1,308 research outputs found
Massive, Topologically Massive, Models
In three dimensions, there are two distinct mass-generating mechanisms for
gauge fields: adding the usual Proca/Pauli-Fierz, or the more esoteric
Chern-Simons (CS), terms. Here we analyze the three-term models where both
types are present, and their various limits. Surprisingly, in the tensor case,
these seemingly innocuous systems are physically unacceptable. If the sign of
the Einstein term is ``wrong'' as is in fact required in the CS case, then the
excitation masses are always complex; with the usual sign, there is a (known)
region of the two mass parameters where reality is restored, but instead we
show that a ghost problem arises, while, for the ``pure mass'' two-term system
without an Einstein action, complex masses are unavoidable. This contrasts with
the smooth behavior of the corresponding vector models. Separately, we show
that the ``partial masslessness'' exhibited by (plain) massive spin-2 models in
de Sitter backgrounds is formally shared by the three-term system: it also
enjoys a reduced local gauge invariance when this mass parameter is tuned to
the cosmological constant.Comment: 7 pages, typos corrected, reference adde
Regret Bounds for Reinforcement Learning with Policy Advice
In some reinforcement learning problems an agent may be provided with a set
of input policies, perhaps learned from prior experience or provided by
advisors. We present a reinforcement learning with policy advice (RLPA)
algorithm which leverages this input set and learns to use the best policy in
the set for the reinforcement learning task at hand. We prove that RLPA has a
sub-linear regret of \tilde O(\sqrt{T}) relative to the best input policy, and
that both this regret and its computational complexity are independent of the
size of the state and action space. Our empirical simulations support our
theoretical analysis. This suggests RLPA may offer significant advantages in
large domains where some prior good policies are provided
Newtonian Counterparts of Spin 2 Massless Discontinuities
Massive spin 2 theories in flat or cosmological () backgrounds
are subject to discontinuities as the masses tend to zero. We show and explain
physically why their Newtonian limits do not inherit this behaviour. On the
other hand, conventional ``Newtonian cosmology'', where is a
constant source of the potential, displays discontinuities: e.g. for any finite
range, can be totally removed.Comment: 6 pages, amplifies the ``Newtonian cosmology'' analysis. To appear as
a Class. Quantum Grav. Lette
Topologically massive gravity as a Pais-Uhlenbeck oscillator
We give a detailed account of the free field spectrum and the Newtonian limit
of the linearized "massive" (Pauli-Fierz), "topologically massive"
(Einstein-Hilbert-Chern-Simons) gravity in 2+1 dimensions about a Minkowski
spacetime. For a certain ratio of the parameters, the linearized free theory is
Jordan-diagonalizable and reduces to a degenerate "Pais-Uhlenbeck" oscillator
which, despite being a higher derivative theory, is ghost-free.Comment: 9 pages, no figures, RevTEX4; version 2: a new paragraph and a
reference added to the Introduction, a new appendix added to review
Pais-Uhlenbeck oscillators; accepted for publication in Class. Quant. Gra
All unitary cubic curvature gravities in D dimensions
We construct all the unitary cubic curvature gravity theories built on the
contractions of the Riemann tensor in D -dimensional (anti)-de Sitter
spacetimes. Our construction is based on finding the equivalent quadratic
action for the general cubic curvature theory and imposing ghost and tachyon
freedom, which greatly simplifies the highly complicated problem of finding the
propagator of cubic curvature theories in constant curvature backgrounds. To
carry out the procedure we have also classified all the unitary quadratic
models. We use our general results to study the recently found cubic curvature
theories using different techniques and the string generated cubic curvature
gravity model. We also study the scattering in critical gravity and give its
cubic curvature extensions.Comment: 24 pages, 1 figure, v2: A subsection on cubic curvature extensions of
critical gravity is added, v3: The part regarding critical gravity is
revised. Version to appear in Class. Quant. Gra
Finite-Dimensional Calculus
We discuss topics related to finite-dimensional calculus in the context of
finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is
called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of
orthofermions. It is shown how to use a matrix approach to implement analytic
representations of the Heisenberg-Weyl algebra in univariate and multivariate
settings. We provide examples for the univariate case. Krawtchouk polynomials
are presented in detail, including a review of Krawtchouk polynomials that
illustrates some curious properties of the Heisenberg-Weyl algebra, as well as
presenting an approach to computing Krawtchouk expansions. From a mathematical
perspective, we are providing indications as to how to implement in finite
terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional
references include
Food Stamps and the Working Poor
The authors show that many households that are eligible for food stamps do not receive them, and that eligible individuals\u27 enrollment is influenced by the states\u27 administrative requirements. Highlighted are the procedures for certifying applicants and recertifying recipients, and policies for treatment of able-bodied adults without dependents.https://research.upjohn.org/up_press/1275/thumbnail.jp
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