New development of the inclusive-cone-based method for linear optimization

The purpose of this dissertation is to present a simple method for linear optimization including linear programming and linear semi-infinite programming, which is termed “the inclusive-cone-based method”. Using the inclusive cone as an analytic tool, theoretical aspects of linear programming are investigated. Sensitivity analysis in linear programming is examined from the perspective of an inclusive cone. The relationship of inclusiveness between correlated linear programming problems is also studied. New inclusive-cone-based ladder algorithms are proposed to solve linear programming problems in inequality form. Numerical experiments are implemented to show effectiveness and efficiency of the new linear programming ladder algorithms. To start the ladder method for linear programming problems, a single artificial constraint technique is introduced to find an initial ladder. Further, in the context of a new category of linear programming problems, an inclusive-cone-based solvability criterion is established to distinguish that a linear programming problem is inclusive-feasible (i.e., optimal), noninclusive-feasible (i.e., unbounded), inclusive-infeasible or noninclusive-infeasible. The inclusive-cone-based method for linear programming is also generalized to linear semi-infinite programming. An optimality result, based upon the concept of the generalized base point, is established. With this optimality result as a theoretical foundation, a ladder algorithm for solving linear semi-infinite programming problems is developed. The new algorithm has several features: at each iteration it only deals with a small fraction of constraints; at each iteration it selects a constraint most violated along a “parameterized centreline”, by solving a one-dimensional global optimization problem using the efficient bridging algorithm; at each iteration the selection of the incoming constraint has a great degree of freedom, which is controlled by a parameter arising in the global optimization problem; it can detect infeasibility and unboundedness after a finite number of iterations; it obviates extra work for feasibility verification as it handles feasibility and optimality simultaneously. A simple convergent result is presented. Numerical behaviour of the algorithm is examined on several test problems

Resolving Boosted Jets with XCone

We show how the recently proposed XCone jet algorithm smoothly interpolates between resolved and boosted kinematics. When using standard jet algorithms to reconstruct the decays of hadronic resonances like top quarks and Higgs bosons, one typically needs separate analysis strategies to handle the resolved regime of well-separated jets and the boosted regime of fat jets with substructure. XCone, by contrast, is an exclusive cone jet algorithm that always returns a fixed number of jets, so jet regions remain resolved even when (sub)jets are overlapping in the boosted regime. In this paper, we perform three LHC case studies---dijet resonances, Higgs decays to bottom quarks, and all-hadronic top pairs---that demonstrate the physics applications of XCone over a wide kinematic range.Comment: 36 pages, 25 figures, 1 table; v2: references added; v3: discussion added and new appendix B to match JHEP versio

The Energy Distribution of Subjets and the Jet Shape

We present a framework that describes the energy distribution of subjets of radius $r$ within a jet of radius $R$. We consider both an inclusive sample of subjets as well as subjets centered around a predetermined axis, from which the jet shape can be obtained. For $r \ll R$ we factorize the physics at angular scales $r$ and $R$ to resum the logarithms of $r/R$. For central subjets, we consider both the standard jet axis and the winner-take-all axis, which involve double and single logarithms of $r/R$, respectively. All relevant one-loop matching coefficients are given, and an inconsistency in some previous results for cone jets is resolved. Our results for the standard jet shape differ from previous calculations at next-to-leading logarithmic order, because we account for the recoil of the standard jet axis due to soft radiation. Numerical results are presented for an inclusive subjet sample for $pp \to {\rm jet}+X$ at next-to-leading order plus leading logarithmic order.Comment: 39 pages, 7 figures, v2: journal versio

XCone: N-jettiness as an exclusive cone jet algorithm

We introduce a new jet algorithm called XCone, for eXclusive Cone, which is based on minimizing the event shape N -jettiness. Because N -jettiness partitions every event into N jet regions and a beam region, XCone is an exclusive jet algorithm that always returns a fixed number of jets. We use a new “conical geometric” measure for which well-separated jets are bounded by circles of radius R in the rapidity-azimuth plane, while overlapping jet regions automatically form nearest-neighbor “clover jets”. This avoids the split/merge criteria needed in inclusive cone algorithms. A key feature of XCone is that it smoothly transitions between the resolved regime where the N signal jets of interest are well separated and the boosted regime where they overlap. The returned value of N -jettiness also provides a quality criterion of how N -jet-like the event looks. We also discuss the N -jettiness factorization theorems that occur for various jet measures, which can be used to compute the associated exclusive N -jet cross sections. In a companion paper [1], the physics potential of XCone is demonstrated using the examples of dijet resonances, Higgs decays to bottom quarks, and all-hadronic top pairs.United States. Department of Energy (Offices of Nuclear and Particle Physics Contracts DE-SC00012567 and DE-SC0011090)Simons Foundation (Investigator grant 327942)United States. Department of Energy (Early Career research program DE-SC0006389)Alfred P. Sloan Foundation (Sloan Research Fellowship)Massachusetts Institute of Technology. Undergraduate Research Opportunities Program (Paul E. Gray Endowed Fund

Jets in Hadron-Hadron Collisions

In this article, we review some of the complexities of jet algorithms and of the resultant comparisons of data to theory. We review the extensive experience with jet measurements at the Tevatron, the extrapolation of this acquired wisdom to the LHC and the differences between the Tevatron and LHC environments. We also describe a framework (SpartyJet) for the convenient comparison of results using different jet algorithms.Comment: 68 pages, 54 figure

Tevatron-for-LHC Report of the QCD Working Group

The experiments at Run 2 of the Tevatron have each accumulated over 1 inverse femtobarn of high-transverse momentum data. Such a dataset allows for the first precision (i.e. comparisons between theory and experiment at the few percent level) tests of QCD at a hadron collider. While the Large Hadron Collider has been designed as a discovery machine, basic QCD analyses will still need to be performed to understand the working environment. The Tevatron-for-LHC workshop was conceived as a communication link to pass on the expertise of the Tevatron and to test new analysis ideas coming from the LHC community. The TeV4LHC QCD Working Group focussed on important aspects of QCD at hadron colliders: jet definitions, extraction and use of Parton Distribution Functions, the underlying event, Monte Carlo tunes, and diffractive physics. This report summarizes some of the results achieved during this workshop.Comment: 156 pages, Tevatron-for-LHC Conference Report of the QCD Working Grou

Asymptotic optimality conditions for linear semi-infinite programming

In this paper, the classical KKT, complementarity and Lagrangian saddle-point conditions are generalized to obtain equivalent conditions characterizing the optimality of a feasible solution to a general linear semi-infinite programming problem without constraint qualifications. The method of this paper differs from the usual convex analysis methods and its main idea is rooted in some fundamental properties of linear programming

Investigation of hydrodynamic scaling relationships in shallow spouted beds

Important global hydrodynamic relationships for shallow spouted beds of high-density particles were characterized in terms of three features: minimum spouting velocity, overall bed pressure drop at minimum spouting velocity; and fountain height. Spouted bed literature is sparse for shallow beds (static particle depth to bed diameter ≤ 1) and beds with heavy particles (density \u3e 3000 kg/m3). Correlations for such beds were developed here by varying column diameter, static bed height, particle diameter, particle density, gas density and gas flow in an ambient temperature and pressure bed. The degree of correlation between each of the observed hydrodynamic features and a set of selected dimensionless groups from the literature was evaluated with principal components analysis. The minimum spouting velocity correlated strongly with the ratios of particle to bed diameter, of particle to gas density, and of static bed height to particle diameter, and weakly with Archimedes number. Overall bed pressure drop at minimum spouting correlated strongly with Archimedes number, the ratio of static bed height to particle diameter and Froude number. Fountain height correlated strongly with the ratios of the superficial gas velocity to minimum spouting velocity, of static bed height to particle diameter and of the particle to the bed diameter. Principal component regression models were developed for minimum spouting velocity, bed pressure drop, and fountain height with respect to a selected set of dimensionless parameters. All models have regression coefficient values exceeding 85%. Predictions using models developed in this study were compared with correlations in the literature and found to give better results for the experimental conditions studied. Most likely the literature models were less accurate because they were extrapolated. Distinct bed pressure drop relationships with gas flow were observed for certain ranges of particle diameter and static bed height. In addition three dynamical spouting modes were observed, and named as regular, erratic and bimodal. A spouting regime map is proposed based on the spouting regimes defined in this investigation. The correspondence between bed pressure drop relationships and spouting regimes is still unclear