Generative statistical models of chord sequences play crucial roles in music processing. To capture syntactic similarities among certain chords (e.g. in C major key, between G and G7 and between F and Dm), we study hidden Markov models and probabilistic context-free grammar models with latent variables describing syntactic categories of chord symbols and their unsupervised learning techniques f...

In  this  paper a  non-linear  model  with  fractional  order  is  presented  for  analyzing  and  controlling the  spread  of  HIV virus.  Both  the  disease-free  equilibrium and the endemic equilibrium are  found  and  their  stability is  discussed. The basic reproduction number , which is a function of the constant parameters in the model, plays an essential  role in the stability of  the ...

A computer conversational system can potentially help a foreign-language student improve his/her fluency through practice dialogues. One of its potential roles could be to correct ungrammatical sentences. This paper describes our research on a sentence-level, generation-based approach to grammar correction: first, a word lattice of candidate corrections is generated from an ill-formed input. A ...

The BMS (Bondi--van der Burg--Metzner--Sachs) symmetry arises as the asymptotic of flat spacetime at null infinity. In particular, algebra for three-dimensional (${\mathrm{BMS}}_{3}$) is generated by super-rotation generators that form a Virasoro subalgebra with central charge ${c}_{L}$, together mutually commuting super-translation generators. and supertranslation have nontrivial commutation r...

Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given difficulty modeling dependence, especially nonstationary cases, model-based prediction intervals are risk of misspecification bias that can negatively affect their validity. Here we present new approach for model-free nonparametric based on conformal machinery. Our key observation data be tre...