Visualizing Rank Deficient Models: A Row Equation Geometry of Rank Deficient Matrices and Constrained-Regression

Situations often arise in which the matrix of independent variables is not of full column rank. That is, there are one or more linear dependencies among the independent variables. This paper covers in detail the situation in which the rank is one less than full column rank and extends this coverage to include cases of even greater rank deficiency. The emphasis is on the row geometry of the solutions based on the normal equations. The author shows geometrically how constrained-regression/generalized-inverses work in this situation to provide a solution in the face of rank deficiency

Energy- and flux-budget (EFB) turbulence closure model for the stably stratified flows. Part I: Steady-state, homogeneous regimes

We propose a new turbulence closure model based on the budget equations for the key second moments: turbulent kinetic and potential energies: TKE and TPE (comprising the turbulent total energy: TTE = TKE + TPE) and vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature). Besides the concept of TTE, we take into account the non-gradient correction to the traditional buoyancy flux formulation. The proposed model grants the existence of turbulence at any gradient Richardson number, Ri. Instead of its critical value separating - as usually assumed - the turbulent and the laminar regimes, it reveals a transition interval, 0.1< Ri <1, which separates two regimes of essentially different nature but both turbulent: strong turbulence at Ri<<1; and weak turbulence, capable of transporting momentum but much less efficient in transporting heat, at Ri>1. Predictions from this model are consistent with available data from atmospheric and lab experiments, direct numerical simulation (DNS) and large-eddy simulation (LES).Comment: 40 pages, 6 figures, Boundary-layer Meteorology, resubmitted, revised versio

Nonrandom Mixing Models of HIV Transmission

Models of HIV transmission and the AIDS epidemic generally assume random mixing among those infected with HIV and those who are not. For sexually transmitted HIV, this implies that individuals select sex partners without regard to attributes such as familiarity, attractiveness, or risk of infection. This paper formulates a model for examining the impact of nonrandom mixing on HIV transmission. We present threshold conditions that determine when HIV epidemics can occur within the framework of this model. Nonrandom mixing is introduced by assuming that sexually active individuals select sex partners to minimize the risk of infection. In addition to variability in risky sex rates, some versions of our model allow for error (or noise) in information exchanged between prospective partners. We investigate several models including random partner selection (or proportionate mixing), segregation of the population by risky sex rates, a probabilistic combination of segregation and random selection induced by imperfect information (or preferred mixing), and a model of costly search with perfect information. We develop examples which show that nonrandom mixing can lead to epidemics that are more severe or less severe than random mixing. For reasonable parameter choices describing the AIDS epidemic, however, the results suggest that random mixing models overstate the number of HIV infections that will occur

Frequent burning promotes invasions of alien plants into a mesic African savanna

Fire is both inevitable and necessary for maintaining the structure and functioning of mesic savannas. Without disturbances such as fire and herbivory, tree cover can increase at the expense of grass cover and over time dominate mesic savannas. Consequently, repeated burning is widely used to suppress tree recruitment and control bush encroachment. However, the effect of regular burning on invasion by alien plant species is little understood. Here, vegetation data from a long-term fire experiment, which began in 1953 in a mesic Zimbabwean savanna, were used to test whether the frequency of burning promoted alien plant invasion. The fire treatments consisted of late season fires, lit at 1-, 2-, 3-, and 4-year intervals, and these regularly burnt plots were compared with unburnt plots. Results show that over half a century of frequent burning promoted the invasion by alien plants relative to areas where fire was excluded. More alien plant species became established in plots that had a higher frequency of burning. The proportion of alien species in the species assemblage was highest in the annually burnt plots followed by plots burnt biennially. Alien plant invasion was lowest in plots protected from fire but did not differ significantly between plots burnt triennially and quadrennially. Further, the abundance of five alien forbs increased significantly as the interval (in years) between fires became shorter. On average, the density of these alien forbs in annually burnt plots was at least ten times as high as the density of unburnt plots. Plant diversity was also altered by long-term burning. Total plant species richness was significantly lower in the unburnt plots compared to regularly burnt plots. These findings suggest that frequent burning of mesic savannas enhances invasion by alien plants, with short intervals between fires favouring alien forbs. Therefore, reducing the frequency of burning may be a key to minimising the risk of alien plant spread into mesic savannas, which is important because invasive plants pose a threat to native biodiversity and may alter savanna functioning

Search for Kaluza-Klein Graviton Emission in ppˉp\bar{p} Collisions at s=1.8\sqrt{s}=1.8 TeV using the Missing Energy Signature

We report on a search for direct Kaluza-Klein graviton production in a data sample of 84 ${pb}^{-1}$ of \ppb collisions at $\sqrt{s}$ = 1.8 TeV, recorded by the Collider Detector at Fermilab. We investigate the final state of large missing transverse energy and one or two high energy jets. We compare the data with the predictions from a $3+1+n$-dimensional Kaluza-Klein scenario in which gravity becomes strong at the TeV scale. At 95% confidence level (C.L.) for $n$=2, 4, and 6 we exclude an effective Planck scale below 1.0, 0.77, and 0.71 TeV, respectively.Comment: Submitted to PRL, 7 pages 4 figures/Revision includes 5 figure

Measurement of the average time-integrated mixing probability of b-flavored hadrons produced at the Tevatron

We have measured the number of like-sign (LS) and opposite-sign (OS) lepton pairs arising from double semileptonic decays of $b$ and $\bar{b}$-hadrons, pair-produced at the Fermilab Tevatron collider. The data samples were collected with the Collider Detector at Fermilab (CDF) during the 1992-1995 collider run by triggering on the existence of $\mu \mu$ and $e \mu$ candidates in an event. The observed ratio of LS to OS dileptons leads to a measurement of the average time-integrated mixing probability of all produced $b$-flavored hadrons which decay weakly, $\bar{\chi} = 0.152 \pm 0.007$ (stat.) $\pm 0.011$ (syst.), that is significantly larger than the world average $\bar{\chi} = 0.118 \pm 0.005$.Comment: 47 pages, 10 figures, 15 tables Submitted to Phys. Rev.

Observation of associated near-side and away-side long-range correlations in √sNN=5.02 TeV proton-lead collisions with the ATLAS detector

Two-particle correlations in relative azimuthal angle (Δϕ) and pseudorapidity (Δη) are measured in √sNN=5.02  TeV p+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using approximately 1  μb-1 of data as a function of transverse momentum (pT) and the transverse energy (ΣETPb) summed over 3.1<η<4.9 in the direction of the Pb beam. The correlation function, constructed from charged particles, exhibits a long-range (2<|Δη|<5) “near-side” (Δϕ∼0) correlation that grows rapidly with increasing ΣETPb. A long-range “away-side” (Δϕ∼π) correlation, obtained by subtracting the expected contributions from recoiling dijets and other sources estimated using events with small ΣETPb, is found to match the near-side correlation in magnitude, shape (in Δη and Δϕ) and ΣETPb dependence. The resultant Δϕ correlation is approximately symmetric about π/2, and is consistent with a dominant cos⁡2Δϕ modulation for all ΣETPb ranges and particle pT

Search for the neutral Higgs bosons of the minimal supersymmetric standard model in pp collisions at root s=7 TeV with the ATLAS detector

A search for neutral Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM) is reported. The analysis is based on a sample of proton-proton collisions at a centre-of-mass energy of 7TeV recorded with the ATLAS detector at the Large Hadron Collider. The data were recorded in 2011 and correspond to an integrated luminosity of 4.7 fb-1 to 4.8 fb-1. Higgs boson decays into oppositely-charged muon or τ lepton pairs are considered for final states requiring either the presence or absence of b-jets. No statistically significant excess over the expected background is observed and exclusion limits at the 95% confidence level are derived. The exclusion limits are for the production cross-section of a generic neutral Higgs boson, φ, as a function of the Higgs boson mass and for h/A/H production in the MSSM as a function of the parameters mA and tan β in the mhmax scenario for mA in the range of 90GeV to 500 GeV. Copyright CERN

Search for R-parity-violating supersymmetry in events with four or more leptons in sqrt(s) =7 TeV pp collisions with the ATLAS detector

A search for new phenomena in final states with four or more leptons (electrons or muons) is presented. The analysis is based on 4.7 fb−1 of $\sqrt{s}=7\;\mathrm{TeV}$ proton-proton collisions delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in two signal regions: one that requires moderate values of missing transverse momentum and another that requires large effective mass. The results are interpreted in a simplified model of R-parity-violating supersymmetry in which a 95% CL exclusion region is set for charged wino masses up to 540 GeV. In an R-parity-violating MSUGRA/CMSSM model, values of m 1/2 up to 820 GeV are excluded for 10 < tan β < 40

Search for high-mass resonances decaying to dilepton final states in pp collisions at s√=7 TeV with the ATLAS detector

The ATLAS detector at the Large Hadron Collider is used to search for high-mass resonances decaying to an electron-positron pair or a muon-antimuon pair. The search is sensitive to heavy neutral Z′ gauge bosons, Randall-Sundrum gravitons, Z * bosons, techni-mesons, Kaluza-Klein Z/γ bosons, and bosons predicted by Torsion models. Results are presented based on an analysis of pp collisions at a center-of-mass energy of 7 TeV corresponding to an integrated luminosity of 4.9 fb−1 in the e + e − channel and 5.0 fb−1 in the μ + μ −channel. A Z ′ boson with Standard Model-like couplings is excluded at 95 % confidence level for masses below 2.22 TeV. A Randall-Sundrum graviton with coupling k/MPl=0.1 is excluded at 95 % confidence level for masses below 2.16 TeV. Limits on the other models are also presented, including Technicolor and Minimal Z′ Models