Exact Post-Selection Inference for Sequential Regression Procedures

We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to perform valid inference after any selection event that can be characterized as y falling into a polyhedral set. This framework allows us to derive conditional (post-selection) hypothesis tests at any step of forward stepwise or least angle regression, or any step along the lasso regularization path, because, as it turns out, selection events for these procedures can be expressed as polyhedral constraints on y. The p-values associated with these tests are exactly uniform under the null distribution, in finite samples, yielding exact type I error control. The tests can also be inverted to produce confidence intervals for appropriate underlying regression parameters. The R package "selectiveInference", freely available on the CRAN repository, implements the new inference tools described in this paper.Comment: 26 pages, 5 figure

Hidden exceptional symmetry in the pure spinor superstring

The pure spinor formulation of superstring theory includes an interacting sector of central charge $c_{\lambda}=22$, which can be realized as a curved $\beta\gamma$ system on the cone over the orthogonal Grassmannian $\text{OG}^{+}(5,10)$. We find that the spectrum of the $\beta\gamma$ system organizes into representations of the $\mathfrak{g}=\mathfrak{e}_6$ affine algebra at level $-3$, whose $\mathfrak{so}(10)_{-3}\oplus {\mathfrak u}(1)_{-4}$ subalgebra encodes the rotational and ghost symmetries of the system. As a consequence, the pure spinor partition function decomposes as a sum of affine $\mathfrak{e}_6$ characters. We interpret this as an instance of a more general pattern of enhancements in curved $\beta\gamma$ systems, which also includes the cases $\mathfrak{g}=\mathfrak{so}(8)$ and $\mathfrak{e}_7$, corresponding to target spaces that are cones over the complex Grassmannian $\text{Gr}(2,4)$ and the complex Cayley plane $\mathbb{OP}^2$. We identify these curved $\beta\gamma$ systems with the chiral algebras of certain $2d$ $(0,2)$ CFTs arising from twisted compactification of 4d $\mathcal{N}=2$ SCFTs on $S^2$.Comment: 8 pages, 1 figure; v2: added references, minor update

HST/WFC3 Observations of an Off-Nuclear Superbubble in Arp 220

We present a high spatial resolution optical and infrared study of the circumnuclear region in Arp 220, a late-stage galaxy merger. Narrowband imaging using HST/WFC3 has resolved the previously observed peak in H$\alpha$+[NII] emission into a bubble-shaped feature. This feature measures 1.6" in diameter, or 600 pc, and is only 1" northwest of the western nucleus. The bubble is aligned with the western nucleus and the large-scale outflow axis seen in X-rays. We explore several possibilities for the bubble origin, including a jet or outflow from a hidden active galactic nucleus (AGN), outflows from high levels of star formation within the few hundred pc nuclear gas disk, or an ultraluminous X-ray source. An obscured AGN or high levels of star formation within the inner $\sim$100 pc of the nuclei are favored based on the alignment of the bubble and energetics arguments.Comment: Accepted for publication in ApJ. 12 pages, 10 figure