The category of finite cardinals (or, equivalently, of finite sets) is the symmetric analogue of the category of finite ordinals, and the ground category of a relevant category of presheaves, the augmented symmetric simplicial sets. We prove here that this ground category has characterisations similar to the classical ones for the category of finite ordinals, by the existence of a universal sym...

An algebraic classification of second order symmetric tensors in 5-dimensional Kaluza-Klein-type Lorentzian spaces is presented by using Jordan matrices. We show that the possible Segre types are [1, 1111], [2111], [311], [z z̄ 111], and the degeneracies thereof. A set of canonical forms for each Segre type is found. The possible continuous groups of symmetry for each canonical form are also stu...

The body of work on multi-body factorization separates between objects whose motions are independent. In this work we show that in many cases objects moving with different 3D motions will be captured as a single object using these approaches. We analyze what causes these degeneracies between objects and suggest an approach for overcoming some of them. We further show that in the case of multipl...

The presence of degeneracies can considerably worsen the measure of the neutrino oscillation parameters θ13 and δ. We study the physics reach of a specific “CERN” setup, using a standard β-Beam and Super-Beam facility. These facilities have a similar sensitivity in both parameters. Their combination does not provide any dramatic improvement as expected due to their almost identical L/E ratio. W...

Calculations of the number of curves on a Calabi-Yau manifold via an instanton expansion do not always agree with what one would expect naively. It is explained how to account for continuous families of instantons via deformation theory and excess intersection theory. The essential role played by degenerate instantons is also explained.