Including Systematic Uncertainties in Confidence Interval Construction for Poisson Statistics

One way to incorporate systematic uncertainties into the calculation of confidence intervals is by integrating over probability density functions parametrizing the uncertainties. In this note we present a development of this method which takes into account uncertainties in the prediction of background processes, uncertainties in the signal detection efficiency and background efficiency and allows for a correlation between the signal and background detection efficiencies. We implement this method with the Feldman & Cousins unified approach with and without conditioning. We present studies of coverage for the Feldman & Cousins and Neyman ordering schemes. In particular, we present two different types of coverage tests for the case where systematic uncertainties are included. To illustrate the method we show the relative effect of including systematic uncertainties the case of dark matter search as performed by modern neutrino tel escopes.Comment: 23 pages, 10 figures, replaced to match published versio

Raman signatures of classical and quantum phases in coupled dots: A theoretical prediction

We study electron molecules in realistic vertically coupled quantum dots in a strong magnetic field. Computing the energy spectrum, pair correlation functions, and dynamical form factor as a function of inter-dot coupling via diagonalization of the many-body Hamiltonian, we identify structural transitions between different phases, some of which do not have a classical counterpart. The calculated Raman cross section shows how such phases can be experimentally singled out.Comment: 9 pages, 2 postscript figures, 1 colour postscript figure, Latex 2e, Europhysics Letters style and epsfig macros. Submitted to Europhysics Letter

Brain amyloid in preclinical Alzheimer\u27s disease is associated with increased driving risk

INTRODUCTION: Postmortem studies suggest that fibrillar brain amyloid places people at higher risk for hazardous driving in the preclinical stage of Alzheimer's disease (AD). METHODS: We administered driving questionnaires to 104 older drivers (19 AD, 24 mild cognitive impairment, and 61 cognitive normal) who had a recent (18)F-florbetapir positron emission tomography scan. We examined associations of amyloid standardized uptake value ratios with driving behaviors: traffic violations or accidents in the past 3 years. RESULTS: The frequency of violations or accidents was curvilinear with respect to standardized uptake value ratios, peaking around a value of 1.1 (model r(2) = 0.10, P = .002); moreover, this relationship was evident for the cognitively normal participants. DISCUSSION: We found that driving risk is strongly related to accumulating amyloid on positron emission tomography, and that this trend is evident in the preclinical stage of AD. Brain amyloid burden may in part explain the increased crash risk reported in older adults

Inference for bounded parameters

The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive discussion by statisticians. The primary focus however in [1] and the accompanying discussion is on the construction of a confidence interval. We argue that the likelihood function and $p$-value function provide a comprehensive presentation of the information available from the model and the data. This is illustrated for Gaussian and Poisson models with lower bounds for the mean parameter

Correspondence between geometrical and differential definitions of the sine and cosine functions and connection with kinematics

In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two forms correspond to two different definitions of trigonometric functions, one geometrical using right triangles and unit circles, and the other employing differential equations. Although the two definitions must be equivalent, this equivalence is not demonstrated in textbooks. In this manuscript, the equivalence between the geometrical and the differential definition is presented assuming no a priori knowledge of the properties of sine and cosine functions. We start with the usual length projections on the unit circle and use elementary geometry and elementary calculus to arrive to harmonic differential equations. This more general and abstract treatment not only reveals the equivalence of the two definitions but also provides an instructive perspective on circular and harmonic motion as studied in kinematics. This exercise can help develop an appreciation of abstract thinking in physics.Comment: 6 pages including 1 figur

Evidence of Female Sex Pheromones and Characterization of the Cuticular Lipids of Unfed, Adult Male Versus Female Blacklegged Ticks, Ixodes scapularis

Copulation in I. scapularis involves physical contact between the male and female (on or off the host), male mounting the female, insertion/maintenance of the male chelicerae in the female genital pore (initiates spermatophore production), and the transfer of the spermatophore by the male into the female genital pore. Bioassays determined that male mounting behavior/chelicerae insertion required direct contact with the female likely requiring non-volatile chemical cues with no evidence of a female volatile sex pheromone to attract males. Unfed virgin adult females and replete mated adult females elicited the highest rates of male chelicerae insertion with part fed virgin adult females exhibiting a much lower response. Whole body surface hexane extracts of unfed virgin adult females and males, separately analyzed by GC-MS, identified a number of novel tick surface associated compounds: fatty alcohols (1-hexadecanol and 1-heptanol), a fatty amide (erucylamid), aromatic hydrocarbons, a short chain alkene (1 heptane), and a carboxylic acid ester (5β-androstane). These compounds are discussed in terms of their potential role in female-male communication. The two most abundant fatty esters found were butyl palmitate and butyl stearate present in ratios that were sex specific. Only 6 n-saturated hydrocarbons were identified in I. scapularis ranging from 10-18 carbons

Projective Ribbon Permutation Statistics: a Remnant of non-Abelian Braiding in Higher Dimensions

In a recent paper, Teo and Kane proposed a 3D model in which the defects support Majorana fermion zero modes. They argued that exchanging and twisting these defects would implement a set R of unitary transformations on the zero mode Hilbert space which is a 'ghostly' recollection of the action of the braid group on Ising anyons in 2D. In this paper, we find the group T_{2n} which governs the statistics of these defects by analyzing the topology of the space K_{2n} of configurations of 2n defects in a slowly spatially-varying gapped free fermion Hamiltonian: T_{2n}\equiv {\pi_1}(K_{2n})$. We find that the group T_{2n}= Z \times T^r_{2n}, where the 'ribbon permutation group' T^r_{2n} is a mild enhancement of the permutation group S_{2n}: T^r_{2n} \equiv \Z_2 \times E((Z_2)^{2n}\rtimes S_{2n}). Here, E((Z_2)^{2n}\rtimes S_{2n}) is the 'even part' of (Z_2)^{2n} \rtimes S_{2n}, namely those elements for which the total parity of the element in (Z_2)^{2n} added to the parity of the permutation is even. Surprisingly, R is only a projective representation of T_{2n}, a possibility proposed by Wilczek. Thus, Teo and Kane's defects realize `Projective Ribbon Permutation Statistics', which we show to be consistent with locality. We extend this phenomenon to other dimensions, co-dimensions, and symmetry classes. Since it is an essential input for our calculation, we review the topological classification of gapped free fermion systems and its relation to Bott periodicity.Comment: Missing figures added. Fixed some typos. Added a paragraph to the conclusio

Paramaterizations of inclusive cross sections for pion production in proton-proton collisions. II. Comparison to new data

A set of new, precise data have recently been made available by the NA49 collaboration for charged pion production in proton-proton and proton-Carbon reactions at 158 GeV. The current paper compares this new data to five currently available arithmetic parameterizations. Although a precise fit is not expected, two of the parameterizations do not work very well but the other three are able to provide a moderately good, but not precise fit to the proton-proton data. The best two of these three parameterizations are scaled to the proton-Carbon data and again provide a moderately good, but not precise fit.Comment: 11 pages, 13 figures, Accepted for publication in Physical Review