Abstract:
In this paper, the author proved that the base change lifting associated to a totally ramified extension of a non-archimedean local field coincides with a map coming from the close fields theory of Kazhdan under some conditions. As a corollary, we can construct a base change lifting for an APF extension of a mixed characteristic local field.

Abstract:
Deligne's conjecture is the Lefschetz trace formula for correspondences defined over a finite field. In this paper, we prove an analogous statement of Deligne's conjecture with respect to $p^n$-torsion \'etale cohomology under certain conditions, where $p$ is the characteristic of the base field.

Abstract:
Dendrite arborization patterns are critical determinants of neuronal connectivity and integration. Planar and highly branched dendrites of the cerebellar Purkinje cell receive specific topographical projections from two major afferent pathways; a single climbing fiber axon from the inferior olive that extend along Purkinje dendrites, and parallel fiber axons of granule cells that contact vertically to the plane of dendrites. It has been believed that murine Purkinje cell dendrites extend in a single parasagittal plane in the molecular layer after the cell polarity is determined during the early postnatal development. By three-dimensional confocal analysis of growing Purkinje cells, we observed that mouse Purkinje cells underwent dynamic dendritic remodeling during circuit maturation in the third postnatal week. After dendrites were polarized and flattened in the early second postnatal week, dendritic arbors gradually expanded in multiple sagittal planes in the molecular layer by intensive growth and branching by the third postnatal week. Dendrites then became confined to a single plane in the fourth postnatal week. Multiplanar Purkinje cells in the third week were often associated by ectopic climbing fibers innervating nearby Purkinje cells in distinct sagittal planes. The mature monoplanar arborization was disrupted in mutant mice with abnormal Purkinje cell connectivity and motor discoordination. The dendrite remodeling was also impaired by pharmacological disruption of normal afferent activity during the second or third postnatal week. Our results suggest that the monoplanar arborization of Purkinje cells is coupled with functional development of the cerebellar circuitry.

Abstract:
Many studies have looked at
how dogs respond to human communicative information. Here, we examined which
human communicative factors were important in influencing dogs’ responses.
Eleven healthy petdogs with no apparent aggressive behaviour toward
people were recruited. Five sensory conditions (all cues presented; either a visual,
an auditory, or an olfactory cue presented;no cues presented) were provided three times
randomly to each dog during the tests. All tests were video recorded, and both
the dogs’behaviour and time taken to reach the person when she
presented each of the sensory cue conditions were observed. Total rates of reaching
the person were as follows: 97.0% (all cues), 87.9% (auditory cues), 84.4%
(visual cues), 84.4% (olfactorycues), and 69.7% (no cues). The time taken for the dog
to notice the person in the box and then obtain a reward from her differed amongthe five conditions: all cues (6.00±0.32 s) and visual cues (6.02±0.91 s) were significantly faster than auditory cues
(18.56±9.57 s) and no cues (26.55±11.72 s). Thus the type of information input was
important in recognition of the person by the dogs and influenced the dogs’response times; visual cues appeared advantageous in
confirming the person’s presence.

Abstract:
We consider 4D quantum-dilaton gravity with the most general coupling in a homogeneous and isotropic universe, especially an inflationary one, which is essentially characterized by an exponentially expanding scale factor with time. We show that on the inflationary background this theory can be miraculously renormalized, at least at the one-loop level, which must be an effective theory during the inflation of the un-constructed complete quantum theory of gravity.

Abstract:
We consider 4D quantum gravity with N-dilatons with the most general couplings. Especially, on constant dilaton and arbitrary metric background, we show the structure of the divergent terms. We show the constraint between the couplings necessary to cancel the coefficient of the square of the Wyle tensor. Next we show the N dependence of a non-renormalizable divergent term, and found that it cannot be canceled in the case of $N \geq 1$ with any fine-tuning of the couplings.

Abstract:
We present a scenario for deriving Maxwell theory from IIB matrix model. Four dimensional spacetime and theories on it relate different dimensional ones by applying appropriate limits of the backgrounds of matrix model. It is understood by looking at open strings bits as bi-local fields on the spacetime, which are decoupled from the bulk in the limits. The origin of electric-magnetic duality is also discussed in matrix model.

Abstract:
We consider electric-magnetic duality(S-duality) in IIB matrix model with a D3-brane background. We propose the duality transformation by considering that of noncommutative Yang-Mills theory(NCYM) in four dimension. NCYM derived from the matrix model has a Yang-Mills coupling related to the noncommutativity of the spacetime. We argue that open strings bits as bi-local fields on the spacetime are decoupled from the bulk in NCOS decoupling limits as it is in string theory approach. We also discuss how our four dimensional spacetime relates to higher, by applying the decoupling and the commutative limits of the backgrounds of the matrix model.

Abstract:
We show that for a twist knot, the A-polynomial can be obtained from recurrences for the summand in Masbaum's formula of the colored Jones polynomial. Our result supports the AJ conjecture due to S.Garoufalidis.

Abstract:
Freed, Hopkins and Teleman constructed an isomorphism between twisted equivariant K-theory of compact Lie group $G$ and the "Verlinde ring" of the loop group of $G$. We call this isomorphism FHT isomorphism. However, it does not hold naturality with respect to group homomorphisms. We construct two "quasi functors" $t.e.K$ (a modification of twisted equivariant K-theory) and $RL$ (a modification of representation group of loop groups) so that FHT isomorphism is natural transformation between two "quasi functors" for tori, that is, we construct two "induced homomorphisms" of the "quasi functors" $t.e.K$ and $RL$ for a group homomorphism whose tangent map is injective between two tori. In fact, we construct another quasi functor $char$ and verify that three quasi functors are naturally isomorphic. Moreover, we extend the quasi functor $t.e.K$ and $char$ to compact connected Lie group with torsion-free fundamental group and group homomorphism satisfying "the decomposable condition", and verify that they are isomorphic. This is a generalization of a result in [FHT1].