Chemical Evolution in VeLLOs

A new type of object called "Very Low Luminosity Objects (VeLLOs)" has been discovered by the Spitzer Space Telescope. VeLLOs might be substellar objects forming by accretion. However, some VeLLOs are associated with strong outflows, indicating the previous existence of massive accretion. The thermal history, which significantly affects the chemistry, between substellar objects with a continuous low accretion rate and objects in a quiescent phase after massive accretion (outburst) must be greatly different. In this study, the chemical evolution has been calculated in an episodic accretion model to show that CO and N2H+ have a relation different from starless cores or Class 0/I objects. Furthermore, the CO2 ice feature at 15.2 micron will be a good tracer of the thermal process in VeLLOs.Comment: corrected e-mail addres

Radio Imaging of the NGC 1333 IRAS 4B Region

The NGC 1333 IRAS 4B region was observed in the 6.9 mm and 1.3 cm continuum with an angular resolution of about 0.4 arcseconds. IRAS 4BI was detected in both bands, and BII was detected in the 6.9 mm continuum only. The 1.3 cm source of BI seems to be a disk-like flattened structure with a size of about 50 AU. IRAS 4BI does not show any sign of multiplicity. Examinations of archival infrared images show that the dominating emission feature in this region is a bright peak in the southern outflow driven by BI, corresponding to the molecular hydrogen emission source HL 9a. Both BI and BII are undetectable in the mid-IR bands. The upper limit on the far-IR flux of IRAS 4BII suggests that it may be a very low luminosity young stellar object.Comment: To appear in the JKA

Importance sampling schemes for evidence approximation in mixture models

The marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete exploration by a simulated Markov chain (e.g., a Gibbs sequence) of the collection of posterior modes, a phenomenon also known as lack of label switching, as all possible label permutations must be simulated by a chain in order to converge and hence overcome the bias. In an importance sampling approach, imposing label switching to the importance function results in an exponential increase of the computational cost with the number of components. In this paper, two importance sampling schemes are proposed through choices for the importance function; a MLE proposal and a Rao-Blackwellised importance function. The second scheme is called dual importance sampling. We demonstrate that this dual importance sampling is a valid estimator of the evidence and moreover show that the statistical efficiency of estimates increases. To reduce the induced high demand in computation, the original importance function is approximated but a suitable approximation can produce an estimate with the same precision and with reduced computational workload.Comment: 24 pages, 5 figure

Modulation of EEG Theta Band Signal Complexity by Music Therapy [Forthcoming]

The primary goal of this study was to investigate the impact of monochord (MC) sounds, a type of archaic sounds used in music therapy, on the neural complexity of EEG signals obtained from patients undergoing chemotherapy. The secondary goal was to compare the EEG signal complexity values for monochords with those for progressive muscle relaxation (PMR), an alternative therapy for relaxation. Forty cancer patients were randomly allocated to one of the two relaxation groups, MC and PMR, over a period of six months; continuous EEG signals were recorded during the first and last sessions. EEG signals were analysed by applying signal mode complexity, a measure of complexity of neuronal oscillations. Across sessions, both groups showed a modulation of complexity of beta-2 band (20-29 Hz) at midfrontal regions, but only MC group showed a modulation of complexity of theta band (3.5 - 7.5 Hz) at posterior regions. Therefore, the neuronal complexity patterns showed different changes in EEG frequency band specific complexity resulting from two different types of interventions. Moreover, the different neural responses to listening to monochords and PMR were observed after regular relaxation interventions over a short time span

Finding branch-decompositions of matroids, hypergraphs, and more

Given $n$ subspaces of a finite-dimensional vector space over a fixed finite field $\mathcal F$, we wish to find a "branch-decomposition" of these subspaces of width at most $k$, that is a subcubic tree $T$ with $n$ leaves mapped bijectively to the subspaces such that for every edge $e$ of $T$, the sum of subspaces associated with leaves in one component of $T-e$ and the sum of subspaces associated with leaves in the other component have the intersection of dimension at most $k$. This problem includes the problems of computing branch-width of $\mathcal F$-represented matroids, rank-width of graphs, branch-width of hypergraphs, and carving-width of graphs. We present a fixed-parameter algorithm to construct such a branch-decomposition of width at most $k$, if it exists, for input subspaces of a finite-dimensional vector space over $\mathcal F$. Our algorithm is analogous to the algorithm of Bodlaender and Kloks (1996) on tree-width of graphs. To extend their framework to branch-decompositions of vector spaces, we developed highly generic tools for branch-decompositions on vector spaces. The only known previous fixed-parameter algorithm for branch-width of $\mathcal F$-represented matroids was due to Hlin\v{e}n\'y and Oum (2008) that runs in time $O(n^3)$ where $n$ is the number of elements of the input $\mathcal F$-represented matroid. But their method is highly indirect. Their algorithm uses the non-trivial fact by Geelen et al. (2003) that the number of forbidden minors is finite and uses the algorithm of Hlin\v{e}n\'y (2005) on checking monadic second-order formulas on $\mathcal F$-represented matroids of small branch-width. Our result does not depend on such a fact and is completely self-contained, and yet matches their asymptotic running time for each fixed $k$.Comment: 73 pages, 10 figure