Abstract:
We study the Hausdorff dimension and measures of full Hausdorff dimension for a compact invariant set of an expanding nonconformal map on the torus given by an integer-valued diagonal matrix. The Hausdorff dimension of a "general Sierpinski carpet" was found by McMullen and Bedford and the uniqueness of the measure of full Hausdorff dimension in some cases was proved by Kenyon and Peres. We extend these results by using compensation functions to study a general Sierpinski carpet represented by a shift of finite type. We give some conditions under which a general Sierpinski carpet has a unique measure of full Hausdorff dimension, and study the properties of the unique measure.

Abstract:
We show the existence of a bounded Borel measurable saturated compensation function for a factor map between subshifts. As an application, we find the Hausdorff dimension and measures of full Hausdorff dimension for a compact invariant set of an expanding nonconformal map on the torus given by an integer-valued diagonal matrix. These problems were studied in [19] for a compact invariant set whose symbolic representation is a shift of finite type under the condition of the existence of a saturated compensation function. We extend the results by presenting a formula for the Hausdorff dimension for a compact invariant set whose symbolic representation is a subshift without the condition and characterizing the invariant ergodic measures of full dimension as the ergodic equilibrium states of a constant multiple of a measurable compensation function. For a compact invariant set whose symbolic representation is a topologically mixing shift of finite type, we study uniqueness and the properties for the unique invariant ergodic measure of full dimension by using a measurable compensation function. Our positive results narrow the possibility of where an example having more than one measure of full dimension can be found.

Abstract:
Let $(X, \sigma_X), (Y, \sigma_Y)$ be one-sided subshifts with the specification property and $\pi:X\rightarrow Y$ a factor map. Let $\mu$ be a unique invariant Gibbs measure for a sequence of continuous functions $\F=\{\log f_n\}_{n=1}^{\infty}$ on $X$, which is an almost additive potential with bounded variation. We show that $\pi\mu$ is also a unique invariant Gibbs measure for a sequence of continuous functions $\G=\{\log g_n\}_{n=1}^{\infty}$ on $Y$. When $(X, \sigma_X)$ is a full shift, we characterize $\G$ and $\mu$ by using relative pressure. This almost additive potential $\G$ is a generalization of a continuous function found by Pollicott and Kempton in their work on the images of Gibbs measures for continuous functions under factor maps. We also consider the following question: Given a unique invariant Gibbs measure $\nu$ for a sequence of continuous functions $\F_2$ on $Y$, can we find an invariant Gibbs measure $\mu$ for a sequence of continuous functions $\F_1$ on $X$ such that $\pi\mu=\nu$? We show that such a measure exists under a certain condition. If $(X, \sigma_X)$ is a full shift and $\nu$ is a unique invariant Gibbs measure for a function in the Bowen class, then we can find a preimage $\mu$ of $\nu$ which is a unique invariant Gibbs measure for a function in the Bowen class.

Abstract:
We give an explicit geometric description of the $\times2,\times3$ system, and use his to study a uniform family of Markov partitions related to those of Wilson and Abramov. The behaviour of these partitions is stable across expansive cones and transitions in this behaviour detects the non-expansive lines.

Abstract:
This paper is devoted to study ergodic optimisation problems for almost-additive sequences of functions (rather than a fixed potential) defined over countable Markov shifts (that is a non-compact space). Under certain assumptions we prove that any accumulation point of a family of Gibbs equilibrium measures is a maximising measure. Applications are given in the study of the joint spectral radius and to multifractal analysis of Lyapunov exponent of non-conformal maps.

Abstract:
In this note we prove that every weak Gibbs measure for an asymptotically additive sequences is a Gibbs measure for another asymptotically additive sequence. In particular, a weak Gibbs measure for a continuous potential is a Gibbs measure for an asymptotically additive sequence. This allows, for example, to apply recent results on dimension theory of asymptotically additive sequences to study multifractal analysis for weak Gibbs measure for continuous potentials.

Abstract:
We introduce a definition of pressure for almost-additive sequences of continuous functions defined over (non-compact) countable Markov shifts. The variational principle is proved. Under certain assumptions we prove the existence of Gibbs and equilibrium measures. Applications are given to the study of maximal Lypaunov exponents of product of matrices.

Abstract:
Inhibition of protein tyrosine phosphatase by orthovanadate induces vasoconstriction, which is mediated by the Rho kinase-dependent inactivation of myosin light chain phosphatase (MLCP) via signaling downstream of Src-induced activation of the epidermal growth factor (EGF) receptor. The present study investigated the potential role of EGF in orthovanadate (OVA)-dependent vaso-constriction. OVA-induced aortic contraction significantly increased in the presence of EGF, and was abolished by inhibitors of Rho kinase (Y27632), extracellular signal-regulated kinase 1 and 2 (Erk1/2) (FR180204), Erk1/2 kinase (PD98059), EGF receptor (AG1478), and Src (PP2). Treatment of the rat endothelium-denuded thoracic aorta with either EGF or OVA augmented the phosphorylation of myosin phosphatase target subunit 1 (MYPT1) at Thr-853 and of the EGF receptor at Tyr-1173. The phosphorylation of MYPT1 was further increased by co-stimulation with EGF and OVA. EGF receptor phosphorylation at Tyr-845 was also increased by EGF or OVA; this effect was augmented by co-stimulation with EGF and OVA, and was abolished by Src inhibition. In addition, Erk1/2 was phosphorylated by EGF or by co-treatment with EGF and OVA; this was abolished by an EGF receptor inhibitor, but not by Src inhibition. These results suggested that OVA-induced EGF-related contraction was mediated by the Rho kinase-dependent inactivation of MLCP via two different signaling cascades: Src-dependent phosphorylation of the EGF receptor at Tyr-845 and EGF-dependent phosphorylation of Erk1/2.

Abstract:
Recently, ontological study has been one of the key concerns of geographic information science, a number of studies have been conducted in both of philosophical and knowledge engineering approach. Some studies pointed out the importance of human cognition and social context for development of ontologies. This paper presents empirical investigation of common sense of land use categories for development of suitable ontologies for each cultural or speech communities. Distinctions and characteristics in perceiving land use categories were described by a psychological method that was submitted to Japanese graduate and undergraduate students. In addition the results were analyzed using corresponddence analysis, a statistical technique for categorical data. This analysis serves to clarify the dominant determining factors for land use categories.

Abstract:
The geometric and biomechanical properties of the larynx strongly influence voice quality and efficiency. A physical understanding of phonation natures in pathological conditions is important for predictions of how voice disorders can be treated using therapy and rehabilitation. Here, we present a continuum-based numerical model of phonation that considers complex fluid-structure interactions occurring in the airway. This model considers a three-dimensional geometry of vocal folds, muscle contractions, and viscoelastic properties to provide a realistic framework of phonation. The vocal fold motion is coupled to an unsteady compressible respiratory flow, allowing numerical simulations of normal and diseased phonations to derive clear relationships between actual laryngeal structures and model parameters such as muscle activity. As a pilot analysis of diseased phonation, we model vocal nodules, the mass lesions that can appear bilaterally on both sides of the vocal folds. Comparison of simulations with and without the nodules demonstrates how the lesions affect vocal fold motion, consequently restricting voice quality. Furthermore, we found that the minimum lung pressure required for voice production increases as nodules move closer to the center of the vocal fold. Thus, simulations using the developed model may provide essential insight into complex phonation phenomena and further elucidate the etiologic mechanisms of voice disorders.