Lines, Circles, Planes and Spheres

Let $S$ be a set of $n$ points in $\mathbb{R}^3$, no three collinear and not all coplanar. If at most $n-k$ are coplanar and $n$ is sufficiently large, the total number of planes determined is at least $1 + k \binom{n-k}{2}-\binom{k}{2}(\frac{n-k}{2})$. For similar conditions and sufficiently large $n$, (inspired by the work of P. D. T. A. Elliott in \cite{Ell67}) we also show that the number of spheres determined by $n$ points is at least $1+\binom{n-1}{3}-t_3^{orchard}(n-1)$, and this bound is best possible under its hypothesis. (By $t_3^{orchard}(n)$, we are denoting the maximum number of three-point lines attainable by a configuration of $n$ points, no four collinear, in the plane, i.e., the classic Orchard Problem.) New lower bounds are also given for both lines and circles.Comment: 37 page

Structure of Fat Jets at the Tevatron and Beyond

Boosted resonances is a highly probable and enthusiastic scenario in any process probing the electroweak scale. Such objects when decaying into jets can easily blend with the cornucopia of jets from hard relative light QCD states. We review jet observables and algorithms that can contribute to the identification of highly boosted heavy jets and the possible searches that can make use of such substructure information. We also review previous studies by CDF on boosted jets and its measurements on specific jet shapes.Comment: invited review for a special "Top and flavour physics in the LHC era" issue of The European Physical Journal C, we invite comments regarding contents of the review; v2 added references and institutional preprint number

Self-diffusion in dense granular shear flows

Diffusivity is a key quantity in describing velocity fluctuations in granular materials. These fluctuations are the basis of many thermodynamic and hydrodynamic models which aim to provide a statistical description of granular systems. We present experimental results on diffusivity in dense, granular shear in a 2D Couette geometry. We find that self-diffusivities are proportional to the local shear rate with diffusivities along the mean flow approximately twice as large as those in the perpendicular direction. The magnitude of the diffusivity is D \approx \dot\gamma a^2 where a is the particle radius. However, the gradient in shear rate, coupling to the mean flow, and drag at the moving boundary lead to particle displacements that can appear sub- or super-diffusive. In particular, diffusion appears superdiffusive along the mean flow direction due to Taylor dispersion effects and subdiffusive along the perpendicular direction due to the gradient in shear rate. The anisotropic force network leads to an additional anisotropy in the diffusivity that is a property of dense systems with no obvious analog in rapid flows. Specifically, the diffusivity is supressed along the direction of the strong force network. A simple random walk simulation reproduces the key features of the data, such as the apparent superdiffusive and subdiffusive behavior arising from the mean flow, confirming the underlying diffusive motion. The additional anisotropy is not observed in the simulation since the strong force network is not included. Examples of correlated motion, such as transient vortices, and Levy flights are also observed. Although correlated motion creates velocity fields qualitatively different from Brownian motion and can introduce non-diffusive effects, on average the system appears simply diffusive.Comment: 13 pages, 20 figures (accepted to Phys. Rev. E

FastJet user manual

FastJet is a C++ package that provides a broad range of jet finding and analysis tools. It includes efficient native implementations of all widely used 2-to-1 sequential recombination jet algorithms for pp and e+e- collisions, as well as access to 3rd party jet algorithms through a plugin mechanism, including all currently used cone algorithms. FastJet also provides means to facilitate the manipulation of jet substructure, including some common boosted heavy-object taggers, as well as tools for estimation of pileup and underlying-event noise levels, determination of jet areas and subtraction or suppression of noise in jets.Comment: 69 pages. FastJet 3 is available from http://fastjet.fr

Fully differential W' production and decay at next-to-leading order in QCD

We present the fully differential production and decay of a W' boson, with arbitrary vector and axial-vector couplings, to any final state at next-to-leading order in QCD. We demonstrate a complete factorization of couplings at next-to-leading order in both the partial width of the W' boson, and in the full two-to-two cross section. We provide numerical predictions for the contribution of a W' boson to single-top-quark production, and separate results based on whether the mass of the right-handed neutrino (nu_R) is light enough for the leptonic decay channel to be open. The single-top-quark analysis will allow for an improved direct W' mass limit of 525-550 GeV using data from run I of the Fermilab Tevatron. We propose a modified tolerance method for estimating parton distribution function uncertainties in cross sections.Comment: 23 pages, revtex3, 13 ps fig

Probabilistic frames: An overview

Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of probabilistic frames, and we characterize one of their subclasses in terms of minimizers of some appropriate potential function. In addition, we survey a range of areas where probabilistic frames, albeit, under different names, appear. These areas include directional statistics, the geometry of convex bodies, and the theory of t-designs

Towards Jetography

As the LHC prepares to start taking data, this review is intended to provide a QCD theorist's understanding and views on jet finding at hadron colliders, including recent developments. My hope is that it will serve both as a primer for the newcomer to jets and as a quick reference for those with some experience of the subject. It is devoted to the questions of how one defines jets, how jets relate to partons, and to the emerging subject of how best to use jets at the LHC.Comment: 95 pages, 28 figures, an extended version of lectures given at the CTEQ/MCNET school, Debrecen, Hungary, August 2008; v2 includes additional discussion in several places, as well as other clarifications and additional references

GRB 011121: A massive star progenitor

Of the cosmological gamma-ray bursts, GRB 011121 has the lowest redshift, z = 0.36. More importantly, the multicolor excess in the afterglow detected in the Hubble Space Telescope (HST) light curves is compelling observational evidence of an underlying supernova. Here we present near-infrared and radio observations of the afterglow, and from our comprehensive afterglow modeling, we find evidence favoring a wind-fed circumburst medium. Lacking X-ray data, we are unable to conclusively measure the mass-loss rate, M, but obtain an estimate, M ∼ 2 × 10-7/νw3 M⊙yr-1, where νw3 is the speed of the wind from the progenitor in units of 103 km s-1. This M is similar to that inferred for the progenitor of the Type Ibc supernova SN 1998bw that has been associated with the peculiar burst GRB 980425. Our data, taken in conjunction with the HST results of Bloom et al., provide a consistent picture: the long-duration GRB 011121 had a massive star progenitor that exploded as a supernova at about the same time as the gamma-ray burst event. Finally, we note that the gamma-ray profile of GRB 011121 is similar to that of GRB 980425

Heavy flavor properties of jets produced in ppˉp\bar{p} interactions at sqrts=sqrt{s}= 1.8 TeV

We present a detailed examination of the heavy flavor properties of jets produced at the Fermilab Tevatron collider. The data set, collected with the Collider Detector at Fermilab, consists of events with two or more jets with transverse energy $E_T \geq 15$ GeV and pseudo-rapidity $|\eta| \leq 1.5$. The heavy flavor content of the data set is enriched by requiring that at least one of the jets (lepton-jet) contains a lepton with transverse momentum larger than 8 GeV/c. Jets containing hadrons with heavy flavor are selected via the identification of secondary vertices. The parton-level cross sections predicted by the {\sc herwig} Monte Carlo generator program are tuned within theoretical and experimental uncertainties to reproduce the secondary-vertex rates in the data. The tuned simulation provides new information on the origin of the discrepancy between the $b\bar{b}$ cross section measurements at the Tevatron and the next-to-leading order QCD prediction. We also compare the rate of away-jets (jets recoiling against the lepton-jet) containing a soft lepton ($p_T \geq 2$ GeV/c) in the data to that in the tuned simulation. We find that this rate is larger than what is expected for the conventional production and semileptonic decay of pairs of hadrons with heavy flavor.Comment: 65 pages, 14 tables, 14 figures. To be submitted to Phys. Rev.

TRY plant trait database – enhanced coverage and open access

Plant traits—the morphological, anatomical, physiological, biochemical and phenological characteristics of plants—determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait‐based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits—almost complete coverage for ‘plant growth form’. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait–environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives