Abstract:
Computed tomography (CT) is commonly used to assess for cerebral hemorrhage and acute ischemic stroke. We investigated the accuracy of CT using a low tube voltage technique in acute ischemic stroke. We compared the standard deviation (SD), contrast between gray and white matter, and contrast-to-noise ratio (CNR) between three groups (120 kV 500 mAs, 100 kV 850 mAs, and 100 kV 750 mAs using hybrid iterative reconstruction) in 50 patients without lesions, and visual evaluation using the normalized rank approach was also performed. The mean value of SD was 4.02, 4.22, and 4.04, respectively, and the contrast between gray and white matter was 7.08, 8.66, and 8.68 HU, respectively; in addition, the CNR was 1.77, 2.06, and 2.15, respectively. The difference between the 100 kV and 120 kV groups was significant (p < 0.01). Visual evaluation showed a significant difference between the 100 and 120 kV groups (p < 0.05).

Apple orchard surface soils in Japan are polluted with copper (Cu), lead (Pb), and arsenic (As) due to long-term use of metal-based pesticides. We investigated the effects of heavy metals accumulated in the surface soils in apple orchards on the microbial biomass and the microbial communities. Soil samples were taken from a chestnut orchard (unpolluted control) and five apple orchards with different degrees of heavy metal pollution. Total concentrations of Cu, Pb, and As in soil ranged from 29 to 931 mg/kg, 35 to 771 mg/kg, and 11 to 198 mg/kg, respectively. The amount of microbial biomass carbon expressed on a soil organic carbon basis decreased with increasing concentrations of heavy metals. Thus, the heavy metals that accumulated in apple orchard surface soils had adverse effects on the soil microbial biomass. The analysis of phospholipid fatty acid (PLFA) composition indicated that the microbial community structure had changed because of the pesticide-derived heavy metals in soil. The relative abundance of gram-positive bacterial marker PLFAs increased and that of fungal marker PLFA decreased with increasing concentrations of heavy metals in soil. Denaturing gradient gel electrophoreses targeting the 16S ribosomal RNA gene of bacteria and the 18S ribosomal RNA gene of fungi also showed shifts in the composition of bacterial and fungal communities induced by soil pollution with heavy metals. However, the diversity of microbial communities was not significantly affected by the heavy metal pollution. This was attributable to the adaptation of the microbial communities in apple orchard surface soils to heavy metals derived from previously used pesticides.

Abstract:
Purpose:
The aim of this study was to develop a method for the direct measurement of
electron beam width and distribution at the scattering foil on the carrousel in
a medical linear accelerator gantry head, which differs from an existing
indirect method for measuring the focal spot size using a camera or metallic
slit located outside the gantry head. Methods: The electron beam emitted by the
linear accelerator was used to irradiate radiochromic film mounted on the
scattering foil on the carrousel, which was not used for clinical treatment.
The electron beam width at the scattering foil position was then evaluated using
the full width at half maximum of the Gaussian distribution approximated from
each one dimensional distribution of the irradiated radiochromic film. Results:
The electron beam width at the scattering foil position was found to be 3.1 to
6.4 mm in the crossline direction and 2.8 to 5.5 mm in the inline direction
with electron energy of 4 to 16 MeV. The two-dimensional distribution of the
electron beam was therefore elliptical or distorted in shape, not circular. Conclusions:
Direct measurement of the electron beam width at the scattering foil in the
carrousel of a medical linear accelerator is possible, though the use of lower
sensitivity film in addition to indirect methods is expected to bring about
better results. However, as this method does not allow for direct measurement
of the incident angle of the accelerated electron beam, further improvements
and refinements are still needed.

Abstract:
By tropical Abel-Jacobi theorem, the Jacobian of a tropical curve is isomorphic to the Picard group. A tropical curve in $\mathbb{R}^2$ corresponds to an immersion from a tropical curve to $\mathbb{R}^2$. In this paper, we show that any principal divisor on a tropical curve is the restriction of a principal divisor on the ambient plane $\mathbb{R}^2$.

Abstract:
The ancestral selection graph in population genetics was introduced by KroneNeuhauser (1997) as an analogue of the coalescent genealogy of a sample of genes from a neutrally evolving population. The number of particles in this graph, followed backwards in time, is a birth and death process with quadratic death and linear birth rates. In this paper an explicit form of the probability distribution of the number of particles is obtained by using the density of the allele frequency in the corresponding diffusion model obtained by Kimura (1955). It is shown that the process of fixation of the allele in the diffusion model corresponds to convergence of the ancestral process to its stationary measure. The time to fixation of the allele conditional on fixation is studied in terms of the ancestral process.

Abstract:
Gene conversion is a mechanism by which a double-strand break in a DNA molecule is repaired using a homologous DNA molecule as a template. As a result, one gene is 'copied and pasted' onto the other gene. It was recently reported that the direction of gene conversion appears to be biased towards G and C nucleotides. In this paper a stochastic model of the dynamics of the bias in gene conversion is developed for a finite population of members in a multigene family. The dual process is the biased voter model, which generates an ancestral random graph for a given sample. An importance-sampling algorithm for computing the likelihood of the sample is also given.

Abstract:
There is a gap in the proof of Lemma VII.4 in [Ann. of Math. (2) 145 (1997), 81--137]. We present an alternative proof of Theorem B (C^1 Omega-stable vector fields satisfy Axiom A). The novel and essential part in the proof of the stability and Omega-stability conjectures for flows is the connecting lemma introduced previously. A mistake in the proof of the last conjecture was pointed out to me by Toyoshiba, who later also provided an independent proof of it, again based on the connecting lemma and previous arguments by Ma\~n\'e and Palis.

Abstract:
A T\"oplitz determinant whose entries are described by a q-analogue of the Narayana polynomials is evaluated by means of Laurent biorthogonal polynomials which allow of a combinatorial interpretation in terms of Schr\"oder paths. As an application, a new proof is given to the Aztec diamond theorem by Elkies, Kuperberg, Larsen and Propp concerning domino tilings of the Aztec diamonds. The proof is based on the correspondence with non-intersecting Schr\"oder paths developed by Eu and Fu.

Abstract:
On tropical geometry in $\rr^2$, the divisor and the Jacobian variety are defined in analogy to algebraic geometry. For study of these objects, it is important to think of the `bunch' of a tropical curve. In this paper, we will show that if the bunch is a bouquet, then the Jacobian is a higher-dimensional torus.

Abstract:
A module $M$ over the tropical semifield $T$ is analogous to a module over a field. We assume that $M$ is straight reflexive, and define the dimension of $M$ to the number of elements of a basis. We study the dimension of a straight reflexive submodule $N \subset M$. Also we find an enough condition to the reflexivity. This result has an application to polytopes in a tropical projective space, and also to a Riemann-Roch theorem for tropical curves.