Geometry and physics of pseudodifferential operators on manifolds

A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: esistence theorem for the function that generalizes the phase; analogue of Taylor's theorem; torsion and curvature terms in the symbolic calculus; the two kinds of derivative acting on smooth sections of the cotangent bundle of the Riemannian manifold; the concept of symbol as an equivalence class. Physical motivations and applications are then outlined, with emphasis on Green functions of quantum field theory and Parker's evaluation of Hawking radiation.Comment: 14 pages, paper in honour of Gaetano Vilas

Towards obtaining Green functions for a Casimir cavity in de Sitter spacetime

Recent work in the literature has studied rigid Casimir cavities in a weak gravitational field, or in de Sitter spacetime, or yet other spacetime models. The present review paper studies the difficult problem of direct evaluation of scalar Green functions for a Casimir-type apparatus in de Sitter spacetime. Working to first order in the small parameter of the problem, i.e. twice the gravity acceleration times the plates' separation divided by the speed of light in vacuum, suitable coordinates are considered for which the differential equations obeyed by the zeroth- and first-order Green functions can be solved in terms of special functions. This result can be used, in turn, to obtain, via the point-split method, the regularized and renormalized energy-momentum tensor both in the scalar case and in the physically more relevant electromagnetic case.Comment: 13 pages, special issue review article. In the final version, the calculations of Sec. III have been improved, two References have been added and their content has been summarize

The Ising model on the random planar causal triangulation: bounds on the critical line and magnetization properties

We investigate a Gibbs (annealed) probability measure defined on Ising spin configurations on causal triangulations of the plane. We study the region where such measure can be defined and provide bounds on the boundary of this region (critical line). We prove that for any finite random triangulation the magnetization of the central spin is sensitive of the boundary conditions. Furthermore, we show that in the infinite volume limit, the magnetization of the central spin vanishes for values of the temperature high enough.Comment: 28 pages, 2 figures, 1 section adde

Generic Ising Trees

The Ising model on an infinite generic tree is defined as a thermodynamic limit of finite systems. A detailed description of the corresponding distribution of infinite spin configurations is given. As an application we study the magnetization properties of such systems and prove that they exhibit no spontaneous magnetization. Furthermore, the values of the Hausdorff and spectral dimensions of the underlying trees are calculated and found to be, respectively, $\bar{d}_h=2$ and $\bar{d}_s=4/3$.Comment: 29 pages, 2 figures; typos corrected, one section and new references adde

Energy-momentum tensor for a scalar Casimir apparatus in a weak gravitational field: Neumann conditions

We consider a Casimir apparatus consisting of two perfectly conducting parallel plates, subject to the weak gravitational field of the Earth. The aim of this paper is the calculation of the energy-momentum tensor of this system for a free, real massless scalar field satisfying Neumann boundary conditions on the plates. The small gravity acceleration (here considered as not varying between the two plates) allows us to perform all calculations to first order in this parameter. Some interesting results are found: a correction, depending on the gravity acceleration, to the well-known Casimir energy and pressure on the plates. Moreover, this scheme predicts a tiny force in the upwards direction acting on the apparatus. These results are supported by two consistency checks: the covariant conservation of the energy-momentum tensor and the vanishing of its regularized trace, when the scalar field is conformally coupled to gravity.Comment: 5 pages in double-column format, Revtex4. The final version is shorter, and the presentation has been improve

Casimir apparatuses in a weak gravitational field

We review and assess a part of the recent work on Casimir apparatuses in the weak gravitational field of the Earth. For a free, real massless scalar field subject to Dirichlet or Neumann boundary conditions on the parallel plates, the resulting regularized and renormalized energy-momentum tensor is covariantly conserved, while the trace anomaly vanishes if the massless field is conformally coupled to gravity. Conformal coupling also ensures a finite Casimir energy and finite values of the pressure upon parallel plates. These results have been extended to an electromagnetic field subject to perfect conductor (hence idealized) boundary conditions on parallel plates, by various authors. The regularized and renormalized energy-momentum tensor has been evaluated up to second order in the gravity acceleration. In both the scalar and the electromagnetic case, studied to first order in the gravity acceleration, the theory predicts a tiny force in the upwards direction acting on the apparatus. This effect is conceptually very interesting, since it means that Casimir energy is indeed expected to gravitate, although the magnitude of the expected force makes it necessary to overcome very severe signal-modulation problems.Comment: 12 pages, prepared for the Fourth International Sakharov Conferenc

Change in mammographic density across birth cohorts of Dutch breast cancer screening participants

Contains fulltext : 208976.pdf (publisher's version ) (Open Access

Rational optimization of tolC as a powerful dual selectable marker for genome engineering

Selection has been invaluable for genetic manipulation, although counter-selection has historically exhibited limited robustness and convenience. TolC, an outer membrane pore involved in transmembrane transport in E. coli, has been implemented as a selectable/counter-selectable marker, but counter-selection escape frequency using colicin E1 precludes using tolC for inefficient genetic manipulations and/or with large libraries. Here, we leveraged unbiased deep sequencing of 96 independent lineages exhibiting counter-selection escape to identify loss-of-function mutations, which offered mechanistic insight and guided strain engineering to reduce counter-selection escape frequency by ∼40-fold. We fundamentally improved the tolC counter-selection by supplementing a second agent, vancomycin, which reduces counter-selection escape by 425-fold, compared colicin E1 alone. Combining these improvements in a mismatch repair proficient strain reduced counter-selection escape frequency by 1.3E6-fold in total, making tolC counter-selection as effective as most selectable markers, and adding a valuable tool to the genome editing toolbox. These improvements permitted us to perform stable and continuous rounds of selection/counter-selection using tolC, enabling replacement of 10 alleles without requiring genotypic screening for the first time. Finally, we combined these advances to create an optimized E. coli strain for genome engineering that is ∼10-fold more efficient at achieving allelic diversity than previous best practices