Hierarchical Data Representation Model - Multi-layer NMF

In this paper, we propose a data representation model that demonstrates hierarchical feature learning using nsNMF. We extend unit algorithm into several layers. Experiments with document and image data successfully discovered feature hierarchies. We also prove that proposed method results in much better classification and reconstruction performance, especially for small number of features. feature hierarchies

Electromagnetic form factors of the baryon decuplet with flavor SU(3) symmetry breaking

We investigate the electromagnetic form factors of the baryon decuplet within the framework of the $\mathrm{SU(3)}$ self-consistent chiral quark-soliton model, taking into account the $1/N_c$ rotational corrections and the effects of flavor $\mathrm{SU(3)}$ symmetry breaking. We first examine the valence- and sea-quark contributions to each electromagnetic form factor of the baryon decuplet and then the effects of the flavor SU(3) symmetry breaking. The present results are in good agreement with the recent lattice data. We also compute the charge radii, the magnetic radii, the magnetic dipole moments and the electric quadrupole moments, comparing their results with those from other theoretical works. We also make a chiral extrapolation to compare the present results with the lattice data in a more quantitative manner. The results show in general similar tendency to the lattice results. In particular, the results of the $M1$ and $E2$ form factors are in good agreement with those of lattice QCD.Comment: 29 pages, 15 figures. Comparison with the lattice data was elaborate

Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic

Let $I$ be a homogeneous Artinian ideal in a polynomial ring $R=k[x_1,...,x_n]$ over a field $k$ of characteristic 0. We study an equivalent condition for the generic initial ideal \gin(I) with respect to reverse lexicographic order to be almost reverse lexicographic. As a result, we show that Moreno-Socias conjecture implies Fr\"{o}berg conjecture. And for the case \Codim I \le 3, we show that $R/I$ has the strong Lefschetz property if and only if \gin(I) is almost reverse lexicographic. Finally for a monomial complete intersection Artinian ideal $I=(x_1^{d_1},...,x_n^{d_n})$, we prove that \gin(I) is almost reverse lexicographic if $d_i > \sum_{j=1}^{i-1} d_j - i + 1$ for each $i \ge 4$. Using this, we give a positive partial answer to Moreno-Socias conjecture, and to Fr\"{o}berg conjecture.Comment: 10 page