Abstract:
Pleomorphic adenoma is the most common benign parotid gland tumor. Although its local recurrence rate is known to be high, the recurrence extending to the cervical region is rare. Here we report a case of a young female (25 years old) with pleomorphic adenoma of the parotid gland which showed multiple recurrences through facial to cervical regions over a span of eight years. We also discuss how this benign tumor with a high recurrence rate has been treated in other cases, and how it should be treated.

Steady and useful culture for chondrocytes is essential for cartilage regenerative medicine. However, in conventional plate culture, the chondrocytes become dedifferentiated and lose their ability to make cartilage matrices. Three-dimensional culture mimicking the physiological environment in native chondrocytes is useful to maintain the chondrocyte properties during the proliferation culture. However, the three-dimensional culture is practically a hard task due to difficult harvest of the cells. Thus, we attempted to apply porous materials, hollow fibers for the three-dimensional culture, and developed their module to realize the effective harvest of the cells. Polyethersulfone-based hollow fibers, whose safety and cell affinity were confirmed by the experiment of the coculture with human chondrocytes, were collected to fabricate a module. The hollow fiber module was installed with screw ends, and enabled the easy removal of chondrocytes from the inner unit. Cultured human chondrocytes embedded within collagen hydrogel were put into the outer lumen of the hollow fiber module, while chondrocyte prolfieration medium was perfused through the inner lumen at 0 to 30 mL/min. After 2 weeks’ culture, the flow rate of 3 to 10 mL/min effectively supported the chondrocyte proliferation. Then, long-term culture using the hollow fiber module at flow rate of 5 mL/min was performed, revealing that the cell growth in this module at 3 weeks was approximately twice larger than that in static culture. The numbers of viable cells could be maintained by week 7. The hollow fiber module installed with screw ends can effectively culture and harvest the chondrocytes.

Abstract:
We have investigated several properties of rapidly rotating dynamic black holes generated by gravitational collapse of rotating relativistic stars. At present, numerical simulations of the binary black hole merger are able to produce a Kerr black hole of J_final / M_final^2 up to = 0.91, of gravitational collapse from uniformly rotating stars up to J_final / M_final^2 ~ 0.75, where J_final is the total angular momentum and M_final the total gravitational mass of the hole. We have succeeded in producing a dynamic black hole of spin J_final / M_final^2 ~ 0.95 through the collapse of differentially rotating relativistic stars. We have investigated those dynamic properties through diagnosing multipole moment of the horizon, and found the following two features. Firstly, two different definitions of the angular momentum of the hole, the approximated Killing vector approach and dipole moment of the current multipole approach, make no significant difference to our computational results. Secondly, dynamic hole approaches a Kerr by gravitational radiation within the order of a rotational period of an equilibrium star, although the dynamic hole at the very forming stage deviates quite far from a Kerr. We have also discussed a new phase of quasi-periodic waves in the gravitational waveform after the ringdown in terms of multipole moment of the dynamic hole.

Abstract:
We investigate the rotational core collapse of a rapidly rotating relativistic star by means of a 3+1 hydrodynamical simulations in conformally flat spacetime of general relativity. We concentrate our investigation to the bounce of the rotational core collapse, since potentially most of the gravitational waves from it are radiated around the core bounce. The dynamics of the star is started from a differentially rotating equilibrium star of T/W ~ 0.16 (T is the rotational kinetic energy and W is the gravitational binding energy of the equilibrium star), depleting the pressure to initiate the collapse and to exceed the threshold of dynamical bar instability. Our finding is that the collapsing star potentially forms a bar when the star has a toroidal structure due to the redistribution of the angular momentum at the core bounce. On the other hand, the collapsing star weakly forms a bar when the star has a spheroidal structure. We also find that the bar structure of the star is destroyed when the torus is destroyed in the rotational core collapse. Since the collapse of a toroidal star potentially forms a bar, it can be a promising source of gravitational waves which will be detected in advanced LIGO.

Abstract:
We investigate the gravitational collapse of rapidly rotating relativistic supermassive stars by means of a 3+1 hydrodynamical simulations in conformally flat spacetime of general relativity. We study the evolution of differentially rotating supermassive stars of $q \equiv J/M^{2} \sim 1$ ($J$ is the angular momentum and $M$ is the gravitational mass of the star) from the onset of radial instability at $R/M \sim 65$ ($R$ is the circumferential radius of the star) to the point where the conformally flat approximation breaks down. We find that the collapse of the star of $q \gtrsim 1$, a radially unstable differentially rotating star form a black hole of $q \lesssim 1$. The main reason to prevent formation of a black hole of $q \gtrsim 1$ is that quite a large amount of angular momentum stays at the surface. We also find that most of the mass density collapses coherently to form a supermassive black hole with no appreciable disk nor bar. In the absence of nonaxisymmetric deformation, the collapse of differentially rotating supermassive stars from the onset of radial instability are the promising sources of burst and quasinormal ringing waves in the Laser Interferometer Space Antenna.

Abstract:
This review examines the organizational principles underlying olfactory learning in three specialized contexts that occur during sensitive periods of enhanced neural plasticity and emphasizes some of their common features. All three forms of olfactory learning are associated with neural changes in the olfactory bulb (OB) at the first stage of sensory processing. These changes require the association of the olfactory and somatosensory signals in the OB. They all depend on somatosensory stimulation-induced release of noradrenaline that induces structural and functional changes at mitral-granule cell reciprocal synapses in the OB, resulting in increases in inhibitory transmission. In the accessory olfactory bulb, this represents the enhanced self-inhibition of mitral cells, which selectively disrupts the transmission of the mating male’s pregnancy-blocking signal at this level. In contrast, an extensive network of secondary dendrites of mitral cells in the main olfactory bulb probably results in a sharpening of the odor-induced pattern of activity, due to increases in lateral inhibition, leading to offspring recognition in sheep and neonatal learning in rats and rabbits. These findings show that inhibitory interneurons play a critical role in olfactory learning. Further work on how these neurons shape olfactory circuit function could provide important clues to understand memory functions of interneurons in other systems. Moreover, recent research has suggested that three forms of olfactory learning are controlled by synergistic, redundant, and distributed neural mechanisms. This has general implications regarding the mechanisms that may contribute to the robustness of memories [Current Zoology 56 (6): 819–833, 2010].

Abstract:
For each simply-laced Dynkin graph $\Delta$ we realize the simple complex Lie algebra of type $\Delta$ as a quotient algebra of the complex degenerate composition Lie algebra $L(A)_{1}^{\mathbb{C}}$ of a domestic canonical algebra $A$ of type $\Delta$ by some ideal $I$ of $L(A)_{1}^{\mathbb{C}}$ that is defined via the Hall algebra of $A$, and give an explicit form of $I$. Moreover, we show that each root space of $L(A)_{1}^{\mathbb{C}}/I$ has a basis given by the coset of an indecomposable $A$-module $M$ with root easily computed by the dimension vector of $M$.

Abstract:
Let $G$ be a group acting on a category $\mathcal{C}$. We give a definition for a functor $F\colon \mathcal{C} \to \mathcal{C}'$ to be a $G$-covering and three constructions of the orbit category $\mathcal{C}/G$, which generalizes the notion of a Galois covering of locally finite-dimensional categories with group $G$ whose action on $\mathcal{C}$ is free and locally bonded defined by Gabriel. Here $\mathcal{C}/G$ is defined for any category $\mathcal{C}$ and we do not require that the action of $G$ is free or locally bounded. We show that a $G$-covering is a universal "$G$-invariant" functor and is essentially given by the canonical functor $\mathcal{C} \to \mathcal{C}/G$. By using this we improve a covering technique for derived equivalence. Also we prove theorems describing the relationships between smash product construction and the orbit category construction by Cibils and Marcos (2006) without the assumption that the $G$-action is free. The orbit category construction by a cyclic group generated by an auto-equivalence modulo natural isomorphisms (e.g., the construction of cluster categories) is justified by a notion of the "colimit orbit category". In addition, we give a presentation of the orbit category of a category with a monoid action by a quiver with relations, which enables us to calculate many examples.

Abstract:
Given a group $G$, we define suitable 2-categorical structures on the class of all small categories with $G$-actions and on the class of all small $G$-graded categories, and prove that 2-categorical extensions of the orbit category construction and of the smash product construction turn out to be 2-equivalences (2-quasi-inverses to each other), which extends the Cohen-Montgomery duality.

Abstract:
Let $\Bbbk$ be a commutative ring and $I$ a category. As a generalization of a $\Bbbk$-category with a (pseudo) action of a group we consider a family of $\Bbbk$-categories with a (pseudo, lax, or oplax) action of $I$, namely an oplax functor from $I$ to the 2-category of small $\Bbbk$-categories. We investigate derived equivalences of those oplax functors, and establish a Morita type theorem for them. This gives a base of investigations of derived equivalences of Grothendieck constructions of those oplax functors.