Trimming for Bounds on Treatment Effects with Missing Outcomes

Empirical researchers routinely encounter sample selection bias whereby 1) the regressor of interest is assumed to be exogenous, 2) the dependent variable is missing in a potentially non-random manner, 3) the dependent variable is characterized by an unbounded (or very large) support, and 4) it is unknown which variables directly affect sample selection but not the outcome. This paper proposes a simple and intuitive bounding procedure that can be used in this context. The proposed trimming procedure yields the tightest bounds on average treatment effects consistent with the observed data. The key assumption is a monotonicity restriction on how the assignment to treatment effects selection -- a restriction that is implicitly assumed in standard formulations of the sample selection problem.

Finite reflection groups and graph norms

Given a graph $H$ on vertex set $\{1,2,\cdots, n\}$ and a function $f:[0,1]^2 \rightarrow \mathbb{R}$, define \begin{align*} \|f\|_{H}:=\left\vert\int \prod_{ij\in E(H)}f(x_i,x_j)d\mu^{|V(H)|}\right\vert^{1/|E(H)|}, \end{align*} where $\mu$ is the Lebesgue measure on $[0,1]$. We say that $H$ is norming if $\|\cdot\|_H$ is a semi-norm. A similar notion $\|\cdot\|_{r(H)}$ is defined by $\|f\|_{r(H)}:=\||f|\|_{H}$ and $H$ is said to be weakly norming if $\|\cdot\|_{r(H)}$ is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. We demonstrate that any graph whose edges percolate in an appropriate way under the action of a certain natural family of automorphisms is weakly norming. This result includes all previously known examples of weakly norming graphs, but also allows us to identify a much broader class arising from finite reflection groups. We include several applications of our results. In particular, we define and compare a number of generalisations of Gowers' octahedral norms and we prove some new instances of Sidorenko's conjecture.Comment: 29 page

Sidorenko's conjecture for higher tree decompositions

This is a companion note to our paper 'Some advances on Sidorenko's conjecture', elaborating on a remark in that paper that the approach which proves Sidorenko's conjecture for strongly tree-decomposable graphs may be extended to a broader class, comparable to that given in work of Szegedy, through further iteration.Comment: 7 pages, unpublished not

Reaction of N,N-Dimethyltryptamine with Dichloromethane Under Common Experimental Conditions.

A large number of clinically used drugs and experimental pharmaceuticals possess the N,N-dimethyltryptamine (DMT) structural core. Previous reports have described the reaction of this motif with dichloromethane (DCM), a common laboratory solvent used during extraction and purification, leading to the formation of an undesired quaternary ammonium salt byproduct. However, the kinetics of this reaction under various conditions have not been thoroughly described. Here, we report a series of experiments designed to simulate the exposure of DMT to DCM that would take place during extraction from plant material, biphasic aqueous work-up, or column chromatography purification. We find that the quaternary ammonium salt byproduct forms at an exceedingly slow rate, only accumulates to a significant extent upon prolonged exposure of DMT to DCM, and is readily extracted into water. Our results suggest that DMT can be exposed to DCM under conditions where contact times are limited (<30 min) with minimal risk of degradation and that this byproduct is not observed following aqueous extraction. However, alternative solvents should be considered when the experimental conditions require longer contact times. Our work has important implications for preparing a wide-range of pharmaceuticals bearing the DMT structural motif in high yields and purities

Vacuum quark condensate, chiral Lagrangian, and Bose-Einstein statistics

In a series of articles it was recently claimed that the quantum chromodynamic (QCD) condensates are not the properties of the vacuum but of the hadrons and are confined inside them. We point out that this claim is incompatible with the chiral Lagrangian and Bose-Einstein statistics of the Goldstone bosons (pions) in chiral limit and conclude that the quark condensate must be the property of the QCD vacuum.Comment: 4 Pages, To appear in Phys. Lett.