An application of a theorem of Sheila Brenner for Hochschild extension algebras of a truncated quiver algebra

Let $A$ be a truncated quiver algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of $A$ is zero in $A$. We give the number of the indecomposable direct summands of the middle term of an almost split sequence for a class of Hochschild extension algebras of $A$ by the standard duality module $D(A)$.Comment: 13pages, 4figure

Monte Carlo simulation of classical spin models with chaotic billiards

It has recently been shown that the computing abilities of Boltzmann machines, or Ising spin-glass models, can be implemented by chaotic billiard dynamics without any use of random numbers. In this paper, we further numerically investigate the capabilities of the chaotic billiard dynamics as a deterministic alternative to random Monte Carlo methods by applying it to classical spin models in statistical physics. First, we verify that the billiard dynamics can yield samples that converge to the true distribution of the Ising model on a small lattice, and we show that it appears to have the same convergence rate as random Monte Carlo sampling. Second, we apply the billiard dynamics to finite-size scaling analysis of the critical behavior of the Ising model and show that the phase transition point and the critical exponents are correctly obtained. Third, we extend the billiard dynamics to spins that take more than two states and show that it can be applied successfully to the Potts model. We also discuss the possibility of extensions to continuous-valued models such as the XY model.Comment: 9 pages, 7 figure

A new proof for the convergence of Picard's filter using partial Malliavin calculus

The discrete-time approximation for nonlinear filtering problems is related to both of strong and weak approximations of stochastic differential equations. In this paper, we propose a new method of proof for the convergence of approximate nonlinear filter analyzed by Jean Picard (1984), and show a more general result than the original one. For the proof, we develop an analysis of Hilbert space valued functionals on Wiener space.Comment: 15 page

Many-body perturbation theory and fluctuation relations for interacting population dynamics

Population dynamics deals with the collective phenomena of living organisms, and it has attracted much attention since it is expected to explain how not only living organisms but also human beings have been adapted to varying environments. However, it is quite difficult to insist on a general statement on living organisms since mathematical models heavily depend on phenomena that we focus on. Recently it was reported that the fluctuation relations on the fitness of living organisms held for a quite general problem setting. But, interactions between organisms were not incorporated in the problem setting, though interaction plays critical roles in collective phenomena in physics and population dynamics. In this paper, we propose interacting models for population dynamics and provide the perturbative theory of population dynamics. Then, we derive the variational principle and fluctuation relations for interacting population dynamics.Comment: 16 pages, 2 figures, accepted by Phys. Rev.

Chaotic Boltzmann machines with two elements

In this brief note, we show that chaotic Boltzmann machines truly yield samples from the probabilistic distribution of the corresponding Boltzmann machines if they are composed of only two elements. This note is an English translation (with slight modifications) of the article originally written in Japanese [H. Suzuki, Seisan Kenkyu 66 (2014), 315-316].Comment: 5 pages, 1 figur

Recent two-photon results at Belle

We review recent measurements of pure neutral final state production, gamma gamma to pi0 pi0 and eta pi0, and observations of new charmoniumlike resonances, X(3915) and X(4350), in the two-photon processes at the Belle experiment.Comment: 4 pages, 5 figures, Proceedings of Lake Louise Winter Institute 201

Pulsation of magnetic stars

Some Ap stars with strong magnetic fields pulsate in high order p-modes; they are called roAp (rapidly oscillating Ap) stars. The p-mode frequencies are modified by the magnetic fields. Although the large frequency separations are hardly affected, small separations are modified considerably. The magnetic field also affects the latitudinal amplitude distribution on the surface. We discuss the property of axisymmetric p-mode oscillations in roAp stars.Comment: 8 pages, 7 figures, conference proceedings, IAU Symp. 301 "Precision asteroseismology" Eds. J.A., Guzik, W.J. Chaplin, G. Handler, and A. Pigulsk

The Faint Stellar Object SDSS J1257+3419 is a Dark Matter Dominated System

A recent study has revealed SDSS J1257+3419 is either a faint and small dwarf galaxy or a faint and widely extended globular cluster. In this Letter, the author suggests this stellar system is a dwarf spheroidal (dSph). Adopting an observational relation between binding energy and mass of old stellar systems, we derive a relation between mass and size of dSphs by assuming that they are dark matter dominated and virialized objects. Letting half-light radius represent size of SDSS J1257+3419, we find that its mass is $\sim 7\times 10^6$ solar mass. This indicates mass-to-light ratio ($M/L$) of SDSS J1257+3419 is about 1000 in the solar unit. This large $M/L$ is expected from a Mateo plot of dSphs. Thus, we insist SDSS J1257+3419 is a dSph.Comment: resubmitte

Relativistic Bullets Ejection from Supernovae and Generation of Gamma Ray Bursts

It is generally believed that cosmological Gamma Ray Bursts (GRBs) are produced by the deceleration of relativistic objects with Lorentz factor (Gamma) >~ 100. We study the possibility that some GRBs are produced along with relativistic matter ejection from supernovae. In this model, it is quite likely that the matter has to travel through the progenitor's thick envelope before generating GRBs. Under the assumption that the ejected matter is described as a single collective matter, we obtain constraints on the matter to have Gamma >~ 100 at the breakout of the progenitor. One advantage of considering this type of model is that the expected GRB energy is sufficiently large, in contrast to the GRB generation model by the shock breakout in the energetic supernova explosion. We find that in general the cross section of the matter has to be very small compared with the progenitor's radius and thus the matter has to be bullet (or jet)-like rather than shell-like.Comment: 8 pages. Accepted for publication in ApJ Letter

R-mode oscillations in accreting white dwarfs in cataclysmic variables

Some cataclysmic variables show short-period ($\sim$200 to $\sim$2000 s) light variations, which are attributable to nonradial pulsations of the accreting primary white dwarf. We regard these periodic variations as r-mode (global Rossby-wave) oscillations which are presumably excited mechanically and confined into hydrogen-rich layers in the white dwarf. Often observed modulations in amplitudes and frequencies even during an observing season may be interpreted as beatings among densely distributed r-mode frequencies. Making the r-mode frequency distribution of a model to be consistent (by adjusting the rotation frequency) with the observed pulsation frequencies, we obtain the best-fit rotation rate for each case. The rotation periods thus obtained for 17 accreting white dwarfs lie between 4 and 10 minutes. Pulsation frequencies observed sometime after a dwarf-nova outburst tend to be higher than the pre-outburst values, so that the best-fit rotation rate for the post-outburst frequencies is also higher. This indicates a spin-up of the hydrogen-rich layers to occur by an enhanced accretion at the outburst. We also discuss the relation between the rotation frequencies of pulsating accreting white dwarfs and the orbital periods.Comment: 15 pages,22 figures, accepted for publication in MNRA