Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds

Given a formula in quantifier-free Presburger arithmetic, if it has a satisfying solution, there is one whose size, measured in bits, is polynomially bounded in the size of the formula. In this paper, we consider a special class of quantifier-free Presburger formulas in which most linear constraints are difference (separation) constraints, and the non-difference constraints are sparse. This class has been observed to commonly occur in software verification. We derive a new solution bound in terms of parameters characterizing the sparseness of linear constraints and the number of non-difference constraints, in addition to traditional measures of formula size. In particular, we show that the number of bits needed per integer variable is linear in the number of non-difference constraints and logarithmic in the number and size of non-zero coefficients in them, but is otherwise independent of the total number of linear constraints in the formula. The derived bound can be used in a decision procedure based on instantiating integer variables over a finite domain and translating the input quantifier-free Presburger formula to an equi-satisfiable Boolean formula, which is then checked using a Boolean satisfiability solver. In addition to our main theoretical result, we discuss several optimizations for deriving tighter bounds in practice. Empirical evidence indicates that our decision procedure can greatly outperform other decision procedures.Comment: 26 page

Latest Results from the Heidelberg-Moscow Double Beta Decay Experiment

New results for the double beta decay of 76Ge are presented. They are extracted from Data obtained with the HEIDELBERG-MOSCOW, which operates five enriched 76Ge detectors in an extreme low-level environment in the GRAN SASSO. The two neutrino accompanied double beta decay is evaluated for the first time for all five detectors with a statistical significance of 47.7 kg y resulting in a half life of (T_(1/2))^(2nu) = [1.55 +- 0.01 (stat) (+0.19) (-0.15) (syst)] x 10^(21) years. The lower limit on the half-life of the 0nu beta-beta decay obtained with pulse shape analysis is (T_(1/2))^(0_nu) > 1.9 x 10^(25) [3.1 x 10^(25)] years with 90% C.L. (68% C.L.) (with 35.5 kg y). This results in an upper limit of the effective Majorana neutrino mass of 0.35 eV (0.27 eV). No evidence for a Majoron emitting decay mode or for the neutrinoless mode is observed.Comment: 14 pages, revtex, 6 figures, Talk was presented at third International Conference ' Dark Matter in Astro and Particle Physics' - DARK2000, to be publ. in Proc. of DARK2000, Springer (2000). Please look into our HEIDELBERG Non-Accelerator Particle Physics group home page: http://www.mpi-hd.mpg.de/non_acc

Effects of quantum space time foam in the neutrino sector

We discuss violations of CPT and quantum mechanics due to interactions of neutrinos with space-time quantum foam. Neutrinoless double beta decay and oscillations of neutrinos from astrophysical sources (supernovae, active galactic nuclei) are analysed. It is found that the propagation distance is the crucial quantity entering any bounds on EHNS parameters. Thus, while the bounds from neutrinoless double beta decay are not significant, the data of the supernova 1987a imply a bound being several orders of magnitude more stringent than the ones known from the literature. Even more stringent limits may be obtained from the investigation of neutrino oscillations from active galactic nuclei sources, which have an impressive potential for the search of quantum foam interactions in the neutrino sector.Comment: 5 page

The one-loop six-dimensional hexagon integral with three massive corners

We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically. After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios. The result can be expressed as a sum of 24 terms involving only one basic function, which is a simple linear combination of logarithms, dilogarithms, and trilogarithms of uniform degree three transcendentality. Our method uses differential equations to determine the symbol of the function, and an algorithm to reconstruct the latter from its symbol. It is known that six-dimensional hexagon integrals are closely related to scattering amplitudes in N=4 super Yang-Mills theory, and we therefore expect our result to be helpful for understanding the structure of scattering amplitudes in this theory, in particular at two loops.Comment: 15 pages, 2 figure

Search for Cold Dark Matter and Solar Neutrinos with GENIUS and GENIUS-TF

The new project GENIUS will cover a wide range of the parameter space of predictions of SUSY for neutralinos as cold dark matter. Further it has the potential to be a real-time detector for low-energy (pp and 7Be) solar neutrinos. A GENIUS Test Facility has just been funded and will come into operation by end of 2002.Comment: 4 pages, revtex, 3 figures, Talk was presented at International School on Nuclear Physics, 23rd Course: Neutrinos in Astro, Particle and Nuclear Physics, Erice, September 18 - 26, 2001, Publ. in Progress in Particle and Nuclear Physics, Vol. 48 (2002) 283 - 286, Home Page of Heidelberg Non-Accelerator Particle Physics Group: http://www.mpi-hd.mpg.de/non_acc

LASER PHYSICS LETTERS

Abstract: Raman spectroscopy offers a powerful alternative analytical method for the detection and identification of lipids/oil in biological samples, such as algae and fish. Recent research in the authors' groups, and experimental data only very recently published by us and a few other groups suggest that Raman spectroscopy can be exploited in instances where fast and accurate determination of the iodine value (associated with the degree of lipid unsaturation) is required. Here the current status of Raman spectroscopy applications on algae is reviewed, and particular attention is given to the efforts of identifying and selecting oil-rich algal strains for the potential mass production of commercial biofuels and for utilization in the food industry. Normalized intensity, a.u

The politics of in/visibility: carving out queer space in Ul'yanovsk

<p>In spite of a growing interest within sexualities studies in the concept of queer space (Oswin 2008), existing literature focuses almost exclusively on its most visible and territorialised forms, such as the gay scene, thus privileging Western metropolitan areas as hubs of queer consumer culture (Binnie 2004). While the literature has emphasised the political significance of queer space as a site of resistance to hegemonic gender and sexual norms, it has again predominantly focused on overt claims to public space embodied in Pride events, neglecting other less open forms of resistance.</p><p> This article contributes new insights to current debates about the construction and meaning of queer space by considering how city space is appropriated by an informal queer network in Ul’ianovsk. The group routinely occupied very public locations meeting and socialising on the street or in mainstream cafés in central Ul’ianovsk, although claims to these spaces as queer were mostly contingent, precarious or invisible to outsiders. The article considers how provincial location affects tactics used to carve out communal space, foregrounding the importance of local context and collective agency in shaping specific forms of resistance, and questioning ethnocentric assumptions about the empowering potential of visibility.</p&gt

Neutrinoless Double Beta Decay in Gauge Theories

Neutrinoless double beta decay is a very important process both from the particle and nuclear physics point of view. Its observation will severely constrain the existing models and signal that the neutrinos are massive Majorana particles. From the elementary particle point of view it pops up in almost every model. In addition to the traditional mechanisms, like the neutrino mass, the admixture of right handed currents etc, it may occur due to the R-parity violating supersymmetric (SUSY) interactions. From the nuclear physics point of view it is challenging, because: 1) The relevant nuclei have complicated nuclear structure. 2) The energetically allowed transitions are exhaust a small part of all the strength. 3) One must cope with the short distance behavior of the transition operators, especially when the intermediate particles are heavy (eg in SUSY models). Thus novel effects, like the double beta decay of pions in flight between nucleons, have to be considered. 4) The intermediate momenta involved are about 100 MeV. Thus one has to take into account possible momentum dependent terms in the nucleon current. We find that, for the mass mechanism, such modifications of the nucleon current for light neutrinos reduce the nuclear matrix elements by about 25 per cent, almost regardless of the nuclear model. In the case of heavy neutrinos the effect is much larger and model dependent. Taking the above effects into account, the available nuclear matrix elements for the experimentally interesting nuclei A = 76, 82, 96, 100, 116, 128, 130, 136 and 150 and the experimental limits on the life times we have extracted new stringent limits on the average neutrino mass and on the R-parity violating coupling for various SUSY models.Comment: Latex, 24 pages, 1 postscript figure, uses iopconf.st

PACS: 32.30.-r, 32.60.+i, 32.70

Abstract: We have measured light shifts, also known as AC Stark shifts, as a function of laser intensity in cold Rubidium atoms by observing sub-natural linewidth gain and loss features in the transmission spectrum of a weak probe beam passing through the atomic sample. The observed energy-level shifts for atoms in a magneto-optical trap (MOT) are found to be consistently higher than that obtained in optical molasses (i.e., when the magnetic field gradient in the MOT is turned off). Using a simple model of a multilevel Rubidium atom interacting with pump and probe beams, we have calculated the theoretical light shift as a function of intensity. A comparison of these calculated values with the light shift data obtained for molasses reveals good agreement between experiment and theory. Further, our model elucidates the role of the Zeeman shifts arising from the magnetic field gradient in the observed probe transmission spectrum for the MOT. A qualitative plot of the transmission spectrum of a probe beam through a fictitious sample of cold J = 1 → J = 2 atoms showing probe absorption at the sum of the pump frequency ω pump and δ , where δ is the difference of the light shifts between the |J = 1,mJ = 0 and the |J = 1,mJ = ± 1 ground state Zeeman sublevels. Probe gain is depicted at ω pump -δ . Se