We present a generative probabilistic model for the topographic mapping of tree structured data. The model is formulated as constrained mixture of hidden Markov tree models. A natural measure of likelihood arises as a cost function that guides the model fitting. We compare our approach with an existing neural-based methodology for constructing topographic maps of directed acyclic graphs. We arg...

We provide a self-similar measure for the self-similar group G acting faithfully on the binary rooted tree, defined as the iterated monodromy group of the quadratic polynomial z + i. We also provide an Lpresentation for G and calculations related to the spectrum of the Markov operator on the Schreier graph of the action of G on the orbit of a point on the boundary of the binary rooted tree.

This paper studies the classification problem of discrete time and continuous time Markov processes of matrix M/G/1 type with a tree structure. It is shown that the Perron-Frobenius eigenvalue of a nonnegative matrix provides information for a complete classification of the Markov process of interest. A computational method is developed to find whether a Markov process of matrix M/G/1 type with...

We propose and study a new approach for the analysis of families of protein sequences. This method is related to the LogDet distances used in phylogenetic reconstructions; it can be viewed as an attempt to embed these distances into a multidimensional framework. The proposed method starts by associating a Markov matrix to each pairwise alignment deduced from a given multiple alignment. The cent...

tributed hypertext repository of information, which users navigate through links and view with browsers. The heavy Internet traffic resulting from the Web’s popularity has significantly increased userperceived latency. The obvious solution—to increase the bandwidth—is not viable, because we cannot easily change the Web’s infrastructure (the Internet) without significant economic cost. However, ...

Most existing algorithms for learning Markov network structure either are limited to learning interactions among few variables or are very slow, due to the large space of possible structures. In this paper, we propose three new methods for using decision trees to learn Markov network structures. The advantage of using decision trees is that they are very fast to learn and can represent complex ...