Dialogue State Induction Using Neural Latent Variable Models

Dialogue state modules are a useful component in a task-oriented dialogue system. Traditional methods find dialogue states by manually labeling training corpora, upon which neural models are trained. However, the labeling process can be costly, slow, error-prone, and more importantly, cannot cover the vast range of domains in real-world dialogues for customer service. We propose the task of dialogue state induction, building two neural latent variable models that mine dialogue states automatically from unlabeled customer service dialogue records. Results show that the models can effectively find meaningful slots. In addition, equipped with induced dialogue states, a state-of-the-art dialogue system gives better performance compared with not using a dialogue state module.Comment: IJCAI 202

POSITIVE SOLUTIONS OF NONLINEAR FRACTIONAL BOUNDARY VALUE PROBLEMS WITH DIRICHLET BOUNDARY CONDITIONS

Abstract. In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of positive solutions is also derived. Several examples are given for demonstration. 1

Positive solutions of boundary value problems with p-Laplacian

In this article, we study a class of boundary value problems with p-Laplacian. By using a Green-like functional and applying the fixed point index theory, we obtain eigenvalue criteria for the existence of positive solutions. Several explicit conditions are derived as consequences, and further results are established for the multiplicity and nonexistence of positive solutions. Extensions are also given to partial differential BVPs with p-Laplacian defined on annular domains

Positive solutions of second order nonlinear difference boundary value problems

We study a class of second order nonlinear difference boundary value problems with separated boundary conditions. A series of criteria are obtained for the existence of one, two, arbitrary number, and even an infinite number of positive solutions. A theorem for the nonexistence of positive solutions is also derived. Several examples are given to demonstrate the applications. Our results improve and supplement several results in the literature

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A FRACTIONAL BOUNDARY VALUE PROBLEM WITH DIRICHLET BOUNDARY CONDITION

Abstract. The authors consider a nonlinear fractional boundary value problem with the Dirichlet boundary condition. An associated Green’s function is constructed as a series of functions by applying spectral theory. Criteria for the existence and uniqueness of solutions are obtained based on it. 1