Random-bit optimal uniform sampling for rooted planar trees with given sequence of degrees and Applications

In this paper, we redesign and simplify an algorithm due to Remy et al. for the generation of rooted planar trees that satisfies a given partition of degrees. This new version is now optimal in terms of random bit complexity, up to a multiplicative constant. We then apply a natural process "simulate-guess-and-proof" to analyze the height of a random Motzkin in function of its frequency of unary nodes. When the number of unary nodes dominates, we prove some unconventional height phenomenon (i.e. outside the universal square root behaviour.)Comment: 19 page

A Guide to the Dagum Distributions

In a series of papers in the 1970s, Camilo Dagum proposed several variants of a new model for the size distribution of personal income. This Chapter traces the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. It also provides interrelations with other statistical distributions as well as aspects that are of special interest in the income distribution eld, including Lorenz curves and the Lorenz order and inequality measures. The Chapter ends with a survey of empirical applications of the Dagum distributions, many published in Romance language periodicals.

Fifty years of similarity relations: a survey of foundations and applications

On the occasion of the 50th anniversary of the publication of Zadeh's significant paper Similarity Relations and Fuzzy Orderings, an account of the development of similarity relations during this time will be given. Moreover, the main topics related to these fuzzy relations will be reviewed.Peer ReviewedPostprint (author's final draft

Fuzzy expert systems in civil engineering

Imperial Users onl

Brain-Inspired Computational Intelligence via Predictive Coding

Artificial intelligence (AI) is rapidly becoming one of the key technologies of this century. The majority of results in AI thus far have been achieved using deep neural networks trained with the error backpropagation learning algorithm. However, the ubiquitous adoption of this approach has highlighted some important limitations such as substantial computational cost, difficulty in quantifying uncertainty, lack of robustness, unreliability, and biological implausibility. It is possible that addressing these limitations may require schemes that are inspired and guided by neuroscience theories. One such theory, called predictive coding (PC), has shown promising performance in machine intelligence tasks, exhibiting exciting properties that make it potentially valuable for the machine learning community: PC can model information processing in different brain areas, can be used in cognitive control and robotics, and has a solid mathematical grounding in variational inference, offering a powerful inversion scheme for a specific class of continuous-state generative models. With the hope of foregrounding research in this direction, we survey the literature that has contributed to this perspective, highlighting the many ways that PC might play a role in the future of machine learning and computational intelligence at large.Comment: 37 Pages, 9 Figure