The chaos theory emerged at the end of the 19th century, and it has given birth to a deep mathematical theory in the 20th century, with a strong practical impact (e.g., weather forecast, turbulence analysis). Periodic orbits play a key role in understanding chaotic systems. Their rigorous computation provides some insights on the chaotic behavior of the system and it enables computer assisted p...

Statistical approaches to natural language parsing and interpretation have a number of advantages but thus far have failed to incorporate compositional generalizations found in traditional structural models. A major reason for this is the inability of most statistical language models being used to represent relational constraints, the connectionist variable binding problem being a prominent cas...

In density estimation task, maximum entropy model (Maxent) can effectively use reliable prior information via certain constraints, i.e., linear constraints without empirical parameters. However, reliable prior information is often insufficient, and the selection of uncertain constraints becomes necessary but poses considerable implementation complexity. Improper setting of uncertain constraints...

In uncertainty theory, quadratic entropy is a type of entropy that provide a quantitative measurement of the uncertainty of uncertain variables. This paper presents the maximum entropy principle for quadratic entropy of uncertain variables, that is, out of all the uncertainty distributions satisfying given constraints, choose the maximum quadratic entropy one.

We present a new approach to inferring a probability distribution which is incompletely specified by a number of linear constraints. We argue that the currently most popular approach of entropy maximization depends on a “constraints as knowledge” interpretation of the constraints, and that a different “constraints as data” perspective leads to a completely different type of inference procedures...