ii Foreword These notes are being written during seminars in Department of Mathematics, University of Bergen, during the spring 2008. I appreciate any comments from the readers. I will pose ques-tions/comments to the readers of draft versions of the manuscript in margin notes like this one. iii iv FOREWORD Preface A fundamental dichotomy in mathematics and computer science is the distinction be...

A trans-coordinate physics is introduced in a previous paper. It is found that the trans-coordinate state of a system cannot be defined along a plane in Minkowski space, so a new non-planar definition of state is proposed in which the notion of simultaneity does not exist. In relativity theory simultaneity is relative. In trans-coordinate physics it is meaningless. The new state definition is i...

Quantum mechanics and general relativity are completely compatible when space-time coordinate systems are eliminated from physics. Standard practice attempts to remove coordinate influence through invariance because it is recognized that coordinates are physically meaningless. But this is shown to be insufficient. This paper investigates a trans-coordinate physics in which space-time coordinate...

Pegasos is a popular and reliable machine learning algorithm for making linear Support Vector Machines solvable at the larger scale. It benefits from the strongly convex optimization objective, faster convergence rates and lower computational and memory costs. In this paper we devise a new weighted formulation of the Pegasos algorithm which favors from the different coordinate-wise λi regulariz...

This paper presents a method to stabilize a group of agents moving in a two-dimensional space to a desired rigid geometric configuration. A common approach is to use information of relative interagent position vectors to carry out this specific control task. However, existing works in this vein either require the agents to express their measurements in a global coordinate reference, or generall...