A New Galactic Extinction Map of the Cygnus Region

We have made a Galactic extinction map of the Cygnus region with 5' spatial resolution. The selected area is 80^\circ to 90^\circ in the Galactic longitude and -4^\circ to 8^\circ in the Galactic latitude. The intensity at 140 \mum is derived from the intensities at 60 and 100 \mum of the IRAS data using the tight correlation between 60, 100, and 140 \mum found in the Galactic plane. The dust temperature and optical depth are calculated with 5' resolution from the 140 and 100 \mum intensity, and Av is calculated from the optical depth. In the selected area, the mean dust temperature is 17 K, the minimum is 16 K, and the maximum is 30 K. The mean Av is 6.5 mag, the minimum is 0.5 mag, and the maximum is 11 mag. The dust temperature distribution shows significant spatial variation on smaller scales down to 5'. Because the present study can trace the 5'-scale spatial variation of the extinction, it has an advantage over the previous studies, such as the one by Schlegel, Finkbeiner, & Davis, who used the COBE/DIRBE data to derive the dust temperature distribution with a spatial resolution of 1^\circ. The difference of Av between our map and Schlegel et al.'s is \pm 3 mag. A new extinction map of the entire sky can be produced by applying the present method.Comment: 27 pages, 14 figures, accepted for publication in Ap

Unimodality Problems in Ehrhart Theory

Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart $h^*$-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart $h^*$-vectors and highlight open questions and problems.Comment: Published in Recent Trends in Combinatorics, Beveridge, A., et al. (eds), Springer, 2016, pp 687-711, doi 10.1007/978-3-319-24298-9_27. This version updated October 2017 to correct an error in the original versio

Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections

We consider testing independence in group-wise selections with some restrictions on combinations of choices. We present models for frequency data of selections for which it is easy to perform conditional tests by Markov chain Monte Carlo (MCMC) methods. When the restrictions on the combinations can be described in terms of a Segre-Veronese configuration, an explicit form of a Gr\"obner basis consisting of moves of degree two is readily available for performing a Markov chain. We illustrate our setting with the National Center Test for university entrance examinations in Japan. We also apply our method to testing independence hypotheses involving genotypes at more than one locus or haplotypes of alleles on the same chromosome.Comment: 25 pages, 5 figure

On positivity of Ehrhart polynomials

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart coefficients are positive (which is not true for all integral polytopes). The main purpose of this article is to survey interesting families of polytopes that are known to be Ehrhart positive and discuss the reasons from which their Ehrhart positivity follows. We also include examples of polytopes that have negative Ehrhart coefficients and polytopes that are conjectured to be Ehrhart positive, as well as pose a few relevant questions.Comment: 40 pages, 7 figures. To appear in in Recent Trends in Algebraic Combinatorics, a volume of the Association for Women in Mathematics Series, Springer International Publishin

A Product Formula for the Normalized Volume of Free Sums of Lattice Polytopes

The free sum is a basic geometric operation among convex polytopes. This note focuses on the relationship between the normalized volume of the free sum and that of the summands. In particular, we show that the normalized volume of the free sum of full dimensional polytopes is precisely the product of the normalized volumes of the summands.Comment: Published in the proceedings of 2017 Southern Regional Algebra Conferenc

Methylation pattern of CDH13 gene in digestive tract cancers

Recently, the loss of CDH13 (T-cadherin, H-cadherin) gene expression accompanied by CDH13 promoter methylation was identified in colon cancers. We examined CDH13 methylation in oesophageal and gastric carcinomas. Five of 37 oesophageal cancers (14%) and 23 of 66 gastric cancers (35%) demonstrated abnormal methylation of the CDH13 promoter. Abnormal methylation was frequently found in gastric cancers of patients at all clinical stages just as in E-cadherin, another of the cadherin family, suggesting that these cancers could be methylated at an early stage. These results suggested that CDH13 might play a variety of roles depending on the tissue type

Relative blocking in posets

Poset-theoretic generalizations of set-theoretic committee constructions are presented. The structure of the corresponding subposets is described. Sequences of irreducible fractions associated to the principal order ideals of finite bounded posets are considered and those related to the Boolean lattices are explored; it is shown that such sequences inherit all the familiar properties of the Farey sequences.Comment: 29 pages. Corrected version of original publication which is available at http://www.springerlink.com, see Corrigendu

Downregulation of functional Reelin receptors in projection neurons implies that primary Reelin action occurs at early/premigratory stages

Reelin signaling is essential for correct development of the mammalian brain. Reelin binds to apolipoprotein E receptor 2 and very low-density lipoprotein receptor and induces phosphorylation of Dab1. However, when and where these reactions occur is essentially unknown, and the primary function(s) of Reelin remain unclear. Here, we used alkaline phosphatase fusion of the receptor-binding region of Reelin to quantitatively investigate the localization of functional Reelin receptors (i.e., those on the plasma membrane as mature forms) in the developing brain. In the wild-type cerebral cortex, they are mainly present in the intermediate and subventricular zones, as well as in radial fibers, but much less in the cell bodies of the cortical plate. Functional Reelin receptors are much more abundant in the Reelin-deficient cortical plate, indicating that Reelin induces their downregulation and that it begins before the neurons migrate out of the intermediate zone. In the wild-type cerebellum, functional Reelin receptors are mainly present in the cerebellar ventricular zone but scarcely expressed by Purkinje cells that have migrated out of it. It is thus strongly suggested that Reelin exerts critical actions on migrating projection neurons at their early/premigratory stages en route to their final destinations, in the developing cerebral cortex and cerebellum. Copyright © 2009 Society for Neuroscience.This work was supported by Grants-in-Aid for Scientific Research from the Ministry of Education, Science, Sports, and Culture (M.H., A.B.), Ono Medical Research Foundation, and Kanae Foundation for the Promotion of Medical Science (M.H.). T.H. is a Research Fellow of Japan Society for the Promotion of Science. J.M.L. is a Ramón y Cajal Research Fellow funded by Grant SAF2004-07685 and Fundación Mutua Madrileña.Peer Reviewe