Nonparametric Dark Energy Reconstruction from Supernova Data

Understanding the origin of the accelerated expansion of the Universe poses one of the greatest challenges in physics today. Lacking a compelling fundamental theory to test, observational efforts are targeted at a better characterization of the underlying cause. If a new form of mass-energy, dark energy, is driving the acceleration, the redshift evolution of the equation of state parameter w(z) will hold essential clues as to its origin. To best exploit data from observations it is necessary to develop a robust and accurate reconstruction approach, with controlled errors, for w(z). We introduce a new, nonparametric method for solving the associated statistical inverse problem based on Gaussian Process modeling and Markov chain Monte Carlo sampling. Applying this method to recent supernova measurements, we reconstruct the continuous history of w out to redshift z=1.5.Comment: 4 pages, 2 figures, accepted for publication in Physical Review Letter

Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process

The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli \rho measure as initial conditions, 0<\rho<1, is stationary in space and time. Let N_t(j) be the number of particles which have crossed the bond from j to j+1 during the time span [0,t]. For j=(1-2\rho)t+2w(\rho(1-\rho))^{1/3} t^{2/3} we prove that the fluctuations of N_t(j) for large t are of order t^{1/3} and we determine the limiting distribution function F_w(s), which is a generalization of the GUE Tracy-Widom distribution. The family F_w(s) of distribution functions have been obtained before by Baik and Rains in the context of the PNG model with boundary sources, which requires the asymptotics of a Riemann-Hilbert problem. In our work we arrive at F_w(s) through the asymptotics of a Fredholm determinant. F_w(s) is simply related to the scaling function for the space-time covariance of the stationary TASEP, equivalently to the asymptotic transition probability of a single second class particle.Comment: 53 pages, 4 figures, Latex2e; Fixed a numerical prefactor in the scaling function (1.10

The One-dimensional KPZ Equation and the Airy Process

Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an n-point generating function and write it in terms of a Fredholm determinant. For long times the generating function converges to a limit, which is established to be equivalent to the standard expression of the n-point distribution of the Airy process.Comment: 15 page

Statistical Self-Similarity of One-Dimensional Growth Processes

For one-dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times. We argue that for self-similar growth from a single seed the universal distribution is the Tracy-Widom distribution from the theory of random matrices and that for growth from a flat substrate it is some other, only numerically determined distribution. In particular, for the polynuclear growth model in the droplet geometry the height maps onto the longest increasing subsequence of a random permutation, from which the height distribution is identified as the Tracy-Widom distribution.Comment: 11 pages, iopart, epsf, 2 postscript figures, submitted to Physica A, in an Addendum the distribution for the flat case is identified analyticall

Nonparametric Reconstruction of the Dark Energy Equation of State

A basic aim of ongoing and upcoming cosmological surveys is to unravel the mystery of dark energy. In the absence of a compelling theory to test, a natural approach is to better characterize the properties of dark energy in search of clues that can lead to a more fundamental understanding. One way to view this characterization is the improved determination of the redshift-dependence of the dark energy equation of state parameter, w(z). To do this requires a robust and bias-free method for reconstructing w(z) from data that does not rely on restrictive expansion schemes or assumed functional forms for w(z). We present a new nonparametric reconstruction method that solves for w(z) as a statistical inverse problem, based on a Gaussian Process representation. This method reliably captures nontrivial behavior of w(z) and provides controlled error bounds. We demonstrate the power of the method on different sets of simulated supernova data; the approach can be easily extended to include diverse cosmological probes.Comment: 16 pages, 11 figures, accepted for publication in Physical Review

Fish Assemblage Shifts and Population Dynamics of Smallmouth Bass (Micropterus dolomieu) in the Beaver Archipelago, Northern Lake Michigan: A Comparison Between Historical and Recent Time Periods Amidst Ecosystem Changes.

The ecological and economic importance of Great Lakes nearshore areas and the paucity of information on nearshore Lake Michigan fish assemblages prompted us to document changes that occurred from a historical time period (1969–1972, 1975, 1977, and 1984) to a recent period (2005–2008) in a nearshore northern Lake Michigan (Beaver Archipelago) fish assemblage, with an emphasis on smallmouth bass Micropterus dolomieu. From historical to recent periods, the Beaver Archipelago fish assemblage shifted from predominantly brown bullheads Ameiurus nebulosus to predominantly smallmouth bass. Relative abundance of brown bullheads and white suckers Catostomus commersonii declined from historical to recent time periods, as did overall species richness. The relative abundance, recruitment variability, and mortality rates of smallmouth bass have not significantly changed since the historical time period, whereas both condition (ages 5–7) and growth (ages 2–7) of this species have significantly increased. Our results suggest that the smallmouth bass population in the Beaver Archipelago area has not been negatively affected by recent ecological changes (i.e., declining primary productivity, increasing benthic invertebrate densities, increasing numbers of double-crested cormorants Phalacrocorax auritus, and increasing introductions of nonnative species). The smallmouth bass is currently the dominant nearshore species and remains a critical component of the nearshore fish assemblage in northern Lake Michigan

Rural nutrition and dietetics research—Future directions

Aim: The aim of this study was to summarise key evidence from recent Australian rural nutrition research and provide recommendations for future nutrition and dietetics research with rural communities. Context: Clear evidence demonstrates that diet plays a role in the health gap between rural and metropolitan Australia. Despite the opportunity to address the health of rural Australians through better nutrition, alarmingly low investment in nutrition and dietetics research has occurred historically, and over the past decade. Approach: A review of the evidence was undertaken by rural nutrition and dietetics leaders to provide a commentary piece to inform future rural nutrition research efforts. Conclusion: Establishing strong, collaborative place-based nutrition and dietetics research teams are necessary to combat the significant gaps in the scientific knowledge of solutions to improve nutrition in rural Australia. Further, dieticians and nutritionists who live in and understand the rural contexts are yet to be fully harnessed in research, and better engaging with these professionals will have the best chance of successfully addressing the nutrition-related disease disparity between rural and metropolitan Australia

Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices

We develop a scaling theory for KPZ growth in one dimension by a detailed study of the polynuclear growth (PNG) model. In particular, we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape. These distribution functions are computed using the partition function of Gaussian random matrices in a cosine potential.Comment: 4 pages, 3 figures, 1 table, RevTeX, revised version, accepted for publication in PR

Infinite N phase transitions in continuum Wilson loop operators

We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character as unitary matrices and undergo a phase transition at infinite N reflected by the eigenvalue distribution closing a gap in its spectrum when the defining smooth loop is dilated from a small size to a large one. If this large N phase transition belongs to a solvable universality class one might be able to calculate analytically the string tension in terms of the perturbative Lambda-parameter. This would be achieved by matching instanton results for small loops to the relevant large-N-universal function which, in turn, would be matched for large loops to an effective string theory. Similarities between our findings and known analytical results in two dimensional space-time indicate that the phase transitions we found only affect the eigenvalue distribution, but the traces of finite powers of the Wilson loop operators stay smooth under scaling.Comment: 31 pages, 9 figures, typos and references corrected, minor clarifications adde