The Magic Number Problem for Subregular Language Families

We investigate the magic number problem, that is, the question whether there exists a minimal n-state nondeterministic finite automaton (NFA) whose equivalent minimal deterministic finite automaton (DFA) has alpha states, for all n and alpha satisfying n less or equal to alpha less or equal to exp(2,n). A number alpha not satisfying this condition is called a magic number (for n). It was shown in [11] that no magic numbers exist for general regular languages, while in [5] trivial and non-trivial magic numbers for unary regular languages were identified. We obtain similar results for automata accepting subregular languages like, for example, combinational languages, star-free, prefix-, suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free languages, showing that there are only trivial magic numbers, when they exist. For finite languages we obtain some partial results showing that certain numbers are non-magic.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Direct measurement of shear-induced cross-correlations of Brownian motion

Shear-induced cross-correlations of particle fluctuations perpendicular and along stream-lines are investigated experimentally and theoretically. Direct measurements of the Brownian motion of micron-sized beads, held by optical tweezers in a shear-flow cell, show a strong time-asymmetry in the cross-correlation, which is caused by the non-normal amplification of fluctuations. Complementary measurements on the single particle probability distribution substantiate this behavior and both results are consistent with a Langevin model. In addition, a shear-induced anti-correlation between orthogonal random-displacements of two trapped and hydrodynamically interacting particles is detected, having one or two extrema in time, depending on the positions of the particles.Comment: 4 pages, 4 figure

The acceleration and propagation of solar flare energetic particles

Observations and theories of particle acceleration in solar flares are reviewed. The most direct signatures of particle acceleration in flares are gamma rays, X-rays and radio emissions produced by the energetic particles in the solar atmosphere and energetic particles detected in interplanetary space and in the Earth's atmosphere. The implication of these observations are discussed. Stochastic and shock acceleration as well as acceleration in direct electric fields are considered. Interplanetary particle propagation is discussed and an overview of the highlights of both current and promising future research is presented

Measurements of heavy ion beam losses from collimation

The collimation efficiency for Pb ion beams in the LHC is predicted to be lower than requirements. Nuclear fragmentation and electromagnetic dissociation in the primary collimators create fragments with a wide range of Z/A ratios, which are not intercepted by the secondary collimators but lost where the dispersion has grown sufficiently large. In this article we present measurements and simulations of loss patterns generated by a prototype LHC collimator in the CERN SPS. Measurements were performed at two different energies and angles of the collimator. We also compare with proton loss maps and find a qualitative difference between Pb ions and protons, with the maximum loss rate observed at different places in the ring. This behavior was predicted by simulations and provides a valuable benchmark of our understanding of ion beam losses caused by collimation.Comment: 12 pages, 20 figure

Phase Rotation, Cooling And Acceleration Of Muon Beams: A Comparison Of Different Approaches

Experimental and theoretical activities are underway at CERN with the aim of examining the feasibility of a very-high-flux neutrino source. In the present scheme, a high-power proton beam (some 4 MW) bombards a target where pions are produced. The pions are collected and decay to muons under controlled optical condition. The muons are cooled and accelerated to a final energy of 50 GeV before being injected into a decay ring where they decay under well-defined conditions of energy and emittance. We present the most challenging parts of the whole scenario, the muon capture, the ionisation-cooling and the first stage of the muon acceleration. Different schemes, their performance and the technical challenges are compared.Comment: LINAC 2000 CONFERENCE, paper ID No. THC1

Analytical solution for the Fermi-sea energy of two-dimensional electrons in a magnetic field: lattice path-integral approach and quantum interference

We derive an exact solution for the total kinetic energy of noninteracting spinless electrons at half-filling in two-dimensional bipartite lattices. We employ a conceptually novel approach that maps this problem exactly into a Feynman-Vdovichenko lattice walker. The problem is then reduced to the analytic study of the sum of magnetic phase factors on closed paths. We compare our results with the ones obtained through numerical calculations.Comment: 5 pages, RevTe

Trends and correlates of marijuana use among late middle-aged and older adults in the United States, 2002–2014

BACKGROUND: Recent trend studies suggest that marijuana use is on the rise among the general population of adults ages 18 and older in the United States. However, little is known about the trends in marijuana use and marijuana-specific risk/protective factors among American adults during the latter part of adulthood. METHOD: Findings are based on repeated, cross-sectional data collected from late middle-aged (ages 50–64) and older adults (ages 65 and older) surveyed as part of the National Survey on Drug Use and Health between 2002 and 2014. RESULTS: The prevalence of past-year marijuana use among late middle-aged adults increased significantly from a low of 2.95% in 2003 to a high of 9.08% in 2014. Similarly, the prevalence of marijuana use increased significantly among older adults from a low of 0.15% in 2003 to a high of 2.04% in 2014. Notably, the upward trends in marijuana use remained significant even when accounting for sociodemographic, substance use, behavioral, and health-related factors. We also found that decreases in marijuana-specific protective factors were associated with the observed trend changes in marijuana use among late middle-aged and older adults, and observed a weakening of the association between late-middle aged marijuana use and risk propensity, other illicit drug use, and criminal justice system involvement over the course of the study. CONCLUSIONS: Findings from the present study provide robust evidence indicating that marijuana use among older Americans has increased markedly in recent years, with the most evident changes observed between 2008 and 2014

Pair dispersion in turbulence

We study the statistics of pair dispersion in two-dimensional turbulence. Direct numerical simulations show that the pdf of pair separations is in agreement with the Richardson prediction. The pdf of doubling times follows dimensional scaling and shows a long tail which is the signature of close approaches between particles initially seeded with a large separation. This phenomenon is related to the formation of fronts in passive scalar advection.Comment: 11 pages, 5 figure

Beam losses from ultra-peripheral nuclear collisions between Pb ions in the Large Hadron Collider and their alleviation

Electromagnetic interactions between colliding heavy ions at the Large Hadron Collider (LHC) at CERN will give rise to localized beam losses that may quench superconducting magnets, apart from contributing significantly to the luminosity decay. To quantify their impact on the operation of the collider, we have used a three-step simulation approach, which consists of optical tracking, a Monte-Carlo shower simulation and a thermal network model of the heat flow inside a magnet. We present simulation results for the case of Pb ion operation in the LHC, with focus on the ALICE interaction region, and show that the expected heat load during nominal Pb operation is 40% above the quench level. This limits the maximum achievable luminosity. Furthermore, we discuss methods of monitoring the losses and possible ways to alleviate their effect.Comment: 17 pages, 20 figure

Consequences of a Change in the Galactic Environment of the Sun

The interaction of the heliosphere with interstellar clouds has attracted interest since the late 1920's, both with a view to explaining apparent quasi-periodic climate "catastrophes" as well as periodic mass extinctions. Until recently, however, models describing the solar wind - local interstellar medium (LISM) interaction self-consistently had not been developed. Here, we describe the results of a two-dimensional (2D) simulation of the interaction between the heliosphere and an interstellar cloud with the same properties as currently, except that the neutral H density is increased from the present value of n(H) ~ 0.2 cm^-3 to 10 cm^-3. The mutual interaction of interstellar neutral hydrogen and plasma is included. The heliospheric cavity is reduced considerably in size (approximately 10 - 14 AU to the termination shock in the upstream direction) and is highly dynamical. The interplanetary environment at the orbit of the Earth changes markedly, with the density of interstellar H increasing to ~2 cm^-3. The termination shock itself experiences periods where it disappears, reforms and disappears again. Considerable mixing of the shocked solar wind and LISM occurs due to Rayleigh-Taylor-like instabilities at the nose, driven by ion-neutral friction. Implications for two anomalously high concentrations of 10Be found in Antarctic ice cores 33 kya and 60 kya, and the absence of prior similar events, are discussed in terms of density enhancements in the surrounding interstellar cloud. The calculation presented here supports past speculation that the galactic environment of the Sun moderates the interplanetary environment at the orbit of the Earth, and possibly also the terrestrial climate.Comment: 23 pages, 2 color plates (jpg), 3 figures (eps