63 research outputs found

    The classification of subfactors of index at most 5

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    A subfactor is an inclusion of von Neumann algebras with trivial centers. The simplest example comes from the fixed points of a group action , and subfactors can be thought of as fixed points of more general group-like algebraic structures. These algebraic structures are closely related to tensor categories and have played important roles in knot theory, quantum groups, statistical mechanics, and topological quantum field theory. There is a measure of size of a subfactor, called the index. Remarkably, the values of the index below 4 are quantized, which suggests that it may be possible to classify subfactors of small index. Subfactors of index at most 4 were classified in the 1980s and early 1990s. The possible index values above 4 are not quantized, but once you exclude a certain family, it turns out that again the possibilities are quantized. Recently, the classification of subfactors has been extended up to index 5, and (outside of the infinite families) there are only 10 subfactors of index between 4 and 5. We give a summary of the key ideas in this classification and discuss what is known about these special small subfactors.The first author was supported by the NSF under Grant No. DMS-0301173 The second author was supported by the Australian Research Council under the Discovery Early Career Researcher Award DE120100232, and Discovery Project DP140100732 The third author was supported by a NSF Postdoctoral Fellowship at Columbia University. All authors were supported by DARPA grants HR0011-11-1-0001 and HR0011-12-1-0009

    Structure and Efficiency in Bacterial Photosynthetic Light Harvesting

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    Photosynthetic organisms use networks of chromophores to absorb sunlight and deliver the energy to reaction centres, where charge separation triggers a cascade of chemical steps to store the energy. We present a detailed model of the light-harvesting complexes in purple bacteria, including explicit interaction with sunlight; energy loss through radiative and non-radiative processes; and dephasing and thermalizing effects of coupling to a vibrational bath. An important feature of the model is that we capture the effect of slow vibrational modes by introducing time-dependent disorder. Our model describes the experimentally observed high efficiency of light harvesting, despite the absence of long-range quantum coherence. The one-exciton part of the quantum state fluctuates due to slow vibrational changes, but remains highly mixed at all times. This lack of long-range coherence suggests a relatively minor role for structure in determining the efficiency of bacterial light harvesting. To investigate this we built hypothetical models with randomly arranged chromophores, but still observed high efficiency when typical nearest-neighbour distances are comparable with those found in nature. This helps to explain the efficiency of energy transport in organisms whose chromophore networks differ widely in structure, while also suggesting new design criteria for efficient artificial light-harvesting devices

    Subfactors of index less than 5, part 3: quadruple points

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    One major obstacle in extending the classification of small index subfactors beyond 3+\sqrt{3} is the appearance of infinite families of candidate principal graphs with 4-valent vertices (in particular, the "weeds" Q and Q' from Part 1 (arXiv:1007.1730)). Thus instead of using triple point obstructions to eliminate candidate graphs, we need to develop new quadruple point obstructions. In this paper we prove two quadruple point obstructions. The first uses quadratic tangles techniques and eliminates the weed Q' immediately. The second uses connections, and when combined with an additional number theoretic argument it eliminates both weeds Q and Q'. Finally, we prove the uniqueness (up to taking duals) of the 3311 Goodman-de la Harpe-Jones subfactor using a combination of planar algebra techniques and connections.Comment: 21 page

    The Micronemal Plasmodium Proteins P36 and P52 Act in Concert to Establish the Replication-Permissive Compartment Within Infected Hepatocytes

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    Within the liver, Plasmodium sporozoites traverse cells searching for a “suitable” hepatocyte, invading these cells through a process that results in the formation of a parasitophorous vacuole (PV), within which the parasite undergoes intracellular replication as a liver stage. It was previously established that two members of the Plasmodium s48/45 protein family, P36 and P52, are essential for productive invasion of host hepatocytes by sporozoites as their simultaneous deletion results in growth-arrested parasites that lack a PV. Recent studies point toward a pathway of entry possibly involving the interaction of P36 with hepatocyte receptors EphA2, CD81, and SR-B1. However, the relationship between P36 and P52 during sporozoite invasion remains unknown. Here we show that parasites with a single P52 or P36 gene deletion each lack a PV after hepatocyte invasion, thereby pheno-copying the lack of a PV observed for the P52/P36 dual gene deletion parasite line. This indicates that both proteins are equally important in the establishment of a PV and act in the same pathway. We created a Plasmodium yoelii P36mCherry tagged parasite line that allowed us to visualize the subcellular localization of P36 and found that it partially co-localizes with P52 in the sporozoite secretory microneme organelles. Furthermore, through co-immunoprecipitation studies in vivo, we determined that P36 and P52 form a protein complex in sporozoites, indicating a concerted function for both proteins within the PV formation pathway. However, upon sporozoite stimulation, only P36 was released as a secreted protein while P52 was not. Our results support a model in which the putatively glycosylphosphatidylinositol (GPI)-anchored P52 may serve as a scaffold to facilitate the interaction of secreted P36 with the host cell during sporozoite invasion of hepatocytes

    Extreme CD8 T Cell Requirements for Anti-Malarial Liver-Stage Immunity following Immunization with Radiation Attenuated Sporozoites

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    Radiation-attenuated Plasmodium sporozoites (RAS) are the only vaccine shown to induce sterilizing protection against malaria in both humans and rodents. Importantly, these “whole-parasite” vaccines are currently under evaluation in human clinical trials. Studies with inbred mice reveal that RAS-induced CD8 T cells targeting liver-stage parasites are critical for protection. However, the paucity of defined T cell epitopes for these parasites has precluded precise understanding of the specific characteristics of RAS-induced protective CD8 T cell responses. Thus, it is not known whether quantitative or qualitative differences in RAS-induced CD8 T cell responses underlie the relative resistance or susceptibility of immune inbred mice to sporozoite challenge. Moreover, whether extraordinarily large CD8 T cell responses are generated and required for protection following RAS immunization, as has been described for CD8 T cell responses following single-antigen subunit vaccination, remains unknown. Here, we used surrogate T cell activation markers to identify and track whole-parasite, RAS-vaccine-induced effector and memory CD8 T cell responses. Our data show that the differential susceptibility of RAS-immune inbred mouse strains to Plasmodium berghei or P. yoelii sporozoite challenge does not result from host- or parasite-specific decreases in the CD8 T cell response. Moreover, the surrogate activation marker approach allowed us for the first time to evaluate CD8 T cell responses and protective immunity following RAS-immunization in outbred hosts. Importantly, we show that compared to a protective subunit vaccine that elicits a CD8 T cell response to a single epitope, diversifying the targeted antigens through whole-parasite RAS immunization only minimally, if at all, reduced the numerical requirements for memory CD8 T cell-mediated protection. Thus, our studies reveal that extremely high frequencies of RAS-induced memory CD8 T cells are required, but may not suffice, for sterilizing anti-Plasmodial immunity. These data provide new insights into protective CD8 T cell responses elicited by RAS-immunization in genetically diverse hosts, information with relevance to developing attenuated whole-parasite vaccines

    CMS physics technical design report : Addendum on high density QCD with heavy ions

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