Comparing the EPA Indoor Air Quality Personal Computer Model and Field Data

The authors recommend caution in using an EPA model for reconstructing past exposure events as well as for predicting future exposures

Sampled forms of functional PCA in reproducing kernel Hilbert spaces

We consider the sampling problem for functional PCA (fPCA), where the simplest example is the case of taking time samples of the underlying functional components. More generally, we model the sampling operation as a continuous linear map from $\mathcal{H}$ to $\mathbb{R}^m$, where the functional components to lie in some Hilbert subspace $\mathcal{H}$ of $L^2$, such as a reproducing kernel Hilbert space of smooth functions. This model includes time and frequency sampling as special cases. In contrast to classical approach in fPCA in which access to entire functions is assumed, having a limited number m of functional samples places limitations on the performance of statistical procedures. We study these effects by analyzing the rate of convergence of an M-estimator for the subspace spanned by the leading components in a multi-spiked covariance model. The estimator takes the form of regularized PCA, and hence is computationally attractive. We analyze the behavior of this estimator within a nonasymptotic framework, and provide bounds that hold with high probability as a function of the number of statistical samples n and the number of functional samples m. We also derive lower bounds showing that the rates obtained are minimax optimal.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1033 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On Exactly Marginal Deformations Dual to BB-Field Moduli of IIB Theory on SE5_5

The complex dimension of the space of exactly marginal deformations for quiver CFTs dual to IIB theory compactified on $Y^{p,q}$ is known to be generically three. Simple general formulas already exist for two of the exactly marginal directions in the space of couplings, one of which corresponds to the sum of the (inverse squared of) gauge couplings, and the other to the $\beta$-deformation. Here we identify the third exactly marginal direction, which is dual to the modulus $\int B_{2}$ on the gravity side. This identification leads to a relation between the field theory gauge couplings and the vacuum expectation value of the gravity modulus that we further support by a computation related to the chiral anomaly induced by added fractional branes. We also present a simple algorithm for finding similar exactly marginal directions in any CFT described by brane tiling, and demonstrate it for the quiver CFTs dual to IIB theory compactified on $L^{1,5,2}$ and the Suspended Pinch Point.Comment: 28 pages, JHEP style. v2: minor corrections, added references and acknowledgements. v3: a number of speculative comments regarding the application of the Konishi anomaly equation to our problem are removed. v4: the proposal in Eq. (2.4) added back as a conjectur