On the Cohomology of the Noncritical WW-string

We investigate the cohomology structure of a general noncritical $W_N$-string. We do this by introducing a new basis in the Hilbert space in which the BRST operator splits into a ``nested'' sum of nilpotent BRST operators. We give explicit details for the case $N=3$. In that case the BRST operator $Q$ can be written as the sum of two, mutually anticommuting, nilpotent BRST operators: $Q=Q_0+Q_1$. We argue that if one chooses for the Liouville sector a $(p,q)$ $W_3$ minimal model then the cohomology of the $Q_1$ operator is closely related to a $(p,q)$ Virasoro minimal model. In particular, the special case of a (4,3) unitary $W_3$ minimal model with central charge $c=0$ leads to a $c=1/2$ Ising model in the $Q_1$ cohomology. Despite all this, noncritical $W_3$ strings are not identical to noncritical Virasoro strings.Comment: 38 pages, UG-7/93, ITP-SB-93-7

Weakly Supervised Domain-Specific Color Naming Based on Attention

The majority of existing color naming methods focuses on the eleven basic color terms of the English language. However, in many applications, different sets of color names are used for the accurate description of objects. Labeling data to learn these domain-specific color names is an expensive and laborious task. Therefore, in this article we aim to learn color names from weakly labeled data. For this purpose, we add an attention branch to the color naming network. The attention branch is used to modulate the pixel-wise color naming predictions of the network. In experiments, we illustrate that the attention branch correctly identifies the relevant regions. Furthermore, we show that our method obtains state-of-the-art results for pixel-wise and image-wise classification on the EBAY dataset and is able to learn color names for various domains.Comment: Accepted at ICPR201

The Schr\"odinger Functional for Improved Gluon and Quark Actions

The Schr\"odinger Functional (quantum/lattice field theory with Dirichlet boundary conditions) is a powerful tool in the non-perturbative improvement and for the study of other aspects of lattice QCD. Here we adapt it to improved gluon and quark actions, on isotropic as well as anisotropic lattices. Specifically, we describe the structure of the boundary layers, obtain the exact form of the classically improved gauge action, and outline the modifications necessary on the quantum level. The projector structure of Wilson-type quark actions determines which field components can be specified at the boundaries. We derive the form of O(a) improved quark actions and describe how the coefficients can be tuned non-perturbatively. There is one coefficient to be tuned for an isotropic lattice, three in the anisotropic case. Our ultimate aim is the construction of actions that allow accurate simulations of all aspects of QCD on coarse lattices.Comment: 39 pages, LaTeX, 11 embedded eps file