An Algorithmic Framework for Strategic Fair Division

We study the paradigmatic fair division problem of allocating a divisible good among agents with heterogeneous preferences, commonly known as cake cutting. Classical cake cutting protocols are susceptible to manipulation. Do their strategic outcomes still guarantee fairness? To address this question we adopt a novel algorithmic approach, by designing a concrete computational framework for fair division---the class of Generalized Cut and Choose (GCC) protocols}---and reasoning about the game-theoretic properties of algorithms that operate in this model. The class of GCC protocols includes the most important discrete cake cutting protocols, and turns out to be compatible with the study of fair division among strategic agents. In particular, GCC protocols are guaranteed to have approximate subgame perfect Nash equilibria, or even exact equilibria if the protocol's tie-breaking rule is flexible. We further observe that the (approximate) equilibria of proportional GCC protocols---which guarantee each of the $n$ agents a $1/n$-fraction of the cake---must be (approximately) proportional. Finally, we design a protocol in this framework with the property that its Nash equilibrium allocations coincide with the set of (contiguous) envy-free allocations

Emergence of a Twisted Magnetic Flux Bundle as a Source of Strong Flare Activity

Sunspot proper motions and flares of a super active region NOAA 5395, which was the biggest and the most flare-active region in the 22nd sunspot cycle, were analyzed in details. We measured sunspot proper motions by using the H-alpha - 5.0 A images obtained with the 60-cm Domeless Solar Telescope (DST) at Hida Observatory, Kyoto University and found some peculiar vortex-like motions of small satellite spots successively emerged from the leading edge of this sunspot group. To explain these motions of small sunspots, we proposed a schematic model of the successive emergence of twisted and winding magnetic flux ropes coiling around a trunk of magnetic flux tube. The location of the strongest flare activity was found to coincide with very the site of the vortex-like motions of sunspots. We conclude that the flare-productive magnetic shear is produced by the emergence of the twisted magnetic flux bundle. Magnetic energy is stored in the twisted flux tubes which are originally formed in the convection zone and released as flares in the course of the emergence of the twisted flux tubes above the photosphere.Comment: 19 pages LaTeX, 8 figures, ApJ accepted high resolution figures : e-mail to [email protected]

A Discrete and Bounded Envy-free Cake Cutting Protocol for Four Agents

We consider the well-studied cake cutting problem in which the goal is to identify a fair allocation based on a minimal number of queries from the agents. The problem has attracted considerable attention within various branches of computer science, mathematics, and economics. Although, the elegant Selfridge-Conway envy-free protocol for three agents has been known since 1960, it has been a major open problem for the last fifty years to obtain a bounded envy-free protocol for more than three agents. We propose a discrete and bounded envy-free protocol for four agents

Double-network acrylamide hydrogel compositions adapted to achieve cartilage-like dynamic stiffness

Since articular cartilage has a limited potential for spontaneous healing, various techniques are employed to repair cartilage lesions. Acrylate-based double-network (DN) hydrogels containing ~90% water have shown promising properties as repair materials for skeletal system soft tissues. Although their mechanical properties approach those of native cartilage, the critical factor—stiffness—of DN-gels does not equal the stiffness of articular cartilage. This study investigated whether revised PAMPS/PAAm compositions with lower water content result in stiffness parameters closer to cartilage. DN-gels containing 61, 86 and 90% water were evaluated using two non-destructive, mm-scale indentation test modes: fast-impact (FI) and slow-sinusoidal (SS) deformation. Deformation resistance (dynamic modulus) and energy handling (loss angle) were determined. The dynamic modulus increased with decreasing water content in both testing modes. In the 61% water DN-gel, the modulus resembled that of cartilage (FI-mode: DN-gel = 12, cartilage = 17; SS-mode: DN-gel = 4, cartilage = 1.7MPa). Loss angle increased with decreasing water content in fast-impact, but not in slow-sinusoidal deformation. However, loss angle was still much lower than cartilage (FI: DN-gel = 5, cartilage = 11; SS: DN-gel = 10, cartilage = 32°), indicating somewhat less ability to dissipate energy. Overall, results show that it is possible to adapt DN-gel composition to produce dynamic stiffness properties close to normal articular cartilag

A simple environment-dependent overlap potential and Cauchy violation in solid argon

We develop an analytic and environment-dependent interatomic potential for the overlap repulsion in solid argon, based on an approximate treatment of the non-orthogonal Tight-Binding theory for the closed-shell systems. The present model can well reproduce the observed elastic properties of solid argon including Cauchy violation at high pressures, yet very simple. A useful and novel analysis is given to show how the elastic properties are related to the environment-dependence incorporated into a generic pairwise potential. The present study has a close link to the broad field of computational materials science, in which the inclusion of environment dependence in short-ranged repulsive part of a potential model is sometimes crucial in predicting the elastic properties correctly.Comment: 10 pages, 3 figure

The X10 Flare on 2003 October 29: Triggered by Magnetic Reconnection between Counter-Helical Fluxes?

Vector magnetograms taken at Huairou Solar Observing Station (HSOS) and Mees Solar Observatory (MSO) reveal that the super active region (AR) NOAA 10486 was a complex region containing current helicity flux of opposite signs. The main positive sunspots were dominated by negative helicity fields, while positive helicity patches persisted both inside and around the main positive sunspots. Based on a comparison of two days of deduced current helicity density, pronounced changes were noticed which were associated with the occurrence of an X10 flare that peaked at 20:49 UT, 2003 October 29. The average current helicity density (negative) of the main sunspots decreased significantly by about 50. Accordingly, the helicity densities of counter-helical patches (positive) were also found to decay by the same proportion or more. In addition, two hard X-ray (HXR) `footpoints' were observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI} during the flare in the 50-100 keV energy range. The cores of these two HXR footpoints were adjacent to the positions of two patches with positive current helicity which disappeared after the flare. This strongly suggested that the X10 flare on 2003 Oct. 29 resulted from reconnection between magnetic flux tubes having opposite current helicity. Finally, the global decrease of current helicity in AR 10486 by ~50% can be understood as the helicity launched away by the halo coronal mass ejection (CME) associated with the X10 flare.Comment: Solar Physics, 2007, in pres

Approximation Algorithms for Computing Maximin Share Allocations

We study the problem of computing maximin share allocations, a recently introduced fairness notion. Given a set of n agents and a set of goods, the maximin share of an agent is the best she can guarantee to herself, if she is allowed to partition the goods in any way she prefers, into n bundles, and then receive her least desirable bundle. The objective then is to find a partition, where each agent is guaranteed her maximin share. Such allocations do not always exist, hence we resort to approximation algorithms. Our main result is a 2/3-approximation that runs in polynomial time for any number of agents and goods. This improves upon the algorithm of Procaccia and Wang (2014), which is also a 2/3-approximation but runs in polynomial time only for a constant number of agents. To achieve this, we redesign certain parts of the algorithm in Procaccia and Wang (2014), exploiting the construction of carefully selected matchings in a bipartite graph representation of the problem. Furthermore, motivated by the apparent difficulty in establishing lower bounds, we undertake a probabilistic analysis. We prove that in randomly generated instances, maximin share allocations exist with high probability. This can be seen as a justification of previously reported experimental evidence. Finally, we provide further positive results for two special cases arising from previous works. The first is the intriguing case of three agents, where we provide an improved 7/8-approximation. The second case is when all item values belong to {0, 1, 2}, where we obtain an exact algorith

The impact of China's vehicle emissions on regional air quality in 2000 and 2020: a scenario analysis

The number of vehicles in China has been increasing rapidly. We evaluate the impact of current and possible future vehicle emissions from China on Asian air quality. We modify the Regional Emission Inventory in Asia (REAS) for China's road transport sector in 2000 using updated Chinese data for the number of vehicles, annual mileage, and emission factors. We develop two scenarios for 2020: a scenario where emission factors remain the same as they were in 2000 (No-Policy, NoPol), and a scenario where Euro 3 vehicle emission standards are applied to all vehicles (except motorcycles and rural vehicles). The Euro 3 scenario is an approximation of what may be the case in 2020 as, starting in 2008, all new vehicles in China (except motorcycles) were required to meet the Euro 3 emission standards. Using the Weather Research and Forecasting model coupled with Chemistry (WRF/Chem), we examine the regional air quality response to China's vehicle emissions in 2000 and in 2020 for the NoPol and Euro 3 scenarios. We evaluate the 2000 model results with observations in Japan, China, Korea, and Russia. Under NoPol in 2020, emissions of carbon monoxide (CO), nitrogen oxides (NO<sub>x</sub>), non-methane volatile organic compounds (NMVOCs), black carbon (BC), and organic carbon (OC) from China's vehicles more than double compared to the 2000 baseline. If all vehicles meet the Euro 3 regulations in 2020, however, these emissions are reduced by more than 50% relative to NoPol. The implementation of stringent vehicle emission standards leads to a large, simultaneous reduction of the surface ozone (O<sub>3</sub>) mixing ratios and particulate matter (PM<sub>2.5</sub>) concentrations. In the Euro 3 scenario, surface O<sub>3</sub> is reduced by more than 10 ppbv and surface PM<sub>2.5</sub> is reduced by more than 10 μg m<sup>−3</sup> relative to NoPol in Northeast China in all seasons. In spring, surface O<sub>3</sub> mixing ratios and PM<sub>2.5</sub> concentrations in neighboring countries are also reduced by more than 3 ppbv and 1 μg m<sup>−3</sup>, respectively. We find that effective regulation of China's road transport sector will be of significant benefit for air quality both within China and across East Asia as well

Fast algorithm for calculating two-photon absorption spectra

We report a numerical calculation of the two-photon absorption coefficient of electrons in a binding potential using the real-time real-space higher-order difference method. By introducing random vector averaging for the intermediate state, the task of evaluating the two-dimensional time integral is reduced to calculating two one-dimensional integrals. This allows the reduction of the computation load down to the same order as that for the linear response function. The relative advantage of the method compared to the straightforward multi-dimensional time integration is greater for the calculation of non-linear response functions of higher order at higher energy resolution.Comment: 4 pages, 2 figures. It will be published in Phys. Rev. E on 1, March, 199