{R}^n, n \ge 2$, we characterize completeness modulus metric $\mu_G$ terms potential-theoretic thickness condition $\partial G\,,$ Martio's $M$-condition. Next, prove that G$ is uniformly perfect if and only admits minorant M\"obius invariant metric. Several applications to qu...

This paper details the developments to date of an unmanned air vehicle (UAV) based on a standard size 60 model helicopter. The design goal is to have the helicopter achieve stable hover with the aid of an INS and stereo vision. The focus of this paper is on the development of an artificial neural network (ANN) that makes use of only the INS data to generate hover commands, which are used to dir...

Results are presented of a simulation which mimics an evolutionary learning process for small networks. Special features of these networks include a high recurrency, a transition function which decreases for large input activities, and the absence of tunable weights attached to the lines the line is either there (weight 1) or absent (weight 0). It is remarkable that already these simple systems...

We present a novel approach to unsupervised temporal sequence processing in the form of an unsupervised, recurrent neural network based on a selforganizing map (SOM). A standard SOM clusters each input vector irrespective of context, whereas the recurrent SOM presented here clusters each input based on an input vector and a context vector. The latter acts as a recurrent conduit feeding back a 2...

In this paper we prove that a conformally compact Einstein manifold with the round sphere as its conformal infinity has to be the hyperbolic space. We do not assume the manifolds to be spin, but our approach relies on the positive mass theorem for asymptotic flat manifolds. The proof is based on understanding of positive eigenfunctions and compactifications obtained by positive eigenfunctions. ...

In this paper we study harmonic maps relative to α-connections, and not always relative to Levi-Civita connections, on statistical manifolds. In particular, harmonic maps on α-conformally equivalent statistical manifolds are discussed, and conditions for harmonicity are given by parameters α and dimensions n. As the application we also describe harmonic maps between level surfaces of a Hessian ...

We prove that for non–linear L = L(R), G = dL/dR 6= 0 the Lagrangians L and L̂(R̂) with L̂ = 2R/G3 − 3L/G4, ĝij = G2 gij and R̂ = 3R/G2 − 4L/G3 give conformally equivalent fourth–order field equations being dual to each other. The proof represents a new application of the fact that the operator 2−R6 is conformally invariant. Gen. Rel. Grav. in print; KEY: Conformal relations in fourth–order gravity