Using Economic Theory to Guide Numerical Analysis: Solving for Equilibria in Models of Asymmetric First-Price Auctions

In models of first-price auctions, when bidders are ex ante heterogeneous, deriving explicit equilibrium bid functions is typically impossible, so numerical methods are often employed to find approximate solutions. Recent theoretical research concerning asymmetric auctions has determined some properties these bid functions must satisfy when certain conditions are met. Plotting the relative expected pay-offs of bidders is a quick, informative way to decide whether the approximate solutions are consistent with theory. We approximate the (inverse-)bid functions by polynomials and employ theoretical results in two ways: to help solve for the polynomial coefficients and to evaluate qualitatively the appropriateness of a given approximation. We simulate auctions from the approximated solutions and find that, for the examples considered, low-degree polynomial approximations perform poorly and can lead to incorrect policy recommendations concerning auction design, suggesting researchers need to take care to obtain quality solutions.     

There are no racial, age, sex, or weight differences in the effect of salt on blood pressure in salt-sensitive hypertensive patients

STUDY DESIGN: A bench-top trauma sled was used to apply four intensities of whiplash trauma to human cadaveric cervical spine specimens and to measure resulting intervertebral rotations using high-speed cinematography. OBJECTIVES: To determine the cervical spine levels most prone to injury from whiplash trauma and to hypothesize a mechanism for such injury. SUMMARY OF BACKGROUND DATA: Whiplash injuries traditionally have been ascribed to hyperextension of the head, but other mechanisms such as hypertranslation also have been suggested. METHODS: Six occiput to T1 (or C7) fresh cadaveric human spines were studied. Physiologic flexion and extension motions were recorded with an Optotrak motion analysis system by loading up to 1.0 Nm. Specimens then were secured in a trauma sled, and a surrogate head was attached. Flags fixed to the head and individual vertebrae were monitored with high-speed cinematography (500 frames/sec). Data were collected for 12 traumas in four classes defined by the maximum sled acceleration. The trauma classes were 2.5 g, 4.5 g, 6.5 g, and 8.5 g. Significance was defined at P < 0.01. RESULTS: In the whiplash traumas, the peak intervertebral rotations of C6-C7 and C7-T1 significantly exceeded the maximum physiologic extension for all trauma classes studied. The maximum extension of these lower levels occurred significantly before full neck extension. In fact, the upper cervical levels were consistently in flexion at the time of maximum lower level extension. CONCLUSIONS: In whiplash, the neck forms an S-shaped curvature, with lower level hyperextension and upper level flexion. This was identified as the injury stage for the lower cervical levels. A subsequent C-shaped curvature with extension of the entire cervical spine produced less lower level extension.     

Xenoendocrine pollutants may reduce size of sexual organs in East Greenland polar bears (Ursus maritimus)

Reproductive organs from 55 male and 44 female East Greenland polar bears were examined to investigate the potential negative impact from organohalogen pollutants (OHCs). Multiple regressions normalizing for age showed a significant inverse relationship between OHCs and testis length and baculum length and weight, respectively, and was found in both subadults (dichlorodiphenyl trichloroethanes, dieldrin, chlordanes, hexacyclohexanes, polychlorinated biphenyls (PCBs), and polybrominated diphenyl ethers (PBDEs)) and adults (hexachlorobenzene [HCB]) (all p < 0.05). Baculum bone mineral densities decreased with increasing chlordanes, DDTs, and HCB in subadults and adults, respectively (all p < 0.05). In females, a significant inverse relationship was found between ovary length and sigma PCB (p = 0.03) and sigma CHL (p < 0.01), respectively, and between ovary weight and sigma PBDE (p < 0.01) and uterine horn length and HCB (p = 0.02). The study suggests thatthere is an impact from xenoendocrine pollutants on the size of East Greenland polar bear genitalia. This may pose a riskto this polar bear subpopulation in the future because of reduced sperm and egg quality/quantity and uterus and penis size/robustness.     

The Reciprocalizer: an Agile Design Tool for Reciprocal Structures

This paper presents the reciprocalizer, a grasshopper plugin developed to design reciprocal structures. The plugin can handle the full set of geometric parameters necessary to describe the geometry of reciprocally connected elements in real-time. This makes it an agile design tool for the exploration of the geometrical richness of reciprocal structures.     

Mapping indoor radon-222 in Denmark: design and test of the statistical model used in the second nationwide survey

In Denmark, a new survey of indoor radon-222 has been carried out, 1-year alpha track measurements (CR-39) have been made in 3019 single-family houses. There are from 3 to 23 house measurements in each of the 275 municipalities. Within each municipality, houses have been selected randomly. One important outcome of the survey is the prediction of the fraction of houses in each municipality with an annual average radon concentration above 200 Bq m(-3). To obtain the most accurate estimate and to assess the associated uncertainties, a statistical model has been developed. The purpose of this paper is to describe the design of this model, and to report results of model tests. The model is based on a transformation of the data to normality and on analytical (conditionally) unbiased estimators of the quantities of interest. Bayesian statistics are used to minimize the effect of small sample size. In each municipality, the correction is dependent on the fraction of area where sand and gravel is a dominating surface geology. The uncertainty analysis is done with a Monte-Carlo technique. It is demonstrated that the weighted sum of all municipality model estimates of fractions above 200 Bq m(-3) (3.9% with 95%-confidence interval = [3.4,4.5]) is consistent with the weighted sum of the observations for Denmark taken as a whole (4.6% with 95%-confidence interval = [3.8,5.6]). The total number of single-family houses within each municipality is used as weight. Model estimates are also found to be consistent with observations at the level of individual counties. These typically include a few hundred house measurements. These tests indicate that the model is well suited for its purpose.     

Experimental and Numerical Study of Damaged Cantilever

The introduction of a crack in a steel structure will cause a local change in the stiffness and damping capacity. The change in stiffness will lead to a change of some of the natural frequencies of the structure and a discontinuity in the associated mode shapes. This paper contains a presentation of the results from experimental and numerical tests with hollow section cantilevers containing fatigue cracks. Two different finite-element (FE) models have been used to estimate the modal parameters numerically. The first FE model consists of beam elements. The second FE model consists of traditional rectangular shell elements and one rectangular shell element with a transverse, internal, open crack. The analytical results from the numerical models are compared with data obtained from experimental tests. The numerical models give good agreements with the experimental data. The beam model takes into account only the first mode of the crack evaluation. In the shell model all three modes of the crack growth are taken into account. Nevertheless, the results obtained for both models are satisfactory because the beam is subjected to bending. It can be concluded that it is sufficient to use crack models for calculating natural frequencies in bending, taking into account the first mode of the crack extension only.     

Patients with acute respiratory distress syndrome mechanically ventilated in prone position

Animal experiments and human studies have shown better oxygenation in mechanically ventilated patients with ARDS when the patient is situated in the prone position. In contradiction to former theories of a gravitational gradient of lung perfusion, a number of investigators have found that lung perfusion is preferentially distributed to the dorsal lung regions regardless of body position. The basal atelectasis and oedema in ARDS are resolved and only partly distributed anteriorly in the prone position, and these areas are thereby better ventilated. The combination of better ventilation and unchanged perfusion improves the ventilation/perfusion ratio and decreases the shunt in the prone position. In two cases of prone position in mechanically ventilated patients the PaO2/FiO2 ratio increased from 7.5 to 14.3 and from 8.8 to 19.8 after one hour in the prone position, and some of the improvement was permanent. Prone position has only minor side effects and is recommended as the first choice amongst adjunct therapies in mechanical ventilation in patients with ARDS remaining hypoxic in conventional therapy in the supine position.