Remarks on the Theory of Cosmological Perturbation

It is shown that the power spectrum defined in the Synchronous Gauge can not be directly used to calculate the predictions of cosmological models on the large-scale structure of universe, which should be calculated directly by a suitable gauge-invariant power spectrum or the power spectrum defined in the Newtonian Gauge.Comment: 13 pages, 1 figure, minor changes, to be published in Chinese Physics Letter

Quark-gluon vertex with an off-shell O(a)-improved chiral fermion action

We perform a study the quark-gluon vertex function with a quenched Wilson gauge action and a variety of fermion actions. These include the domain wall fermion action (with exponentially accurate chiral symmetry) and the Wilson clover action both with the non-perturbatively improved clover coefficient as well as with a number of different values for this coefficient. We find that the domain wall vertex function behaves very well in the large momentum transfer region. The off-shell vertex function for the on-shell improved clover class of actions does not behave as well as the domain wall case and, surprisingly, shows only a weak dependence on the clover coefficient $c_{SW}$ for all components of its Dirac decomposition and across all momenta. Including off-shell improvement rotations for the clover fields can make this action yield results consistent with those from the domain wall approach, as well as helping to determine the off-shell improved coefficient $c_q^\prime$.Comment: 11 pages, 13 figures, REVTeX

Evaluation of Formal posterior distributions via Markov chain arguments

We consider evaluation of proper posterior distributions obtained from improper prior distributions. Our context is estimating a bounded function $\phi$ of a parameter when the loss is quadratic. If the posterior mean of $\phi$ is admissible for all bounded $\phi$, the posterior is strongly admissible. We give sufficient conditions for strong admissibility. These conditions involve the recurrence of a Markov chain associated with the estimation problem. We develop general sufficient conditions for recurrence of general state space Markov chains that are also of independent interest. Our main example concerns the $p$-dimensional multivariate normal distribution with mean vector $\theta$ when the prior distribution has the form $g(\|\theta\|^2) d\theta$ on the parameter space $\mathbb{R}^p$. Conditions on $g$ for strong admissibility of the posterior are provided.Comment: Published in at http://dx.doi.org/10.1214/07-AOS542 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Fringe Center Detection Technique Based on a Sub-Pixel Resolution, and Its Applications Using Sinusoidal Gratings

A common problem in optical profilometry is the accuracy in locating fringe centers. This paper presents an accurate fringe center detection technique based on sub-pixel resolution using the fringe projection method. An optimum reconstruction filter is developed which has low sensitivity to noise. In fringe center detection, computer simulation results of using one-pixel and sub-pixel resolutions are compared. The detection technique is then applied to radius measurement of cylindrical objects and surface profile measurement of diffuse objects. The experimental results thus obtained through the proposed optimum reconstruction filter show significant improvement in measurement accuracy

A Fringe Center Detection Technique Based on a Sub-Pixel Resolution, and Its Applications Using Sinusoidal Gratings

A common problem in optical profilometry is the accuracy in locating fringe centers. This paper presents an accurate fringe center detection technique based on sub-pixel resolution using the fringe projection method. An optimum reconstruction filter is developed which has low sensitivity to noise. In fringe center detection, computer simulation results of using one-pixel and sub-pixel resolutions are compared. The detection technique is then applied to radius measurement of cylindrical objects and surface profile measurement of diffuse objects. The experimental results thus obtained through the proposed optimum reconstruction filter show significant improvement in measurement accuracy

Realization of random-field dipolar Ising ferromagnetism in a molecular magnet

The longitudinal magnetic susceptibility of single crystals of the molecular magnet Mn$_{12}$-acetate obeys a Curie-Weiss law, indicating a transition to a ferromagnetic phase due to dipolar interactions. With increasing magnetic field applied transverse to the easy axis, the transition temperature decreases considerably more rapidly than predicted by mean field theory to a T=0 quantum critical point. Our results are consistent with an effective Hamiltonian for a random-field Ising ferromagnet in a transverse field, where the randomness is induced by an external field applied to Mn$_{12}$-acetate crystals that are known to have an intrinsic distribution of locally tilted magnetic easy axes.Comment: 4 pages, 4 figure

Electrical coupling between ventricular myocytes and myofibroblasts in the infarcted mouse heart

Aims: Recent studies have demonstrated electrotonic coupling between scar tissue and the surrounding myocardium in cryoinjured hearts. However, the electrical dynamics occurring at the myocyte-nonmyocyte interface in the fibrotic heart remain undefined. Here, we sought to develop an assay to interrogate the nonmyocyte cell type contributing to heterocellular coupling and to characterize, on a cellular scale, its voltage response in the infarct border zone of living hearts. Methods and results: We used two-photon laser scanning microscopy in conjunction with a voltage-sensitive dye to record transmembrane voltage changes simultaneously from cardiomyocytes and adjoined nonmyocytes in Langendorff-perfused mouse hearts with healing myocardial infarction. Transgenic mice with cardiomyocyte-restricted expression of a green fluorescent reporter protein underwent permanent coronary artery ligation and their hearts were subjected to voltage imaging 7-10 days later. Reporter-negative cells, i.e. nonmyocytes, in the infarct border zone exhibited depolarizing transients at a 1:1 coupling ratio with action potentials recorded simultaneously from adjacent, reporter-positive ventricular myocytes. The electrotonic responses in the nonmyocytes exhibited slower rates of de- and repolarization compared to the action potential waveform of juxtaposed myocytes. Voltage imaging in infarcted hearts expressing a fluorescent reporter specifically in myofibroblasts revealed that the latter were electrically coupled to border zone myocytes. Their voltage transient properties were indistinguishable from those of nonmyocytes in hearts with cardiomyocyte-restricted reporter expression. The density of connexin43 expression at myofibroblast-cardiomyocyte junctions was ∼5% of that in the intercalated disc regions of paired ventricular myocytes in the remote, uninjured myocardium, whereas the ratio of connexin45 to connexin43 expression levels at heterocellular contacts was ∼1%. Conclusion: Myofibroblasts contribute to the population of electrically coupled nonmyocytes in the infarct border zone. The slower kinetics of myofibroblast voltage responses may reflect low electrical conductivity across heterocellular junctions, in accordance with the paucity of connexin expression at myofibroblast-cardiomyocyte contacts

Fidelity, dynamic structure factor, and susceptibility in critical phenomena

Motivated by the growing importance of fidelity in quantum critical phenomena, we establish a general relation between fidelity and structure factor of the driving term in a Hamiltonian through a newly introduced concept: fidelity susceptibility. Our discovery, as shown by some examples, facilitates the evaluation of fidelity in terms of susceptibility using well developed techniques such as density matrix renormalization group for the ground state, or Monte Carlo simulations for the states in thermal equilibrium.Comment: 4 pages, 2 figures, final version accepted by PR