A Near-Optimal Sampling Strategy for Sparse Recovery of Polynomial Chaos Expansions

Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations in the parameter space. It was later shown that the choice of sample locations could significantly impact the accuracy of resulting surrogates. This motivated new sampling strategies or design-of-experiment approaches, such as coherence-optimal sampling, which aim at improving the coherence property. In this paper, we propose a sampling strategy that can identify near-optimal sample locations that lead to improvement in local-coherence property and also enhancement of cross-correlation properties of measurement matrices. We provide theoretical motivations for the proposed sampling strategy along with several numerical examples that show that our near-optimal sampling strategy produces substantially more accurate results, compared to other sampling strategies

Thermodynamic geometry of black holes in f(R) gravity

In this paper, we consider three types (static, static charged and rotating charged) of black holes in f(R) gravity. We study the thermodynamical behavior, stability conditions and phase transition of these black holes. It will be shown that, the number and type of phase transition points are related to different parameters, which shows the dependency of stability conditions to these parameters. Also, we extended our study to different thermodynamic geometry methods (Ruppeiner, Weinhold and GTD). Next, we investigate the compatibility of curvature scalar of geothermodynamic methods with phase transition points of the above balck holes. In addition, we point out the effect of different values of spacetime parameters on stability conditions of mentioned black holes.Comment: 45 figures,35 page

Effects of Corruption on Poverty and Economic Growth

Promoting economic growth and poverty reduction have become important in national and international policy framework; however in low-income countries, corruption threatens the global fight against poverty. Therefore, there is a strong correlation between economic performance and a country’s ranking on the corruption indices, however, no causality between poverty and corruption can be derived from this correlation. Since most of the studies which have investigated the link between corruption and poverty may draw conclusions on causality in the form of models that only show correlation, this study is set out to investigate the Granger causal relationship between corruption and poverty as the first objective. It uses dynamic panel system GMM estimators, focuses on capability poverty using human poverty index (HPI) and is based on a sample of 97 countries during 1997-2006. The empirical findings reveal that corruption and poverty go together, with bidirectional causality. Although ASEAN has recorded good economic growth, corruption and poverty are high in the region. This may lead to some doubt as to whether ASEAN countries are outlier. The second objective of this study is to investigate the effects of corruption on long run growth for ASEAN countries and compare it with the other developing countries during 1997-2006 using GMM estimators. The estimated growth equation used in this study is the growth equation popularized by Barro (1991). The basic model is modified to include corruption but as the robustness check in other specifications, additional variables are included. The results of linear growth equation show that corruption increases economic growth both in ASEAN and developing countries and support the idea that in economies with low level of governance, corruption is beneficial for economic growth. Additionally, the empirical evidence reveals a non linear relationship between corruption and growth with the results indicating corruption increases economic growth at low incidence levels of and hampers it at higher level. The results of non linear growth equation also confirm that in economies with low level of governance, small amount of corruption increases growth. This study also traces the transmission channels including investment in physical capital and human capital. While the results of the linear physical capital equation indicate that corruption increases growth through its positive effect on investment in physical capital, the results of nonlinear equation show that the relationship between investment in physical capital and corruption is justified by an inverted U shape function. The results of human capital equation also suggest that corruption hampers growth through its adverse effects on the human capital stock. Overall, the total positive effect of corruption on growth is verified in low level of incidence and low level of governance for ASEAN countries as well as developing countries. Finally the third objective is to study the effects of corruption on poverty for the same countries and in the same time period. The empirical results indicate that in addition to the direct effects of corruption on poverty, it has an indirect effect through economic growth. While economic growth adversely affects poverty, the increased growth that is due to increased corruption is not pro poor and increases poverty

Contextual Bandits with Cross-learning

In the classical contextual bandits problem, in each round $t$, a learner observes some context $c$, chooses some action $a$ to perform, and receives some reward $r_{a,t}(c)$. We consider the variant of this problem where in addition to receiving the reward $r_{a,t}(c)$, the learner also learns the values of $r_{a,t}(c')$ for all other contexts $c'$; i.e., the rewards that would have been achieved by performing that action under different contexts. This variant arises in several strategic settings, such as learning how to bid in non-truthful repeated auctions (in this setting the context is the decision maker's private valuation for each auction). We call this problem the contextual bandits problem with cross-learning. The best algorithms for the classical contextual bandits problem achieve $\tilde{O}(\sqrt{CKT})$ regret against all stationary policies, where $C$ is the number of contexts, $K$ the number of actions, and $T$ the number of rounds. We demonstrate algorithms for the contextual bandits problem with cross-learning that remove the dependence on $C$ and achieve regret $O(\sqrt{KT})$ (when contexts are stochastic with known distribution), $\tilde{O}(K^{1/3}T^{2/3})$ (when contexts are stochastic with unknown distribution), and $\tilde{O}(\sqrt{KT})$ (when contexts are adversarial but rewards are stochastic).Comment: 48 pages, 5 figure