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This paper derives the Fokker-Planck (FP) equation for a particle moving in potential by a randomly modulated dipole. The FP equation describes the anomalous diffusion observed in the companion paper [1] and breaks the conservation of the total probability at the singularity by the dipole. It also shows anisotropic diffusion, which is typical in fluid turbulence. We need to modify the probability density by introducing a mechanism to recover the particle. After the modification, the latent fractal dimension matches with the results of the companion paper. We hope that our model gives a new example of fractional diffusion, where the random singularity triggers fractionality., Comment: 35 pages, 6 figures

Type I X-ray bursts are thermonuclear explosions on the neutron star (NS) surface caused by mass accretion from a companion star. Observations of X-ray bursts provide valuable information on X-ray binary systems, e.g., binary parameters, the chemical composition of accreted matter, and the nuclear equation of state (EOS) of NSs. There have been several theoretical studies to constrain the physics of X-ray bursters. However, they have mainly focused on the burning layers above the solid crust of the NS, which brings up issues of the treatment of NS gravitation and internal energy. In this study, focusing on the microphysics inside NSs, we calculate a series of X-ray bursts using a general-relativistic stellar-evolution code with several NS EOSs. We compare the X-ray-burst models with the burst parameters of a clocked burster associated with GS 1826-24. We find a monotonic correlation between the NS radius and the light-curve profile. A larger radius shows a higher recurrence time and a large peak luminosity. In contrast, the dependence of light curves on the NS mass becomes more complicated, where the neutrino cooling suppresses the efficiency of nuclear ignition. We also constrain the EOS and mass of GS 1826-24, i.e., stiffer EOSs, corresponding to larger NS radii, are not preferred due to too-high peak luminosity. The EOS and the cooling and heating of NSs are important to discuss the theoretical and observational properties of X-ray bursts., Comment: 19 pages, 16 figures, 3 tables, updated to match published version (ApJ)

The logarithmic $R^2$-corrected $F(R)$ gravity is investigated as a prototype model of modified gravity theories with quantum corrections. By using the auxiliary field method, the model is described by the general relativity with a scalaron field. The scalaron field can be identified as an inflaton at the primordial inflation era. It is also one of the dark matter candidates in the dark energy era. It is found that a wide range of the parameters is consistent with the current observations of CMB fluctuations, dark energy and dark matter., Comment: 11 pages, 5 figures

We report on the operation of co-located ${}^{129}$Xe and ${}^{131}$Xe nuclear spin masers with an external feedback scheme, and discuss the use of ${}^{131}$Xe as a comagnetometer in measurements of the ${}^{129}$Xe spin precession frequency. By applying a correction based on the observed change in the ${}^{131}$Xe frequency, the frequency instability due to magnetic field and cell temperature drifts are eliminated by two orders of magnitude. The frequency precision of 6.2 $\mu$Hz is obtained for a 10$^4$ s averaging time, suggesting the possibility of future improvement to $\approx$ 1 nHz by improving the signal-to-noise ratio of the observation., Comment: 8 pages, 5 figures

A new laser ion source configuration based on resonant photoionization in a gas cell has been developed at RIBF RIKEN. This system is intended for the future PArasitic RI-beam production by Laser Ion-Source (PALIS) project which will be installed at RIKEN's fragment separator, BigRIPS. A novel implementation of differential pumping, in combination with a sextupole ion beam guide (SPIG), has been developed. A few small scroll pumps create a pressure difference from 1000 hPa - 10^-3 Pa within a geometry drastically miniaturized compared to conventional systems. This system can utilize a large exit hole for fast evacuation times, minimizing the decay loss for short-lived nuclei during extraction from a buffer gas cell, while sufficient gas cell pressure is maintained for stopping high energy RI-beams. In spite of the motion in a dense pressure gradient, the photo-ionized ions inside the gas cell are ejected with an assisting force gas jet and successfully transported to a high-vacuum region via SPIG followed by a quadrupole mass separator. Observed behaviors agree with the results of gas flow and Monte Carlo simulations.

The reduced transition probability B(E2;0 ->2+) for 28S was obtained experimentally using Coulomb excitation at 53 MeV/nucleon. The resultant B(E2) value 181(31) e2fm4 is smaller than the expectation based on empirical B(E2) systematics. The double ratio |M_n/M_p|/(N/Z) of the 0+ ->2+ transition in 28S was determined to be 1.9(2) by evaluating the M_n value from the known B(E2) value of the mirror nucleus 28Mg, showing the hindrance of proton collectivity relative to that of neutrons. These results indicate the emergence of the magic number Z=16 in the |T_z|=2 nucleus 28S., Comment: 10 pages, 3 figures. Published in Phys. Rev. Lett (http://link.aps.org/doi/10.1103/PhysRevLett.108.222501)

The effects of a new triple-$\alpha$ reaction rate (OKK rate) on the helium flash of a helium accreting neutron star in a binary system have been investigated. Since the ignition points determine the properties of a thermonuclear flash of type I X-ray bursts, we examine the cases of different accretion rates, $dM/dt (\dot{M})$, of helium from $3\times10^{-10} M_{\odot} \rm yr^{-1}$ to $3\times10^{-8} M_{\odot} \rm yr^{-1}$, which could cover the observed accretion rates. We find that for the cases of low accretion rates, nuclear burnings are ignited at the helium layers of rather low densities. As a consequence, helium deflagration would be triggered for all cases of lower accretion rate than $\dot{M}\simeq 3\times10^{-8} M_{\odot} \rm yr^{-1}$. We find that OKK rate could be barely consistent with the available observations of the X-ray bursts on the helium accreting neutron star. However this coincidence is found to depend on the properties of crustal heating and the neutron star model.We suggest that OKK rate would be reduced by a factor of $10^{2-3}$ for $10^8$ K in the range of the observational errors., Comment: 10 pages, 4 figures

We study the interactions of Maldacena's long folded strings in two-dimensional string theory. We find the amplitude for a state containing two long folded strings to come and go back to infinity. We calculate this amplitude both in the worldsheet theory and in the dual matrix model, the Matrix Quantum Mechanics. The matrix model description allows to evaluate the amplitudes involving any number of long strings, which are given by the mixed trace correlators in an effective two-matrix model., Comment: 39 pages, 6 figures

The ALL-1 gene is directly involved in 5-10% of ALLs and AMLs by fusion to other genes or through internal rearrangements. DNA microarrays were utilized to determine expression profiles of ALLs and AMLs with ALL-1 rearrangements. These profiles distinguish those tumors from other ALLs and AMLs. The expression patterns of ALL-1-associated tumors, in particular ALLs, involve oncogenes, tumor suppressors, anti apoptotic genes, drug resistance genes etc., and correlate with the aggressive nature of the tumors. The genes whose expression differentiates between ALLs with and without ALL-1 rearrangement were further divided into several groups enabling separation of ALL-1- associated ALLs into two subclasses. Further, AMLs with partial duplication of ALL-1 vary in their expression pattern from AMLs in which ALL-1 had undergone fusion to other genes. The extensive analysis described here draws attention to genes which might have a direct role in pathogenesis.

The nonperturbative aspects of string theory are explored for non-critical string in two distinct formulations: loop equations and matrix models. The effects corresponding to D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations can not. This implies that string theory may not be nonperturbatively formulated solely in terms of closed strings., Comment: 58 pages, 3 figures, PTPTeX, published version

We complete the construction of the Moyal star formulation of bosonic open string field theory (MSFT) by providing a detailed study of the fermionic ghost sector. In particular, as in the case of the matter sector, (1) we construct a map from Witten's star product to the Moyal product, (2) we propose a regularization scheme which is consistent with the matter sector and (3) as a check of the formalism, we derive the ghost Neumann coefficients algebraically directly from the Moyal product. The latter satisfy the Gross-Jevicki nonlinear relations even in the presence of the regulator, and when the regulator is removed they coincide numerically with the expression derived from conformal field theory. After this basic construction, we derive a regularized action of string field theory in the Siegel gauge and define the Feynman rules. We give explicitly the analytic expression of the off-shell four point function for tachyons, including the ghost contribution. Some of the results in this paper have already been used in our previous publications. This paper provides the technical details of the computations which were omitted there., Comment: 65 pages, typos corrected

We propose an analytic framework to study the nonperturbative solutions of Witten's open string field theory. The method is based on the Moyal star formulation where the kinetic term can be split into two parts. The first one describes the spectrum of two identical half strings which are independent from each other. The second one, which we call midpoint correction, shifts the half string spectrum to that of the standard open string. We show that the nonlinear equation of motion of string field theory is exactly solvable at zeroth order in the midpoint correction. An infinite number of solutions are classified in terms of projection operators. Among them, there exists only one stable solution which is identical to the standard butterfly state. We include the effect of the midpoint correction around each exact zeroth order solution as a perturbation expansion which can be formally summed to the complete exact solution., Comment: 29 pages

We illustrate a basic framework for analytic computations of Feynman graphs using the Moyal star formulation of string field theory. We present efficient methods of computation based on (a) the monoid algebra in noncommutative space and (b) the conventional Feynman rules in Fourier space. The methods apply equally well to perturbative string states or nonperturbative string states involving D-branes. The ghost sector is formulated using Moyal products with fermionic (b,c) ghosts. We also provide a short account on how the purely cubic theory and/or VSFT proposals may receive some clarification of their midpoint structures in our regularized framework., Comment: 19 pages, LaTeX, typos corrected, comments added, Eqs.(27-32)(55-59) added. Eq.(27) includes a more explicit result of the four point function

We discuss noncommutative solitons on a noncommutative torus and their application to tachyon condensation. In the large B limit, they can be exactly described by the Powers-Rieffel projection operators known in the mathematical literature. The resulting soliton spectrum is consistent with T-duality and is surprisingly interesting. It is shown that an instability arises for any D-branes, leading to the decay into many smaller D-branes. This phenomenon is the consequence of the fact that K-homology for type II von Neumann factor is labeled by R., Comment: LaTeX, 17 pages, 1 figure

We give a representation of the volume preserving diffeomorphism of $\bR^p$ in terms of the noncommutative (p-2)-branes whose kinetic term is described by the Hopf term. In the static gauge, the (p-2)-brane can be described by the free fields and it suggests that the quantization of the algebra is possible., Comment: 14 pages, LaTeX file

We discuss tachyon configuration for the unoriented bosonic string theory which produces a bosonic string theory with SO(32) gauge symmetry in ten dimensions. It is closely related to the tachyon condensation scenario proposed by A. Sen. We also give the boundary state description of the tachyon condensation process, with some emphasis on the r\^ole of orbifold conformal field theory., Comment: Proceeding of the talk given at YITP workshop ``Tachyon condensation and boundary state''(October 27-29, 1999), latex file

By a toroidal compactification with a vortex like configuration of tachyon fields, the unoriented bosonic string in 26 dimensions becomes equivalent to 10 dimensional string theory with gauge group $SO(32)\times G$ where $G$ has rank 16. The reduction from SO(8192) to SO(32) is induced by the action of non-abelian Wilson lines which twists the tachyon. The additional enhanced gauge symmetry $G$ appears from closed string sector by Frenkel-Kac construction. We also examine the consistency of the tachyon condensation., Comment: 12 pages, LaTeX file; v2 a few references added; v3 topological aspect is discussed. some terminology chage, and some references added

We discuss the open string ending on D $p$-branes in IKKT framework. First we determine the boundary conditions of Green-Schwarz superstring which are consistent with supersymmetry and $\kappa$-symmetry. We point out some subtleties arising from taking the Schild gauge and show that in this gauge the system incorporates the limited dimensional D $p$-branes ($p=3,7$). The matrix regularization for the Dirichlet open string is given by gauge group SO(N). When $p=3$, the matrix model becomes the dimensional reduction of a 6 dimensional ${\cal N}=1$ super Yang-Mills theory., Comment: 9 pages, LaTeX

We study open supermembranes in 11 dimensional rigid superspace with 6 dimensional topological defects (M-theory five-branes). After rederiving in the Green-Schwarz formalism the boundary conditions for open superstrings in the type IIA theory, we determine the boundary conditions for open supermembranes by imposing kappa symmetry and invariance under a fraction of 11 dimensional supersymmetry. The result seems to imply the self-duality of the three-form field strength on the five-brane world volume. We show that the light-cone gauge formulation is regularized by a dimensional reduction of a 6 dimensional N=1 super Yang-Mills theory with the gauge group SO(N\to\infty). We also analyze the SUSY algebra and BPS states in the light-cone gauge., Comment: 30 pages, Latex, references and Appendix E added, some minor changes made

We study de Wit-Hoppe-Nicolai supermembrane with emphasis on the winding in M-direction. We propose a SUSY algebra of the supermembrane in the Lorentz invariant form. We analyze the BPS conditions and argue that the area preserving diffeomorphism constraints associated with the harmonic vector fields play an essential role. We derive the first order partial differential equation that describes the BPS state with one quarter SUSY., Comment: 10 pages latex, references added