Real-Time Audio-to-Score Alignment of Music Performances Containing Errors and Arbitrary Repeats and Skips

This paper discusses real-time alignment of audio signals of music performance to the corresponding score (a.k.a. score following) which can handle tempo changes, errors and arbitrary repeats and/or skips (repeats/skips) in performances. This type of score following is particularly useful in automatic accompaniment for practices and rehearsals, where errors and repeats/skips are often made. Simple extensions of the algorithms previously proposed in the literature are not applicable in these situations for scores of practical length due to the problem of large computational complexity. To cope with this problem, we present two hidden Markov models of monophonic performance with errors and arbitrary repeats/skips, and derive efficient score-following algorithms with an assumption that the prior probability distributions of score positions before and after repeats/skips are independent from each other. We confirmed real-time operation of the algorithms with music scores of practical length (around 10000 notes) on a modern laptop and their tracking ability to the input performance within 0.7 s on average after repeats/skips in clarinet performance data. Further improvements and extension for polyphonic signals are also discussed.Comment: 12 pages, 8 figures, version accepted in IEEE/ACM Transactions on Audio, Speech, and Language Processin

Monte Carlo Study of Two-Color QCD with Finite Chemical Potential - Status report of Wilson fermion simulation

Using Wilson fermions, we study SU(2) lattice QCD with the chemical potential at $\beta=1.6$. The ratio of fermion determinants is evaluated at each Metropolis link update step. We calculate the baryon number density, the Polyakov loops and the pseudoscalar and vector masses on $4^4$ and $4^3\times 8$ lattices. Preliminary data show the pseudoscalar meson becomes massive around $\mu=0.4$, which indicates the chiral symmetry restoration. The calculation is broken down when approaching to the transition region. We analyze the behavior of the fermion determinant and eigen value distributions of the determinant, which shows a peculiar ``Shell-and-Bean'' pattern near the transition.Comment: 4 pages, 5 figures, Lattice 2000 (Finite Density

Decay Rates of Fixed Planes and Closed-string Tachyons on Unstable Orbifolds

We consider closed-string tachyon condensation in the twisted sectors on the C/Z_{2n+1} \times R^{7,1} orbifold. We calculate the localized energy density in the fixed plane on the orbifold at the one-loop level, and we obtain the decay rate per unit volume of the fixed plane to leading order. We show that the decay rate increases monotonically as a function of n.Comment: 19 pages, 2 figures, LaTeX. v2: typos corrected. v3: section 5 is modified, main results unchanged. v4: published version in Prog. Theor. Phy

On Isosystolic Inequalities for T^n, RP^n, and M^3

If a closed smooth n-manifold M admits a finite cover whose Z/2Z-cohomology has the maximal cup-length, then for any riemannian metric g on M, we show that the systole Sys(M,g) and the volume Vol(M,g) of the riemannian manifold (M,g) are related by the following isosystolic inequality: Sys(M,g)^n \leq n! Vol(M,g). The inequality can be regarded as a generalization of Burago and Hebda's inequality for closed essential surfaces and as a refinement of Guth's inequality for closed n-manifolds whose Z/2Z-cohomology has the maximal cup-length. We also establish the same inequality in the context of possibly non-compact manifolds under a similar cohomological condition. The inequality applies to (i) T^n and all other compact euclidean space forms, (ii) RP^n and many other spherical space forms including the Poincar\'e dodecahedral space, and (iii) most closed essential 3-manifolds including all closed aspherical 3-manifolds.Comment: 34 pages, 0 figures. v2 contains expository revisions and some additional reference

Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --

Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We derive the all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that the second order vector and tensor modes may be generated due to the mode-mode coupling of the linear order scalar perturbations. We also briefly discuss the main progress of this work by the comparison with some literatures.Comment: 58 pages, no figure. Complete version of gr-qc/0605107; some typos are corrected (v2); References and some typos are corrected. To be appeard Progress of Theoretical Physic

Some classical views on the parameters of the Grothendieck-Teichmüeller group

We present two new formulas concerning behaviors of the standard parameters of the Grothendieck-Teichmüller group GT , and discuss their relationships with classical mathematics. First, considering a non-Galois etale cover of P1 {0 1 infinity} of degree 4, we present a newtype equation satisfied by the Galois image in GT . Second, a certain equation in GL 2 (Z||Z2 ) satisfied by every element of GT is derived as an application of (profinite) free differential calculus.</p