Categorical formulation of quantum algebras

We describe how dagger-Frobenius monoids give the correct categorical description of certain kinds of finite-dimensional 'quantum algebras'. We develop the concept of an involution monoid, and use it to construct a correspondence between finite-dimensional C*-algebras and certain types of dagger-Frobenius monoids in the category of Hilbert spaces. Using this technology, we recast the spectral theorems for commutative C*-algebras and for normal operators into an explicitly categorical language, and we examine the case that the results of measurements do not form finite sets, but rather objects in a finite Boolean topos. We describe the relevance of these results for topological quantum field theory.Comment: 34 pages, to appear in Communications in Mathematical Physic

Photosensitive epilepsy: report of two cases

Reports on photosensitive epilepsy are uncommon. The authors review the literature, and special attention is given to television epilepsy. Two cases are reported and discussed.Epilepsia fotossensível é tema ainda pouco descrito. Os autores revisam a literatura pertinente e descrevem dois casos de epilepsia fotossensível, dando ênfase à assim chamada epilepsia da televisão.Escola Paulista de Medicina Setor de Investigação e Tratamento das EpilepsiasUNIFESP, EPM, Setor de Investigação e Tratamento das EpilepsiasSciEL

Astrophysical and Cosmological Tests of Quantum Theory

We discuss several proposals for astrophysical and cosmological tests of quantum theory. The tests are motivated by deterministic hidden-variables theories, and in particular by the view that quantum physics is merely an effective theory of an equilibrium state. The proposed tests involve searching for nonequilibrium violations of quantum theory in: primordial inflaton fluctuations imprinted on the cosmic microwave background, relic cosmological particles, Hawking radiation, photons with entangled partners inside black holes, neutrino oscillations, and particles from very distant sources.Comment: 25 pages. Amendment to section 7. Contribution to: "The Quantum Universe", special issue of Journal of Physics A, dedicated to Prof. G.-C. Ghirardi on the occasion of his seventieth birthda

AQFT from n-functorial QFT

There are essentially two different approaches to the axiomatization of quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and functorial QFT, going back to Atiyah and Segal. More recently, based on ideas by Baez and Dolan, the latter is being refined to "extended" functorial QFT by Freed, Hopkins, Lurie and others. The first approach uses local nets of operator algebras which assign to each patch an algebra "of observables", the latter uses n-functors which assign to each patch a "propagator of states". In this note we present an observation about how these two axiom systems are naturally related: we demonstrate under mild assumptions that every 2-dimensional extended Minkowskian QFT 2-functor ("parallel surface transport") naturally yields a local net. This is obtained by postcomposing the propagation 2-functor with an operation that mimics the passage from the Schroedinger picture to the Heisenberg picture in quantum mechanics. The argument has a straightforward generalization to general pseudo-Riemannian structure and higher dimensions.Comment: 39 pages; further examples added: Hopf spin chains and asymptotic inclusion of subfactors; references adde

Picturing classical and quantum Bayesian inference

We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators rather than probability distributions as representative of degrees of belief. The diagrammatic framework is stated in the graphical language of symmetric monoidal categories and of compact structures and Frobenius structures therein, in which Bayesian inversion boils down to transposition with respect to an appropriate compact structure. We characterize classical Bayesian inference in terms of a graphical property and demonstrate that our approach eliminates some purely conventional elements that appear in common representations thereof, such as whether degrees of belief are represented by probabilities or entropic quantities. We also introduce a quantum-like calculus wherein the Frobenius structure is noncommutative and show that it can accommodate Leifer's calculus of `conditional density operators'. The notion of conditional independence is also generalized to our graphical setting and we make some preliminary connections to the theory of Bayesian networks. Finally, we demonstrate how to construct a graphical Bayesian calculus within any dagger compact category.Comment: 38 pages, lots of picture

Methionine Adenosyltransferase α1 Is Targeted to the Mitochondrial Matrix and Interacts with Cytochrome P450 2E1 to Lower Its Expression

Methionine adenosyltransferase α1 (MATα1, encoded by MAT1A) is responsible for hepatic biosynthesis of S‐adenosyl methionine, the principal methyl donor. MATα1 also act as a transcriptional cofactor by interacting and influencing the activity of several transcription factors. Mat1a knockout (KO) mice have increased levels of cytochrome P450 2E1 (CYP2E1), but the underlying mechanisms are unknown. The aims of the current study were to identify binding partners of MATα1 and elucidate how MATα1 regulates CYP2E1 expression. We identified binding partners of MATα1 by coimmunoprecipitation (co‐IP) and mass spectrometry. Interacting proteins were confirmed using co‐IP using recombinant proteins, liver lysates, and mitochondria. Alcoholic liver disease (ALD) samples were used to confirm relevance of our findings. We found that MATα1 negatively regulates CYP2E1 at mRNA and protein levels, with the latter being the dominant mechanism. MATα1 interacts with many proteins but with a predominance of mitochondrial proteins including CYP2E1. We found that MATα1 is present in the mitochondrial matrix of hepatocytes using immunogold electron microscopy. Mat1a KO hepatocytes had reduced mitochondrial membrane potential and higher mitochondrial reactive oxygen species, both of which were normalized when MAT1A was overexpressed. In addition, KO hepatocytes were sensitized to ethanol and tumor necrosis factor α–induced mitochondrial dysfunction. Interaction of MATα1 with CYP2E1 was direct, and this facilitated CYP2E1 methylation at R379, leading to its degradation through the proteasomal pathway. Mat1a KO livers have a reduced methylated/total CYP2E1 ratio. MATα1’s influence on mitochondrial function is largely mediated by its effect on CYP2E1 expression. Patients with ALD have reduced MATα1 levels and a decrease in methylated/total CYP2E1 ratio. Conclusion: Our findings highlight a critical role of MATα1 in regulating mitochondrial function by suppressing CYP2E1 expression at multiple levels

Immunotherapies in neuromyelitis optica spectrum disorder: efficacy and predictors of response

OBJECTIVE: To analyse predictors for relapses and number of attacks under different immunotherapies in patients with neuromyelitis optica spectrum disorder (NMOSD). DESIGN: This is a retrospective cohort study conducted in neurology departments at 21 regional and university hospitals in Germany. Eligible participants were patients with aquaporin-4-antibody-positive or aquaporin-4-antibody-negative NMOSD. Main outcome measures were HRs from Cox proportional hazard regression models adjusted for centre effects, important prognostic factors and repeated treatment episodes. RESULTS: 265 treatment episodes with a mean duration of 442 days (total of 321 treatment years) in 144 patients (mean age at first attack: 40.9 years, 82.6% female, 86.1% aquaporin-4-antibody-positive) were analysed. 191 attacks occurred during any of the treatments (annual relapse rate=0.60). The most common treatments were rituximab (n=77, 111 patient-years), azathioprine (n=52, 68 patient-years), interferon-beta (n=32, 61 patient-years), mitoxantrone (n=34, 32.1 patient-years) and glatiramer acetate (n=17, 10 patient-years). Azathioprine (HR=0.4, 95% CI 0.3 to 0.7, p=0.001) and rituximab (HR=0.6, 95% CI 0.4 to 1.0, p=0.034) reduced the attack risk compared with interferon-beta, whereas mitoxantrone and glatiramer acetate did not. Patients who were aquaporin-4-antibody-positive had a higher risk of attacks (HR=2.5, 95% CI 1.3 to 5.1, p=0.009). Every decade of age was associated with a lower risk for attacks (HR=0.8, 95% CI 0.7 to 1.0, p=0.039). A previous attack under the same treatment tended to be predictive for further attacks (HR=1.5, 95% CI 1.0 to 2.4, p=0.065). CONCLUSIONS: Age, antibody status and possibly previous attacks predict further attacks in patients treated for NMOSD. Azathioprine and rituximab are superior to interferon-beta

Cardy condition for open-closed field algebras

Let $V$ be a vertex operator algebra satisfying certain reductivity and finiteness conditions such that $\mathcal{C}_V$, the category of V-modules, is a modular tensor category. We study open-closed field algebras over V equipped with nondegenerate invariant bilinear forms for both open and closed sectors. We show that they give algebras over certain \C-extension of the Swiss-cheese partial dioperad, and we obtain Ishibashi states easily in such algebras. We formulate Cardy condition algebraically in terms of the action of the modular transformation $S: \tau \mapsto -\frac{1}{\tau}$ on the space of intertwining operators. We then derive a graphical representation of S in the modular tensor category $\mathcal{C}_V$. This result enables us to give a categorical formulation of Cardy condition and modular invariant conformal full field algebra over $V\otimes V$. Then we incorporate the modular invariance condition for genus-one closed theory, Cardy condition and the axioms for open-closed field algebra over V equipped with nondegenerate invariant bilinear forms into a tensor-categorical notion called Cardy $\mathcal{C}_V|\mathcal{C}_{V\otimes V}$-algebra. We also give a categorical construction of Cardy $\mathcal{C}_V|\mathcal{C}_{V\otimes V}$-algebra in Cardy case.Comment: 70 page, 105 figures, references are updated. less typos, to appear in Comm. Math. Phy

Contrasting disease patterns in seropositive and seronegative neuromyelitis optica: A multicentre study of 175 patients

BACKGROUND: The diagnostic and pathophysiological relevance of antibodies to aquaporin-4 (AQP4-Ab) in patients with neuromyelitis optica spectrum disorders (NMOSD) has been intensively studied. However, little is known so far about the clinical impact of AQP4-Ab seropositivity. OBJECTIVE: To analyse systematically the clinical and paraclinical features associated with NMO spectrum disorders in Caucasians in a stratified fashion according to the patients' AQP4-Ab serostatus. METHODS: Retrospective study of 175 Caucasian patients (AQP4-Ab positive in 78.3%). RESULTS: Seropositive patients were found to be predominantly female (p 1 myelitis attacks in the first year were identified as possible predictors of a worse outcome. CONCLUSION: This study provides an overview of the clinical and paraclinical features of NMOSD in Caucasians and demonstrates a number of distinct disease characteristics in seropositive and seronegative patients