When is it Better to Compare than to Score?

When eliciting judgements from humans for an unknown quantity, one often has the choice of making direct-scoring (cardinal) or comparative (ordinal) measurements. In this paper we study the relative merits of either choice, providing empirical and theoretical guidelines for the selection of a measurement scheme. We provide empirical evidence based on experiments on Amazon Mechanical Turk that in a variety of tasks, (pairwise-comparative) ordinal measurements have lower per sample noise and are typically faster to elicit than cardinal ones. Ordinal measurements however typically provide less information. We then consider the popular Thurstone and Bradley-Terry-Luce (BTL) models for ordinal measurements and characterize the minimax error rates for estimating the unknown quantity. We compare these minimax error rates to those under cardinal measurement models and quantify for what noise levels ordinal measurements are better. Finally, we revisit the data collected from our experiments and show that fitting these models confirms this prediction: for tasks where the noise in ordinal measurements is sufficiently low, the ordinal approach results in smaller errors in the estimation

Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence

Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector $w^* \in \mathbb{R}^d$ that represents the "qualities" of the $d$ items being compared; this class of models includes the two most widely used parametric models--the Bradley-Terry-Luce (BTL) and the Thurstone models. Working within a standard minimax framework, we provide tight upper and lower bounds on the optimal error in estimating the quality score vector $w^*$ under this class of models. The bounds depend on the topology of the comparison graph induced by the subset of pairs being compared via its Laplacian spectrum. Thus, in settings where the subset of pairs may be chosen, our results provide principled guidelines for making this choice. Finally, we compare these error rates to those under cardinal measurement models and show that the error rates in the ordinal and cardinal settings have identical scalings apart from constant pre-factors.Comment: 39 pages, 5 figures. Significant extension of arXiv:1406.661

Heterodyne Ladar System Efficiency Enhancement Using Single-mode Optical Fiber Mixers

A theoretical performance analysis of a heterodyne ladar system incorporating a single-mode fiber receiver has been performed. For our purposes, the performance parameters of interest are the coupling and mixing efficiency of the ladar receiver, as they relate to the overall system carrier-to-noise ratio. For a receiver incorporating a single-mode fiber mixer, the received and local-oscillator fields are matched both spatially and temporally at the detector, yielding 100% mixing efficiency. We have therefore focused our efforts on determining an expression for the efficiency with which a diffuse return from a purely speckle target can be coupled into the receiving leg of a monostatic, untruncated cw ladar system. Through numerical analysis, the expected coupling efficiency for a ladar system with negligible truncation of the transmit beam has been determined to be 30.6%

Analysis of Ladar Range Resolution Enhancement by Sinusoidal Phase Modulation

The ability of a ladar system to resolve two or more separate returns from a combined echo is related to the effective correlation bandwidth of the pulse emitted by the ladar system. Phase modulation of an outgoing pulse introduces additional frequency components, which increases the effective correlation bandwidth of the pulse and thus improves the range resolution of the system. In this paper, we discuss the general theoretical basis for achieving improved range resolution using a modulated waveform and a matched filter receiver. We then demonstrate these concepts by considering the particular case of improved range resolution for a sinusoidally phase modulated carrier with a rectangular amplitude function. We also perform computer simulations with a realistic pulsed ladar envelope possessing the same modulation function. Our calculations indicate that the resolution of a pulsed ladar system may be improved by a factor of 70 with a phase-modulated pulse and a matched-filter receiver

A comparison of broad-spectrum and narrow-spectrum dry cow therapy used alone and in combination with a teat sealant

The dry period is a critical time in the lactation cycle, offering the optimum time for cure of existing intramammary infection (IMI), while also encompassing the periods of highest susceptibility to new intramammary infection. Until recent years, intramammary infection in the dry period has been controlled with the use of antibiotic dry cow therapy. The aim of this study was to investigate 3 different dry cow therapy regimens, in low-somatic cell count (SCC; bulk milk SCC < 250,000 cells/mL) herds in southwest England. A total of 489 cows was recruited to the study and randomly allocated to receive either the broad-spectrum antibiotic cefquinome, a combination treatment comprising the narrow-spectrum antibiotic cloxacillin and an internal teat sealant, or the narrow-spectrum antibiotic cloxacillin alone. All quarters were sampled for bacteriology at drying off and again in the week immediately postcalving; 2 quarters were also sampled 2 wk before the estimated calving date to allow an assessment of infection dynamics during the dry period. Quarters were subsequently monitored for clinical mastitis for the first 100 d of lactation. Conventional multilevel (random effects) models were constructed to assess the efficacy of products in preventing IMI. Survival analysis was used to examine factors that influenced the risk of clinical mastitis using conventional Cox proportional hazards models. No differences were identified between the treatment groups in terms of cure of IMI caused by the major pathogens. Quarters in both the combination and cefquinome-treated groups were more likely to be free of a major pathogen or enterobacterial pathogen postcalving. With respect to clinical mastitis, the cefquinome-treated group was less likely to develop clinical mastitis than was the cloxacillin treated group

Equivalent-source acoustic holography for projecting measured ultrasound fields through complex media

Holographic projections of experimental ultrasound measurements generally use the angular spectrum method or Rayleigh integral, where the measured data is imposed as a Dirichlet boundary condition. In contrast, full-wave models, which can account for more complex wave behaviour, often use interior mass or velocity sources to introduce acoustic energy into the simulation. Here, a method to generate an equivalent interior source that reproduces the measurement data is proposed based on gradient-based optimisation. The equivalent-source can then be used with full-wave models (for example, the open-source k-Wave toolbox) to compute holographic projections through complex media including nonlinearity and heterogeneous material properties. Numerical and experimental results using both time-domain and continuous-wave sources are used to demonstrate the accuracy of the approach

A Search for Scalar Chameleons with ADMX

Scalar fields with a "chameleon" property, in which the effective particle mass is a function of its local environment, are common to many theories beyond the standard model and could be responsible for dark energy. If these fields couple weakly to the photon, they could be detectable through the "afterglow" effect of photon-chameleon-photon transitions. The ADMX experiment was used in the first chameleon search with a microwave cavity to set a new limit on scalar chameleon-photon coupling excluding values between 2*10^9 and 5*10^14 for effective chameleon masses between 1.9510 and 1.9525 micro-eV.Comment: 4 pages, 3 figure

Coherent Versus Incoherent Ladar Detection at 2.09 μm

A 2.09-μm ladar system is built to compare coherent to incoherent detection. The 2.09-μm wavelength is of interest because of its high atmospheric transmission and because it is eyesafe. The 2.09-μm system presented is capable of either a coherent or incoherent operational mode, is tunable in a small region around 2.09 μm, and is being used to look at the statistical nature of the ladar return pulses for typical glint and speckle targets. To compare coherent to incoherent detection the probability of detection is investigated as the primary performance criterion of interest. The probability of detection is dependent on both the probability of false alarm and the probability density function, representing the signal current output from the detector. These probability distributions are different for each detection technique and for each type of target. Furthermore, the probability of detection and the probability of false alarm are both functions of the dominating noise source(s) in the system. A description of the theoretical expectations of this system along with the setup of the ladar system and how it is being used to collect data for both coherent and incoherent detection is presented

Numerical method for evolving the dipolar projected Gross-Pitaevskii equation

We describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for an interacting Bose gas in a harmonic oscillator potential, with the inclusion of a long-range dipolar interaction. The central difficulty in solving this equation is the requirement that the field is restricted to a small set of prescribed modes that constitute the low energy c-field region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the dipolar PGPE. We introduce a set of auxiliary oscillator states to perform a Fourier transform necessary to evaluate the dipolar interaction in reciprocal space. We extensively characterize the accuracy of our approach, and derive Ehrenfest equations for the evolution of the angular momentum.Comment: 16 pages, 6 figures. Updated to published versio