We define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic Λ in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/r...

In this paper we show that model categories of a very broad class can be replaced up to Quillen equivalence by simplicial model categories.

A 0-1 matrix where in each column the 1s occur consecutively is said to have the consecutive ones property. This property and its approximations are important in a variety of applications, e.g., in DNA analysis and paleontology. Checking whether the matrix rows can be permuted so that this property holds can be done in polynomial time. However, an exact solution rarely exists in applications. T...

It has been believed that stochastic feedforward neural networks (SFNN) have several advantages beyond deterministic deep neural networks (DNN): they have more expressive power allowing multi-modal mappings and regularize better due to their stochastic nature. However, training SFNN is notoriously harder. In this paper, we aim at developing efficient training methods for large-scale SFNN, in pa...