Algorithms for Highly Symmetric Linear and Integer Programs

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of lower dimension. Combining this approach with knowledge of the geometry of feasible integer solutions yields an algorithm for solving highly symmetric integer linear programs which only takes time which is linear in the number of constraints and quadratic in the dimension.Comment: 21 pages, 1 figure; some references and further comments added, title slightly change

Templates for Convex Cone Problems with Applications to Sparse Signal Recovery

This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic formulation of the problem; second, determine its dual; third, apply smoothing; and fourth, solve using an optimal first-order method. A merit of this approach is its flexibility: for example, all compressed sensing problems can be solved via this approach. These include models with objective functionals such as the total-variation norm, ||Wx||_1 where W is arbitrary, or a combination thereof. In addition, the paper also introduces a number of technical contributions such as a novel continuation scheme, a novel approach for controlling the step size, and some new results showing that the smooth and unsmoothed problems are sometimes formally equivalent. Combined with our framework, these lead to novel, stable and computationally efficient algorithms. For instance, our general implementation is competitive with state-of-the-art methods for solving intensively studied problems such as the LASSO. Further, numerical experiments show that one can solve the Dantzig selector problem, for which no efficient large-scale solvers exist, in a few hundred iterations. Finally, the paper is accompanied with a software release. This software is not a single, monolithic solver; rather, it is a suite of programs and routines designed to serve as building blocks for constructing complete algorithms.Comment: The TFOCS software is available at http://tfocs.stanford.edu This version has updated reference

Manipulating Scrip Systems: Sybils and Collusion

Game-theoretic analyses of distributed and peer-to-peer systems typically use the Nash equilibrium solution concept, but this explicitly excludes the possibility of strategic behavior involving more than one agent. We examine the effects of two types of strategic behavior involving more than one agent, sybils and collusion, in the context of scrip systems where agents provide each other with service in exchange for scrip. Sybils make an agent more likely to be chosen to provide service, which generally makes it harder for agents without sybils to earn money and decreases social welfare. Surprisingly, in certain circumstances it is possible for sybils to make all agents better off. While collusion is generally bad, in the context of scrip systems it actually tends to make all agents better off, not merely those who collude. These results also provide insight into the effects of allowing agents to advertise and loan money. While many extensions of Nash equilibrium have been proposed that address collusion and other issues relevant to distributed and peer-to-peer systems, our results show that none of them adequately address the issues raised by sybils and collusion in scrip systems.Comment: 20 pages, 5 figures. To appear in the Proceedings of The First Conference on Auctions, Market Mechanisms and Their Applications (AMMA '09

Evolution of density perturbations in a realistic universe

Prompted by the recent more precise determination of the basic cosmological parameters and growing evidence that the matter-energy content of the universe is now dominated by dark energy and dark matter we present the general solution of the equation that describes the evolution of density perturbations in the linear approximation. It turns out that as in the standard CDM model the density perturbations grow very slowly during the radiation dominated epoch and their amplitude increases by a factor of about 4000 in the matter and later dark energy dominated epoch of expansion of the universe.Comment: 19 pages, 4 figure

Explaining participation in regional transnational social movement organizations

Since the late 1980s, governments have focused intensely on formalizing political and economic relationships within regions. There has also been a concurrent rise in transnational, regional level organizing among social movement activists globally, suggesting the regionalization of 'global civil society.' However, opportunities for participation in transnational associations vary widely across countries. In this article, we examine the influence of international (both global and regional) institutional contexts, citizen participation in international society, and national level factors on varying levels of participation in regional transnational social movement organizations (TSMOs). We use negative binomial regression to examine relationships among these factors at three time points: 1980, 1990, and 2000. We find that in the early time period, citizen network connections to international society facilitated the formation of and participation in regionally organized TSMOs. Over time, however, regional and global institutional contexts were more predictive of participation in regional TSMOs than were international network ties. Our analysis also uncovered how qualitatively different forms of regionalism translated into significantly different levels of TSMO regionalization. In Europe, where the regional institutional structure is more elaborated than elsewhere in the world, the number of regional TSMOs in which citizens participated greatly outpaced that found elsewhere. Irrespective of international, institutional factors, however, state-level features remained crucial to explaining the development of regional TSMO sectors and the variable levels of participation in them. Citizens in states with restrictions on political rights and civil liberties had significantly lower participation in these organizations in 1990 and 2000. Even so, over time, citizens in states with more ties to global and regional multilateral processes found more ways to overcome this disadvantage and strengthen their participation in regional, transnational civil society. © 2007 SAGE Publications

Thoracic Aortic Calcium Versus Coronary Artery Calcium for the Prediction of Coronary Heart Disease and Cardiovascular Disease Events

ObjectivesThis study compared the ability of coronary artery calcium (CAC) and thoracic aortic calcium (TAC) to predict coronary heart disease (CHD) and cardiovascular disease (CVD) events.BackgroundCoronary artery calcium has been shown to strongly predict CHD and CVD events, but it is unknown whether TAC, also measured within a single cardiac computed tomography (CT) scan, is of further value in predicting events.MethodsA total of 2,303 asymptomatic adults (mean age 55.7 years, 38% female) with CT scans were followed up for 4.4 years for CHD (myocardial infarction, cardiac death, or late revascularizations) and CVD (CHD plus stroke). Cox regression, adjusted for Framingham risk score (FRS), examined the relation of Agatston CAC and TAC categories, and log-transformed CAC and TAC with the incidence of CHD and CVD events and receiver-operator characteristic (ROC) curves tested whether TAC improved prediction of events over CAC and FRS.ResultsA total of 53% of subjects had Agatston CAC scores of 0; 8% 1 to 9; 19% 10 to 99; 12% 100 to 399; and 8% ≥400. For TAC, proportions were 69%, 5%, 12%, 8%, and 7%, respectively; 41 subjects (1.8%) experienced CHD and 47 (2.0%) CVD events. The FRS-adjusted hazard ratios (HR) across increasing CAC groups (relative to <10) ranged from 3.7 (p = 0.04) to 19.6 (p < 0.001) for CHD and from 2.8 (p = 0.07) to 13.1 (p < 0.001) for CVD events; only TAC scores of 100 to 399 predicted CHD and CVD (HR: 3.0, p = 0.008, and HR: 2.3, p = 0.04, respectively); these risks were attenuated after accounting for CAC. Findings were consistent when using log-transformed CAC and TAC Agatston and volume scores. The ROC curve analyses showed CAC predicted CHD and CVD events over FRS alone (p < 0.01); however, TAC did not further add to predicting events over FRS or CAC.ConclusionsThis study found that CAC, but not TAC, is strongly related to CHD and CVD events. Moreover, TAC does not further improve event prediction over CAC

Caloric Curves and Nuclear Expansion

Nuclear caloric curves have been analyzed using an expanding Fermi gas hypothesis to extract average nuclear densities. In this approach the observed flattening of the caloric curves reflects progressively increasing expansion with increasing excitation energy. This expansion results in a corresponding decrease in the density and Fermi energy of the excited system. For nuclei of medium to heavy mass apparent densities ~ 0.4 rho_0 are reached at the higher excitation energies.Comment: 4 pages, 3 figure

Three-body non-additive forces between spin-polarized alkali atoms

Three-body non-additive forces in systems of three spin-polarized alkali atoms (Li, Na, K, Rb and Cs) are investigated using high-level ab initio calculations. The non-additive forces are found to be large, especially near the equilateral equilibrium geometries. For Li, they increase the three-atom potential well depth by a factor of 4 and reduce the equilibrium interatomic distance by 0.9 A. The non-additive forces originate principally from chemical bonding arising from sp mixing effects.Comment: 4 pages, 3 figures (in 5 files

Regulation and role of differential ethylene biosynthesis in gravistimulated Antirrhinum majus L. cut flower stems

Gravistimulation induced differential ethylene production in Antirrhinum majus L. cut flower stems with highest levels in the lower halves of the gravistimulated stems. Expression levels of three different 1-aminocyclopropane-1-carboxylate (ACC) synthase (ACS) genes, an ACC oxidase (ACO) and an ethylene receptor (ETR/ERS homolog) gene were studied in the bending zone after 9 h of gravistimulation. One of the ACS genes (Am-ACS3) was abundantly expressed in the lower halves but not in the upper halves of gravistimulated stems. This strongly suggests that Am-ACS3 is responsible for the observed differential ethylene production in gravistimulated stems. Am-ACO and Am-ETR/ERS gene expression was increased in both the lower and upper halves of gravistimulated stems, suggesting that they play no role in differential ethylene production. When gravistimulation was performed in an environment enriched with either 20 µL/L ethylene or 100 nL/L 1-methylcyclopropene (1-MCP), a slight stimulation of bending by 1-MCP and a slight inhibition of bending by ethylene were observed. The regulation and role of ethylene in gravitropism of cut snapdragon flowering stems is discussed

Stroke-prone salt-sensitive spontaneously hypertensive rats show higher susceptibility to spreading depolarization (SD) and altered hemodynamic responses to SD

Spreading depolarization (SD) occurs in a plethora of clinical conditions including migraine aura, delayed ischemia after subarachnoid hemorrhage and malignant hemispheric stroke. It describes waves of near-breakdown of ion homeostasis, particularly Na(+) homeostasis in brain gray matter. SD induces tone alterations in resistance vessels, causing either hyperperfusion in healthy tissue; or hypoperfusion (inverse hemodynamic response = spreading ischemia) in tissue at risk. Observations from mice with genetic dysfunction of the ATP1A2-encoded α(2)-isoform of Na(+)/K(+)-ATPase (α(2)NaKA) suggest a mechanistic link between (1) SD, (2) vascular dysfunction, and (3) salt-sensitive hypertension via α(2)NaKA. Thus, α(2)NaKA-dysfunctional mice are more susceptible to SD and show a shift toward more inverse hemodynamic responses. α(2)NaKA-dysfunctional patients suffer from familial hemiplegic migraine type 2, a Mendelian model disease of SD. α(2)NaKA-dysfunctional mice are also a genetic model of salt-sensitive hypertension. To determine whether SD thresholds and hemodynamic responses are also altered in other genetic models of salt-sensitive hypertension, we examined these variables in stroke-prone spontaneously hypertensive rats (SHRsp). Compared with Wistar Kyoto control rats, we found in SHRsp that electrical SD threshold was significantly reduced, propagation speed was increased, and inverse hemodynamic responses were prolonged. These results may have relevance to both migraine with aura and stroke