Journal de théorie et applications du mensonge généralisé

A time-tree is a rooted phylogenetic tree with all internal and leaf nodes equipped with absolute divergence and sampling dates, respectively. Although these time-trees have emerged as a major focus of phylogenetics research, little is known about their parameter space. From a graphtheoretic and algorithmic point of view, we present and investigate a hierarchy of discrete time-tree space approximations in this article. The NNI graph, one of the most fundamental and widely used phylogenetic graphs, is our hierarchy's lowest level and roughest approximation. The sampling dates and relative timing of evolutionary divergence are discretized by more refined approximations.

Analyses of brain activity revealed that arithmetic activated more of the bilateral supplementary motor area, left insula and left inferior parietal lobule, while algebra activated more of the angular gyrus. For algebra, significant brain-behavior correlations were found in the semantic network, including the middle temporal gyri, inferior frontal gyri, dorsomedial prefrontal cortices and left angular gyrus. Interindividual single-trial brainbehavior correlation The phonological network, which included the precentral gyrus and supplementary motor area and the visuospatial network, which included the bilateral superior parietal lobules, contained the significant brain-behavior correlations for arithmetic. The visuospatial and semantic networks were found to have significant positive functional connectivity in algebra, while only the visuospatial and phonological networks were found to have significant positive functional connectivity in arithmetic.

This paper aims at studying a new integrable Hamiltonian system due to valent. This is a Hamiltonian system with two degrees of freedom where the additional integral is polynomial of degree 3. The critical points and the bifurcation diagram of the Hamiltonian are obtained and the non-degeneracy conditions are verified. Thereafter the topology of iso-energy surfaces is found. Also for zero value of one of the parameters, the type of non-degenerate critical points of rank zero is calculated, the bifurcation diagram of the momentum map is constructed and finally the molecules (fomenko invariants) are found.