Efficient Set Sharing Using ZBDDs

Set sharing is an abstract domain in which each concrete object is represented by the set of local variables from which it might be reachable. It is a useful abstraction to detect parallelism opportunities, since it contains definite information about which variables do not share in memory, i.e., about when the memory regions reachable from those variables are disjoint. Set sharing is a more precise alternative to pair sharing, in which each domain element is a set of all pairs of local variables from which a common object may be reachable. However, the exponential complexity of some set sharing operations has limited its wider application. This work introduces an efficient implementation of the set sharing domain using Zero-suppressed Binary Decision Diagrams (ZBDDs). Because ZBDDs were designed to represent sets of combinations (i.e., sets of sets), they naturally represent elements of the set sharing domain. We show how to synthesize the operations needed in the set sharing transfer functions from basic ZBDD operations. For some of the operations, we devise custom ZBDD algorithms that perform better in practice. We also compare our implementation of the abstract domain with an efficient, compact, bit set-based alternative, and show that the ZBDD version scales better in terms of both memory usage and running time

Chain Reduction for Binary and Zero-Suppressed Decision Diagrams

Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the others' ability to symbolically represent Boolean functions in compact form. For any Boolean function, its chain-reduced ZDD (CZDD) representation will be no larger than its ZDD representation, and at most twice the size of its BDD representation. The chain-reduced BDD (CBDD) of a function will be no larger than its BDD representation, and at most three times the size of its CZDD representation. Extensions to the standard algorithms for operating on BDDs and ZDDs enable them to operate on the chain-reduced versions. Experimental evaluations on representative benchmarks for encoding word lists, solving combinatorial problems, and operating on digital circuits indicate that chain reduction can provide significant benefits in terms of both memory and execution time

Grain charging in protoplanetary discs

Recent work identified a growth barrier for dust coagulation that originates in the electric repulsion between colliding particles. Depending on its charge state, dust material may have the potential to control key processes towards planet formation such as MHD (magnetohydrodynamic) turbulence and grain growth which are coupled in a two-way process. We quantify the grain charging at different stages of disc evolution and differentiate between two very extreme cases: compact spherical grains and aggregates with fractal dimension D_f = 2. Applying a simple chemical network that accounts for collisional charging of grains, we provide a semi-analytical solution. This allowed us to calculate the equilibrium population of grain charges and the ionisation fraction efficiently. The grain charging was evaluated for different dynamical environments ranging from static to non-stationary disc configurations. The results show that the adsorption/desorption of neutral gas-phase heavy metals, such as magnesium, effects the charging state of grains. The greater the difference between the thermal velocities of the metal and the dominant molecular ion, the greater the change in the mean grain charge. Agglomerates have more negative excess charge on average than compact spherical particles of the same mass. The rise in the mean grain charge is proportional to N**(1/6) in the ion-dust limit. We find that grain charging in a non-stationary disc environment is expected to lead to similar results. The results indicate that the dust growth and settling in regions where the dust growth is limited by the so-called "electro-static barrier" do not prevent the dust material from remaining the dominant charge carrier.Comment: 18 pages, 10 figures, accepted for publication in Astronomy and Astrophysic

Search for the Supersymmetric Partner of the Top-Quark in ppˉp \bar{p} Collisions at s=1.8TeV\sqrt{s} = 1.8 {\rm TeV}

We report on a search for the supersymmetric partner of the top quark (stop) produced in $t \bar{t}$ events using $110 {\rm pb}^{-1}$ of $p \bar{p}$ collisions at $\sqrt{s} = 1.8 {\rm TeV}$ recorded with the Collider Detector at Fermilab. In the case of a light stop squark, the decay of the top quark into stop plus the lightest supersymmetric particle (LSP) could have a significant branching ratio. The observed events are consistent with Standard Model $t \bar{t}$ production and decay. Hence, we set limits on the branching ratio of the top quark decaying into stop plus LSP, excluding branching ratios above 45% for a LSP mass up to 40 {\rm GeV/c}$^{2}$.Comment: 11 pages, 4 figure

Measurement of the Associated γ+μ±\gamma + \mu^\pm Production Cross Section in ppˉp \bar p Collisions at s=1.8\sqrt{s} = 1.8 TeV

We present the first measurement of associated direct photon + muon production in hadronic collisions, from a sample of 1.8 TeV $p \bar p$ collisions recorded with the Collider Detector at Fermilab. Quantum chromodynamics (QCD) predicts that these events are primarily from the Compton scattering process $cg \to c\gamma$, with the final state charm quark producing a muon. Hence this measurement is sensitive to the charm quark content of the proton. The measured cross section of $29\pm 9 pb^{-1}$ is compared to a leading-order QCD parton shower model as well as a next-to-leading-order QCD calculation.Comment: 12 pages, 4 figures Added more detailed description of muon background estimat

Inclusive jet cross section in pˉp{\bar p p} collisions at s=1.8\sqrt{s}=1.8 TeV

The inclusive jet differential cross section has been measured for jet transverse energies, $E_T$, from 15 to 440 GeV, in the pseudorapidity region 0.1$\leq | \eta| \leq$0.7. The results are based on 19.5 pb$^{-1}$ of data collected by the CDF collaboration at the Fermilab Tevatron collider. The data are compared with QCD predictions for various sets of parton distribution functions. The cross section for jets with $E_T>200$ GeV is significantly higher than current predictions based on O($\alpha_s^3$) perturbative QCD calculations. Various possible explanations for the high-$E_T$ excess are discussed.Comment: 8 pages with 2 eps uu-encoded figures Submitted to Physical Review Letter

Characterisation and categorisation of the diversity in viscoelastic vibrational properties between 98 wood types

International audienceContext Increased knowledge on diversity in wood properties would have implications both for fundamental research and for promoting a diversification of uses as material. *Aims The objective is to contribute to overcoming the critical lack of data on the diversity of wood dynamic mechanical/viscoelastic vibrational properties, by testing lesser-known species and categorizing sources of variability. *Methods Air-dry axial specific dynamic modulus of elasticity (E'/γ) and damping coefficient (tanδ) were measured on a wide sampling (1792 specimens) of 98 wood types from 79 species. An experimental device and protocol was designed for conducting systematic (i.e. rapid and reproducible) characterizations. *Results Diversity at the specimens' level corroborates the "standard" relationship between tanδ and E'/γ, which is discussed in terms of orientation of wood elements and of chemical composition. Diversity at the species level is expressed on the basis of results for normal heartwood, with specific gravity (γ) ranging from 0.2 to 1.3. Axial E'/γ ranges from 9 to 32 GPa and tanδ from 4×10-3 to 19×10-3. Properties distribution follows a continuum, but with group characteristics. The lowest values of tanδ are only found in certain tropical hardwoods. Results can also suggest alternative species for musical instruments making

Measurement of the B0 anti-B0 oscillation frequency using l- D*+ pairs and lepton flavor tags

The oscillation frequency Delta-md of B0 anti-B0 mixing is measured using the partially reconstructed semileptonic decay anti-B0 -> l- nubar D*+ X. The data sample was collected with the CDF detector at the Fermilab Tevatron collider during 1992 - 1995 by triggering on the existence of two lepton candidates in an event, and corresponds to about 110 pb-1 of pbar p collisions at sqrt(s) = 1.8 TeV. We estimate the proper decay time of the anti-B0 meson from the measured decay length and reconstructed momentum of the l- D*+ system. The charge of the lepton in the final state identifies the flavor of the anti-B0 meson at its decay. The second lepton in the event is used to infer the flavor of the anti-B0 meson at production. We measure the oscillation frequency to be Delta-md = 0.516 +/- 0.099 +0.029 -0.035 ps-1, where the first uncertainty is statistical and the second is systematic.Comment: 30 pages, 7 figures. Submitted to Physical Review