Smooth Inequalities and Equilibrium Inefficiency in Scheduling Games

We study coordination mechanisms for Scheduling Games (with unrelated machines). In these games, each job represents a player, who needs to choose a machine for its execution, and intends to complete earliest possible. Our goal is to design scheduling policies that always admit a pure Nash equilibrium and guarantee a small price of anarchy for the l_k-norm social cost --- the objective balances overall quality of service and fairness. We consider policies with different amount of knowledge about jobs: non-clairvoyant, strongly-local and local. The analysis relies on the smooth argument together with adequate inequalities, called smooth inequalities. With this unified framework, we are able to prove the following results. First, we study the inefficiency in l_k-norm social costs of a strongly-local policy SPT and a non-clairvoyant policy EQUI. We show that the price of anarchy of policy SPT is O(k). We also prove a lower bound of Omega(k/log k) for all deterministic, non-preemptive, strongly-local and non-waiting policies (non-waiting policies produce schedules without idle times). These results ensure that SPT is close to optimal with respect to the class of l_k-norm social costs. Moreover, we prove that the non-clairvoyant policy EQUI has price of anarchy O(2^k). Second, we consider the makespan (l_infty-norm) social cost by making connection within the l_k-norm functions. We revisit some local policies and provide simpler, unified proofs from the framework's point of view. With the highlight of the approach, we derive a local policy Balance. This policy guarantees a price of anarchy of O(log m), which makes it the currently best known policy among the anonymous local policies that always admit a pure Nash equilibrium.Comment: 25 pages, 1 figur

Microwave remote sensing of soil moisture, volume 1

Multifrequency sensor data from NASA's C-130 aircraft were used to determine which of the all weather microwave sensors demonstrated the highest correlation to surface soil moisture over optimal bare soil conditions, and to develop and test techniques which use visible/infrared sensors to compensate for the vegetation effect in this sensor's response to soil moisture. The L-band passive microwave radiometer was found to be the most suitable single sensor system to estimate soil moisture over bare fields. The perpendicular vegetation index (PVI) as determined from the visible/infrared sensors was useful as a measure of the vegetation effect on the L-band radiometer response to soil moisture. A linear equation was developed to estimate percent field capacity as a function of L-band emissivity and the vegetation index. The prediction algorithm improves the estimation of moisture significantly over predictions from L-band emissivity alone

Multifrequency remote sensing of soil moisture

Multifrequency sensor data collected at Guymon, Oklahoma and Dalhart, Texas using NASA's C-130 aircraft were used to determine which of the all-weather microwave sensors demonstrated the highest correlation to surface soil moisture over optimal bare soil conditions, and to develop and test techniques which use visible/infrared sensors to compensate for the vegetation effect in this sensor's response to soil moisture. The L-band passive microwave radiometer was found to be the most suitable single sensor system to estimate soil moisture over bare fields. In comparison to other active and passive microwave sensors the L-band radiometer (1) was influenced least by ranges in surface roughness; (2) demonstrated the most sensitivity to soil moisture differences in terms of the range of return from the full range of soil moisture; and (3) was less sensitive to errors in measurement in relation to the range of sensor response. L-band emissivity related more strongly to soil moisture when moisture was expressed as percent of field capacity. The perpendicular vegetation index as determined from the visible/infrared sensors was useful as a measure of the vegetation effect on the L-band radiometer response to soil moisture

Development of visible/infrared/microwave agriculture classification and biomass estimation algorithms, volume 2

Agricultural crop classification models using two or more spectral regions (visible through microwave) were developed and tested and biomass was estimated by including microwave with visible and infrared data. The study was conducted at Guymon, Oklahoma and Dalhart, Texas utilizing aircraft multispectral data and ground truth soil moisture and biomass information. Results indicate that inclusion of C, L, and P band active microwave data from look angles greater than 35 deg from nadir with visible and infrared data improved crop discrimination and biomass estimates compared to results using only visible and infrared data. The active microwave frequencies were sensitive to different biomass levels. In addition, two indices, one using only active microwave data and the other using data from the middle and near infrared bands, were well correlated to total biomass

Development of visible/infrared/microwave agriculture classification and biomass estimation algorithms

Agricultural crop classification models using two or more spectral regions (visible through microwave) are considered in an effort to estimate biomass at Guymon, Oklahoma Dalhart, Texas. Both grounds truth and aerial data were used. Results indicate that inclusion of C, L, and P band active microwave data, from look angles greater than 35 deg from nadir, with visible and infrared data improve crop discrimination and biomass estimates compared to results using only visible and infrared data. The microwave frequencies were sensitive to different biomass levels. The K and C band were sensitive to differences at low biomass levels, while P band was sensitive to differences at high biomass levels. Two indices, one using only active microwave data and the other using data from the middle and near infrared bands, were well correlated to total biomass. It is implied that inclusion of active microwave sensors with visible and infrared sensors on future satellites could aid in crop discrimination and biomass estimation

Orbital evolution of a test particle around a black hole: Indirect determination of the self force in the post Newtonian approximation

Comparing the corrections to Kepler's law with orbital evolution under a self force, we extract the finite, already regularized part of the latter in a specific gauge. We apply this method to a quasi-circular orbit around a Schwarzschild black hole of an extreme mass ratio binary, and determine the first- and second-order conservative gravitational self force in a post Newtonian expansion. We use these results in the construction of the gravitational waveform, and revisit the question of the relative contribution of the self force and spin-orbit coupling.Comment: 5 pages, 2 figure