Show Me the Data: Statistical Representation

Statistical representation is the science and art of using data to describe the world around us. Statistical representation is based on the fundamental concept that data consists of structure plus noise. The challenge facing the statistician is to use the noisy data to learn about the underlying structure. This framework accommodates the analysis of data generated by almost all other scientific disciplines. There are numerous ways of constructing statistical representations. The methods discussed here include tables, graphs, and models. The proper representation depends on the nature of the data and the particular issues being addressed. A combination of methods is often appropriate

THE USE OF INVERSE THEORY ON AN ILL-POSED ENVIRONMENTAL COMPOSITE SAMPLING PROBLEM

As an alternative to retesting, the use of inverse theory techniques is proposed to resolve the lack of information inherent in composite sampling methods. This paper evaluates the feasibility of combining composite sampling with the inverse theory technique of linear regularization on an environmental site characterization investigation. Federal legislation has mandated the cleanup of hazardous waste sites, creating the need to characterize these sites for various chemical constituents. An abundance of samples, high measurement costs, and limited budgets create the appeal of compositing samples. We propose that the number of costly laboratory analyses can be reduced by combining composite sampling and inverse theory techniques. The goal of the paper is to estimate the constituent concentration for the sample units used to construct the composite . A novel application of linear regularization is illustrated with a data set from an environmental investigation into mercury contamination at a waste disposal site in New Mexico. The disposal site has measurements at both the composite and sample unit level. This allows for a rare opportunity to evaluate the assumptions made about the compositing process and to compare estimates based on composite measurements with estimates based on sample unit measurements

Applied Mathematics at the U.S. Department of Energy: Past, Present and a View to the Future

Over the past half-century, the Applied Mathematics program in the U.S. Department of Energy's Office of Advanced Scientific Computing Research has made significant, enduring advances in applied mathematics that have been essential enablers of modern computational science. Motivated by the scientific needs of the Department of Energy and its predecessors, advances have been made in mathematical modeling, numerical analysis of differential equations, optimization theory, mesh generation for complex geometries, adaptive algorithms and other important mathematical areas. High-performance mathematical software libraries developed through this program have contributed as much or more to the performance of modern scientific computer codes as the high-performance computers on which these codes run. The combination of these mathematical advances and the resulting software has enabled high-performance computers to be used for scientific discovery in ways that could only be imagined at the program's inception. Our nation, and indeed our world, face great challenges that must be addressed in coming years, and many of these will be addressed through the development of scientific understanding and engineering advances yet to be discovered. The U.S. Department of Energy (DOE) will play an essential role in providing science-based solutions to many of these problems, particularly those that involve the energy, environmental and national security needs of the country. As the capability of high-performance computers continues to increase, the types of questions that can be answered by applying this huge computational power become more varied and more complex. It will be essential that we find new ways to develop and apply the mathematics necessary to enable the new scientific and engineering discoveries that are needed. In August 2007, a panel of experts in applied, computational and statistical mathematics met for a day and a half in Berkeley, California to understand the mathematical developments required to meet the future science and engineering needs of the DOE. It is important to emphasize that the panelists were not asked to speculate only on advances that might be made in their own research specialties. Instead, the guidance this panel was given was to consider the broad science and engineering challenges that the DOE faces and identify the corresponding advances that must occur across the field of mathematics for these challenges to be successfully addressed. As preparation for the meeting, each panelist was asked to review strategic planning and other informational documents available for one or more of the DOE Program Offices, including the Offices of Science, Nuclear Energy, Fossil Energy, Environmental Management, Legacy Management, Energy Efficiency & Renewable Energy, Electricity Delivery & Energy Reliability and Civilian Radioactive Waste Management as well as the National Nuclear Security Administration. The panelists reported on science and engineering needs for each of these offices, and then discussed and identified mathematical advances that will be required if these challenges are to be met. A review of DOE challenges in energy, the environment and national security brings to light a broad and varied array of questions that the DOE must answer in the coming years. A representative subset of such questions includes: (1) Can we predict the operating characteristics of a clean coal power plant? (2) How stable is the plasma containment in a tokamak? (3) How quickly is climate change occurring and what are the uncertainties in the predicted time scales? (4) How quickly can an introduced bio-weapon contaminate the agricultural environment in the US? (5) How do we modify models of the atmosphere and clouds to incorporate newly collected data of possibly of new types? (6) How quickly can the United States recover if part of the power grid became inoperable? (7) What are optimal locations and communication protocols for sensing devices in a remote-sensing network? (8) How can new materials be designed with a specified desirable set of properties? In comparing and contrasting these and other questions of importance to DOE, the panel found that while the scientific breadth of the requirements is enormous, a central theme emerges: Scientists are being asked to identify or provide technology, or to give expert analysis to inform policy-makers that requires the scientific understanding of increasingly complex physical and engineered systems. In addition, as the complexity of the systems of interest increases, neither experimental observation nor mathematical and computational modeling alone can access all components of the system over the entire range of scales or conditions needed to provide the required scientific understanding

Measurement of the Forward-Backward Asymmetry in the B -> K(*) mu+ mu- Decay and First Observation of the Bs -> phi mu+ mu- Decay

We reconstruct the rare decays $B^+ \to K^+\mu^+\mu^-$, $B^0 \to K^{*}(892)^0\mu^+\mu^-$, and $B^0_s \to \phi(1020)\mu^+\mu^-$ in a data sample corresponding to $4.4 {\rm fb^{-1}}$ collected in $p\bar{p}$ collisions at $\sqrt{s}=1.96 {\rm TeV}$ by the CDF II detector at the Fermilab Tevatron Collider. Using $121 \pm 16$ $B^+ \to K^+\mu^+\mu^-$ and $101 \pm 12$ $B^0 \to K^{*0}\mu^+\mu^-$ decays we report the branching ratios. In addition, we report the measurement of the differential branching ratio and the muon forward-backward asymmetry in the $B^+$ and $B^0$ decay modes, and the $K^{*0}$ longitudinal polarization in the $B^0$ decay mode with respect to the squared dimuon mass. These are consistent with the theoretical prediction from the standard model, and most recent determinations from other experiments and of comparable accuracy. We also report the first observation of the $B^0_s \to \phi\mu^+\mu^- decay and measure its branching ratio${\mathcal{B}}(B^0_s \to \phi\mu^+\mu^-) = [1.44 \pm 0.33 \pm 0.46] \times 10^{-6}$using$27 \pm 6$signal events. This is currently the most rare$B^0_s$ decay observed.Comment: 7 pages, 2 figures, 3 tables. Submitted to Phys. Rev. Let

Measurements of the properties of Lambda_c(2595), Lambda_c(2625), Sigma_c(2455), and Sigma_c(2520) baryons

We report measurements of the resonance properties of Lambda_c(2595)+ and Lambda_c(2625)+ baryons in their decays to Lambda_c+ pi+ pi- as well as Sigma_c(2455)++,0 and Sigma_c(2520)++,0 baryons in their decays to Lambda_c+ pi+/- final states. These measurements are performed using data corresponding to 5.2/fb of integrated luminosity from ppbar collisions at sqrt(s) = 1.96 TeV, collected with the CDF II detector at the Fermilab Tevatron. Exploiting the largest available charmed baryon sample, we measure masses and decay widths with uncertainties comparable to the world averages for Sigma_c states, and significantly smaller uncertainties than the world averages for excited Lambda_c+ states.Comment: added one reference and one table, changed order of figures, 17 pages, 15 figure

Search for a New Heavy Gauge Boson Wprime with Electron + missing ET Event Signature in ppbar collisions at sqrt(s)=1.96 TeV

We present a search for a new heavy charged vector boson $W^\prime$ decaying to an electron-neutrino pair in $p\bar{p}$ collisions at a center-of-mass energy of 1.96\unit{TeV}. The data were collected with the CDF II detector and correspond to an integrated luminosity of 5.3\unit{fb}^{-1}. No significant excess above the standard model expectation is observed and we set upper limits on $\sigma\cdot{\cal B}(W^\prime\to e\nu)$. Assuming standard model couplings to fermions and the neutrino from the $W^\prime$ boson decay to be light, we exclude a $W^\prime$ boson with mass less than 1.12\unit{TeV/}c^2 at the 95\unit{%} confidence level.Comment: 7 pages, 2 figures Submitted to PR

Observation of the Decay Λ0b→Λ+cτ−¯ν

The first observation of the semileptonic b-baryon decay Λb0→Λc+τ-ν¯τ, with a significance of 6.1σ, is reported using a data sample corresponding to 3 fb-1 of integrated luminosity, collected by the LHCb experiment at center-of-mass energies of 7 and 8 TeV at the LHC. The τ- lepton is reconstructed in the hadronic decay to three charged pions. The ratio K=B(Λb0→Λc+τ-ν¯τ)/B(Λb0→Λc+π-π+π-) is measured to be 2.46±0.27±0.40, where the first uncertainty is statistical and the second systematic. The branching fraction B(Λb0→Λc+τ-ν¯τ)=(1.50±0.16±0.25±0.23)% is obtained, where the third uncertainty is from the external branching fraction of the normalization channel Λb0→Λc+π-π+π-. The ratio of semileptonic branching fractions R(Λc+)B(Λb0→Λc+τ-ν¯τ)/B(Λb0→Λc+μ-ν¯μ) is derived to be 0.242±0.026±0.040±0.059, where the external branching fraction uncertainty from the channel Λb0→Λc+μ-ν¯μ contributes to the last term. This result is in agreement with the standard model prediction