The transfer matrix: A geometrical perspective

A Geometrical Perspective on the Insulin Evolution

We study the molecular evolution of insulin from metric geometry point of view. In mathematics, and in particular in geometry, distances and metrics between objects are of fundamental importance. Using a weaker notion than the classical distance, namely the weighted quasi-metrics, one can study the geometry of biological sequences (DNA, mRNA, or proteins) space. We analyze from geometrical poin...

A Geometrical Perspective for the Bargaining Problem

A new treatment to determine the Pareto-optimal outcome for a non-zero-sum game is presented. An equilibrium point for any game is defined here as a set of strategy choices for the players, such that no change in the choice of any single player will increase the overall payoff of all the players. Determining equilibrium for multi-player games is a complex problem. An intuitive conceptual tool f...

A geometrical interpretation of the inverse matrix

Feed-forward neural networks: a geometrical perspective

The convex hull of any subset o f vertices of an n-dimensional hypercube contains no other vertex of the hypercube. This result permits the application of some theorems of n-dimensional geometry lo digital reed-forward neural networks. Also. the construction Of the convex hull is proposed as an alternative to more traditional learning algorithms. Some preliminary simulation results are reponed.

Efficiency and Robustness in a Geometrical Perspective

A geometrical setting is constructed, based on Hilbert space, in which the asymptotic properties of estimators can be studied. Estimators are defined in the context of parametrised models, which are treated as submanifolds of an underlying Hilbert manifold, on which a parameter-defining mapping is defined as a submersion on to a finite-dimensional parameter space. Robustness of an estimator is ...