Noncommutative/Nonlinear BPS Equations without Zero Slope Limit

It is widely believed that via the Seiberg-Witten map, the linearly realized BPS equation in the non-commutative space is related to the non-linearly realized BPS equation in the commutative space in the zero slope limit. We show that the relation also holds without taking the zero slope limit as is expected from the arguments of the BPS equation for the non-Abelian Born-Infeld theory. This is regarded as an evidence for the relation between the two BPS equations. As a byproduct of our analysis, the non-linear instanton equation is solved exactly.Comment: 9 pages, LaTeX, no figures, v2: discussion on the string tension removed, v3: minor modification

A new method of joint nonparametric estimation of probability density and its support

In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density is not the whole real line. To avoid the unknown boundary effects, our estimator detects the boundary, and eliminates the boundary-bias of the estimator simultaneously. Moreover, we refer an extension to a simple multivariate case, and propose an improved estimator free from the unknown boundary bias

Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas

We consider the partition function of the superconformal Chern-Simons theories with the quiver diagram being the affine D-type Dynkin diagram. Rewriting the partition function into that of a Fermi gas system, we show that the perturbative expansions in 1/N are summed up to an Airy function, as in the ABJM theory or more generally the theories of the affine A-type quiver. As a corollary, this provides a proof for the previous proposal in the large N limit. For special values of the Chern-Simons levels, we further identify three species of the membrane instantons and also conjecture an exact expression of the overall constant, which corresponds to the constant map in the topological string theory.Comment: 23 pages, 4 figures; v2: section 4.2 added, one figure adde

Descent Relation of Tachyon Condensation from Boundary String Field Theory

We analyze how lower-dimensional bosonic D-branes further decay, using the boundary string field theory. Especially we find that the effective tachyon potential of the lower-dimensional D-brane has the same profile as that of D25-brane.Comment: 10 pages, LaTeX, 1 figure, v2: reference added, v3: typos corrected and text improve

A new kernel estimator of hazard ratio and its asymptotic mean squared error

The hazard function is a ratio of a density and survival function, and it is a basic tool of the survival analysis. In this paper we propose a kernel estimator of the hazard ratio function, which are based on a modification of \'{C}wik and Mielniczuk's method. We study nonparametric estimators of the hazard function and compare those estimators by means of asymptotic mean squared error ($AMSE$). We obtain asymptotic bias and variance of the new estimator, and compare them with a naive estimator. The asymptotic variance of the new estimator is always smaller than the naive estimator's, so we also discuss an improvement of $AMSE$ using Terrell and Scott's bias reduction method. The new modified estimator ensures the non-negativity, and we demonstrate the numerical improvement

Instanton Effects in Orientifold ABJM Theory

We investigate another supersymmetric Chern-Simons theory called the orientifold ABJM theory, which replaces the unitary supergroup structure of the ABJM theory with an orthosymplectic one. Its non-perturbative structure is completely clarified by considering the duplication of the quiver.Comment: 21 pages, 1 figure, v2: a reference added, minor changes, v3: typos corrected, published versio