On Semiclassical Limits of String States

We explore the relation between classical and quantum states in both open and closed (super)strings discussing the relevance of coherent states as a semiclassical approximation. For the closed string sector a gauge-fixing of the residual world-sheet rigid translation symmetry of the light-cone gauge is needed for the construction to be possible. The circular target-space loop example is worked out explicitly.Comment: 12 page

Topics on global analysis of manifolds and representation theory of reductive groups

Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect representation theoretic properties on function spaces, with focus on multiplicities and spectrum.Comment: 14 page

Effectiveness of different post-diagnostic dementia care models delivered by primary care: a systematic review

BACKGROUND: Global policy recommendations suggest a task-shifted model of post-diagnostic dementia care, moving towards primary and community-based care. It is unclear how this may best be delivered. AIM: To assess the effectiveness and cost-effectiveness of primary care-based models of post-diagnostic dementia care. DESIGN AND SETTING: A systematic review of trials and economic evaluations of post-diagnostic dementia care interventions where primary care was substantially involved in care plan decision making. METHOD: Searches were undertaken of MEDLINE, PsychINFO, EMBASE, Web of Science, and CINAHL (from inception to March 2019). Two authors independently critically appraised studies and inductively classified interventions into types of care models. Random effects meta-analysis or narrative synthesis was conducted for each model where appropriate. RESULTS: From 4506 unique references and 357 full texts, 23 papers were included from 10 trials of nine interventions, delivered in four countries. Four types of care models were identified. Primary care provider (PCP)-led care (n = 1) led to better caregiver mental health and reduced hospital and memory clinic costs compared with memory clinics. PCP-led care with specialist consulting support (n = 2) did not have additional effects on clinical outcomes or costs over usual primary care. PCP-case management partnership models (n = 6) offered the most promise, with impact on neuropsychiatric symptoms, caregiver burden, distress and mastery, and healthcare costs. Integrated primary care memory clinics (n = 1) had limited evidence for improved quality of life and cost-effectiveness compared with memory clinics. CONCLUSION: Partnership models may impact on some clinical outcomes and healthcare costs. More rigorous evaluation of promising primary care-led care models is needed

Conformal algebra: R-matrix and star-triangle relation

The main purpose of this paper is the construction of the R-operator which acts in the tensor product of two infinite-dimensional representations of the conformal algebra and solves Yang-Baxter equation. We build the R-operator as a product of more elementary operators S_1, S_2 and S_3. Operators S_1 and S_3 are identified with intertwining operators of two irreducible representations of the conformal algebra and the operator S_2 is obtained from the intertwining operators S_1 and S_3 by a certain duality transformation. There are star-triangle relations for the basic building blocks S_1, S_2 and S_3 which produce all other relations for the general R-operators. In the case of the conformal algebra of n-dimensional Euclidean space we construct the R-operator for the scalar (spin part is equal to zero) representations and prove that the star-triangle relation is a well known star-triangle relation for propagators of scalar fields. In the special case of the conformal algebra of the 4-dimensional Euclidean space, the R-operator is obtained for more general class of infinite-dimensional (differential) representations with nontrivial spin parts. As a result, for the case of the 4-dimensional Euclidean space, we generalize the scalar star-triangle relation to the most general star-triangle relation for the propagators of particles with arbitrary spins.Comment: Added references and corrected typo

Application and comparison of large-scale solution-based DNA capture-enrichment methods on ancient DNA

The development of second-generation sequencing technologies has greatly benefitted the field of ancient DNA (aDNA). Its application can be further exploited by the use of targeted capture-enrichment methods to overcome restrictions posed by low endogenous and contaminating DNA in ancient samples. We tested the performance of Agilent's SureSelect and Mycroarray's MySelect in-solution capture systems on Illumina sequencing libraries built from ancient maize to identify key factors influencing aDNA capture experiments. High levels of clonality as well as the presence of multiple-copy sequences in the capture targets led to biases in the data regardless of the capture method. Neither method consistently outperformed the other in terms of average target enrichment, and no obvious difference was observed either when two tiling designs were compared. In addition to demonstrating the plausibility of capturing aDNA from ancient plant material, our results also enable us to provide useful recommendations for those planning targeted-sequencing on aDNA

The Heat Kernel on AdS_3 and its Applications

We derive the heat kernel for arbitrary tensor fields on S^3 and (Euclidean) AdS_3 using a group theoretic approach. We use these results to also obtain the heat kernel on certain quotients of these spaces. In particular, we give a simple, explicit expression for the one loop determinant for a field of arbitrary spin s in thermal AdS_3. We apply this to the calculation of the one loop partition function of N=1 supergravity on AdS_3. We find that the answer factorizes into left- and right-moving super Virasoro characters built on the SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds.Comment: 46 pages, LaTeX, v2: Reference adde

Warped Riemannian metrics for location-scale models

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimensional Riemannian manifolds. Indeed, a warped Riemannian metric is fully determined by only two functions of a single variable, irrespective of the dimension of the underlying Riemannian manifold. Starting from this theorem, several original contributions are made. The expression of the Rao-Fisher information metric of the Riemannian Gaussian model is provided, for the first time in the literature. A generalised definition of the Mahalanobis distance is introduced, which is applicable to any location-scale model defined on a Riemannian manifold. The solution of the geodesic equation is obtained, for any Rao-Fisher information metric defined in terms of warped Riemannian metrics. Finally, using a mixture of analytical and numerical computations, it is shown that the parameter space of the von Mises-Fisher model of $n$-dimensional directional data, when equipped with its Rao-Fisher information metric, becomes a Hadamard manifold, a simply-connected complete Riemannian manifold of negative sectional curvature, for $n = 2,\ldots,8$. Hopefully, in upcoming work, this will be proved for any value of $n$.Comment: first version, before submissio

The Beta Ansatz: A Tale of Two Complex Structures

Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi-Yau threefolds. An efficient way of encoding this information exploits the theory of dessin d’enfants, expressing the structure in terms of a permutation triple, which is in turn related to a Belyi pair, namely a holomorphic map from a torus to a P1 with three marked points. The procedure of a-maximization, in the context of isoradial embeddings of the dimer, also associates a complex structure to the torus, determined by the R-charges in the SCFT, which can be compared with the Belyi complex structure. Algorithms for the explicit construction of the Belyi pairs are described in detail. In the case of orbifolds, these algorithms are related to the construction of covers of elliptic curves, which exploits the properties of Weierstraß elliptic functions. We present a counter example to a previous conjecture identifying the complex structure of the Belyi curve to the complex structure associated with R-charges

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

PeptX: Using Genetic Algorithms to optimize peptides for MHC binding

<p>Abstract</p> <p>Background</p> <p>The binding between the major histocompatibility complex and the presented peptide is an indispensable prerequisite for the adaptive immune response. There is a plethora of different <it>in silico </it>techniques for the prediction of the peptide binding affinity to major histocompatibility complexes. Most studies screen a set of peptides for promising candidates to predict possible T cell epitopes. In this study we ask the question vice versa: Which peptides do have highest binding affinities to a given major histocompatibility complex according to certain <it>in silico </it>scoring functions?</p> <p>Results</p> <p>Since a full screening of all possible peptides is not feasible in reasonable runtime, we introduce a heuristic approach. We developed a framework for Genetic Algorithms to optimize peptides for the binding to major histocompatibility complexes. In an extensive benchmark we tested various operator combinations. We found that (1) selection operators have a strong influence on the convergence of the population while recombination operators have minor influence and (2) that five different binding prediction methods lead to five different sets of "optimal" peptides for the same major histocompatibility complex. The consensus peptides were experimentally verified as high affinity binders.</p> <p>Conclusion</p> <p>We provide a generalized framework to calculate sets of high affinity binders based on different previously published scoring functions in reasonable runtime. Furthermore we give insight into the different behaviours of operators and scoring functions of the Genetic Algorithm.</p