7,445 research outputs found
Graph complexes in deformation quantization
Kontsevich's formality theorem and the consequent star-product formula rely
on the construction of an -morphism between the DGLA of polyvector
fields and the DGLA of polydifferential operators. This construction uses a
version of graphical calculus. In this article we present the details of this
graphical calculus with emphasis on its algebraic features. It is a morphism of
differential graded Lie algebras between the Kontsevich DGLA of admissible
graphs and the Chevalley-Eilenberg DGLA of linear homomorphisms between
polyvector fields and polydifferential operators. Kontsevich's proof of the
formality morphism is reexamined in this light and an algebraic framework for
discussing the tree-level reduction of Kontsevich's star-product is described.Comment: 39 pages; 3 eps figures; uses Xy-pic. Final version. Details added,
mainly concerning the tree-level approximation. Typos corrected. An abridged
version will appear in Lett. Math. Phy
Exchange rate pass-through to import prices in South Africa: Is there asymmetry?
There is growing emphasis on the role played by the private sector in alleviating poverty in Africa. At the same time, greater focus is being placed on cash transfers as a poverty alleviation tool. This paper provides an economic rationale for private sector involvement in the provision of cash transfers. Previous research has focused on how the financial sector can provide payment solutions. In addition to payment mechanisms, the paper examines other avenues through which the private sector can contribute to cash transfer programmes .business taxes and Corporate Social Responsibility (CSR). Reducing corruption in tax administration and an enabling investment climate are essential if business taxes are to be a sustainable financing source for cash transfers. Governments can incorporate CSR into national policies and strategies which identify cash transfers as a poverty alleviation instrument. Cell phone banking, mobile branches, Point of sale (POS) technology and low cost banking are increasing access to financial services by the poor. These financial innovations can be used to make cash transfer payments.Exchange rate pass-through, Asymmetric pass-through, VECM, South Africa
The Relative Space: Space Measurements on a Rotating Platform
We introduce here the concept of relative space, an extended 3-space which is
recognized as the only space having an operational meaning in the study of the
space geometry of a rotating disk. Accordingly, we illustrate how space
measurements are performed in the relative space, and we show that an old-aged
puzzling problem, that is the Ehrenfest's paradox, is explained in this purely
relativistic context. Furthermore, we illustrate the kinematical origin of the
tangential dilation which is responsible for the solution of the Ehrenfest's
paradox.Comment: 14 pages, 2 EPS figures, LaTeX, to appear in the European Journal of
Physic
The alpha-effect in rotating convection: a comparison of numerical simulations
Numerical simulations are an important tool in furthering our understanding
of turbulent dynamo action, a process that occurs in a vast range of
astrophysical bodies. It is important in all computational work that
comparisons are made between different codes and, if non-trivial differences
arise, that these are explained. Kapyla et al (2010: MNRAS 402, 1458) describe
an attempt to reproduce the results of Hughes & Proctor (2009: PRL 102, 044501)
and, by employing a different methodology, they arrive at very different
conclusions concerning the mean electromotive force and the generation of
large-scale fields. Here we describe why the simulations of Kapyla et al (2010)
are simply not suitable for a meaningful comparison, since they solve different
equations, at different parameter values and with different boundary
conditions. Furthermore we describe why the interpretation of Kapyla et al
(2010) of the calculation of the alpha-effect is inappropriate and argue that
the generation of large-scale magnetic fields by turbulent convection remains a
problematic issue.Comment: Submitted to MNRAS. 5 pages, 3 figure
Hawking Radiation as Tunneling: the D-dimensional rotating case
The tunneling method for the Hawking radiation is revisited and applied to
the dimensional rotating case. Emphasis is given to covariance of results.
Certain ambiguities afflicting the procedure are resolved.Comment: Talk delivered at the Seventh International Workshop Quantum Field
Theory under the influence of External Conditions, QFEXT'05, september
05,Barcelona, Spain. To appear in Journal of Phys.
On the Observables Describing a Quantum Reference Frame
A reference frame F is described by the element g of the Poincare' group P
which connects F with a given fixed frame F_0. If F is a quantum frame, defined
by a physical object following the laws of quantum physics, the parameters of g
have to be considered as quantum observables. However, these observables are
not compatible and some of them, namely the coordinates of the origin of F,
cannot be represented by self-adjoint operators. Both these difficulties can be
overcome by considering a positive-operator-valued measure (POVM) on P,
covariant with respect to the left translations of the group, namely a
covariance system. We develop a construction procedure for this kind of
mathematical structure. The formalism is also used to discuss the quantum
observables measured with respect to a quantum reference frame.Comment: 23 pages, no figure
AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz-
Zaboronsky superfield formalism using the language of graded manifolds. As a
main illustarting example, to every Courant algebroid structure we associate
canonically a three-dimensional topological sigma-model. Using the AKSZ
formalism, we construct the Batalin-Vilkovisky master action for the model.Comment: 13 pages, based on lectures at Rencontres mathematiques de Glanon
200
On the Pointwise Behavior of Recursive Partitioning and Its Implications for Heterogeneous Causal Effect Estimation
Decision tree learning is increasingly being used for pointwise inference.
Important applications include causal heterogenous treatment effects and
dynamic policy decisions, as well as conditional quantile regression and design
of experiments, where tree estimation and inference is conducted at specific
values of the covariates. In this paper, we call into question the use of
decision trees (trained by adaptive recursive partitioning) for such purposes
by demonstrating that they can fail to achieve polynomial rates of convergence
in uniform norm, even with pruning. Instead, the convergence may be
poly-logarithmic or, in some important special cases, such as honest regression
trees, fail completely. We show that random forests can remedy the situation,
turning poor performing trees into nearly optimal procedures, at the cost of
losing interpretability and introducing two additional tuning parameters. The
two hallmarks of random forests, subsampling and the random feature selection
mechanism, are seen to each distinctively contribute to achieving nearly
optimal performance for the model class considered
Symplectic Microgeometry II: Generating functions
We adapt the notion of generating functions for lagrangian submanifolds to
symplectic microgeometry. We show that a symplectic micromorphism always admits
a global generating function. As an application, we describe hamiltonian flows
as special symplectic micromorphisms whose local generating functions are the
solutions of Hamilton-Jacobi equations. We obtain a purely categorical
formulation of the temporal evolution in classical mechanics.Comment: 27 pages, 1 figur
One-dimensional Chern-Simons theory
We study a one-dimensional toy version of the Chern-Simons theory. We
construct its simplicial version which comprises features of a low-energy
effective gauge theory and of a topological quantum field theory in the sense
of Atiyah.Comment: 37 page
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