introduction: the selection of suitable beam angles and weights in external-beam radiotherapy is at present generally based upon the experience of the planner. therefore, automated selection of beam angles and weights in forward-planned radiotherapy will be beneficial. material and methods: in this work, an efficient method is presented within the matlab environment to investigate how to improv...

We address the problem of the apparently very small magnitude of CP violation in the standard model, measured by the Jarlskog invariant J . In order to make statements about probabilities for certain values of J , we seek to find a natural measure on the space of Kobayashi-Maskawa matrices, the double quotient U(1)\SU(3)/U(1). We review several possible, geometrically motivated choices of the m...

We find solutions of the Yang-Mills field equations with gauge group SU(2) in 4k dimensions which have the interpretation of four-dimensional instantons at angles. These configurations satisfy a BPS-like condition which arises in the context of two-dimensional (4,0)-supersymmetric sigma models. Moreover we show that these solutions are examples of Hermitian-Einstein connections on E. In the pas...

Imitation learning is a powerful approach to humanoid behavior generation, however, the most existing methods assume the availability of the information on the internal state of a demonstrator such as joint angles, while humans usually cannot directly access to imitate the observed behavior. This paper presents a method of imitation learning based on visuosomatic mapping from observing the demo...

Almost everyone knows that the inner angles of a triangle sum to 180o. But if you ask the typical mathematician how to sum the solid inner angles over the vertices of a tetrahedron, you are likely to receive a blank stare or a mystified shrug. In some cases you may be directed to the Gram-Euler relations for higher dimensional polytopes [3, 4, 6, 7], a 19th century result unjustly consigned to ...

In contrast to the current rapid evolution in our understanding of the microscopic degrees of freedom of M-theory, the macroscopic picture has changed very little over the past year. The ‘basic’ ingredients remain D=11 supergravity and its 1/2-supersymmetic solutions: the M-wave, the M-2-brane, the M-5-brane and, in the S KaluzaKlein vacuum, the M-monopole (i.e. EuclideanTaub-Nut times 7-dimens...

We interpret a class of 4k-dimensional instanton solutions found by Ward, Corrigan, Goddard and Kent as four-dimensional instantons at angles. The super-position of each pair of four-dimensional instantons is associated with four angles which depend on some of the ADHM parameters. All these solutions are associated with the group Sp(k) and are examples of Hermitian-Einstein connections on E 4k....