We study bilinear embedding models for the task of multirelational link prediction and knowledge graph completion. Bilinear models belong to the most basic models for this task, they are comparably efficient to train and use, and they can provide good prediction performance. The main goal of this paper is to explore the expressiveness of and the connections between various bilinear models propo...

In this paper, we show that the Garnier system in n-variables has affine Weyl group symmetry of type B (1) n+3. We also formulate the τ functions for the Garnier system (or the Schlesinger system of rank 2) on the root lattice Q(Cn+3) and show that they satisfy Toda equations, Hirota-Miwa equations and bilinear differential equations.

A class of bilinear differential operators is introduced through assigning appropriate signs and used to create bilinear differential equations which generalize Hirota bilinear equations. The resulting bilinear differential equations are characterized by a special kind of Bell polynomials and the linear superposition principle is applied to the construction of their linear subspaces of solution...

In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarević operators. By exhibiting a generalized “taxi-cab” metric, we show that the graph of a bilinear fractal interpolant is the attractor of an underlying contractive bilinear IFS. We present an explicit formula for the box-counting dimension of the ...

In this paper we obtain one and two soliton solutions to HirotaSatsuma KdV system with the aid of Hirota’s bilinear method. We also obtain some rational solutions. Mathematics Subject Classification: 35C05

• TOP OF ARTICLE • INPUT-OUTPUT SYSTEM REPRESENTATION • NONLINEAR DIFFERENTIAL ALGEBRAIC REPRESENTATION • VOLTERRA REPRESENTATION • STATE-SPACE REPRESENTATION • BILINEAR REPRESENTATION • NARMA REPRESENTATION • FUZZY-LOGIC NONLINEAR REPRESENTATION • NONLINEAR REPRESENTATION USING NEURAL NETWORKS • MODEL-FREE REPRESENTATION • FEATURES OF NONLINEAR REPRESENTATIONS • EXAMPLE • CONCLUDING REMARKS • ...