1,208 research outputs found
Comparison theory and smooth minimal C*-dynamics
We prove that the C*-algebra of a minimal diffeomorphism satisfies
Blackadar's Fundamental Comparability Property for positive elements. This
leads to the classification, in terms of K-theory and traces, of the
isomorphism classes of countably generated Hilbert modules over such algebras,
and to a similar classification for the closures of unitary orbits of
self-adjoint elements. We also obtain a structure theorem for the Cuntz
semigroup in this setting, and prove a conjecture of Blackadar and Handelman:
the lower semicontinuous dimension functions are weakly dense in the space of
all dimension functions. These results continue to hold in the broader setting
of unital simple ASH algebras with slow dimension growth and stable rank one.
Our main tool is a sharp bound on the radius of comparison of a recursive
subhomogeneous C*-algebra. This is also used to construct uncountably many
non-Morita-equivalent simple separable amenable C*-algebras with the same
K-theory and tracial state space, providing a C*-algebraic analogue of McDuff's
uncountable family of II_1 factors. We prove in passing that the range of the
radius of comparison is exhausted by simple C*-algebras.Comment: 30 pages, no figure
Twisted k-graph algebras associated to Bratteli diagrams
Given a system of coverings of k-graphs, we show that the cohomology of the
resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the
system. We then consider Bratteli diagrams of 2-graphs whose twisted
C*-algebras are matrix algebras over noncommutative tori. For such systems we
calculate the ordered K-theory and the gauge-invariant semifinite traces of the
resulting 3-graph C*-algebras. We deduce that every simple C*-algebra of this
form is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the
sense of Pask-Raeburn-R{\o}rdam-Sims.Comment: 28 pages, pictures prepared using tik
A mixed-mode shell-model theory for nuclear structure studies
We introduce a shell-model theory that combines traditional spherical states,
which yield a diagonal representation of the usual single-particle interaction,
with collective configurations that track deformations, and test the validity
of this mixed-mode, oblique basis shell-model scheme on Mg. The correct
binding energy (within 2% of the full-space result) as well as low-energy
configurations that have greater than 90% overlap with full-space results are
obtained in a space that spans less than 10% of the full space. The results
suggest that a mixed-mode shell-model theory may be useful in situations where
competing degrees of freedom dominate the dynamics and full-space calculations
are not feasible.Comment: 20 pages, 8 figures, revtex 12p
Inelastic light, neutron, and X-ray scatterings related to the heterogeneous elasticity of glasses
The effects of plasticization of poly(methyl methacrylate) glass on the boson
peaks observed by Raman and neutron scattering are compared. In plasticized
glass the cohesion heterogeneities are responsible for the neutron boson peak
and partially for the Raman one, which is enhanced by the composition
heterogeneities. Because the composition heterogeneities have a size similar to
that of the cohesion ones and form quasiperiodic clusters, as observed by small
angle X-ray scattering, it is inferred that the cohesion heterogeneities in a
normal glass form nearly periodic arrangements too. Such structure at the
nanometric scale explains the linear dispersion of the vibrational frequency
versus the transfer momentum observed by inelastic X-ray scattering.Comment: 9 pages, 2 figures, to be published in J. Non-Cryst. Solids
(Proceedings of the 4th IDMRCS
Dynamic modeling of mean-reverting spreads for statistical arbitrage
Statistical arbitrage strategies, such as pairs trading and its
generalizations, rely on the construction of mean-reverting spreads enjoying a
certain degree of predictability. Gaussian linear state-space processes have
recently been proposed as a model for such spreads under the assumption that
the observed process is a noisy realization of some hidden states. Real-time
estimation of the unobserved spread process can reveal temporary market
inefficiencies which can then be exploited to generate excess returns. Building
on previous work, we embrace the state-space framework for modeling spread
processes and extend this methodology along three different directions. First,
we introduce time-dependency in the model parameters, which allows for quick
adaptation to changes in the data generating process. Second, we provide an
on-line estimation algorithm that can be constantly run in real-time. Being
computationally fast, the algorithm is particularly suitable for building
aggressive trading strategies based on high-frequency data and may be used as a
monitoring device for mean-reversion. Finally, our framework naturally provides
informative uncertainty measures of all the estimated parameters. Experimental
results based on Monte Carlo simulations and historical equity data are
discussed, including a co-integration relationship involving two
exchange-traded funds.Comment: 34 pages, 6 figures. Submitte
Perturbations of nuclear C*-algebras
Kadison and Kastler introduced a natural metric on the collection of all
C*-subalgebras of the bounded operators on a separable Hilbert space. They
conjectured that sufficiently close algebras are unitarily conjugate. We
establish this conjecture when one algebra is separable and nuclear. We also
consider one-sided versions of these notions, and we obtain embeddings from
certain near inclusions involving separable nuclear C*-algebras. At the end of
the paper we demonstrate how our methods lead to improved characterisations of
some of the types of algebras that are of current interest in the
classification programme.Comment: 45 page
Classification of graph C*-algebras with no more than four primitive ideals
We describe the status quo of the classification problem of graph C*-algebras
with four primitive ideals or less
Physical Origin of the Boson Peak Deduced from a Two-Order-Parameter Model of Liquid
We propose that the boson peak originates from the (quasi-) localized
vibrational modes associated with long-lived locally favored structures, which
are intrinsic to a liquid state and are randomly distributed in a sea of
normal-liquid structures. This tells us that the number density of locally
favored structures is an important physical factor determining the intensity of
the boson peak. In our two-order-parameter model of the liquid-glass
transition, the locally favored structures act as impurities disturbing
crystallization and thus lead to vitrification. This naturally explains the
dependence of the intensity of the boson peak on temperature, pressure, and
fragility, and also the close correlation between the boson peak and the first
sharp diffraction peak (or prepeak).Comment: 5 pages, 1 figure, An error in the reference (Ref. 7) was correcte
Seasonal Arctic sea ice forecasting with probabilistic deep learning
Anthropogenic warming has led to an unprecedented year-round reduction in Arctic sea ice extent. This has far-reaching consequences for indigenous and local communities, polar ecosystems, and global climate, motivating the need for accurate seasonal sea ice forecasts. While physics-based dynamical models can successfully forecast sea ice concentration several weeks ahead, they struggle to outperform simple statistical benchmarks at longer lead times. We present a probabilistic, deep learning sea ice forecasting system, IceNet. The system has been trained on climate simulations and observational data to forecast the next 6 months of monthly-averaged sea ice concentration maps. We show that IceNet advances the range of accurate sea ice forecasts, outperforming a state-of-the-art dynamical model in seasonal forecasts of summer sea ice, particularly for extreme sea ice events. This step-change in sea ice forecasting ability brings us closer to conservation tools that mitigate risks associated with rapid sea ice loss
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