Directed Projection Graph of N-Dimensional Hypercube and Subhypercube Decomposition of Balanced Linearly Separable Boolean Functions

A directed projection graph of the [Formula: see text]-dimensional hypercube on the two-dimensional plane is successfully created. Any [Formula: see text]-variable Boolean function can be easily transformed to an induced subgraph of the projection. Therefore, the discussions on [Formula: see text]-variable Boolean functions only need to focus on a two-dimensional planar graph. Some mathematical theories on the projection graph and the induced subgraph are established, and some properties and characteristics of a balanced linearly separable Boolean function (BLSBF) are uncovered. In particular, the sub-hypercube decompositions of BLSBF is easily represented on the projection, and meanwhile, the enumeration scheme for counting the number of [Formula: see text]-variable BLSBFs is developed by using equivalence classification and conformal transformation. With the aid of the directed projection grap constructed in this paper, one can further study many difficult problems in some fields such as Boolean functions and artificial neural networks.

Pedestrian Attribute Recognition by Joint Visual-semantic Reasoning and Knowledge Distillation

Pedestrian attribute recognition in surveillance is a challenging task in computer vision due to significant pose variation, viewpoint change and poor image quality. To achieve effective recognition, this paper presents a graph-based global reasoning framework to jointly model potential visual-semantic relations of attributes and distill auxiliary human parsing knowledge to guide the relational learning. The reasoning framework models attribute groups on a graph and learns a projection function to adaptively assign local visual features to the nodes of the graph. After feature projection, graph convolution is utilized to perform global reasoning between the attribute groups to model their mutual dependencies. Then, the learned node features are projected back to visual space to facilitate knowledge transfer. An additional regularization term is proposed by distilling human parsing knowledge from a pre-trained teacher model to enhance feature representations. The proposed framework is verified on three large scale pedestrian attribute datasets including PETA, RAP, and PA-100k. Experiments show that our method achieves state-of-the-art results.

AN EXTENSION OF THE JONES POLYNOMIAL OF CLASSICAL KNOTS

We define a linear algebraic extension of the Jones polynomial of classical knots, and prove that certain key properties of the classical Jones polynomial are properties of the extension. This shows that these properties are linear algebraic in nature, not topological. We identify a topological property of the classical Jones polynomial, that is, a property of the classical Jones polynomial that the extension does not possess. We discuss ortho-projection matrices, ortho-projection graphs, and their Jones polynomials. We classify, up to isomorphism, the connected ortho-projection graphs with at most eight vertices, and show that each such isomorphism class corresponds to a prime alternating classical knot diagram. We give an example of a connected ortho-projection graph with nine vertices that does not correspond to such a diagram.