A Characterization of the Uniform Rule with Several Commodities and Agents

We consider the problem of allocating infinitely divisible commodities among a group of agents. Especially, we focus on the case where there are several commodities to be allocated, and agents have continuous, strictly convex, and separable preferences. In this paper, we establish that the uniform rule is the only rule satisfying strategy-proofness, unanimity, symmetry, and nonbossiness.

Accession Rules and Trade Agreements: The Case of the WTO

This paper models the accession process to the World Trade Organization (WTO) as a two stage game. In the first stage, member countries choose tariff rates to be applied on trade with each other. In the second stage a non-member country applies for membership in the agreement and negotiates with the member countries over the tariff rates to be applied. Based on the rules of the WTO accession process, we model this negotiation using the Nash bargaining solution. The analysis focuses on the question of how the pattern of trade between the acceding country and the member countries affects the distribution of gains from accession between the members and the acceding countries, given the rules of the WTO negotiation process. We consider two n good, n country trade models which highlight features of the WTO tariff negotiations. The first is a model in which each country imports one good from all of the other countries (competing supplier model). This model highlights the role of the MFN principle, since member countries are forced to extend the same tariff treatment to non-members when they join. We show that the non-member will free ride on tariff reductions among the member countries in this case, and that the non-member will gain a larger fraction of the gains from accession if transport costs are sufficiently low. The second model considers a case in which each country exports a single good to the other countries (principal supplier model). We show that in this case tariff reductions by the member countries reduce the welfare of the non-member country, and the member countries gain a larger share of the gains from accession.

Robust Control of Burst Suppression Amid Physical and Neurological Uncertainty

Burst suppression is a clinical term describing a phenomenon in which the electroencephalogram (EEG) of a sedated patient produces behavior that switches between higher frequency and amplitude bursting to lower frequency and lower amplitude suppression. This phenomenon can be observed during general anesthesia, hypothermia, or in an otherwise induced coma state. In a clinical setting, this phenomenon is typically induced by sedation from a drug such as propofol (2,6-diisopropylphenol). The level of sedation can be quantified by something called the burst suppression ratio (BSR), which is defined as the amount of time that a patient’s EEG is in a suppressed state over the amount of time measured. One can vary this ratio by either increasing or decreasing the propofol infusion rate that the patient is given to bring them to a deeper or lighter state of sedation. By measuring the EEG data, one can form a closed loop feedback system where the EEG data is monitored for signs of burst suppression and the propofol is increased or decreased accordingly. Therefore, it becomes desirable to create models of this closed loop system to simulate the kind of behavior that would be expected from a clinical setting such as the one described. Many methods and experimental paradigms have been developed to address this problem including development of pharmacokinetic (PK) models that describe the dynamics of drug infusion in the body as well as signal processing methods for computing the burst suppression estimation such as the burst suppression probability. Some of these paradigms have been tested in rodent experiments, though human studies remain elusive. In this regard, simulations and detailed physiological modeling and control design can play a key role. This thesis seeks to add on the rich body of work that has been done thus far by incorporating a Schnider PK model with the Wilson-Cowan neural mass model to form a closed loop model which we can use as a basis for more detailed analysis which includes real-time burst suppression estimation as well as uncertainty modeling in both the patient’s physical characteristics (such as weight, height, age and gender) in addition to neurological phenomena such as the recovery and consumption rates of neurons during burst suppression behavior. By creating a conversion from the physiological parameters that describe the PK models to the dimensionless and more abstract parameters which guide the Wilson-Cowan equations, and implementing an actuator and burst suppression ratio estimation algorithm, we have effectively modeled the clinical setting with which the BSR is sought to be controlled. Thus, in this study we wished to show that with PID control, one could control this model at a nominal condition (i.e., the patient and neurological parameters which the gains were designed for) as well as at various uncertainty conditions that include both physical and neurological uncertainty, as described above. Using the Zeigler-Nichols tuning method, we were able to design gains to sufficiently control this system at set points of 0.8, 0.5 and 0.2 BSR over a simulation time of roughly 18 hours in both nominal, patient varied with noise added and with reduced performance when including patient variation and noise as well as neurological uncertainty. This time duration was chosen because it was convenient for the model’s time constants but also because it is representative of the time a patient may be sedated. The BSR ranges were chosen so as to show the closed loop system’s ability to maintain control at multiple levels of sedation. The reduced performance due to neurological uncertainty was due to the BSR estimation algorithm estimating a lower bound that was too high for the system to be controlled at a BSR of 0.2. The minimum BSR the system with added neurological uncertainty could be controlled to was 0.38, which is where the system held at during the portion of the trajectory that a BSR of 0.2 was commanded. During the achievable parts of the envelope, however, the control scheme worked with similar performance to that of the nominal case. This would suggest that an adaptive estimation algorithm needs to be developed to estimate the neurological deviations from the nominal case. Further, this suggests that if variations in the BSR of a patient due to neurological uncertainty is expected, then accurate estimation of these parameters are vital to reaching a robust solution in a real-time system

The relationship between foot arch measurements and walking parameters in children

BACKGROUND: Walking mechanics are influenced by body morphology. Foot arch height is one aspect of body morphology central to walking. However, generalizations about the relationship between arch height and walking are limited due to previous methodologies used for measuring the arch and the populations that have been studied. To gain the knowledge needed to support healthy gait in children and adults, we need to understand this relationship in unimpaired, typically developing children and adults using dynamic measures. The purpose of the current study was to examine the relationship between arch height and gait in a sample of healthy children and adults using dynamic measures. METHODS: Data were collected from 638 participants (n = 254 children and n = 384 adults) at the Museum of Science, Boston (MOS) and from 18 4- to 8-year-olds at the Motor Development and Motor Control Laboratories. Digital footprints were used to calculate two arch indices: the Chippaux-Smirak (CSI) and the Keimig Indices (KI). The height of the navicular bone was measured. Gait parameters were captured with a mechanized gait carpet at the MOS and three-dimensional motion analyses and in-ground force plates in the Motor Development and Motor Control Laboratories. RESULTS: Linear regression analyses on data from the MOS confirmed that as age increases, step length increases. With a linear mixed effect regression model, we found that individuals who took longer steps had higher arches as measured by the KI. However, this relationship was no longer significant when only adults were included in the model. A model restricted to children found that amongst this sample, those with higher CSI and higher KI values take longer relative step lengths. Data from the Motor Development and Motor Control Laboratories showed that both CSI and KI added to the prediction; children with lower anterior ground reaction forces had higher CSI and higher KI values. Arch height indices were correlated with navicular height. CONCLUSIONS: These results suggest that more than one measure of the arch may be needed elucidate the relationship between arch height and gait.K12 HD055931 - NICHD NIH HHS; K12HD055931 - NICHD NIH HH