17,891 research outputs found
An application of a theorem of Sheila Brenner for Hochschild extension algebras of a truncated quiver algebra
Let be a truncated quiver algebra over an algebraically closed field such
that any oriented cycle in the ordinary quiver of is zero in . 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 by
the standard duality module .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
solar mass. This indicates mass-to-light ratio () of SDSS J1257+3419 is
about 1000 in the solar unit. This large 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 (200 to 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
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