Algebraic K-theory of quotient stacks

We prove some fundamental results like localization, excision, Nisnevich descent and the Mayer-Vietoris property for equivariant regular blow-up for the equivariant K-theory of schemes with an affine group scheme action. We also show that the equivariant K-theory with finite coefficients is invariant under equivariant vector bundle morphisms. We show that the equivariant homotopy K-theory is invariant under equivariant vector bundle morphisms and satisfies all the above properties, including nil-invariance.Comment: 21 pages, Title changed, Final version, to appear in Annals of K-Theor

Collaborative Learning of Stochastic Bandits over a Social Network

We consider a collaborative online learning paradigm, wherein a group of agents connected through a social network are engaged in playing a stochastic multi-armed bandit game. Each time an agent takes an action, the corresponding reward is instantaneously observed by the agent, as well as its neighbours in the social network. We perform a regret analysis of various policies in this collaborative learning setting. A key finding of this paper is that natural extensions of widely-studied single agent learning policies to the network setting need not perform well in terms of regret. In particular, we identify a class of non-altruistic and individually consistent policies, and argue by deriving regret lower bounds that they are liable to suffer a large regret in the networked setting. We also show that the learning performance can be substantially improved if the agents exploit the structure of the network, and develop a simple learning algorithm based on dominating sets of the network. Specifically, we first consider a star network, which is a common motif in hierarchical social networks, and show analytically that the hub agent can be used as an information sink to expedite learning and improve the overall regret. We also derive networkwide regret bounds for the algorithm applied to general networks. We conduct numerical experiments on a variety of networks to corroborate our analytical results.Comment: 14 Pages, 6 Figure

Long term monitoring of trichloroethylene degradation indicator parameters using sensors

Past operations at Savannah River Site (SRS) have resulted in significant amount of groundwater contamination with trichloroethylene. Natural attenuation of chlorinated solvents via reductive dechlorination is one of the most important processes occurring at SRS, which requires monitoring. Many traditional monitoring techniques require manual sampling and analysis at an onsite or offsite laboratory, which is costly and time consuming. Therefore the need for a system, which can accurately and cost-effectively conduct real-time analysis using automated sensors, is important. There are several characteristics of groundwater like pH, ORP, conductivity and chloride that may be monitored to assess the TCE degradation. To evaluate the effectiveness of the sensors to measure the required parameters, a series of tests were conducted by varying the parameters that can affect the performance of the sensors. Interference by the other ions is neither strong nor permanent but can cause interference during measurement. So a thorough testing of the ISE is necessary to obtain reliable data

Equivariant vector bundles, their derived category and KK-theory on affine schemes

Let $G$ be an affine group scheme over a noetherian commutative ring $R$. We show that every $G$-equivariant vector bundle on an affine toric scheme over $R$ with $G$-action is extended from \Spec(R) for several cases of $R$ and $G$. We show that given two affine schemes with group scheme actions, an equivalence of the equivariant derived categories implies isomorphism of the equivariant $K$-theories as well as equivariant $K'$-theories.Comment: 34 pages, minor corrections, final version, to appear in Annals of K-Theor