284,555 research outputs found
Extending Nearly-Linear Models
Nearly-Linear Models are a family of neighbourhood models, obtaining lower/upper probabilities from a given probability by a linear affine transformation with barriers. They include a number of known models as special cases, among them the Pari-Mutuel Model, the \u3b5-contamination model, the Total Variation Model and the vacuous lower/upper probabilities. We classified Nearly-Linear models, investigating their consistency properties, in previous work. Here we focus on how to extend those Nearly-Linear Models that are coherent or at least avoid sure loss. We derive formulae for their natural extensions, interpret a specific model as a natural extension itself of a certain class of lower probabilities, and supply a risk measurement interpretation for one of the natural extensions we compute
Modelling the transitional boundary layer
Recent developments in the modelling of the transition zone in the boundary layer are reviewed (the zone being defined as extending from the station where intermittency begins to depart from zero to that where it is nearly unity). The value of using a new non-dimensional spot formation rate parameter, and the importance of allowing for so-called subtransitions within the transition zone, are both stressed. Models do reasonably well in constant pressure 2-dimensional flows, but in the presence of strong pressure gradients further improvements are needed. The linear combination approach works surprisingly well in most cases, but would not be so successful in situations where a purely laminar boundary layer would separate but a transitional one would not. Intermittency-weighted eddy viscosity methods do not predict peak surface parameters well without the introduction of an overshooting transition function whose connection with the spot theory of transition is obscure. Suggestions are made for further work that now appears necessary for developing improved models of the transition zone
Magnetic Energy and Helicity Budgets in the Active-Region Solar Corona. I. Linear Force-Free Approximation
We self-consistently derive the magnetic energy and relative magnetic
helicity budgets of a three-dimensional linear force-free magnetic structure
rooted in a lower boundary plane. For the potential magnetic energy we derive a
general expression that gives results practically equivalent to those of the
magnetic Virial theorem. All magnetic energy and helicity budgets are
formulated in terms of surface integrals applied to the lower boundary, thus
avoiding computationally intensive three-dimensional magnetic field
extrapolations. We analytically and numerically connect our derivations with
classical expressions for the magnetic energy and helicity, thus presenting a
so-far lacking unified treatment of the energy/helicity budgets in the
constant-alpha approximation. Applying our derivations to photospheric vector
magnetograms of an eruptive and a noneruptive solar active regions, we find
that the most profound quantitative difference between these regions lies in
the estimated free magnetic energy and relative magnetic helicity budgets. If
this result is verified with a large number of active regions, it will advance
our understanding of solar eruptive phenomena. We also find that the
constant-alpha approximation gives rise to large uncertainties in the
calculation of the free magnetic energy and the relative magnetic helicity.
Therefore, care must be exercised when this approximation is applied to
photospheric magnetic field observations. Despite its shortcomings, the
constant-alpha approximation is adopted here because this study will form the
basis of a comprehensive nonlinear force-free description of the energetics and
helicity in the active-region solar corona, which is our ultimate objective.Comment: 44 pages, 8 figures, 2 tables. The Astrophysical Journal, in pres
No way out? The double-bind in seeking global prosperity alongside mitigated climate change
In a prior study, I introduced a simple economic growth model designed to be
consistent with general thermodynamic laws. Unlike traditional economic models,
civilization is viewed only as a well-mixed global whole with no distinction
made between individual nations, economic sectors, labor, or capital
investments. At the model core is an observationally supported hypothesis that
the global economy's current rate of primary energy consumption is tied through
a constant to a very general representation of its historically accumulated
wealth. Here, this growth model is coupled to a linear formulation for the
evolution of globally well-mixed atmospheric CO2 concentrations. While very
simple, the coupled model provides faithful multi-decadal hindcasts of
trajectories in gross world product (GWP) and CO2. Extending the model to the
future, the model suggests that the well-known IPCC SRES scenarios
substantially underestimate how much CO2 levels will rise for a given level of
future economic prosperity. For one, global CO2 emission rates cannot be
decoupled from wealth through efficiency gains. For another, like a long-term
natural disaster, future greenhouse warming can be expected to act as an
inflationary drag on the real growth of global wealth. For atmospheric CO2
concentrations to remain below a "dangerous" level of 450 ppmv, model forecasts
suggest that there will have to be some combination of an unrealistically rapid
rate of energy decarbonization and nearly immediate reductions in global
civilization wealth. Effectively, it appears that civilization may be in a
double-bind. If civilization does not collapse quickly this century, then CO2
levels will likely end up exceeding 1000 ppmv; but, if CO2 levels rise by this
much, then the risk is that civilization will gradually tend towards collapse
Dialogue Act Recognition via CRF-Attentive Structured Network
Dialogue Act Recognition (DAR) is a challenging problem in dialogue
interpretation, which aims to attach semantic labels to utterances and
characterize the speaker's intention. Currently, many existing approaches
formulate the DAR problem ranging from multi-classification to structured
prediction, which suffer from handcrafted feature extensions and attentive
contextual structural dependencies. In this paper, we consider the problem of
DAR from the viewpoint of extending richer Conditional Random Field (CRF)
structural dependencies without abandoning end-to-end training. We incorporate
hierarchical semantic inference with memory mechanism on the utterance
modeling. We then extend structured attention network to the linear-chain
conditional random field layer which takes into account both contextual
utterances and corresponding dialogue acts. The extensive experiments on two
major benchmark datasets Switchboard Dialogue Act (SWDA) and Meeting Recorder
Dialogue Act (MRDA) datasets show that our method achieves better performance
than other state-of-the-art solutions to the problem. It is a remarkable fact
that our method is nearly close to the human annotator's performance on SWDA
within 2% gap.Comment: 10 pages, 4figure
Numerical Simulations of Coronal Heating through Footpoint Braiding
Advanced 3D radiative MHD simulations now reproduce many properties of the
outer solar atmosphere. When including a domain from the convection zone into
the corona, a hot chromosphere and corona are self-consistently maintained.
Here we study two realistic models, with different simulated area, magnetic
field strength and topology, and numerical resolution. These are compared in
order to characterize the heating in the 3D-MHD simulations which
self-consistently maintains the structure of the atmosphere. We analyze the
heating at both large and small scales and find that heating is episodic and
highly structured in space, but occurs along loop shaped structures, and moves
along with the magnetic field. On large scales we find that the heating per
particle is maximal near the transition region and that widely distributed
opposite-polarity field in the photosphere leads to a greater heating scale
height in the corona. On smaller scales, heating is concentrated in current
sheets, the thicknesses of which are set by the numerical resolution. Some
current sheets fragment in time, this process occurring more readily in the
higher-resolution model leading to spatially highly intermittent heating. The
large scale heating structures are found to fade in less than about five
minutes, while the smaller, local, heating shows time scales of the order of 2
minutes in one model and 1 minutes in the other, higher-resolution, model.Comment: 20 pages, accepted by Ap
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