5,241 research outputs found
Coronal mass ejection initiation: On the nature of the Flux Cancellation Model
We consider a three-dimensional bipolar force-free magnetic field with non
zero magnetic helicity, occupying a half-space, and study the problem of its
evolution driven by an imposed photospheric flux decrease. For this specific
setting of the Flux Cancellation Model describing coronal mass ejections
occuring in active regions, we address the issues of the physical meaning of
flux decrease, of the influence on field evolution of the size of the domain
over which this decrease is imposed, and of the existence of an energetic
criterion characterizing the possible onset of disruption of the configuration.
We show that: (1) The imposed flux disappearance can be interpreted in terms of
transport of positive and negative fluxes towards the inversion line, where
they get annihilated. (2) For the particular case actually computed, in which
the initial state is quite sheared, the formation of a twisted flux rope and
the subsequent global disruption of the configuration are obtained when the
flux has decreased by only a modest amount over a limited part of the whole
active region. (3) The disruption is produced when the magnetic energy becomes
of the order of the decreasing energy of a semi-open field, and then before
reaching the energy of the associated fully open field. This suggests that the
mechanism leading to the disruption is nonequilibrium as in the case where flux
is imposed to decrease over the whole region.Comment: In press in ApJ Letter
On the Limiting Behaviour of the Fundamental Geodesics of Information Geometry
The Information Geometry of extended exponential families has received much recent attention in a variety of important applications, notably categorical data analysis, graphical modelling and, more specifically, log-linear modelling. The essential geometry here comes from the closure of an exponential family in a high-dimensional simplex. In parallel, there has been a great deal of interest in the purely Fisher Riemannian structure of (extended) exponential families, most especially in the Markov chain Monte Carlo literature. These parallel developments raise challenges, addressed here, at a variety of levels: both theoretical and practical—relatedly, conceptual and methodological. Centrally to this endeavour, this paper makes explicit the underlying geometry of these two areas via an analysis of the limiting behaviour of the fundamental geodesics of Information Geometry, these being Amari’s (+1) and (0)-geodesics, respectively. Overall, a substantially more complete account of the Information Geometry of extended exponential families is provided than has hitherto been the case. We illustrate the importance and benefits of this novel formulation through applications
A Neural Network model with Bidirectional Whitening
We present here a new model and algorithm which performs an efficient Natural
gradient descent for Multilayer Perceptrons. Natural gradient descent was
originally proposed from a point of view of information geometry, and it
performs the steepest descent updates on manifolds in a Riemannian space. In
particular, we extend an approach taken by the "Whitened neural networks"
model. We make the whitening process not only in feed-forward direction as in
the original model, but also in the back-propagation phase. Its efficacy is
shown by an application of this "Bidirectional whitened neural networks" model
to a handwritten character recognition data (MNIST data).Comment: 16page
On-Line Learning Theory of Soft Committee Machines with Correlated Hidden Units - Steepest Gradient Descent and Natural Gradient Descent -
The permutation symmetry of the hidden units in multilayer perceptrons causes
the saddle structure and plateaus of the learning dynamics in gradient learning
methods. The correlation of the weight vectors of hidden units in a teacher
network is thought to affect this saddle structure, resulting in a prolonged
learning time, but this mechanism is still unclear. In this paper, we discuss
it with regard to soft committee machines and on-line learning using
statistical mechanics. Conventional gradient descent needs more time to break
the symmetry as the correlation of the teacher weight vectors rises. On the
other hand, no plateaus occur with natural gradient descent regardless of the
correlation for the limit of a low learning rate. Analytical results support
these dynamics around the saddle point.Comment: 7 pages, 6 figure
3D magnetic configuration of the Halpha filament and X-ray sigmoid in NOAA AR 8151
We investigate the structure and relationship of an H filament and an X-ray sigmoid observed in active region NOAA 8151. We first examine the presence of such structures in the reconstructed 3D coronal magnetic field obtained from the non-constant- force-free field hypothesis using a photospheric vector magnetogram (IVM, Mees Solar Observatory). This method allows us to identify several flux systems: a filament (height 30 Mm, aligned with the polarity inversion line (PIL), magnetic field strength at the apex 49 G, number of turns 0.5-0.6), a sigmoid (height 45 Mm, aligned with the PIL, magnetic field strength at the apex 56 G, number of turns 0.5-0.6) and a highly twisted flux tube (height 60 Mm, magnetic field strength at the apex 36 G, number of turns 1.1-1.2). By searching for magnetic dips in the configuration, we identify a filament structure which is in good agreement with the H observations. We find that both filament and sigmoidal structures can be described by a long twisted flux tube with a number of turns less than 1 which means that these structures are stable against kinking. The filament and the sigmoid have similar absolute values of and Jz in the photosphere. However, the electric current density is positive in the filament and negative in the sigmoid: the filament is right-handed whereas the sigmoid is left-handed. This fact can explain the discrepancies between the handedness of magnetic clouds (twisted flux tubes ejected from the Sun) and the handedness of their solar progenitors (twisted flux bundles in the low corona). The mechanism of eruption in AR 8151 is more likely not related to the development of instability in the filament and/or the sigmoid but is associated with the existence of the highly twisted flux tube (~1.1-1.2 turns)
Flat connections and Wigner-Yanase-Dyson metrics
On the manifold of positive definite matrices, we investigate the existence
of pairs of flat affine connections, dual with respect to a given monotone
metric. The connections are defined either using the -embeddings and
finding the duals with respect to the metric, or by means of contrast
functionals. We show that in both cases, the existence of such a pair of
connections is possible if and only if the metric is given by the
Wigner-Yanase-Dyson skew information.Comment: 17 page
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