19,699 research outputs found
A note on spin rescalings in post-Newtonian theory
Usually, the reduced mass is viewed as a dropped factor in and
, where and are dimensionless Lagrangian and Hamiltonian
functions. However, it must be retained in post-Newtonian systems of spinning
compact binaries under a set of scaling spin transformations
because and do not keep the
consistency of the orbital equations and the spin precession equations but
and do. When another set of scaling spin
transformations are adopted, the consistency
of the orbital and spin equations is kept in or , and the factor
can be eliminated. In addition, there are some other interesting results as
follows. The next-to-leading-order spin-orbit interaction is induced in the
accelerations of the simple Lagrangian of spinning compact binaries with the
Newtonian and leading-order spin-orbit contributions, and the
next-to-leading-order spin-spin coupling is present in a post-Newtonian
Hamiltonian that is exactly equivalent to the Lagrangian formalism. If any
truncations occur in the Euler-Lagrangian equations or the Hamiltonian, then
the Lagrangian and Hamiltonian formulations lose their equivalence. In fact,
the Lagrangian including the accelerations with or without truncations can be
chaotic for the two bodies spinning, whereas the Hamiltonian without the
spin-spin term is integrable.Comment: 10 pages, 1 figur
-index of observable algebra in the field algebra determined by a normal group
Let be a finite group and a normal subgroup. is the crossed
product of and which is only a subalgebra of , the
quantum double of . One can construct a -subalgebra
of the field algebra of -spin models,
such that is a -module algebra. The concrete
construction of -invariant subalgebra of
is given. By constructing the quasi-basis of conditional
expectation of onto ,
the -index of is given
The construction of observable algebra in field algebra of -spin models determined by a normal subgroup
Let be a finite group and a normal subgroup. Starting from -spin
models, in which a non-Abelian field w.r.t. carries an
action of the Hopf -algebra , a subalgebra of the quantum double
, the concrete construction of the observable algebra
is given, as -invariant subspace. Furthermore,
using the iterated twisted tensor product, one can prove that the observable
algebra , where denotes the algebra of
complex functions on , and the group algebra.Comment: 12 page
A Hierarchical Bayesian Approach for Aerosol Retrieval Using MISR Data
Atmospheric aerosols can cause serious damage to human health and life
expectancy. Using the radiances observed by NASA's Multi-angle Imaging
SpectroRadiometer (MISR), the current MISR operational algorithm retrieves
Aerosol Optical Depth (AOD) at a spatial resolution of 17.6 km x 17.6 km. A
systematic study of aerosols and their impact on public health, especially in
highly-populated urban areas, requires a finer-resolution estimate of the
spatial distribution of AOD values.
We embed MISR's operational weighted least squares criterion and its forward
simulations for AOD retrieval in a likelihood framework and further expand it
into a Bayesian hierarchical model to adapt to a finer spatial scale of 4.4 km
x 4.4 km. To take advantage of AOD's spatial smoothness, our method borrows
strength from data at neighboring pixels by postulating a Gaussian Markov
Random Field prior for AOD. Our model considers both AOD and aerosol mixing
vectors as continuous variables. The inference of AOD and mixing vectors is
carried out using Metropolis-within-Gibbs sampling methods. Retrieval
uncertainties are quantified by posterior variabilities. We also implement a
parallel MCMC algorithm to reduce computational cost. We assess our retrievals
performance using ground-based measurements from the AErosol RObotic NETwork
(AERONET), a hand-held sunphotometer and satellite images from Google Earth.
Based on case studies in the greater Beijing area, China, we show that a 4.4
km resolution can improve the accuracy and coverage of remotely-sensed aerosol
retrievals, as well as our understanding of the spatial and seasonal behaviors
of aerosols. This improvement is particularly important during high-AOD events,
which often indicate severe air pollution.Comment: 39 pages, 15 figure
Symmetry-broken states on networks of coupled oscillators
When identical oscillators are coupled together in a network, dynamical
steady states are often assumed to reflect network symmetries. Here we show
that alternative persistent states may also exist that break the symmetries of
the underlying coupling network. We further show that these symmetry-broken
coexistent states are analogous to those dubbed "chimera states," which can
occur when identical oscillators are coupled to one another in identical ways.Comment: 6 pages, 6 figure
Pure Nash Equilibria: Complete Characterization of Hard and Easy Graphical Games
We consider the computational complexity of pure Nash equilibria in graphical
games. It is known that the problem is NP-complete in general, but tractable
(i.e., in P) for special classes of graphs such as those with bounded
treewidth. It is then natural to ask: is it possible to characterize all
tractable classes of graphs for this problem? In this work, we provide such a
characterization for the case of bounded in-degree graphs, thereby resolving
the gap between existing hardness and tractability results. In particular, we
analyze the complexity of PUREGG(C, -), the problem of deciding the existence
of pure Nash equilibria in graphical games whose underlying graphs are
restricted to class C. We prove that, under reasonable complexity theoretic
assumptions, for every recursively enumerable class C of directed graphs with
bounded in-degree, PUREGG(C, -) is in polynomial time if and only if the
reduced graphs (the graphs resulting from iterated removal of sinks) of C have
bounded treewidth. We also give a characterization for PURECHG(C,-), the
problem of deciding the existence of pure Nash equilibria in colored
hypergraphical games, a game representation that can express the additional
structure that some of the players have identical local utility functions. We
show that the tractable classes of bounded-arity colored hypergraphical games
are precisely those whose reduced graphs have bounded treewidth modulo
homomorphic equivalence. Our proofs make novel use of Grohe's characterization
of the complexity of homomorphism problems.Comment: 8 pages. To appear in AAMAS 201
On the Hyperbolizing metric spaces
In this paper, we prove that the metric space defined by
Z.Ibragimov is asymptotically if the metric space is
, where is a nonempty closed proper subset of . Secondly, based
on the metric , we define a new kind of metric on the set
and show that the new metric space is
also asymptotically without the assumption of on the metric
space .Comment: This paper has been withdrawn by the author due to a crucial sign
error in equation
Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials
Measuring thermal properties of materials is not only of fundamental
importance in understanding the transport processes of energy carriers
(electrons and phonons) but also of practical interest in developing novel
materials with desired thermal conductivity for applications in energy,
electronics, and photonic systems. Over the past two decades, ultrafast
laser-based time-domain thermoreflectance (TDTR) has emerged and evolved as a
reliable, powerful, and versatile technique to measure the thermal properties
of a wide range of bulk and thin film materials and their interfaces. This
tutorial discusses the basics as well as the recent advances of the TDTR
technique and its applications in the thermal characterization of a variety of
materials. The tutorial begins with the fundamentals of the TDTR technique,
serving as a guideline for understanding the basic principles of this
technique. A diverse set of TDTR configurations that have been developed to
meet different measurement conditions are then presented, followed by several
variations of the TDTR technique that function similarly as the standard TDTR
but with their own unique features. This tutorial closes with a summary that
discusses the current limitations and proposes some directions for future
development.Comment: 82 pages, 23 figures, invited tutorial submitted to Journal of
Applied Physic
Jones type basic construction on field algebras of -spin models
Let be a finite group. Starting from the field algebra of
-spin models, one can construct the crossed product -algebra
such that it coincides with the -basic
construction for the field algebra and the -invariant
subalgebra of , where is the quantum double of . Under
the natural -module action on ,the
iterated crossed product -algebra can be obtained, which is
-isomorphic to the -basic construction for and the field algebra . Furthermore, one can show that the
iterated crossed product -algebra is a new field algebra and give the
concrete structure with the order and disorder operators.Comment: 14 page
Minimax Optimal Rates for Poisson Inverse Problems with Physical Constraints
This paper considers fundamental limits for solving sparse inverse problems
in the presence of Poisson noise with physical constraints. Such problems arise
in a variety of applications, including photon-limited imaging systems based on
compressed sensing. Most prior theoretical results in compressed sensing and
related inverse problems apply to idealized settings where the noise is i.i.d.,
and do not account for signal-dependent noise and physical sensing constraints.
Prior results on Poisson compressed sensing with signal-dependent noise and
physical constraints provided upper bounds on mean squared error performance
for a specific class of estimators. However, it was unknown whether those
bounds were tight or if other estimators could achieve significantly better
performance. This work provides minimax lower bounds on mean-squared error for
sparse Poisson inverse problems under physical constraints. Our lower bounds
are complemented by minimax upper bounds. Our upper and lower bounds reveal
that due to the interplay between the Poisson noise model, the sparsity
constraint and the physical constraints: (i) the mean-squared error does not
depend on the sample size other than to ensure the sensing matrix satisfies
RIP-like conditions and the intensity of the input signal plays a critical
role; and (ii) the mean-squared error has two distinct regimes, a low-intensity
and a high-intensity regime and the transition point from the low-intensity to
high-intensity regime depends on the input signal . In the low-intensity
regime the mean-squared error is independent of while in the high-intensity
regime, the mean-squared error scales as , where is the
sparsity level, is the number of pixels or parameters and is the signal
intensity.Comment: 30 pages, 5 figure
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