In this paper, we study the concept of $mathcal C$-reticulation for the category $mathcal C$ whose objects are lattice-valued maps. The relation between the free objects in $mathcal C$ and the $mathcal C$-reticulation of rings and modules is discussed. Also, a method to construct $mathcal C$-reticulation is presented, in the case where $mathcal C$ is equational. Some relations between the conce...

Phylogenetic networks are mathematical structures for modeling and visualization of reticulation processes in the study of evolution. Galled networks, reticulation visible networks, nearly-stable networks and stable-child networks are the four classes of phylogenetic networks that are recently introduced to study the topological and algorithmic aspects of phylogenetic networks. We prove the fol...

The Agabus bipustulatus complex includes one of Europe's most widely distributed and common diving beetles. This complex, which is known for its large morphological variation, has a complex demographic and altitudinal variation in elytral reticulation. The various depth of the reticulation imprint, both in smaller and larger meshes, results in both mat and shiny individuals, as well as intermed...

Reticulation networks are now frequently used to model the history of life for various groups of species whose evolutionary past is likely to include reticulation events such as horizontal gene transfer or hybridization. However, the reconstructed networks are rarely guaranteed to be temporal. If a reticulation network is temporal, then it satisfies the two biologically motivated timing constra...

Molecular phylogenetics, the study of reconstructing evolutionary trees, is a well-established field of scientific endeavor. However, in certain circumstances evolution is not completely tree-like. For example, a comparison of gene trees representing a set of present-day species and reconstructed for different genetic loci often reveals conflicting tree topologies. These discrepancies are not a...

Let X be a finite set, N be a reticulation-visible network on X, and T be a rooted binary phylogenetic tree. We show that there is a polynomial-time algorithm for deciding whether or not N displays T . Furthermore, for all |X| ≥ 1, we show that N has at most 8|X| − 7 vertices in total and at most 3|X| − 3 reticulation vertices, and that these upper bounds are sharp.

PURPOSE We aimed to prospectively evaluate anatomic chest computed tomography (CT) with tissue characterization late gadolinium-enhanced magnetic resonance imaging (MRI) in the evaluation of pulmonary fibrosis (PF). METHODS Twenty patients with idiopathic pulmonary fibrosis (IPF) and twelve control patients underwent late-enhanced MRI and high-resolution CT. Tissue characterization of PF was ...

The reticulation of an algebra was first defined for commutative rings by Simmons [19] and it was extended by Belluce to non-commutative rings [3]. As for the algebras of fuzzy logics, Belluce also constructed the reticulation of an MV-algebra [2], G. Georgescu defined the reticulation of a quantale [8] and L. Leuştean made this construction for BL-algebras [13, 14]. In each of the papers cited...

Galled trees, evolutionary networks with isolated reticulation cycles, have appeared under several slightly different definitions in the literature. In this paper, we establish the actual relationships between the main four such alternative definitions: namely, the original galled trees, level-1 networks, nested networks with nesting depth 1, and evolutionary networks with arc-disjoint reticula...