Open string theory and planar algebras

In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real rational functions. These moduli spaces appear naturally in the formulation of open string theory on the projective line. We also show two geometric ways to obtain planar algebras from real algebraic geometry, one based on string topology and one on Gromov-Witten theory. In particular, through the well known relation between planar algebras and subfactors, these results establish a connection between open string theory, real algebraic geometry, and subfactors of von Neumann algebras.Comment: 13 pages, LaTeX, 7 eps figure

Cyclotomic integers, fusion categories, and subfactors

Dimensions of objects in fusion categories are cyclotomic integers, hence number theoretic results have implications in the study of fusion categories and finite depth subfactors. We give two such applications. The first application is determining a complete list of numbers in the interval (2, 76/33) which can occur as the Frobenius-Perron dimension of an object in a fusion category. The smallest number on this list is realized in a new fusion category which is constructed in the appendix written by V. Ostrik, while the others are all realized by known examples. The second application proves that in any family of graphs obtained by adding a 2-valent tree to a fixed graph, either only finitely many graphs are principal graphs of subfactors or the family consists of the A_n or D_n Dynkin diagrams. This result is effective, and we apply it to several families arising in the classification of subfactors of index less then 5.Comment: 47 pages, with an appendix by Victor Ostri

On Haagerup's list of potential principal graphs of subfactors

We show that any graph, in the sequence given by Haagerup in 1991 as that of candidates of principal graphs of subfactors, is not realized as a principal graph except for the smallest two. This settles the remaining case of a previous work of the first author.Comment: 19 page

On intermediate subfactors of Goodman-de la Harpe-Jones subfactors

In this paper we present a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. Motivated by this conjecture, we determine all intermediate subfactors of Goodman-Harpe-Jones subfactors, and as a result we verify that Goodman-Harpe-Jones subfactors verify our conjecture. Our result also gives a negative answer to a question motivated by a conjecture of Aschbacher-Guralnick.Comment: To appear in Comm. Math. Phy

Quantum subgroups of the Haagerup fusion categories

We answer three related questions concerning the Haagerup subfactor and its even parts, the Haagerup fusion categories. Namely we find all simple module categories over each of the Haagerup fusion categories (in other words, we find the `"quantum subgroups" in the sense of Ocneanu), we find all subfactors whose principal even part is one of the Haagerup fusion categories, and we compute the Brauer-Picard groupoid of Morita equivalences of the Haagerup fusion categories. In addition to the two even parts of the Haagerup subfactor, there is exactly one more fusion category which is Morita equivalent to each of them. This third fusion category has six simple objects and the same fusion rules as one of the even parts of the Haagerup subfactor, but has not previously appeared in the literature. We also find the full lattice of intermediate subfactors for every subfactor whose even part is one of these three fusion categories, and we discuss how our results generalize to Izumi subfactors.Comment: Final version. 40 pages, many figure

Two phase 3 trials of inclisiran in patients with elevated LDL cholesterol

BACKGROUND Inclisiran inhibits hepatic synthesis of proprotein convertase subtilisin-kexin type 9. Previous studies suggest that inclisiran might provide sustained reductions in low-density lipoprotein (LDL) cholesterol levels with infrequent dosing. METHODS We enrolled patients with atherosclerotic cardiovascular disease (ORION-10 trial) and patients with atherosclerotic cardiovascular disease or an atherosclerotic cardiovascular disease risk equivalent (ORION-11 trial) who had elevated LDL cholesterol levels despite receiving statin therapy at the maximum tolerated dose. Patients were randomly assigned in a 1:1 ratio to receive either inclisiran (284 mg) or placebo, administered by subcutaneous injection on day 1, day 90, and every 6 months thereafter over a period of 540 days. The coprimary end points in each trial were the placebo-corrected percentage change in LDL cholesterol level from baseline to day 510 and the time-adjusted percentage change in LDL cholesterol level from baseline after day 90 and up to day 540. RESULTS A total of 1561 and 1617 patients underwent randomization in the ORION-10 and ORION-11 trials, respectively. Mean (SD) LDL cholesterol levels at baseline were 104.738.3 mg per deciliter (2.710.99 mmol per liter) and 105.539.1 mg per deciliter (2.731.01 mmol per liter), respectively. At day 510, inclisiran reduced LDL cholesterol levels by 52.3% (95% confidence interval [CI], 48.8 to 55.7) in the ORION-10 trial and by 49.9% (95% CI, 46.6 to 53.1) in the ORION-11 trial, with corresponding time-adjusted reductions of 53.8% (95% CI, 51.3 to 56.2) and 49.2% (95% CI, 46.8 to 51.6) (P<0.001 for all comparisons vs. placebo). Adverse events were generally similar in the inclisiran and placebo groups in each trial, although injection-site adverse events were more frequent with inclisiran than with placebo (2.6% vs. 0.9% in the ORION-10 trial and 4.7% vs. 0.5% in the ORION-11 trial); such reactions were generally mild, and none were severe or persistent. CONCLUSIONS Reductions in LDL cholesterol levels of approximately 50% were obtained with inclisiran, administered subcutaneously every 6 months. More injection-site adverse events occurred with inclisiran than with placebo

Constructing the extended Haagerup planar algebra

We construct a new subfactor planar algebra, and as a corollary a new subfactor, with the `extended Haagerup' principal graph pair. This completes the classification of irreducible amenable subfactors with index in the range $(4,3+\sqrt{3})$, which was initiated by Haagerup in 1993. We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein theoretic description, and a description as a subalgebra generated by a certain element in the graph planar algebra of its principal graph. In the skein theoretic description there is an explicit algorithm for evaluating closed diagrams. This evaluation algorithm is unusual because intermediate steps may increase the number of generators in a diagram.Comment: 45 pages (final version; improved introduction

Evolutionary Mechanisms of Long-Term Genome Diversification Associated With Niche Partitioning in Marine Picocyanobacteria.

Marine picocyanobacteria of the genera Prochlorococcus and Synechococcus are the most abundant photosynthetic organisms on Earth, an ecological success thought to be linked to the differential partitioning of distinct ecotypes into specific ecological niches. However, the underlying processes that governed the diversification of these microorganisms and the appearance of niche-related phenotypic traits are just starting to be elucidated. Here, by comparing 81 genomes, including 34 new Synechococcus, we explored the evolutionary processes that shaped the genomic diversity of picocyanobacteria. Time-calibration of a core-protein tree showed that gene gain/loss occurred at an unexpectedly low rate between the different lineages, with for instance 5.6 genes gained per million years (My) for the major Synechococcus lineage (sub-cluster 5.1), among which only 0.71/My have been fixed in the long term. Gene content comparisons revealed a number of candidates involved in nutrient adaptation, a large proportion of which are located in genomic islands shared between either closely or more distantly related strains, as identified using an original network construction approach. Interestingly, strains representative of the different ecotypes co-occurring in phosphorus-depleted waters (Synechococcus clades III, WPC1, and sub-cluster 5.3) were shown to display different adaptation strategies to this limitation. In contrast, we found few genes potentially involved in adaptation to temperature when comparing cold and warm thermotypes. Indeed, comparison of core protein sequences highlighted variants specific to cold thermotypes, notably involved in carotenoid biosynthesis and the oxidative stress response, revealing that long-term adaptation to thermal niches relies on amino acid substitutions rather than on gene content variation. Altogether, this study not only deciphers the respective roles of gene gains/losses and sequence variation but also uncovers numerous gene candidates likely involved in niche partitioning of two key members of the marine phytoplankton

Spatial Bistability Generates hunchback Expression Sharpness in the Drosophila Embryo

During embryonic development, the positional information provided by concentration gradients of maternal factors directs pattern formation by providing spatially dependent cues for gene expression. In the fruit fly, Drosophila melanogaster, a classic example of this is the sharp on–off activation of the hunchback (hb) gene at midembryo, in response to local concentrations of the smooth anterior–posterior Bicoid (Bcd) gradient. The regulatory region for hb contains multiple binding sites for the Bcd protein as well as multiple binding sites for the Hb protein. Some previous studies have suggested that Bcd is sufficient for properly sharpened Hb expression, yet other evidence suggests a need for additional regulation. We experimentally quantified the dynamics of hb gene expression in flies that were wild-type, were mutant for hb self-regulation or Bcd binding, or contained an artificial promoter construct consisting of six Bcd and two Hb sites. In addition to these experiments, we developed a reaction–diffusion model of hb transcription, with Bcd cooperative binding and hb self-regulation, and used Zero Eigenvalue Analysis to look for multiple stationary states in the reaction network. Our model reproduces the hb developmental dynamics and correctly predicts the mutant patterns. Analysis of our model indicates that the Hb sharpness can be produced by spatial bistability, in which hb self-regulation produces two stable levels of expression. In the absence of self-regulation, the bistable behavior vanishes and Hb sharpness is disrupted. Bcd cooperative binding affects the position where bistability occurs but is not itself sufficient for a sharp Hb pattern. Our results show that the control of Hb sharpness and positioning, by hb self-regulation and Bcd cooperativity, respectively, are separate processes that can be altered independently. Our model, which matches the changes in Hb position and sharpness observed in different experiments, provides a theoretical framework for understanding the data and in particular indicates that spatial bistability can play a central role in threshold-dependent reading mechanisms of positional information

The SPIRAL radioactive ion beam facility

This document describes the scientific goals as well as the technical choices of the SPIRAL project (Système de Production d'Ions Radioactifs et d'Accélération en Ligne)