Abstract:
Human T lymphotropic virus type 1 (HTLV-1) is endemic in the southern part of Japan. Infection of the virus can cause adult T cell leukemia/lymphoma (ATL), while most infected individuals remain in a carrier state for a long period of time. Although rare cases of carriers, like ATL patients, who developed opportunistic infections, have been reported, hematological changes of carriers who are prone to opportunistic infections have not been well defined. Here, we present a case of an HTLV-1 carrier who developed Mycobacterium intracellulare infection and Pneumocystis jirovecii pneumonia (PcP) simultaneously. Flow cytometric analysis of bone marrow cells revealed an aberrant compositional change similar to that in ATL patients. This suggests the presence of a pre-ATL state prior to the development of ATL, which is notable in terms of underlying cellular immunodeficiency.

Abstract:
We construct some classes of instanton solutions of eight dimensional noncommutative ADHM equations generalizing the solutions of eight dimensional commutative ADHM equations found by Papadopoulos and Teschendorff, and interpret them as supersymmetric $D0$-$D8$ bound states in a NS $B$-field. Especially, we consider the $D0$-$D8$ system with anti-self-dual $B$-field preserving 3/16 of supercharges. This system and self-duality conditions are related with the group $Sp(2)$ which is a subgroup of the eight dimensional rotation group SO(8).

Abstract:
We study the noncommutative version of the extended ADHM construction in the eight dimensional U(1) Yang-Mills theory. This construction gives rise to the solutions of the BPS equations in the Yang-Mills theory, and these solutions preserve at least 3/16 of supersymmetries. In a wide subspace of the extended ADHM data, we show that the integer $k$ which appears in the extended ADHM construction should be interpreted as the $D4$-brane charge rather than the $D0$-brane charge by explicitly calculating the topological charges in the case that the noncommutativity parameter is anti-self-dual. We also find the relationship with the solution generating technique and show that the integer $k$ can be interpreted as the charge of the $D0$-brane bound to the $D8$-brane with the $B$-field in the case that the noncommutativity parameter is self-dual.

Abstract:
We study the 1/4 BPS equations in the eight dimensional noncommutative Yang-Mills theory found by Bak, Lee and Park. We explicitly construct some solutions of the 1/4 BPS equations using the noncommutative version of the ADHM-like construction in eight dimensions. From the calculation of topological charges, we show that our solutions can be interpreted as the bound states of the $D0$-$D4$-$D8$ with a $B$-field. We also discuss the structure of the moduli space of the 1/4 BPS solutions and determine the metric of the moduli space of the U(2) one-instanton in four and eight dimensions.

Abstract:
We used three kinds of tungsten sheets in this study. First, we examined microstructure such as grain size distribution using an optical microscope. Secondly, we carried out three-point bend tests at temperatures between about 290 and 500？K. Then, we examined fracture surface of a failed specimen using a scanning electron microscope. Lastly, by analyzing all these results, we evaluated apparent intergranular and transgranular fracture strengths and discussed strengths and ductility of tungsten. Additionally, we compared mechanical properties of tungsten with those of molybdenum. 1. Introduction Generally, pure molybdenum after recrystallization indicates a certain amount of ductility at room temperature. In contrast, pure tungsten after recrystallization does not deform plastically near room temperature, since its ductile-to-brittle transition temperature is much above 400？K [1]. Such brittleness of tungsten is principally attributed to high hardness which leads to high yield strength and difficulty of plastic deformation. However, detailed discussion on such difference in the strengths and ductility between tungsten and molybdenum has not been carried out until now. Materials used in this study are pure tungsten, K-doped tungsten, and La-doped tungsten. All these materials are subjected to recrystallization treatments in various conditions. First, we examined microstructure such as average grain size and size distribution of the specimen after recrystallization using an optical microscope (OM). Secondly, we carried out three-point bend tests at temperatures between about 290？K and 500？K and obtained yield and maximum strengths. From the temperature dependences of the yield and the maximum strengths, we evaluated two parameters (critical stress and critical temperature) [2, 3]. Lastly, we carried out fracture surface observation of a failed specimen by a scanning electron microscope (SEM). Analyzing these experimental data, we estimated apparent intergranular and/or transgranular fracture strengths. Furthermore, we compared and discussed difference in the mechanical properties between tungsten and molybdenum. 2. Experimental Procedures Three kinds of tungsten sheets were used in this study. One is pure tungsten sheet (designated as “W” in the text). The others are K-doped tungsten sheet (K: about 50？mass ppm, designated as “KDW” in the text) and La-doped tungsten sheet (La2O3: about 1 mass%, designated as “LDW” in the text). Thickness of these sheets is about 1 mm. The materials are produced by powder metallurgy, sintered, hot-rolled, and stress

Abstract:
This study investigated abnormalities of the first three steps of gait initiation in patients with Parkinson’s disease without freezing of gait (PD ？ FOG) and investigated which abnormalities are related to FOG. Seven PD ？ FOG and seven age-matched healthy controls performed self-generated or cue-triggered gait initiation. Data for PD patients with FOG (PD + FOG) were cited from a previous study using a procedure similar to that used in the present study. Gait initiation was abnormal, and external cue normalized some abnormalities in PD ？ FOG. The initial swing side was fairly consistent among the trials in both PD ？ FOG and in healthy controls, although the initial swing side was inconsistent in PD + FOG. The duration of the first double limb support (DLS) was the only parameter that depends on FOG severity and that was abnormal in PD + FOG but was not abnormal in PD ？ FOG. The variability of the initial swing side and prolonged first DLS are abnormalities specifically related to FOG.

Abstract:
We present a review of the normal form theory for weakly dispersive nonlinear wave equations where the leading order phenomena can be described by the KdV equation. This is an infinite dimensional extension of the well-known Poincar\'e-Dulac normal form theory for ordinary differential equations. We also provide a detailed analysis of the interaction problem of solitary wavesas an important application of the normal form theory. Several explicit examples are discussed based on the normal form theory, and the results are compared with their numerical simulations. Those examples include the ion acoustic wave equation, the Boussinesq equation as a model of the shallow water waves, the regularized long wave equation and the Hirota bilinear equation having a 7th order linear dispersion.

Abstract:
This paper studies maximum likelihood(ML) decoding in error-correcting codes as rational maps and proposes an approximate ML decoding rule by using a Taylor expansion. The point for the Taylor expansion, which will be denoted by $p$ in the paper, is properly chosen by considering some dynamical system properties. We have two results about this approximate ML decoding. The first result proves that the order of the first nonlinear terms in the Taylor expansion is determined by the minimum distance of its dual code. As the second result, we give numerical results on bit error probabilities for the approximate ML decoding. These numerical results show better performance than that of BCH codes, and indicate that this proposed method approximates the original ML decoding very well.

Abstract:
To the coverage problem of sensor networks, V. de Silva and R. Ghrist (2007) developed several approaches based on (persistent) homology theory. Their criteria for the coverage are formulated on the Rips complexes constructed by the sensors, in which their locations are supposed to be fixed. However, the sensors are in general affected by perturbations (e.g., natural phenomena), and hence the stability of the coverage criteria should be also discussed. In this paper, we present a coverage theorem stable under perturbation. Furthermore, we also introduce a method of eliminating redundant cover after perturbation. The coverage theorem is derived by extending the Rips interleaving theorem studied by F. Chazal, V. de Silva, and S. Oudot (2013) into an appropriate relative version.

Abstract:
This paper studies a higher dimensional generalization of Frieze's $\zeta(3)$-limit theorem in the Erd\"os-R\'enyi graph process. Frieze's theorem states that the expected weight of the minimum spanning tree converges to $\zeta(3)$ as the number of vertices goes to infinity. In this paper, we study the $d$-Linial-Meshulam process as a model for random simplicial complexes, where $d=1$ corresponds to the Erd\"os-R\'enyi graph process. First, we define spanning acycles as a higher dimensional analogue of spanning trees, and connect its minimum weight to persistent homology. Then, our main result shows that the expected weight of the minimum spanning acycle behaves in $O(n^{d-1})$.