Lower Limits on Soft Supersymmetry-Breaking Scalar Masses

Working in the context of the CMSSM, we argue that phenomenological constraints now require the universal soft supersymmetry-breaking scalar mass m_0 be non-zero at the input GUT scale. This conclusion is primarily imposed by the LEP lower limit on the Higgs mass and the requirement that the lightest supersymmetric particle not be charged. We find that m_0 > 0 for all tan beta if mu 0 only when tan beta sim 8 and one allows an uncertainty of 3+ GeV in the theoretical calculation of the Higgs mass. Upper limits on flavour-changing neutral interactions in the MSSM squark sector allow substantial violations of non-universality in the m_0 values, even if their magnitudes are comparable to the lower limit we find in the CMSSM. Also, we show that our lower limit on m_0 at the GUT scale in the CMSSM is compatible with the no-scale boundary condition m_0 = 0 at the Planck scale.Comment: 11 pages, latex, 6 eps figure

Persistent homology of groups

We introduce and investigate notions of persistent homology for p-groups and for coclass trees of p-groups. Using computer techniques we show that persistent homology provides fairly strong homological invariants for p-groups of order at most 81. The strength of these invariants, and some elementary theoretical properties, suggest that persistent homology may be a useful tool in the study of prime-power groups.Comment: 12 pages, 6 figure

More on Electric Dipole Moment Constraints on Phases in the Constrained MSSM

We reconsider constraints on \cp-violating phases in the Constrained Minimal Supersymmetric Standard Model. We include the recent calculations of Ibrahim and Nath on the chromoelectric and purely gluonic contributions to the quark electric dipole moment and combine cosmological limits on gaugino masses with experimental bounds on the neutron (and electron) electric dipole moments. The constraint on the phase of the Higgs mixing mass $\mu$, |\thm|, is dependent on the value of the trilinear mass parameter, $A$, in the model and on $\tan \beta$. For values of |A| < 300 \gev at the GUT scale, we find |\thm|/\pi \la 0.05, while for |A| < 1500 \gev, |\thm|/\pi \la 0.3. Thus, we find that in principle, large CP violating phases are compatible with the bounds on the electric dipole moments of the neutron and electron, as well as remaining compatible with the cosmological upper bound on the relic density of neutralinos. The other \cp-violating phase \tha is essentially unconstrained.Comment: 11 pages in LaTeX + 4 postscript figures, uses epsf.sty. Added two references, clarified figures. Accepted to Physics Letter

A Note on Infinities in Eternal Inflation

In some well-known scenarios of open-universe eternal inflation, developed by Vilenkin and co-workers, a large number of universes nucleate and thermalize within the eternally inflating mega-universe. According to the proposal, each universe nucleates at a point, and therefore the boundary of the nucleated universe is a space-like surface nearly coincident with the future light cone emanating from the point of nucleation, all points of which have the same proper-time. This leads the authors to conclude that at the proper-time t = t_{nuc} at which any such nucleation occurs, an infinite open universe comes into existence. We point out that this is due entirely to the supposition of the nucleation occurring at a single point, which in light of quantum cosmology seems difficult to support. Even an infinitesimal space-like length at the moment of nucleation gives a rather different result -- the boundary of the nucleating universe evolves in proper-time and becomes infinite only in an infinite time. The alleged infinity is never attained at any finite time.Comment: 13 pages and 6 figure

A Penrose polynomial for embedded graphs

We extend the Penrose polynomial, originally defined only for plane graphs, to graphs embedded in arbitrary surfaces. Considering this Penrose polynomial of embedded graphs leads to new identities and relations for the Penrose polynomial which can not be realized within the class of plane graphs. In particular, by exploiting connections with the transition polynomial and the ribbon group action, we find a deletion-contraction-type relation for the Penrose polynomial. We relate the Penrose polynomial of an orientable checkerboard colourable graph to the circuit partition polynomial of its medial graph and use this to find new combinatorial interpretations of the Penrose polynomial. We also show that the Penrose polynomial of a plane graph G can be expressed as a sum of chromatic polynomials of twisted duals of G. This allows us to obtain a new reformulation of the Four Colour Theorem

Automatic Detection of Clear-Sky Periods From Irradiance Data

Recent degradation studies have highlighted the importance of considering cloud cover when calculating degradation rates, finding more reliable values when the data are restricted to clear sky periods. Several automated methods of determining clear sky periods have been previously developed, but parameterizing and testing the models has been difficult. In this paper, we use clear sky classifications determined from satellite data to develop an algorithm that determines clear sky periods using only measured irradiance values and modeled clear sky irradiance as inputs. This method is tested on global horizontal irradiance (GHI) data from ground collectors at six sites across the United States and compared against independent satellite-based classifications. First, 30 separate models were optimized on each individual site at GHI data intervals of 1, 5, 10, 15, and 30 min (sampled on the first minute of the interval). The models had an average F0.5 score of 0.949 ± 0.035 on a holdout test set. Next, optimizations were performed by aggregating data from different locations at the same interval, yielding one model per data interval. This paper yielded an average F0.5 of 0.946 ± 0.037. A final, 'universal' optimization that was trained on data from all sites at all intervals provided an F0.5 score of 0.943 ± 0.040. The optimizations all provide improvements on a prior, unoptimized clear sky detection algorithm that produces F0.5 scores that average to 0.903 ± 0.067. Our paper indicates that a single algorithm can accurately classify clear sky periods across locations and data sampling intervals