We describe an O(n) time algorithm for computing the exact probability that two d-dimensional probabilistic point sets are linearly separable, for any fixed d ≥ 2. A probabilistic point in d-space is the usual point, but with an associated (independent) probability of existence. We also show that the d-dimensional separability problem is equivalent to a (d + 1)-dimensional convex hull membershi...

The effect of setting all T=0 two body interaction matrix elements equal to a constant (or zero) in shell model calculations (designated as < T = 0 >= 0) are investigated. Despite the apparent severity of such a procedure, one gets fairly reasonable spectra. We find that using < T = 0 >= 0 in single j shell calculations degeneracies appear e.g. the I =

We show that triangulating a set of points with elevations such that the number of local minima of the resulting terrain is minimized is NP-hard for degenerate point sets. The same result applies when there are no degeneracies for higher-order Delaunay triangulations. Two heuristics are presented to minimize the number of local minima for higher-order Delaunay triangulations, and they are compa...

We consider certain naturalness questions in supersymmetric theories. Various suggestions which give rise to squark degeneracies are reviewed. A stringy scenario, discussed by Kaplunovsky and Louis, is the only one which leads to complete degeneracy of squarks and sleptons at the high scale. Alternatives include the possible existence of a gauged non-Abelian horizontal symmetry, broken at some ...

A method of calculating analytical energy gradient of high-spin multiplet state by the SAC-CI (symmetry-adaptedcluster configuration-interaction) method is developed and implemented. This method is expected to be a powerful tool in studying the dynamics and properties of molecules having high spin-multiplicities. Good performance of this method is shown for the quartet states of BHþ and C2 and ...

Note that both the eigen-Majoranas γn,α and the eigenvalues n are time dependent. Degeneracies of the many-body spectrum can arise when one or more of the eigenvalues n vanish or when some nonzero n is degenerate, independent of time. The various Majorana operators associated with each single-particle eigenvalue n are labeled by the index α. If the single-particle eigenvalue n is N-fold degener...

We study how the eightfold-degeneracy in the (θ13, δ) plane observed in γ ∼ 100 β-beams can be reduced by periodically changing the ions in the storage ring. This “ions cocktail” allows to change the neutrino energy, at fixed γ, by choosing ions with different decay energies. We propose to combine the standard He and Ne beams with Li and B ones. These latter two ions have peaked νe → νμ oscilla...

We examine the use of two superbeam neutrino oscillation experiments with baselines <∼ 1000 km to resolve parameter degeneracies inherent in the three-neutrino analysis of such experiments. We find that with appropriate choices of neutrino energies and baselines two experiments with different baselines can provide a much better determination of the neutrino mass ordering than a single experimen...

Abstract In the nuclear f7/2 shell, the nucleon–nucleon interaction can be represented by the eight values E(J) = 〈(f2 7/2) J |V |(f2 7/2) J〉, J = 0, 1, · · · , 7, where for even J the isospin is 1, and for odd J it is 0. If we set the T = 0 (odd J) two-body matrix elements to zero (or to a constant), we find several degeneracies which we attempt to explain in this work. We also give more detai...

We discuss the physics of superbeam upgrades, where we focus on T2KK, a NuMI beam line based experiment NOνA*, and a wide band beam (WBB) experiment independent of the NuMI beam line. For T2KK, we find that the Japan-Korea baseline helps resolve parameter degeneracies, but the improvement due to correlated systematics between the two detectors (using identical detectors) is only moderate. For a...