Open-string vertex algebras, tensor categories and operads

We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the notions of vertex algebra and of conformal vertex algebra. Given an open-string vertex algebra, we show that there exists a vertex algebra, which we call the ``meromorphic center,'' inside the original algebra such that the original algebra yields a module and also an intertwining operator for the meromorphic center. This result gives us a general method for constructing open-string vertex algebras. Besides obvious examples obtained from associative algebras and vertex (super)algebras, we give a nontrivial example constructed from the minimal model of central charge c=1/2. We establish an equivalence between the associative algebras in the braided tensor category of modules for a suitable vertex operator algebra and the grading-restricted conformal open-string vertex algebras containing a vertex operator algebra isomorphic to the given vertex operator algebra. We also give a geometric and operadic formulation of the notion of grading-restricted conformal open-string vertex algebra, we prove two isomorphism theorems, and in particular, we show that such an algebra gives a projective algebra over what we call the ``Swiss-cheese partial operad.''Comment: 53 page

Roles of reconstituted high-density lipoprotein nanoparticles in cardiovascular disease: A new paradigm for drug discovery

Epidemiological results revealed that there is an inverse correlation between high-density lipoprotein (HDL) cholesterol levels and risks of atherosclerotic cardiovascular disease (ASCVD). Mounting evidence supports that HDLs are atheroprotective, therefore, many therapeutic approaches have been developed to increase HDL cholesterol (HDL-C) levels. Nevertheless, HDL-raising therapies, such as cholesteryl ester transfer protein (CETP) inhibitors, failed to ameliorate cardiovascular outcomes in clinical trials, thereby casting doubt on the treatment of cardiovascular disease (CVD) by increasing HDL-C levels. Therefore, HDL-targeted interventional studies were shifted to increasing the number of HDL particles capable of promoting ATP-binding cassette transporter A1 (ABCA1)-mediated cholesterol efflux. One such approach was the development of reconstituted HDL (rHDL) particles that promote ABCA1-mediated cholesterol efflux from lipid-enriched macrophages. Here, we explore the manipulation of rHDL nanoparticles as a strategy for the treatment of CVD. In addition, we discuss technological capabilities and the challenge of relating preclinical in vivo mice research to clinical studies. Finally, by drawing lessons from developing rHDL nanoparticles, we also incorporate the viabilities and advantages of the development of a molecular imaging probe with HDL nanoparticles when applied to ASCVD, as well as gaps in technology and knowledge required for putting the HDL-targeted therapeutics into full gear