Analytic Confidence Level Calculations using the Likelihood Ratio and Fourier Transform

The interpretation of new particle search results involves a confidence level calculation on either the discovery hypothesis or the background-only ("null") hypothesis. A typical approach uses toy Monte Carlo experiments to build an expected experiment estimator distribution against which an observed experiment's estimator may be compared. In this note, a new approach is presented which calculates analytically the experiment estimator distribution via a Fourier transform, using the likelihood ratio as an ordering estimator. The analytic approach enjoys an enormous speed advantage over the toy Monte Carlo method, making it possible to quickly and precisely calculate confidence level results.Comment: 11 pages, 2 figure

Constraining models of f(R)f(R) gravity with Planck and WiggleZ power spectrum data

In order to explain cosmic acceleration without invoking "dark" physics, we consider $f(R)$ modified gravity models, which replace the standard Einstein-Hilbert action in General Relativity with a higher derivative theory. We use data from the WiggleZ Dark Energy survey to probe the formation of structure on large scales which can place tight constraints on these models. We combine the large-scale structure data with measurements of the cosmic microwave background from the Planck surveyor. After parameterising the modification of the action using the Compton wavelength parameter $B_0$, we constrain this parameter using ISiTGR, assuming an initial non-informative log prior probability distribution of this cross-over scale. We find that the addition of the WiggleZ power spectrum provides the tightest constraints to date on $B_0$ by an order of magnitude, giving ${\rm log}_{10}(B_0) < -4.07$ at 95% confidence limit. Finally, we test whether the effect of adding the lensing amplitude $A_{\rm Lens}$ and the sum of the neutrino mass $\sum m_\nu$ is able to reconcile current tensions present in these parameters, but find $f(R)$ gravity an inadequate explanation.Comment: 21 pages, 7 figures, matches version published in JCAP. The modified version of ISiTGR used to produce the results in this paper is available at http://isit.g

Giant topological insulator gap in graphene with 5d adatoms

Two-dimensional topological insulators (2D TIs) have been proposed as platforms for many intriguing applications, ranging from spintronics to topological quantum information processing. Realizing this potential will likely be facilitated by the discovery of new, easily manufactured materials in this class. With this goal in mind we introduce a new framework for engineering a 2D TI by hybridizing graphene with impurity bands arising from heavy adatoms possessing partially filled d-shells, in particular osmium and iridium. First principles calculations predict that the gaps generated by this means exceed 0.2 eV over a broad range of adatom coverage; moreover, tuning of the Fermi level is not required to enter the TI state. The mechanism at work is expected to be rather general and may open the door to designing new TI phases in many materials.Comment: 7 pages, 8 figure

Optimal Auctions for Correlated Buyers with Sampling

Cr\'emer and McLean [1985] showed that, when buyers' valuations are drawn from a correlated distribution, an auction with full knowledge on the distribution can extract the full social surplus. We study whether this phenomenon persists when the auctioneer has only incomplete knowledge of the distribution, represented by a finite family of candidate distributions, and has sample access to the real distribution. We show that the naive approach which uses samples to distinguish candidate distributions may fail, whereas an extended version of the Cr\'emer-McLean auction simultaneously extracts full social surplus under each candidate distribution. With an algebraic argument, we give a tight bound on the number of samples needed by this auction, which is the difference between the number of candidate distributions and the dimension of the linear space they span

Engineering a robust quantum spin Hall state in graphene via adatom deposition

The 2007 discovery of quantized conductance in HgTe quantum wells delivered the field of topological insulators (TIs) its first experimental confirmation. While many three-dimensional TIs have since been identified, HgTe remains the only known two-dimensional system in this class. Difficulty fabricating HgTe quantum wells has, moreover, hampered their widespread use. With the goal of breaking this logjam we provide a blueprint for stabilizing a robust TI state in a more readily available two-dimensional material---graphene. Using symmetry arguments, density functional theory, and tight-binding simulations, we predict that graphene endowed with certain heavy adatoms realizes a TI with substantial band gap. For indium and thallium, our most promising adatom candidates, a modest 6% coverage produces an estimated gap near 80K and 240K, respectively, which should be detectable in transport or spectroscopic measurements. Engineering such a robust topological phase in graphene could pave the way for a new generation of devices for spintronics, ultra-low-dissipation electronics and quantum information processing.Comment: 14 pages, 7 figure