Comparing and characterizing some constructions of canonical bases from Coxeter systems

The Iwahori-Hecke algebra $\mathcal{H}$ of a Coxeter system $(W,S)$ has a "standard basis" indexed by the elements of $W$ and a "bar involution" given by a certain antilinear map. Together, these form an example of what Webster calls a pre-canonical structure, relative to which the well-known Kazhdan-Lusztig basis of $\mathcal{H}$ is a canonical basis. Lusztig and Vogan have defined a representation of a modified Iwahori-Hecke algebra on the free $\mathbb{Z}[v,v^{-1}]$-module generated by the set of twisted involutions in $W$, and shown that this module has a unique pre-canonical structure satisfying a certain compatibility condition, which admits its own canonical basis which can be viewed as a generalization of the Kazhdan-Lusztig basis. One can modify the parameters defining Lusztig and Vogan's module to obtain other pre-canonical structures, each of which admits a unique canonical basis indexed by twisted involutions. We classify all of the pre-canonical structures which arise in this fashion, and explain the relationships between their resulting canonical bases. While some of these canonical bases are related in a trivial fashion to Lusztig and Vogan's construction, others appear to have no simple relation to what has been previously studied. Along the way, we also clarify the differences between Webster's notion of a canonical basis and the related concepts of an IC basis and a $P$-kernel.Comment: 32 pages; v2: additional discussion of relationship between canonical bases, IC bases, and P-kernels; v3: minor revisions; v4: a few corrections and updated references, final versio

On the Commutative Equivalence of Context-Free Languages

The problem of the commutative equivalence of context-free and regular languages is studied. In particular conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

MiR-31 modulates dystrophin expression: New implications for Duchenne muscular dystrophy therapy

Duchenne muscular dystrophy (DMD)--which is caused by mutations in the dystrophin gene-is one of the most severe myopathies. Among therapeutic strategies, exon skipping allows the rescue of dystrophin synthesis through the production of a shorter but functional messenger RNA. Here, we report the identification of a microRNA--miR-31--that represses dystrophin expression by targeting its 3' untranslated region. In human DMD myoblasts treated with exon skipping, we demonstrate that miR-31 inhibition increases dystrophin rescue. These results indicate that interfering with miR-31 activity can provide an ameliorating strategy for those DMD therapies that are aimed at efficiently recovering dystrophin synthesis

2-(2-thienyl)-5,6-dihydroxy-4-carboxypyrimidines as inhibitors of the hepatitis C virus NS5B polymerase: Discovery, SAR, modeling, and mutagenesis

Infections caused by hepatitis C virus (HCV) are a significant world health problem for which novel therapies are in urgent demand. The polymerase of HCV is responsible for the replication of viral RNA. We recently disclosed dihydroxypyrimidine carboxylates 2 as novel, reversible inhibitors of the HCV NS5B polymerase. This series was further developed into 5,6-dihydroxy-2-(2- thienyl)pyrimidine-4-carboxylic acids such as 34 (EC50 9.3 \u3bcM), which now show activity in the cell-based HCV replication assay. The structure-activity relationship of these inhibitors is discussed in the context of their physicochemical properties and of the polymerase crystal structure. We also report the results of mutagenesis experiments which support the proposed binding model, which involves pyrophosphate-like chelation of the active site Mg ions