Scaling Behaviors of Branched Polymers

We study the thermodynamic behavior of branched polymers. We first study random walks in order to clarify the thermodynamic relation between the canonical ensemble and the grand canonical ensemble. We then show that correlation functions for branched polymers are given by those for $\phi^3$ theory with a single mass insertion, not those for the $\phi^3$ theory themselves. In particular, the two-point function behaves as $1/p^4$, not as $1/p^2$, in the scaling region. This behavior is consistent with the fact that the Hausdorff dimension of the branched polymer is four.Comment: 17 pages, 3 figure

Little IIB Matrix Model

We study the zero-dimensional reduced model of D=6 pure super Yang-Mills theory and argue that the large N limit describes the (2,0) Little String Theory. The one-loop effective action shows that the force exerted between two diagonal blocks of matrices behaves as 1/r^4, implying a six-dimensional spacetime. We also observe that it is due to non-gravitational interactions. We construct wave functions and vertex operators which realize the D=6, (2,0) tensor representation. We also comment on other "little" analogues of the IIB matrix model and Matrix Theory with less supercharges.Comment: 17 pages, references adde

Intra-Day Variation of Urinary Nuclear Matrix Protein 22

Nuclear Matrix Protein 22 (NMP22), a urinary tumor marker for urothelial cancers, is directly released into the urine from the nucleus after cell death, Accordingly, values of NMP22 do not requlre adjustment using other substances such as urinary creatinine. On the other hand, its values might vary according to urine concentration. This study investigated the intra-day variation in the urinary level of NMP22. NMP22 and urinary creatinine were measured in a 24-hour urine sample and 4 spot urine samples obtained from 20 inpatients (10 with bladder cancer, and 10 with non-urothelial cancer or benign tumors). The spot urine samples were collected at 6 a.m., 10 a.m., 2p.m. and 9 p.m. There were no significant differences in NMP22 values between the 24-hour and spot samples in all patients. Out of 10 bladder cancer patients, 6 had positive 24-hour samples. Among these 6 patients, only 3 had 4 positive spot samples (>12.O U/ml): one had 3 positive samples, and 2 had one positive sample. Among the controls, only one patient with renal cancer had a positive 24-hour sample. Only 3 controls, 2 With prostatic cancer and one with renal cancer, had a single positive spot sample. The highest margin between the maximum and minimum levels in the 4 spot samples was 237.8 U/ml in the bladder cancer patients and 16.6 U/ml in the controIs. When the ratios of NMP22 and urinary creatinine values for the 24-hour to spot samples were calculated in each patient, a significant correlation was observed between the ratios of NMP22 and urinary creatinine (r=0.575, p<0.001). The urinary level of NMP22 shows intra-day variation and might be affected by the extent of the concentration of urine samples. The measurement results must be judged with this in mind, especially when judging the results around the cut-off value

Noncommutative Yang-Mills in IIB Matrix Model

We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix model with D-brane backgrounds serve as a concrete definition of noncommutative Yang-Mills. We investigate D-instanton solutions as local excitations on D3-branes. When instantons overlap, their interaction can be well described in gauge theory and AdS/CFT correspondence. We show that IIB matrix model gives us the consistent potential with IIB supergravity when they are well separated.Comment: 21pages, LaTeX, no figures, typos correcte

Bi-local Fields in Noncommutative Field Theory

We propose a bi-local representation in noncommutative field theory. It provides a simple description for high momentum degrees of freedom. It also shows that the low momentum modes can be well approximated by ordinary local fields. Long range interactions are generated in the effective action for the lower momentum modes after integrating out the high momentum bi-local fields. The low momentum modes can be represented by diagonal blocks in the matrix model picture and the high momentum bi-local fields correspond to off-diagonal blocks. This block-block interaction picture simply reproduces the infrared singular behaviors of nonplanar diagrams in noncommutative field theory.Comment: 27 pages, 2 figure

Effective Actions of Matrix Models on Homogeneous Spaces

We evaluate the effective actions of supersymmetric matrix models on fuzzy S^2\times S^2 up to the two loop level. Remarkably it turns out to be a consistent solution of IIB matrix model. Based on the power counting and SUSY cancellation arguments, we can identify the 't Hooft coupling and large N scaling behavior of the effective actions to all orders. In the large N limit, the quantum corrections survive except in 2 dimensional limits. They are O(N) and O(N^{4\over 3}) for 4 and 6 dimensional spaces respectively. We argue that quantum effects single out 4 dimensionality among fuzzy homogeneous spaces.Comment: 28 pages, 1 figure, published version in Nucl. Phys.

IIB Matrix Model with D1-D5 Backgrounds

We consider IIB matrix model with D1-D5-brane backgrounds. Using the fact that noncommutative gauge theory on the D-branes can be obtained as twisted reduced model in IIB matrix model, we study two-dimensional gauge theory on D1-branes and D5-branes. Especially the spectrum of the zero modes in the off-diagonal parts is examined. We also consider the description of D1-branes as local excitations of gauge theory on D5-branes. Relation to supergravity solution is also discussed.Comment: 17 pages, LaTe

Supercurrent Interactions in Noncommutative Yang-Mills and IIB Matrix Model

It is known that noncommutative Yang-Mills is equivalent to IIB matrix model with a noncommutative background, which is interpreted as a twisted reduced model. In noncommutative Yang-Mills, long range interactions can be seen in nonplanar diagrams after integrating high momentum modes. These interactions can be understood as block-block interactions in the matrix model. Using this relation, we consider long range interactions in noncommutative Yang-Mills associated with fermionic backgrounds. Exchanges of gravitinos, which couple to a supersymmetry current, are examined.Comment: 16 pages, LaTex, minor change

Behavioral analysis of relaxin-3 deficient mice

Relaxin-3 is a neuropeptide belonging to the relaxin/insulin superfamily. Studies using rodents have revealed that relaxin-3 is predominantly expressed in neurons in the nucleus incertus of the pons, projecting axons to forebrain regions including the hypothalamus. There is evidence that relaxin-3 is involved in several functions, including food intake and stress responses. We generated relaxin-3 gene knockout (KO) mice and examined them using a battery of behavioral tests of sensory/motor functions and emotion-related behaviors. Relaxin-3 KO mice exhibited normal growth and appearance. There was no difference in bodyweight among genotypes in both normal and high fat diet feeding. In addition, there were no significant differences between wild-type and KO mice in social interaction, depression-like behavior, and short memory test. However, in the elevated plus maze test, KO mice exhibited a robust increase in the tendency to enter open arms, although they exhibited normal performance in a light/dark transition test and showed no difference from wild-type mice in the open field test. Taken together, these results indicate that relaxin-3 KO mice exhibit mild anxiolytic characteristics relative to wild-type mice, suggesting that this peptide is involved in anxiety-related behavior

Matrix Models in Homogeneous Spaces

We investigate non-commutative gauge theories in homogeneous spaces G/H. We construct such theories by adding cubic terms to IIB matrix model which contain the structure constants of G. The isometry of a homogeneous space, G must be a subgroup of SO(10) in our construction. We investigate CP^2=SU(3)/U(2) case in detail which gives rise to 4 dimensional non-commutative gauge theory. We show that non-commutative gauge theory on R^4 can be realized in the large N limit by letting the action approach IIB matrix model in a definite way. We discuss possible relevances of these theories to the large N limit of IIB matrix model.Comment: 21 pages, sign errors in one loop effective action are correcte