7,316 research outputs found
On the structure and applications of the Bondi-Metzner-Sachs group
This work is a pedagogical review dedicated to a modern description of the
Bondi-Metzner-Sachs group. The curved space-times that will be taken into
account are the ones that suitably approach, at infinity, Minkowski space-time.
In particular we will focus on asymptotically flat space-times. In this work
the concept of asymptotic symmetry group of those space-times will be studied.
In the first two sections we derive the asymptotic group following the
classical approach which was basically developed by Bondi, van den Burg,
Metzner and Sachs. This is essentially the group of transformations between
coordinate systems of a certain type in asymptotically flat space-times. In the
third section the conformal method and the notion of asymptotic simplicity are
introduced, following mainly the works of Penrose. This section prepares us for
another derivation of the Bondi-Metzner-Sachs group which will involve the
conformal structure, and is thus more geometrical and fundamental. In the
subsequent sections we discuss the properties of the Bondi-Metzner-Sachs group,
e.g. its algebra and the possibility to obtain as its subgroup the Poincar\'e
group, as we may expect. The paper ends with a review of the
Bondi-Metzner-Sachs invariance properties of classical gravitational scattering
discovered by Strominger, that are finding application to black hole physics
and quantum gravity in the literature.Comment: 62 pages, 9 figures. Misprints have been amended and two important
references have been adde
A fuzzy bipolar celestial sphere
We introduce a non-commutative deformation of the algebra of bipolar
spherical harmonics supporting the action of the full Lorentz algebra. Our
construction is close in spirit to the one of the non-commutative spherical
harmonics associated to the fuzzy sphere and, as such, it leads to a maximal
value of the angular momentum. We derive the action of Lorentz boost generators
on such non-commutative spherical harmonics and show that it is compatible with
the existence of a maximal angular momentum.Comment: 15 pages, 4 figures; v2: typos corrected, references added; v3 title
slightly changed, minor adjustments in the presentation, results unchanged.
References added, matches published versio
Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data
We develop a Bayesian approach for selecting the model which is the most
supported by the data within a class of marginal models for categorical
variables formulated through equality and/or inequality constraints on
generalised logits (local, global, continuation or reverse continuation),
generalised log-odds ratios and similar higher-order interactions. For each
constrained model, the prior distribution of the model parameters is formulated
following the encompassing prior approach. Then, model selection is performed
by using Bayes factors which are estimated by an importance sampling method.
The approach is illustrated through three applications involving some datasets,
which also include explanatory variables. In connection with one of these
examples, a sensitivity analysis to the prior specification is also considered
Differentiable Genetic Programming
We introduce the use of high order automatic differentiation, implemented via
the algebra of truncated Taylor polynomials, in genetic programming. Using the
Cartesian Genetic Programming encoding we obtain a high-order Taylor
representation of the program output that is then used to back-propagate errors
during learning. The resulting machine learning framework is called
differentiable Cartesian Genetic Programming (dCGP). In the context of symbolic
regression, dCGP offers a new approach to the long unsolved problem of constant
representation in GP expressions. On several problems of increasing complexity
we find that dCGP is able to find the exact form of the symbolic expression as
well as the constants values. We also demonstrate the use of dCGP to solve a
large class of differential equations and to find prime integrals of dynamical
systems, presenting, in both cases, results that confirm the efficacy of our
approach
Verification of Agent-Based Artifact Systems
Artifact systems are a novel paradigm for specifying and implementing
business processes described in terms of interacting modules called artifacts.
Artifacts consist of data and lifecycles, accounting respectively for the
relational structure of the artifacts' states and their possible evolutions
over time. In this paper we put forward artifact-centric multi-agent systems, a
novel formalisation of artifact systems in the context of multi-agent systems
operating on them. Differently from the usual process-based models of services,
the semantics we give explicitly accounts for the data structures on which
artifact systems are defined. We study the model checking problem for
artifact-centric multi-agent systems against specifications written in a
quantified version of temporal-epistemic logic expressing the knowledge of the
agents in the exchange. We begin by noting that the problem is undecidable in
general. We then identify two noteworthy restrictions, one syntactical and one
semantical, that enable us to find bisimilar finite abstractions and therefore
reduce the model checking problem to the instance on finite models. Under these
assumptions we show that the model checking problem for these systems is
EXPSPACE-complete. We then introduce artifact-centric programs, compact and
declarative representations of the programs governing both the artifact system
and the agents. We show that, while these in principle generate infinite-state
systems, under natural conditions their verification problem can be solved on
finite abstractions that can be effectively computed from the programs. Finally
we exemplify the theoretical results of the paper through a mainstream
procurement scenario from the artifact systems literature
Giant electroresistance and tunable magnetoelectricity in a multiferroic junction
First-principles density functional calculations show that the
multiferroic
junction with asymmetric (RuO/PbO and TiO/SrO) interfaces has a
large ferroelectric depolarizing field, whose switching changes the interface
transmission probabilities for tunneling electrons, leading to
electroresistance modulation over several orders of magnitude. The switching
further affects the interface spin density, naturally driving magnetoresistance
as well as modulated spin-dependent in-plane resistivity, which may be
exploited in field-effect devices.Comment: 7 pages, 10 figures, 1 table; extended upon revie
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