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

Little Core Based System on Chip Platform for Internet of Thing

Although the technology scaling has enabled designers to integrate a large number of hardware blocks onto a single chip realizing System on Chip (SoC), problems arising from leakage current have made power reduction an important issue. The IoT platform has restricted power consumption because of battery power. In this paper, we propose our little core based IoT platform focusing on the low power and expandability. The experimental results demonstrate the feasibility of our proposal to the IoT

A Scalable Large Format Display Based on Zero Client Processor

This paper proposes zero client module that targets Large  Format Display (LFD) system for display wall. Increased resolution in modern LFD requires a high bandwidth channel and a high performance display controller to transfer the image data to the monitor. The key idea is to use a Gagabit-Etherent communication based Daisy-Chain to transfer an image data. This communication supports sufficient bandwidth for image data transfer. As a result, we implement the LFD system using tha zero  client module and LFDmonitors

Two-point discrimination values vary depending on test site, sex and test modality in the orofacial region: a preliminary study

The two-point discrimination (TPD) test is one of the most commonly used neurosensory tests to assess mechanoperception in the clinical settings. While there have been numerous studies of functional sensibility of the hand using TPD test, there have been relatively not enough reports on TPD in the orofacial region. Objective The aims of the present study were to determine the normal values of TPD in the six trigeminal sites (the forehead, cheek, mentum, upper lip, lower lip, and the tongue tip) and to investigate the effect of the site, sex, and test modality on the TPD perception. Material and Methods Forty healthy volunteers consisting of age-matched men (20) and women (20) with a mean age of 27.1 years were recruited. One examiner performed the TPD test using a simple hand-operated device, i.e., by drawing compass with a blunt or sharp-pointed tip. The static TPD with a blunt-pointed tip (STPDB), moving TPD with a blunt-pointed tip (MTPDB), and static TPD with a sharp-pointed tip (STPDS) were measured. The predictors were the site, sex, and test modality, and the outcome variable was the TPD value. Three-way ANOVA was used for statistics. Results The analysis showed a significant effect of the site, sex and test modality on the TPD values. Significant differences between the test sites were observed with the descending order from the forehead and cheek>;mentum>;upper lip and lower lip>;tongue tip and index finger. Women showed lower TPD values than those of men. The STPDS measurements were consistently lower than those of the STPDB and MTPDB. Conclusions The normal values of TPD in this study suggest that the cheek and forehead were less sensitive than other regions evaluated and women were more sensitive than men. The STPDS was the most sensitive test modality

Multi-cultural, multi-course collaborative project: Learning outcomes and project impact

A multi-course collaborative project is an effective way to enhance student learning because it not only facilitates the development of social skills, but also provides students an opportunity to understand the importance of collaboration with people in diverse areas in the industry (Kim, LaFleur, & Schaeffer, 2008). A collaborative project in a multi-cultural setting enhances student learning by exposing students to other cultures and broadening their scope of knowledge and applications (Chen, Hsu, & Caropreso, 2006)

Soft X-ray Circular Reflectivity from Ferromagnetic Transition-Metal Films Near the Brewster's Angle: Theoretical and Numerical X-ray Resonant Magnetic Scattering Study

We first report a novel phenomenon that manifests itself in a colossal difference in soft x-ray reflectivity from ferromagnetic transition-metal films between the left- and right-handed circular polarization (LCP and RCP) modes at a resonance near normal Brewster's angle. Theoretical and numerical studies of sft x-ray resonant magnetic scattering using the circular-polarization-mode basis reveal that this effect arises from a totally destructive interference of photons scattered individually from chargem orbital, and spin degrees of freedom in magnetized thin films that selectively occurs only for one helicity of the opposite circular modes when the required criteria are fulfilled. Across the normal Brewster's angle. the polarization state of scattered soft x-ray is continuously variable from the RCP to the LCP mode (or vice versa) through the linear s polarization mode by changing the incidence angle of linear p-polarized x rays at the resonance.Comment: 16 pages, 3 figures, 1 tabl