Abstract:
We propose a stochastic model of a fragmentation process, developed by taking into account fragment lifetime as a function of their size based on the Gibrat process. If lifetime is determined by a power function of fragment size, numerical results indicate that size distributions at different times can be collapsed into a single time-invariant curve by scaling size by average fragment size (i.e., the distribution obeys the dynamical scaling law). If lifetime is determined by a logarithmic function of fragment size, the distribution does not obey the scaling law. The necessary and sufficient condition that the scaling law is obeyed is obtained by a scaling analysis of the master equation.

Abstract:
We reproduce patterns of drying paste by means of smoothed particle hydrodynamics which is the one of methods for solving the equations of continuum in the Lagrangian description. In addition to reproduce a realistic pattern, we find that average size of fragments decays in proportion to inverse time in the case of a linear drying process. Distributions of the size of the fragments are obtained depending on the time. We find a universal scaling distribution by scaling analysis with the average size of the fragment.

Structure of semantic memory was investigated in the way of neural network simulations in detail. In the literature, it is well-known that brain damaged patients often showed category specific disorder in various cognitive neuropsychological tasks like picture naming, categorisation, identification tasks and so on. In order to describe semantic memory disorder of brain damaged patients, the attractor neural network model originally proposed Hinton and Shallice (1991) was employed and was tried to re-evaluate the model performance. Especially, in order to answer the question about organization of semantic memory, how our semantic memories are organized, computer simulations were conducted. After the model learned data set (Tyler, Moss, Durrant-Peatfield, & Levy, 2000), units in hidden and cleanup layers were removed and observed its performances. The results showed category specificity. This model could also explain the double dissociation phenomena. In spite of the simplicity of its architecture, the attractor neural network might be considered to mimic human behavior in the meaning of semantic memory organization and its disorder. Although this model could explain various phenomenon in cognitive neuropsychology, it might become obvious that this model had one limitation to explain human behavior. As far as investigation in this study, asymmetry in category specificity between animate and inanimate objects might not be explained on this model without any additional assumptions. Therefore, further studies must be required to improve our understanding for semantic memory organisation.

Abstract:
The morphology and anatomy of leaves of rheophytic and non-rheophytic types of Adenophora triphylla (Thunb.) ADC var. japonica (Regel) H. Hara were compared in order to clarify how leaf characteristics differ. Our results revealed that the leaf of the rheophytic type of A. triphylla var. japonica was narrower than the leaf of the non-rheophytic type because of fewer cells that were also smaller. Moreover, surprisingly, the rheophytic ecotype of A. triphylla var. japonica was thinner than that of the non-rheophytic type, although the general tendency is that the rheophytic leaf is thicker than the closely related non-rheophytic species, suggesting that the rheophytic type of A. triphylla var. japonica adapts differently, as compared to other rheophytic plants, to solar radiation and evaporation.

Abstract:
Arisaema iyoanum Makino subsp. nakaianum (Ohba) H. Ohashi et J. Murata and A. ovale Nakai var. ovale are known to have one-leaved phenotype in both males and females; however, we discovered two-leaved individuals of these species. To elucidate the relationship between growth stage and leaf number of A. iyoanum subsp. nakaianum and A. ovale var. ovale, we conducted a morphological analysis of these plants. Our analysis suggested that the two-leaved individuals of A. iyoanum subsp. nakaianum and A. ovale var. ovale appeared only at the female phase. This suggested that one-leaved A. iyoanum subsp. nakaianum and A. ovale var. ovale individuals could not store the resources and hence changed to two-leaved individuals. This transformation could be explained by the fact that these species occur at high altitudes in mountain areas or regions covered in snow of the Japan Sea side, and their flowering time is also late compared with that in other sympatric Arisaema

The comparative morphology and anatomy of leaves between the coastal ecotype and the normal type of Adenophora triphylla (Thunb.) A.DC. var. japonica (Regel) H.Hara (Campanulaceae) were examined to clarify the differences in morphological characters between the 2 groups. Morphological and anatomical analyses revealed that the coastal ecotype had a thicker leaf than the normal type, because of the increased size of epidermal and spongy cells. Thus, the main morphological change from the normal type into the coastal ecotype of A. triphylla var. japonica is the increase in leaf size, suggesting that the coastal ecotype may have evolved from the normal type via a heterochronic process.

To determine the size and the density of stomata among different environments, we conducted anatomical analyses using Aster hispidusvar. hispidus (open field), As. hispidus var. leptocladus (serpentine soil), and As. hispidus var. insularis (coastal). The stomatal size was not significantly different among these ecotypes but the density of stomata in the serpentine and coastal ecotypes was significantly lower than that of As. hispidusvar. hispidus, which suggests that these ecotypes have experienced selection that reduced the density of stomata for adaptation to the dry conditions of serpentine and coastal areas.

To determine the effects of sika deer (Cervus nippon) browsing on the physical defences of the Japanese pricklyash “Zanthoxylum ailanthoides Sieb. et Zucc.” (Rutaceae), we compared the length and density of prickles on Japanese
islands which were under different browsing
pressures. We measured the length and density of prickles on the midribs, leaf rachis, and stems. We found that the
prickles of Z. ailanthoides on
Kashima island were not significantly longer or at higher densities than those
in the neighbouring areas; the longest pickles at the highest densities were
found on Akune island. The density of sika deer on Akune (ca. 520-600/km^{2}) was higher than that on Kashima (ca. 38.5/km^{2}),
and consequently, Akune was under greater browsing pressure. Our results
suggest that the increased length and density of prickles on Akune is a response by Z. ailanthoides to the high density of sika deer found on the

Abstract:
A graph $G=(V,E)$ is called $(k,\ell)$-full if $G$ contains a subgraph $H=(V,F)$ of $k|V|-\ell$ edges such that, for any non-empty $F' \subseteq F$, $|F'| \leq k|V(F')| - \ell$ holds. Here, $V(F')$ denotes the set of vertices incident to $F'$. It is known that the family of edge sets of $(k,\ell)$-full graphs forms a family of matroid, known as the sparsity matroid of $G$. In this paper, we give a constant-time approximation algorithm for the rank of the sparsity matroid of a degree-bounded undirected graph. This leads to a constant-time tester for $(k,\ell)$-fullness in the bounded-degree model, (i.e., we can decide with high probability whether an input graph satisfies a property $P$ or far from $P$). Depending on the values of $k$ and $\ell$, it can test various properties of a graph such as connectivity, rigidity, and how many spanning trees can be packed. Based on this result, we also propose a constant-time tester for $(k,\ell)$-edge-connected-orientability in the bounded-degree model, where an undirected graph $G$ is called $(k,\ell)$-edge-connected-orientable if there exists an orientation $\vec{G}$ of $G$ with a vertex $r \in V$ such that $\vec{G}$ contains $k$ arc-disjoint dipaths from $r$ to each vertex $v \in V$ and $\ell$ arc-disjoint dipaths from each vertex $v \in V$ to $r$. A tester is called a one-sided error tester for $P$ if it always accepts a graph satisfying $P$. We show, for $k \geq 2$ and (proper) $\ell \geq 0$, any one-sided error tester for $(k,\ell)$-fullness and $(k,\ell)$-edge-connected-orientability requires $\Omega(n)$ queries.

Abstract:
We give a new algorithm of slow continued fraction expansion related to any real cubic number field as a 2-dimensional version of the Farey map. Using our algorithm, we can find the generators of dual substitutions (so-called tiling substitutions) for any stepped surface for any cubic direction.