Incomplete Transition Complexity of Basic Operations on Finite Languages

The state complexity of basic operations on finite languages (considering complete DFAs) has been in studied the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of boolean operations, concatenation, star, and reversal. For all operations we give tight upper bounds for both description measures. We correct the published state complexity of concatenation for complete DFAs and provide a tight upper bound for the case when the right automaton is larger than the left one. For all binary operations the tightness is proved using family languages with a variable alphabet size. In general the operational complexities depend not only on the complexities of the operands but also on other refined measures.Comment: 13 page

Neutrino Masses from Large Extra Dimensions

Recently it was proposed that the standard model (SM) degrees of freedom reside on a $(3+1)$-dimensional wall or ``3-brane'' embedded in a higher-dimensional spacetime. Furthermore, in this picture it is possible for the fundamental Planck mass \mst to be as small as the weak scale \mst\simeq O(\tev) and the observed weakness of gravity at long distances is due the existence of new sub-millimeter spatial dimensions. We show that in this picture it is natural to expect neutrino masses to occur in the 10^{-1} - 10^{-4}\ev range, despite the lack of any fundamental scale higher than \mst. Such suppressed neutrino masses are not the result of a see-saw, but have intrinsically higher-dimensional explanations. We explore two possibilities. The first mechanism identifies any massless bulk fermions as right-handed neutrinos. These give naturally small Dirac masses for the same reason that gravity is weak at long distances in this framework. The second mechanism takes advantage of the large {\it infrared} desert: the space in the extra dimensions. Here, small Majorana neutrino masses are generated by breaking lepton number on distant branes.Comment: 17 pages, late

Gauge coupling unification with large extra dimensions

We make a detailed study of the unification of gauge couplings in the MSSM with large extra dimensions. We find some scenarios where unification can be achieved (with the strong coupling constant at the Z mass within one standard deviation of the experimental value) with both the compactification scale and the SUSY breaking scale in the few TeV range. No enlargement of the gauge group or particle content is needed. One particularly interesting scenario is when the SUSY breaking scale is larger than the compactification scale, but both are small enough to be probed at the CERN LHC. Unification in two scales scenarios is also investigated and found to give results within the LHC.Comment: 17 pages, 3 figures, some discussions added, few additional references included. Version to appear in Phys. Rev.

United States’ neighborhood park use and physical activity over two years: The National Study of Neighborhood Parks

The United States lacks surveillance to monitor park use and conditions. The purpose of this study was to use the System for Observing Play and Recreation in Communities (SOPARC) as a surveillance tool to describe the conditions, user characteristics, and physical activity of a national sample of neighborhood parks at two time points. Using a stratified multistage sampling strategy, a representative sample of 174 neighborhood parks in 25 major United States’ cities were selected. During 2014 and 2016, park-related use, conditions, and physical activity were assessed using SOPARC in 169 parks. Overall, 74,106 park users were observed at baseline and 69,150 park users were observed two years later (p = 0.37). There were persistent disparities in park use by gender and age, with disproportionately more male than female users in each age group (child, teenager, adult, older adult). Older adults used the park less than other age groups. Almost two-thirds of park users were observed being sedentary (61.9% in 2014, 60.7% in 2016), followed by moderate (30.8%, 32.0%) and vigorous (7.3%, 7.3%) activity. Empty target areas increased over two years (75.3%, 77.6%; p = 0.01) and those that were equipped (2.6%, 1.2%; p = 0.0003), accessible (95.4%, 94.3%; p = 0.01), and organized (2.6%, 1.7%; p = 0.01) decreased. Areas that were usable (97.5%, 97.4%) or provided supervised activities (2.0%, 2.4%) did not change significantly. The findings demonstrate the value of SOPARC as a surveillance tool, identify user groups under represented at parks, and suggest an opportunity to encourage more park-based physical activity among park visitors

Effects of Extra Dimensions on Unitarity and Higgs Boson Mass

We study the unitarity constraint on the two body Higgs boson elastic scattering in the presence of extra dimensions. The contributions from exchange of spin-2 and spin-0 Kaluza-Klein states can have large effect on the partial wave amplitude. Unitarity condition restrict the maximal allowed value for the ratio $r$ of the center of mass energy to the gravity scale to be less than one. Although the constraint on the standard Higgs boson mass for $r$ of order one is considerably relaxed, for small $r$ the constraint is similar to that in the Standard Model. The resulting bound on the Higgs boson mass is not dramatically altered if perturbative calculations are required to be valid up to the maximal allowed value for $r$.Comment: References added, RevTex, 9 pages with two figure

Using Scalars to Probe Theories of Low Scale Quantum Gravity

Arkani-Hamed, Dimopoulos and Dvali have recently suggested that gravity may become strong at energies near 1 TeV which would remove the hierarchy problem. Such a scenario can be tested at present and future colliders since the exchange of towers of Kaluza-Klein gravitons leads to a set of new dimension-8 operators that can play important phenomenological roles. In this paper we examine how the production of pairs of scalars at $e^+e^-$, $\gamma \gamma$ and hadron colliders can be used to further probe the effects of graviton tower exchange. In particular we examine the tree-level production of pairs of identical Higgs fields which occurs only at the loop level in both the Standard Model and its extension to the Minimal Supersymmetric Standard Model. Cross sections for such processes are found to be potentially large at the LHC and the next generation of linear colliders. For the $\gamma\gamma$ case the role of polarization in improving sensitivity to graviton exchange is emphasized.Comment: 32 pages, 12 figures, latex, remarks added to tex

Island nucleation in the presence of step edge barriers: Theory and applications

We develop a theory of nucleation on top of two-dimensional islands bordered by steps with an additional energy barrier $\Delta E_S$ for descending atoms. The theory is based on the concept of the residence time of an adatom on the island,and yields an expression for the nucleation rate which becomes exact in the limit of strong step edge barriers. This expression differs qualitatively and quantitatively from that obtained using the conventional rate equation approach to nucleation [J. Tersoff et al., Phys. Rev. Lett.72, 266 (1994)]. We argue that rate equation theory fails because nucleation is dominated by the rare instances when two atoms are present on the island simultaneously. The theory is applied to two distinct problems: The onset of second layer nucleation in submonolayer growth, and the distribution of the sizes of top terraces of multilayer mounds under conditions of strong step edge barriers. Application to homoepitaxial growth on Pt(111) yields the estimate $\Delta E_S \geq 0.33$ eV for the additional energy barrier at CO-decorated steps.Comment: 13 pages, 3 figure

Minimal Higher-Dimensional Extensions of the Standard Model and Electroweak Observables

We consider minimal 5-dimensional extensions of the Standard Model compactified on an $S^1/Z_2$ orbifold, in which the SU(2)$_L$ and U(1)$_Y$ gauge fields and Higgs bosons may or may not all propagate in the fifth dimension while the observable matter is always assumed to be confined to a 4-dimensional subspace. We pay particular attention to consistently quantize the higher-dimensional models in the generalized $R_\xi$ gauge and derive analytic expressions for the mass spectrum of the resulting Kaluza-Klein states and their couplings to matter. Based on recent data from electroweak precision tests, we improve previous limits obtained in the 5-dimensional Standard Model with a common compactification radius and extend our analysis to other possible 5-dimensional Standard-Model constructions. We find that the usually derived lower bound of $\sim 4$ TeV on an universal compactification scale may be considerably relaxed to $\sim 3$ TeV in a minimal scenario, in which the SU(2)$_L$ gauge boson is the only field that feels the presence of the fifth dimension.Comment: 48 pages, LaTeX, 1 eps figure, typos correcte

Using systematic observations to understand conditions that promote interracial experiences in neighbourhood parks

We analysed observations from 31 neighbourhood parks, with each park mapped into smaller target areas for study, across five US cities generated using the System for Observing Play and Recreation in the Community (SOPARC). In areas where at least two people were observed, less than one-third (31.6%) were populated with at least one white and one non-white person. Park areas that were supervised, had one or more people engaged in vigorous activity, had at least one male and one female present, and had one or more teens present were significantly more likely to involve interracial groups (p < 0.01 for each association). Observations in parks located in interracial neighbourhoods were also more likely to involve interracial groups (p < 0.05). Neighbourhood poverty rate had a significant and negative relationship with the presence of interracial groups, particularly in neighbourhoods that are predominantly non-white. Additional research is needed to confirm the impact of these interactions. Urban planning and public health practitioners should consider the health benefits of interracial contact in the design and programming of neighbourhood parks

Supersymmetry and Electroweak breaking from extra dimensions at the TeV-scale

We analyze some features of the role that extra dimensions, of radius $R$ in the TeV$^{-1}$ range, can play in the soft breaking of supersymmetry and the spontaneous breaking of electroweak symmetry. We use a minimal model where the gauge and Higgs sector of the MSSM are living in the bulk of five dimensions and the chiral multiplets in a four-dimensional boundary. Supersymmetry is broken in the bulk by the Scherk-Schwarz mechanism and transmitted to the boundary by radiative corrections. The particle spectrum is completely predicted as a function of a unique $R$-charge. The massless sector corresponds to the pure Standard Model and electroweak symmetry is radiatively broken with a light Higgs weighing \simlt 110 GeV. The $\mu$-problem is solved and Higgsinos, gauginos and heavy Higgses acquire masses $\sim 1/R$. Chiral sfermions acquire radiative squared-masses $\sim \alpha_i/R^2$. The effective potential is explicitly computed in the bulk of extra dimensions and some cosmological consequences can be immediately drawn from it. Gauge coupling running and unification is studied in the presence of Scherk-Schwarz supersymmetry breaking. The unification is similar to that in the supersymmetric theory.Comment: 27 pages, Latex, 7 figures. Minor change