Laplace's rule of succession in information geometry

Laplace's "add-one" rule of succession modifies the observed frequencies in a sequence of heads and tails by adding one to the observed counts. This improves prediction by avoiding zero probabilities and corresponds to a uniform Bayesian prior on the parameter. The canonical Jeffreys prior corresponds to the "add-one-half" rule. We prove that, for exponential families of distributions, such Bayesian predictors can be approximated by taking the average of the maximum likelihood predictor and the \emph{sequential normalized maximum likelihood} predictor from information theory. Thus in this case it is possible to approximate Bayesian predictors without the cost of integrating or sampling in parameter space

Parametric Fokker-Planck equation

We derive the Fokker-Planck equation on the parametric space. It is the Wasserstein gradient flow of relative entropy on the statistical manifold. We pull back the PDE to a finite dimensional ODE on parameter space. Some analytical example and numerical examples are presented

Tests of Dynamical Flux Emergence as a Mechanism for CME Initiation

Current coronal mass ejection (CME) models set their lower boundary to be in the lower corona. They do not calculate accurately the transfer of free magnetic energy from the convection zone to the magnetically dominated corona because they model the effects of flux emergence using kinematic boundary conditions or simply assume the appearance of flux at these heights. We test the importance of including dynamical flux emergence in CME modeling by simulating, in 2.5D, the emergence of sub-surface flux tubes into different coronal magnetic field configurations. We investigate how much free magnetic energy, in the form of shear magnetic field, is transported from the convection zone to the corona, and whether dynamical flux emergence can drive CMEs. We find that multiple coronal flux ropes can be formed during flux emergence, and although they carry some shear field into the corona, the majority of shear field is confined to the lower atmosphere. Less than 10% of the magnetic energy in the corona is in the shear field, and this, combined with the fact that the coronal flux ropes bring up significant dense material, means that they do not erupt. Our results have significant implications for all CME models which rely on the transfer of free magnetic energy from the lower atmosphere into the corona but which do not explicitly model this transfer. Such studies of flux emergence and CMEs are timely, as we have new capabilities to observe this with Hinode and SDO, and therefore to test the models against observations

SIMS chemical analysis of extended impacts on the leading and trailing edges of LDEF experiment AO187-2

Numerous 'extended impacts' found in both leading and trailing edge capture cells were successfully analyzed for the chemical composition of projectile residues by secondary ion mass spectrometry (SIMS). Most data were obtained from the trailing edge cells where 45 of 58 impacts were classified as 'probably natural' and the remainder as 'possibly man-made debris.' This is in striking contrast to leading edge cells where 9 of 11 impacts so far measured are definitely classified as orbital debris. Although all the leading edge cells had lost their plastic entrance foils during flight, the rate of foil failure was similar to that of the trailing edge cells, 10 percent of which were recovered intact. Ultraviolet embrittlement is suspected as the major cause of failure on both leading and trailing edges. The major impediment to the accurate determination of projectile chemistry is the fractionation of volatile and refractory elements in the hypervelocity impact and redeposition processes. This effect had been noted in a simulation experiment but is more pronounced in the LDEF capture cells, probably due to the higher average velocities of the space impacts. Surface contamination of the pure Ge surfaces with a substance rich in Si, but also containing Mg and Al, provides an additional problem for the accurate determination of impactor chemistry. The effect is variable, being much larger on surfaces that were exposed to space than in those cells that remained intact. Future work will concentrate on the analyses of more leading edge impacts and the development of new SIMS techniques for the measurement of elemental abundances in extended impacts

Observational Evidence for Coronal Twisted Flux Rope

Multi-instrument data sets of NOAA AR10938 on Jan. 16, 2007, (e.g., {\emph{Hinode}}, {\it{STEREO}}, {\it{GOES}}, {\it{MLSO}} and {\it{ISOON}} H$\alpha$) are utilized to study the fine structure and evolution of a magnetic loop system exhibiting multiple crossing threads, whose arrangement and individual shapes are very suggestive of individual field lines in a flux rope. The footpoints of the magnetic threads are closely rooted into pores and plage areas. A C-class flare recorded by {\it{GOES}} at approximately 2:35 UT near one of the footpoints of the multi-thread system (along with a wisp of loop material shown by EUV data) led to the brightening of the magnetic structure revealing its fine structure with several threads that indicate a high degree of linking (suggesting a left-handed helical pattern as shown by the filament structure formed later-on). EUV observations by {\emph{Hinode}}/EIS of hot spectral lines at 2:46 UT show a complex structure of coronal loops. The same features were observed about 20 minutes later in X-ray images from {\emph{Hinode}}/XRT and about 30 minutes further in EUV images of {\it{STEREO}}/SECCHI/EUVI with much better resolution. H$\alpha$ and 304 {\AA} images revealed the presence of several filament fibrils in the same area. They evolved a few hours later into a denser structure seemingly showing helical structure, which persistently lasted for several days forming a segment of a larger scale filament. The present observations provide an important indication for a flux robe as a precursor of a solar filament.Comment: 13 pages, 4 figure

Transient dynamics for sequence processing neural networks

An exact solution of the transient dynamics for a sequential associative memory model is discussed through both the path-integral method and the statistical neurodynamics. Although the path-integral method has the ability to give an exact solution of the transient dynamics, only stationary properties have been discussed for the sequential associative memory. We have succeeded in deriving an exact macroscopic description of the transient dynamics by analyzing the correlation of crosstalk noise. Surprisingly, the order parameter equations of this exact solution are completely equivalent to those of the statistical neurodynamics, which is an approximation theory that assumes crosstalk noise to obey the Gaussian distribution. In order to examine our theoretical findings, we numerically obtain cumulants of the crosstalk noise. We verify that the third- and fourth-order cumulants are equal to zero, and that the crosstalk noise is normally distributed even in the non-retrieval case. We show that the results obtained by our theory agree with those obtained by computer simulations. We have also found that the macroscopic unstable state completely coincides with the separatrix.Comment: 21 pages, 4 figure

STEREO quadrature observations of coronal dimming at the onset of mini-CMEs

Context: Using unique quadrature observations with the two STEREO spacecraft, we investigate coronal dimmings at the onset of small-scale eruptions. In CMEs they are believed to indicate the opening up of the coronal magnetic fields at the start of the eruption. Aims: It is to determine whether coronal dimming seen in small-scale eruptions starts before or after chromospheric plasma ejection. Methods: One STEREO spacecraft obtained high cadence, 75 s, images in the He II 304A channel, and the other simultaneous images in the Fe IX/FeX 171A channel. We concentrate on two well-positioned chromospheric eruptions that occurred at disk center in the 171A images, and on the limb in 304A. One was in the quiet Sun and the other was in an equatorial coronal hole. We compare the timing of chromospheric eruption seen in the 304A limb images with the brightenings and dimmings seen on disk in the 171A images. Further we use off-limb images of the low frequency 171A power to infer the coronal structure near the eruptions. Results: In both the quiet Sun and the coronal hole eruption, on disk 171A dimming was seen before the chromospheric eruption, and in both cases it extends beyond the site of the chromospheric eruption. The quiet Sun eruption occurred on the outer edge of the enclosing magnetic field of a prominence and may be related to a small disruption of the prominence just before the 171A dimming. Conclusions: These small-scale chromospheric eruptions started with a dimming in coronal emission just like their larger counterparts. We therefore suggest that a fundamental step in triggering them was the removal of overlying coronal field.Comment: 4 pages, 8 figures. To appear A&A Letters. Movies accompanying this Letter are at http://www.mps.mpg.de/data/outgoing/innes/dims

From neurons to epidemics: How trophic coherence affects spreading processes

Trophic coherence, a measure of the extent to which the nodes of a directed network are organised in levels, has recently been shown to be closely related to many structural and dynamical aspects of complex systems, including graph eigenspectra, the prevalence or absence of feed-back cycles, and linear stability. Furthermore, non-trivial trophic structures have been observed in networks of neurons, species, genes, metabolites, cellular signalling, concatenated words, P2P users, and world trade. Here we consider two simple yet apparently quite different dynamical models -- one a Susceptible-Infected-Susceptible (SIS) epidemic model adapted to include complex contagion, the other an Amari-Hopfield neural network -- and show that in both cases the related spreading processes are modulated in similar ways by the trophic coherence of the underlying networks. To do this, we propose a network assembly model which can generate structures with tunable trophic coherence, limiting in either perfectly stratified networks or random graphs. We find that trophic coherence can exert a qualitative change in spreading behaviour, determining whether a pulse of activity will percolate through the entire network or remain confined to a subset of nodes, and whether such activity will quickly die out or endure indefinitely. These results could be important for our understanding of phenomena such as epidemics, rumours, shocks to ecosystems, neuronal avalanches, and many other spreading processes

Nonlinear force-free models for the solar corona I. Two active regions with very different structure

With the development of new instrumentation providing measurements of solar photospheric vector magnetic fields, we need to develop our understanding of the effects of current density on coronal magnetic field configurations. The object is to understand the diverse and complex nature of coronal magnetic fields in active regions using a nonlinear force-free model. From the observed photospheric magnetic field we derive the photospheric current density for two active regions: one is a decaying active region with strong currents (AR8151), and the other is a newly emerged active region with weak currents (AR8210). We compare the three-dimensional structure of the magnetic fields for both active region when they are assumed to be either potential or nonlinear force-free. The latter is computed using a Grad-Rubin vector-potential-like numerical scheme. A quantitative comparison is performed in terms of the geometry, the connectivity of field lines, the magnetic energy and the magnetic helicity content. For the old decaying active region the connectivity and geometry of the nonlinear force-free model include strong twist and strong shear and are very different from the potential model. The twisted flux bundles store magnetic energy and magnetic helicity high in the corona (about 50 Mm). The newly emerged active region has a complex topology and the departure from a potential field is small, but the excess magnetic energy is stored in the low corona and is enough to trigger powerful flares.Comment: 11 pages, 11 figure

An Information-Geometric Reconstruction of Quantum Theory, I: The Abstract Quantum Formalism

In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few elementary features of quantum phenomena, such as the statistical nature of measurements, complementarity, and global gauge invariance. It is shown that these features can be traced to experimental observations characteristic of quantum phenomena and to general theoretical principles, and thus can reasonably be taken as a starting point of the derivation. When appropriately formulated within an information geometric framework, these features lead to (i) the abstract quantum formalism for finite-dimensional quantum systems, (ii) the result of Wigner's theorem, and (iii) the fundamental correspondence rules of quantum theory, such as the canonical commutation relationships. The formalism also comes naturally equipped with a metric (and associated measure) over the space of pure states which is unitarily- and anti-unitarily invariant. The derivation suggests that the information geometric framework is directly or indirectly responsible for many of the central structural features of the quantum formalism, such as the importance of square-roots of probability and the occurrence of sinusoidal functions of phases in a pure quantum state. Global gauge invariance is seen to play a crucial role in the emergence of the formalism in its complex form.Comment: 26 page