Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Non-Abelian Anyons and Topological Quantum Computation

Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as {it Non-Abelian anyons}, meaning that they obey {it non-Abelian braiding statistics}. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations which are necessary for quantum computation are carried out by braiding quasiparticles, and then measuring the multi-quasiparticle states. The fault-tolerance of a topological quantum computer arises from the non-local encoding of the states of the quasiparticles, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the nu=5/2 state, although several other prospective candidates have been proposed in systems as disparate as ultra-cold atoms in optical lattices and thin film superconductors. In this review article, we describe current research in this field, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. We address both the mathematical underpinnings of topological quantum computation and the physics of the subject using the nu=5/2 fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

The first suggestion that physical exercise results in free radical-mediated damage to tissues appeared in 1978, and the past three decades have resulted in a large growth of knowledge regarding exercise and oxidative stress. Although the sources of oxidant production during exercise continue to be debated, it is now well established that both resting and contracting skeletal muscles produce reactive oxygen species and reactive nitrogen species. Importantly, intense and prolonged exercise can result in oxidative damage to both proteins and lipids in the contracting myocytes. Furthermore, oxidants can modulate a number of cell signaling pathways and regulate the expression of multiple genes in eukaryotic cells. This oxidant-mediated change in gene expression involves changes at transcriptional, mRNA stability, and signal transduction levels. Furthermore, numerous products associated with oxidant-modulated genes have been identified and include antioxidant enzymes, stress proteins, DNA repair proteins, and mitochondrial electron transport proteins. Interestingly, low and physiological levels of reactive oxygen species are required for normal force production in skeletal muscle, but high levels of reactive oxygen species promote contractile dysfunction resulting in muscle weakness and fatigue. Ongoing research continues to probe the mechanisms by which oxidants influence skeletal muscle contractile properties and to explore interventions capable of protecting muscle from oxidant-mediated dysfunction.

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Exercise-induced oxidative stress: cellular mechanisms and impact on muscle force production

UV radiation (UV) is classified as a "complete carcinogen" because it is both a mutagen and a non-specific damaging agent and has properties of both a tumor initiator and a tumor promoter. In environmental abundance, UV is the most important modifiable risk factor for skin cancer and many other environmentally-influenced skin disorders. However, UV also benefits human health by mediating natural synthesis of vitamin D and endorphins in the skin, therefore UV has complex and mixed effects on human health. Nonetheless, excessive exposure to UV carries profound health risks, including atrophy, pigmentary changes, wrinkling and malignancy. UV is epidemiologically and molecularly linked to the three most common types of skin cancer, basal cell carcinoma, squamous cell carcinoma and malignant melanoma, which together affect more than a million Americans annually. Genetic factors also influence risk of UV-mediated skin disease. Polymorphisms of the melanocortin 1 receptor (MC1R) gene, in particular, correlate with fairness of skin, UV sensitivity, and enhanced cancer risk. We are interested in developing UV-protective approaches based on a detailed understanding of molecular events that occur after UV exposure, focusing particularly on epidermal melanization and the role of the MC1R in genome maintenance.

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UV Radiation and the Skin

https://www.math.uni-hamburg.de/home/runkel/PDF/tft1.pdf

TFT construction of RCFT correlators I: partition functions

"NATURAL OCCURRENCE AND TISSUE LEVELS Plants Natural Sources of Tocotrienols, Augustine S. H. Ong Analysis and Distribution of Vitamin E in Vegetable Oils and Foods, Alan J. Sheppard, John L. Weihrauch, and Jean A.T. Pennington Animals and Humans Absorption, Transport and Delivery to Tissues, Maret G. Traber, William Cohn, and David P. R. Muller Interrelationships of Vitamin E with Other Nutrients, Harold H. Draper Effects of ss-Carotene and Related Caritenoids on Vitamin E, Shirley R. Blakely, Geraldine V. Mitchell, Mamie Leah Young Jenkins, and Erich Grundel CHEMISTRY, BIOCHEMISTRY, AND CELL BIOLOGY Chemical Reactions, Antioxidant Action, and Biomembranes Pulse Radioysis as a Tool in Vitamin E Research, Wolf Bors, Manfred Saran, and Christs Michel Peroxyl Radical Trapping Reactions of Alpha-Tocopherol in Biomimetic Systems, Daniel C. Liebler Synthesis and Kinetic Study of Antioxidant and Prooxidant Actions of Vitamin E Derivatives, Kazou Mukai Rates and Products of Reactions of Vitamin E with Oxygen Radicals, Etsuo Niki and Mitsuyoshi Matsuo Relative Importance of Vitamin E in Antiperoxidative Defenses in Human Blood Plasma and Low-Density Lipoprotein (LDL), Balz B. Frei and Bruce N. Ames Scavenging of Singlet Molecular Oxygen by Tocopherols, Helmut Sies, Stephan Kaiser, Paulo Di Mascio, and Michael E. Murphy Relationship Between Vitamin E and a More Electronegatively Charged LDL of Human Plasma, Gabriele Bittolo-Bon, Giuseppe Cazzolato, and Pietro Avogaro The Role of Vitamin E in Blood and Cellular Aging, Shiro Urano Pharamacology Biokinetics of Vitamin E Using Deuterated Tocopherols, Graham W. Burton and Keith U. Ingold Vitamin E Status of Exotic Animals Compared with Livestock and Domestics, Ellen S. Dierenfeld and Maret G. Traber Alpha-Tocopherol and Protein Kinase C Regulation of Intracellular Signaling, Angelo Manfredo Azzi, Gianna Bartoli, Daniel Boscoboinik, Carmel Hensey, and Adam Szewczyk Vitamin E Action in Modulating the Arachidonic Acid Cascade, David G. Cornwell and Rao V. Panganamala The Safety of Oral Intake of Vitamin E: Data from Clinical Studies from 1986 to 1991, Adrianne Bendich and Lawrence J. Machlin Reduction in the Toxicity of Doxorubicin (Adriamycin) in the Heart by Vitamin E, Jose Milei and Susana Llesuy PATHOPHYSIOLOGICAL CONDITIONS AND VITAMIN E Metabolism and Aging Vitamin E and the Aging Process, Abraham Z. Reznick, Bruce Rappaport, Sharon V. Landvik, Irene Simon-Schnass, and Lester Packer Vitamin E and High-Altitude Exercise, Irene Simon-Schnass Significance of Vitamin E for the Athlete, Lester Packer, Abraham Z. Reznick, Irene Simon-Schnass, and Sharon V. Landvik Plasma Alpha-Tocopherol and Ubiquinone and Their Relations to Muscle Function in Healthy Humans and in Cardiac Diseases, Jan Karlsson, Bertil Diamant, Henning Theorell, Kurt Johansen, and Karl Folkers Cancer Effects of Vitamin E on Oral Carcinogenesis and Oral Cancer, Gerald Shklar and Joel L. Schwartz Epidemiology of Vitamin E: Evidence for Anticancer Effects in Humans, Paul Knekt Antitumor Activity of Tocotrienols, Kanki Komiyama and Masakazu Yamaoka Impact of Palm Oil on Experimental Carcinogenesis, Charles E. Elson Immunity and Disease Resistance Vitamin E and Immune Response, Simin Nikbin Meydani and Robert P. Tengerdy MEDICAL APPLICATIONS Dermatology Vitamin E in Dermatological Therapy, Jurgen Fuchs and Lester Packer Vitamin E and Coenzyme Q10 in Normal Human Skin and in Basal Cell Epitheliomas, Luigi Rusciani, Giuseppina Petrelli, and Silvio Lippa Vitamin E in Skin: Antioxidant and Prooxidant Balance, Eric Witt, Valerian E. Kagan, and Lester Packer Neurology Vitamin E and Parkinson's Disease, Lawrence I. Golbe and J. William Langston Vitamin E Therapy in Neurological Diseases, Tuomas Westermarck, Erkki Antila, and Faik Atroshi Effects of Palm Oil Vitamin E on Atherogenesis, Erkki Antila, Faik Atroshi, and Tuomas Westermarck Vitamin E Deficiency and Neurological Disorders, Ronald J. Sokol Effects of Vitamin E and Its Derivative on Posttraumatic Epilepsy and Seizures, Akitane Mori, Isao Yokoi, and Hideaki Kabuto Pediatrics Vitamin E in the Newborn, Sunil Sinha and Malcolm Chiswick FUTURE PERSPECTIVES "

Vitamin E in Health and Disease

We formulate rational conformal field theory in terms of a symmetric special Frobenius algebra A and its representations. A is an algebra in the modular tensor category of Moore-Seiberg data of the underlying chiral CFT. The multiplication on A corresponds to the OPE of boundary fields for a single boundary condition. General boundary conditions are A-modules, and (generalised) defect lines are A-A-bimodules. 
The relation with three-dimensional TFT is used to express CFT data, like structure constants or torus and annulus coefficients, as invariants of links in three-manifolds. We compute explicitly the ordinary and twisted partition functions on the torus and the annulus partition functions. We prove that they satisfy consistency conditions, like modular invariance and NIM-rep properties. 
We suggest that our results can be interpreted in terms of non-commutative geometry over the modular tensor category of Moore-Seiberg data.

Jürgen Fuchs

Papers

TFT construction of RCFT correlators I: partition functions

Vitamin E in Health and Disease

TFT construction of RCFT correlators I: Partition functions

Duality and defects in rational conformal field theory

Affine Lie Algebras and Quantum Groups