Discovering a junction tree behind a Markov network by a greedy algorithm

In an earlier paper we introduced a special kind of k-width junction tree, called k-th order t-cherry junction tree in order to approximate a joint probability distribution. The approximation is the best if the Kullback-Leibler divergence between the true joint probability distribution and the approximating one is minimal. Finding the best approximating k-width junction tree is NP-complete if k>2. In our earlier paper we also proved that the best approximating k-width junction tree can be embedded into a k-th order t-cherry junction tree. We introduce a greedy algorithm resulting very good approximations in reasonable computing time. In this paper we prove that if the Markov network underlying fullfills some requirements then our greedy algorithm is able to find the true probability distribution or its best approximation in the family of the k-th order t-cherry tree probability distributions. Our algorithm uses just the k-th order marginal probability distributions as input. We compare the results of the greedy algorithm proposed in this paper with the greedy algorithm proposed by Malvestuto in 1991.Comment: The paper was presented at VOCAL 2010 in Veszprem, Hungar

Calculating energy storage due to topological changes in emerging active region NOAA AR 11112

The Minimum Current Corona (MCC) model provides a way to estimate stored coronal energy using the number of field lines connecting regions of positive and negative photospheric flux. This information is quantified by the net flux connecting pairs of opposing regions in a connectivity matrix. Changes in the coronal magnetic field, due to processes such as magnetic reconnection, manifest themselves as changes in the connectivity matrix. However, the connectivity matrix will also change when flux sources emerge or submerge through the photosphere, as often happens in active regions. We have developed an algorithm to estimate the changes in flux due to emergence and submergence of magnetic flux sources. These estimated changes must be accounted for in order to quantify storage and release of magnetic energy in the corona. To perform this calculation over extended periods of time, we must additionally have a consistently labeled connectivity matrix over the entire observational time span. We have therefore developed an automated tracking algorithm to generate a consistent connectivity matrix as the photospheric source regions evolve over time. We have applied this method to NOAA Active Region 11112, which underwent a GOES M2.9 class flare around 19:00 on Oct.16th, 2010, and calculated a lower bound on the free magnetic energy buildup of ~8.25 x 10^30 ergs over 3 days.Comment: 36 pages, 14 figures. Published in 2012 ApJ, 749, 64. Published version available at http://stacks.iop.org/0004-637X/749/64 Animation available at http://solar.physics.montana.edu/tarrl/data/AR11112.mp

Communication Bottlenecks in Scale-Free Networks

We consider the effects of network topology on the optimality of packet routing quantified by $\gamma_c$, the rate of packet insertion beyond which congestion and queue growth occurs. The key result of this paper is to show that for any network, there exists an absolute upper bound, expressed in terms of vertex separators, for the scaling of $\gamma_c$ with network size $N$, irrespective of the routing algorithm used. We then derive an estimate to this upper bound for scale-free networks, and introduce a novel static routing protocol which is superior to shortest path routing under intense packet insertion rates.Comment: 5 pages, 3 figure

Relating magnetic reconnection to coronal heating

It is clear that the solar corona is being heated and that coronal magnetic fields undergo reconnection all the time. Here we attempt to show that these two facts are in fact related - i.e. coronal reconnection generates heat. This attempt must address the fact that topological change of field lines does not automatically generate heat. We present one case of flux emergence where we have measured the rate of coronal magnetic reconnection and the rate of energy dissipation in the corona. The ratio of these two, $P/\dot{\Phi}$, is a current comparable to the amount of current expected to flow along the boundary separating the emerged flux from the pre-existing flux overlying it. We can generalize this relation to the overall corona in quiet Sun or in active regions. Doing so yields estimates for the contribution to corona heating from magnetic reconnection. These estimated rates are comparable to the amount required to maintain the corona at its observed temperature.Comment: To appear in Phil. Trans. Royal Soc.

Revised metallicity classes for low-mass stars: dwarfs (dM), subdwarfs (sdM), extreme subdwarfs (esdM), and ultra subdwarfs (usdM)

The current classification system of M stars on the main sequence distinguishes three metallicity classes (dwarfs - dM, subdwarfs - sdM, and extreme subdwarfs - esdM). The spectroscopic definition of these classes is based on the relative strength of prominent CaH and TiO molecular absorption bands near 7000A, as quantified by three spectroscopic indices (CaH2, CaH3, and TiO5). We re-examine this classification system in light of our ongoing spectroscopic survey of stars with proper motion \mu > 0.45 "/yr, which has increased the census of spectroscopically identified metal-poor M stars to over 400 objects. Kinematic separation of disk dwarfs and halo subdwarfs suggest deficiencies in the current classification system. Observations of common proper motion doubles indicates that the current dM/sdM and sdM/esdM boundaries in the [TiO5,CaH2+CaH3] index plane do not follow iso-metallicity contours, leaving some binaries inappropriately classified as dM+sdM or sdM+esdM. We propose a revision of the classification system based on an empirical calibration of the TiO/CaH ratio for stars of near solar metallicity. We introduce the parameter \zeta_{TiO/CaH} which quantifies the weakening of the TiO bandstrength due to metallicity effect, with values ranging from \zeta_{TiO/CaH}=1 for stars of near-solar metallicity to \zeta_{TiO/CaH}~0 for the most metal-poor (and TiO depleted) subdwarfs. We redefine the metallicity classes based on the value of the parameter \zeta_{TiO/CaH}; and refine the scheme by introducing an additional class of ultra subdwarfs (usdM). We introduce sequences of sdM, esdM, and usdM stars to be used as formal classification standards.Comment: 15 pages, accepted for publication in the Astrophysical Journa

Formation of bacterial streamers during filtration in microfluidic systems

Bacterial behavior during filtration is complex and is influenced by numerous factors. The aim of this paper is to report on experiments designed to make progress in the understanding of bacterial transfer in filters and membranes. Polydimethylsiloxane (PDMS) microsystems were built to allow direct dynamic observation of bacterial transfer across different microchannel geometries mimicking filtration processes. When filtering Escherichia coli suspensions in such devices, the bacteria accumulated in the downstream zone of the filter forming long streamers undulating in the flow. Confocal microscopy and 3D reconstruction of streamers showed how the streamers are connected to the filter and how they form in the stream. Streamer development was found to be influenced by the flow configuration and the presence of connections or tortuosity between channels. Experiments showed that streamer formation was greatest in a filtration system composed of staggered arrays of squares 10 μm apart

Single parameter galaxy classification: The Principal Curve through the multi-dimensional space of galaxy properties

We propose to describe the variety of galaxies from SDSS by using only one affine parameter. To this aim, we build the Principal Curve (P-curve) passing through the spine of the data point cloud, considering the eigenspace derived from Principal Component Analysis of morphological, physical and photometric galaxy properties. Thus, galaxies can be labeled, ranked and classified by a single arc length value of the curve, measured at the unique closest projection of the data points on the P-curve. We find that the P-curve has a "W" letter shape with 3 turning points, defining 4 branches that represent distinct galaxy populations. This behavior is controlled mainly by 2 properties, namely u-r and SFR. We further present the variations of several galaxy properties as a function of arc length. Luminosity functions variate from steep Schechter fits at low arc length, to double power law and ending in Log-normal fits at high arc length. Galaxy clustering shows increasing autocorrelation power at large scales as arc length increases. PCA analysis allowed to find peculiar galaxy populations located apart from the main cloud of data points, such as small red galaxies dominated by a disk, of relatively high stellar mass-to-light ratio and surface mass density. The P-curve allows not only dimensionality reduction, but also provides supporting evidence for relevant physical models and scenarios in extragalactic astronomy: 1) Evidence for the hierarchical merging scenario in the formation of a selected group of red massive galaxies. These galaxies present a log-normal r-band luminosity function, which might arise from multiplicative processes involved in this scenario. 2) Connection between the onset of AGN activity and star formation quenching, which appears in green galaxies when transitioning from blue to red populations. (Full abstract in downloadable version)Comment: Full abstract in downloadable versio