Class Of Tree Models Research Articles

Axiomatizing Hybrid XPath with Data

In this paper we introduce sound and strongly complete axiomatizations for XPath with data constraints extended with hybrid operators. First, we present HXPath=, a multi-modal version of XPath with data, extended with nominals and the hybrid operator @. Then, we introduce an axiomatic system for HXPath=, and we prove it is strongly complete with respect to the class of abstract data models, i.e., data models in which data values are abstracted as equivalence relations. We prove a general completeness result similar to the one presented in, e.g., [BtC06], that ensures that certain extensions of the axiomatic system we introduce are also complete. The axiomatic systems that can be obtained in this way cover a large family of hybrid XPath languages over different classes of frames, for which we present concrete examples. In addition, we investigate axiomatizations over the class of tree models, structures widely used in practice. We show that a strongly complete, finitary, first-order axiomatization of hybrid XPath over trees does not exist, and we propose two alternatives to deal with this issue. We finally introduce filtrations to investigate the status of decidability of the satisfiability problem for these languages.

Inferring the Total-Evidence Timescale of Marattialean Fern Evolution in the Face of Model Sensitivity.

Phylogenetic divergence-time estimation has been revolutionized by two recent developments: 1) total-evidence dating (or "tip-dating") approaches that allow for the incorporation of fossils as tips in the analysis, with their phylogenetic and temporal relationships to the extant taxa inferred from the data and 2) the fossilized birth-death (FBD) class of tree models that capture the processes that produce the tree (speciation, extinction, and fossilization) and thus provide a coherent and biologically interpretable tree prior. To explore the behavior of these methods, we apply them to marattialean ferns, a group that was dominant in Carboniferous landscapes prior to declining to its modest extant diversity of slightly over 100 species. We show that tree models have a dramatic influence on estimates of both divergence times and topological relationships. This influence is driven by the strong, counter-intuitive informativeness of the uniform tree prior, and the inherent nonidentifiability of divergence-time models. In contrast to the strong influence of the tree models, we find minor effects of differing the morphological transition model or the morphological clock model. We compare the performance of a large pool of candidate models using a combination of posterior-predictive simulation and Bayes factors. Notably, an FBD model with epoch-specific speciation and extinction rates was strongly favored by Bayes factors. Our best-fitting model infers stem and crown divergences for the Marattiales in the mid-Devonian and Late Cretaceous, respectively, with elevated speciation rates in the Mississippian and elevated extinction rates in the Cisuralian leading to a peak diversity of n}{}{sim}2800 species at the end of the Carboniferous, representing the heyday of the Psaroniaceae. This peak is followed by the rapid decline and ultimate extinction of the Psaroniaceae, with their descendants, the Marattiaceae, persisting at approximately stable levels of diversity until the present. This general diversification pattern appears to be insensitive to potential biases in the fossil record; despite the preponderance of available fossils being from Pennsylvanian coal balls, incorporating fossilization-rate variation does not improve model fit. In addition, by incorporating temporal data directly within the model and allowing for the inference of the phylogenetic position of the fossils, our study makes the surprising inference that the clade of extant Marattiales is relatively young, younger than any of the fossils historically thought to be congeneric with extant species. This result is a dramatic demonstration of the dangers of node-based approaches to divergence-time estimation, where the assignment of fossils to particular clades is made a priori (earlier node-based studies that constrained the minimum ages of extant genera based on these fossils resulted in much older age estimates than in our study) and of the utility of explicit models of morphological evolution and lineage diversification. [Bayesian model comparison; Carboniferous; divergence-time estimation; fossil record; fossilized birth–death; lineage diversification; Marattiales; models of morphological evolution; Psaronius; RevBayes.]

Inferring Tree Models for Oncogenesis from Comparative Genome Hybridization Data

Comparative genome hybridization (CGH) is a laboratory method to measure gains and losses of chromosomal regions in tumor cells. It is believed that DNA gains and losses in tumor cells do not occur entirely at random, but partly through some flow of causality. Models that relate tumor progression to the occurrence of DNA gains and losses could be very useful in hunting cancer genes and in cancer diagnosis. We lay some mathematical foundations for inferring a model of tumor progression from a CGH data set. We consider a class of tree models that are more general than a path model that has been developed for colorectal cancer. We derive a tree model inference algorithm based on the idea of a maximum-weight branching in a graph, and we show that under plausible assumptions our algorithm infers the correct tree. We have implemented our methods in software, and we illustrate with a CGH data set for renal cancer.