A Note on Odd Periodic derived Hall algebras

Let $m$ be an odd positive integer and $D_m(\mathcal {A})$ be the $m$-periodic derived category of a finitary hereditary abelian category $\mathcal {A}$. In this note, we prove that there is an embedding of algebras from the derived Hall algebra of $D_m(\mathcal {A})$ defined by Xu-Chen [12] to the extended derived Hall algebra of $D_m(\mathcal {A})$ defined in [15]. This homomorphism is given on basis elements, rather than just on generating elements, and thus it improves the main result of [5].Comment: 13 page

The role of randomization inference in unraveling individual treatment effects in clinical trials: Application to HIV vaccine trials

Randomization inference is a powerful tool in early phase vaccine trials to estimate the causal effect of a regimen against a placebo or another regimen. Traditionally, randomization-based inference often focuses on testing either Fisher's sharp null hypothesis of no treatment effect for any unit or Neyman's weak null hypothesis of no sample average treatment effect. Many recent efforts have explored conducting exact randomization-based inference for other summaries of the treatment effect profile, for instance, quantiles of the treatment effect distribution function. In this article, we systematically review methods that conduct exact, randomization-based inference for quantiles of individual treatment effects (ITEs) and extend some results by incorporating auxiliary information often available in a vaccine trial. These methods are suitable for four scenarios: (i) a randomized controlled trial (RCT) where the potential outcomes under one regimen are constant; (ii) an RCT with no restriction on any potential outcomes; (iii) an RCT with some user-specified bounds on potential outcomes; and (iv) a matched study comparing two non-randomized, possibly confounded treatment arms. We then conduct two extensive simulation studies, one comparing the performance of each method in many practical clinical settings and the other evaluating the usefulness of the methods in ranking and advancing experimental therapies. We apply these methods to an early-phase clinical trail, HIV Vaccine Trials Network Study 086 (HVTN 086), to showcase the usefulness of the methods

Hydrogenation and Hydro-Carbonation and Etching of Single-Walled Carbon Nanotubes

We present a systematic experimental investigation of the reactions between hydrogen plasma and single-walled carbon nanotubes (SWNTs) at various temperatures. Microscopy, infrared (IR) and Raman spectroscopy and electrical transport measurements are carried out to investigate the properties of SWNTs after hydrogenation. Structural deformations, drastically reduced electrical conductance and increased semiconducting nature of SWNTs upon sidewall hydrogenation are observed. These changes are reversible upon thermal annealing at 500C via dehydrogenation. Harsh plasma or high temperature reactions lead to etching of nanotube likely via hydro-carbonation. Smaller SWNTs are markedly less stable against hydro-carbonation than larger tubes. The results are fundamental and may have implications to basic and practical applications including hydrogen storage, sensing, band-gap engineering for novel electronics and new methods of manipulation, functionalization and etching of nanotubes.Comment: 3 pages, 4 figure