Time and Geometric Quantization

In this paper we briefly review the functional version of the Koopman-von Neumann operatorial approach to classical mechanics. We then show that its quantization can be achieved by freezing to zero two Grassmannian partners of time. This method of quantization presents many similarities with the one known as Geometric Quantization.Comment: Talk given by EG at "Spacetime and Fundamental Interactions: Quantum Aspects. A conference to honour A.P.Balachandran's 65th birthday

Religious Relationships with the Environment in a Tibetan Rural Community : Interactions and Contrasts with Popular Notions of Indigenous Environmentalism

Acknowledgments: We thank Beijing Forestry University, our field assistants Tashi Rabden, Pema Dechin, Tsewang Chomtso and Gele Chopel for their invaluable help, the Forest Bureau of Daocheng county for permission and support, and the people of Samdo for their hospitality and participation. The research was funded by the ESRC and the World Pheasant Association. This paper is a contribution to Imperial College’s Grand Challenges in Ecosystems and the Environment initiative. Two anonymous reviewers gave valuable comments on the manuscript.Peer reviewedPublisher PD

Influence of Pichia pastoris cellular material on polymerase chain reaction performance as a synthetic biology standard for genome monitoring

Advances in synthetic genomics are now well underway in yeasts due to the low cost of synthetic DNA. These new capabilities also bring greater need for quantitating the presence, loss and rearrangement of loci within synthetic yeast genomes. Methods for achieving this will ideally; i) be robust to industrial settings, ii) adhere to a global standard and iii) be sufficiently rapid to enable at-line monitoring during cell growth. The methylotrophic yeast Pichia pastoris (P. pastoris) is increasingly used for industrial production of biotherapeutic proteins so we sought to answer the following questions for this particular yeast species. Is time-consuming DNA purification necessary to obtain accurate end-point polymerase chain reaction (e-pPCR) and quantitative PCR (qPCR) data? Can the novel linear regression of efficiency qPCR method (LRE qPCR), which has properties desirable in a synthetic biology standard, match the accuracy of conventional qPCR? Does cell cultivation scale influence PCR performance? To answer these questions we performed e-pPCR and qPCR in the presence and absence of cellular material disrupted by a mild 30s sonication procedure. The e-pPCR limit of detection (LOD) for a genomic target locus was 50 pg (4.91 × 103 copies) of purified genomic DNA (gDNA) but the presence of cellular material reduced this sensitivity sixfold to 300 pg gDNA (2.95 × 104 copies). LRE qPCR matched the accuracy of a conventional standard curve qPCR method. The presence of material from bioreactor cultivation of up to OD600 = 80 did not significantly compromise the accuracy of LRE qPCR. We conclude that a simple and rapid cell disruption step is sufficient to render P. pastoris samples of up to OD600 = 80 amenable to analysis using LRE qPCR which we propose as a synthetic biology standard

The Computational Power of Minkowski Spacetime

The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another's physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an $n$th order polynomial time reduction at the completion of an observer's journey. These results enable a comparison between the optimal quadratic \emph{Grover speedup} from quantum computing and an $n=2$ speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation.Comment: 6 pages, LaTeX, feedback welcom

A canonical transformation and the tunneling probability for the birth of an asymptotically DeSitter universe with dust

In the present work, we study the quantum cosmology description of closed Friedmann-Robertson-Walker models in the presence of a positive cosmological constant and a generic perfect fluid. We work in the Schutz's variational formalism. If one uses the scale factor and its canonically conjugated momentum as the phase space variables that describe the geometrical sector of these models, one obtains Wheeler-DeWitt equations with operator ordering ambiguities. In order to avoid those ambiguities and simplify the quantum treatment of the models, we introduce new phase space variables. We explicitly demonstrate that the transformation leading from the old set of variables to the new one is canonical. In order to show that the above canonical transformations simplify the quantum treatment of those models, we consider a particular model where the perfect fluid is dust. We solve the Wheeler-DeWitt equation numerically using the Crank-Nicholson scheme and determine the time evolution of the initial wave function. Finally, we compare the results for the present model with the ones for another model where the only difference is the presence of a radiative perfect fluid, instead of dust.Comment: Revtex4, 18 pages, 2 EPS figure

Autistic spectrum disorder symptoms in children and adolescents with attention-deficit/hyperactivity disorder: a meta-analytical review

BACKGROUND: Research identifies highly variable prevalence estimates for autism spectrum disorder (ASD) in children and adolescents with attention deficit hyperactivity disorder (ADHD), particularly between community and clinical samples, warranting quantitative meta-analyses to investigate the true prevalence of ASD in children and adolescents with ADHD. // METHODS: Studies were identified through a systematic literature search of PsycINFO, MEDLINE and Web of Science through January 2018. Twenty-two publications met inclusion criteria (total N = 61 985). Two random effects meta-analyses were conducted: (1) to identify the proportion of children and adolescents with ADHD that met criteria for ASD; and (2) to compare the severity of dimensionally-measured ASD symptomology in children and adolescents with and without ADHD. // RESULTS: The overall pooled effect for children and adolescents with ADHD who met threshold for ASD was 21%. There was no significant difference between community samples (19%) and clinical samples (24%) or between US studies v. those from other countries. Children and adolescents with ADHD had substantially more dimensionally-measured ASD traits compared with those who did not have ADHD (d = 1.23). // CONCLUSION: The findings provide further evidence that ADHD and ASD are associated in nature. Clinical and research implications are discussed

Models for Modules

We recall the structure of the indecomposable sl(2) modules in the Bernstein-Gelfand-Gelfand category O. We show that all these modules can arise as quantized phase spaces of physical models. In particular, we demonstrate in a path integral discretization how a redefined action of the sl(2) algebra over the complex numbers can glue finite dimensional and infinite dimensional highest weight representations into indecomposable wholes. Furthermore, we discuss how projective cover representations arise in the tensor product of finite dimensional and Verma modules and give explicit tensor product decomposition rules. The tensor product spaces can be realized in terms of product path integrals. Finally, we discuss relations of our results to brane quantization and cohomological calculations in string theory.Comment: 18 pages, 6 figure

Chern-Simons Quantization of (2+1)-Anti-De Sitter Gravity on a Torus

Chern-Simons formulation of 2+1 dimensional Einstein gravity with a negative cosmological constant is investigated when the spacetime has the topology $R\times T^{2}$. The physical phase space is shown to be a direct product of two sub-phase spaces each of which is a non-Hausdorff manifold plus a set with nonzero codimensions. Spacetime geometrical interpretation of each point in the phase space is also given and we explain the 1 to 2 correspondence with the ADM formalism from the geometrical viewpoint. In quantizing this theory, we construct a "modified phase space" which is a cotangnt bundle on a torus. We also provide a modular invariant inner product and investigate the relation to the quantum theory which is directly related to the spinor representation of the ADM formalism. (This paper is the revised version of a previous paper(hep-th/9312151). The wrong discussion on the topology of the phase space is corrected.)Comment: latex 28 page

A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry

We introduce an antisymplectic Dirac operator and antisymplectic gamma matrices. We explore similarities between, on one hand, the Schroedinger-Lichnerowicz formula for spinor bundles in Riemannian spin geometry, which contains a zeroth-order term proportional to the Levi-Civita scalar curvature, and, on the other hand, the nilpotent, Grassmann-odd, second-order \Delta operator in antisymplectic geometry, which in general has a zeroth-order term proportional to the odd scalar curvature of an arbitrary antisymplectic and torsionfree connection that is compatible with the measure density. Finally, we discuss the close relationship with the two-loop scalar curvature term in the quantum Hamiltonian for a particle in a curved Riemannian space.Comment: 55 pages, LaTeX. v2: Subsection 3.10 expanded. v3: Reference added. v4: Published versio

Duality through the symplectic embedding formalism

In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method (NDM). We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method (SEM) is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.Comment: RevTeX4, 10 pages. To appear in Int. J. Mod. Phys.