Ramified rectilinear polygons: coordinatization by dendrons

Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic $l_1$-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3. Ramified rectilinear polygons are particular instances of rectangular complexes obtained from cube-free median graphs, or equivalently simply connected rectangular complexes with triangle-free links. The underlying graphs of finite ramified rectilinear polygons can be recognized among graphs in linear time by a Lexicographic Breadth-First-Search. Whereas the symmetry of a simple rectilinear polygon is very restricted (with automorphism group being a subgroup of the dihedral group $D_4$), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure

On retracts, absolute retracts, and folds in cographs

Let G and H be two cographs. We show that the problem to determine whether H is a retract of G is NP-complete. We show that this problem is fixed-parameter tractable when parameterized by the size of H. When restricted to the class of threshold graphs or to the class of trivially perfect graphs, the problem becomes tractable in polynomial time. The problem is also soluble when one cograph is given as an induced subgraph of the other. We characterize absolute retracts of cographs.Comment: 15 page

What is a 'novel' mtDNA mutation - And does 'novelty' really matter?

The hunt for pathogenic mitochondrial DNA (mtDNA) mutations is often fueled by the seeming novelty of mutations that are either nonsynonymous or affect the protein synthesis machinery in patients. In order to determine the novelty of a detected mutation, the working geneticist nearly always consults MITOMAP - often exclusively. By reanalyzing some case studies of refractory anemia with ring sideroblasts, prostate cancer, and hearing impairment, we demonstrate that the practice of solely relying on MITOMAP can be most misleading. A notorious example is the T1243C mutation, which was assessed to be novel and deemed to be associated with some (rare) disease simply because researchers did not realize that T1243C defines a deep branch in the Eurasian mtDNA phylogeny. The majority of 'novel' mutations suspected of being pathogenic are in actual fact known (and presumably neutral) polymorphisms (although unknown to MITOMAP), and this becomes glaringly evident when proper database searches and straightforward Internet queries are carried out.Instituto Multidisciplinario de Biología Celula

Mitochondrial portrait of the Cabo Verde archipelago: the Senegambian outpost of Atlantic slave trade

In order to study the matrilineal genetic composition in Cabo Verde (Republic of Cape Verde), an archipelago that used to serve as a Portuguese entrepôt of the Atlantic slave trade, we have analysed a total of 292 mtDNAs sampled from the seven inhabited islands for the hypervariable segment I (HVS-I) and some characteristic RFLPs of the coding regions. The different settlement history of the northwestern group of the islands is well reflected in the mtDNA pool. The total Cabo Verde sample clearly displays the characteristic mitochondrial features of the Atlantic fringe of western Africa and testifies to almost no mitochondrial input from the Portuguese colonizers.info:eu-repo/semantics/publishedVersio

Recognizing Treelike k-Dissimilarities

A k-dissimilarity D on a finite set X, |X| >= k, is a map from the set of size k subsets of X to the real numbers. Such maps naturally arise from edge-weighted trees T with leaf-set X: Given a subset Y of X of size k, D(Y) is defined to be the total length of the smallest subtree of T with leaf-set Y . In case k = 2, it is well-known that 2-dissimilarities arising in this way can be characterized by the so-called "4-point condition". However, in case k > 2 Pachter and Speyer recently posed the following question: Given an arbitrary k-dissimilarity, how do we test whether this map comes from a tree? In this paper, we provide an answer to this question, showing that for k >= 3 a k-dissimilarity on a set X arises from a tree if and only if its restriction to every 2k-element subset of X arises from some tree, and that 2k is the least possible subset size to ensure that this is the case. As a corollary, we show that there exists a polynomial-time algorithm to determine when a k-dissimilarity arises from a tree. We also give a 6-point condition for determining when a 3-dissimilarity arises from a tree, that is similar to the aforementioned 4-point condition.Comment: 18 pages, 4 figure

High Mitochondrial DNA Stability in B-Cell Chronic Lymphocytic Leukemia

BACKGROUND: Chronic Lymphocytic Leukemia (CLL) leads to progressive accumulation of lymphocytes in the blood, bone marrow, and lymphatic tissues. Previous findings have suggested that the mtDNA could play an important role in CLL. METHODOLOGY/PRINCIPAL FINDINGS: The mitochondrial DNA (mtDNA) control-region was analyzed in lymphocyte cell DNA extracts and compared with their granulocyte counterpart extract of 146 patients suffering from B-Cell CLL; B-CLL (all recruited from the Basque country). Major efforts were undertaken to rule out methodological artefacts that would render a high false positive rate for mtDNA instabilities and thus lead to erroneous interpretation of sequence instabilities. Only twenty instabilities were finally confirmed, most of them affecting the homopolymeric stretch located in the second hypervariable segment (HVS-II) around position 310, which is well known to constitute an extreme mutational hotspot of length polymorphism, as these mutations are frequently observed in the general human population. A critical revision of the findings in previous studies indicates a lack of proper methodological standards, which eventually led to an overinterpretation of the role of the mtDNA in CLL tumorigenesis. CONCLUSIONS/SIGNIFICANCE: Our results suggest that mtDNA instability is not the primary causal factor in B-CLL. A secondary role of mtDNA mutations cannot be fully ruled out under the hypothesis that the progressive accumulation of mtDNA instabilities could finally contribute to the tumoral process. Recommendations are given that would help to minimize erroneous interpretation of sequencing results in mtDNA studies in tumorigenesis

What is a 'novel' mtDNA mutation - And does 'novelty' really matter?

The hunt for pathogenic mitochondrial DNA (mtDNA) mutations is often fueled by the seeming novelty of mutations that are either nonsynonymous or affect the protein synthesis machinery in patients. In order to determine the novelty of a detected mutation, the working geneticist nearly always consults MITOMAP - often exclusively. By reanalyzing some case studies of refractory anemia with ring sideroblasts, prostate cancer, and hearing impairment, we demonstrate that the practice of solely relying on MITOMAP can be most misleading. A notorious example is the T1243C mutation, which was assessed to be novel and deemed to be associated with some (rare) disease simply because researchers did not realize that T1243C defines a deep branch in the Eurasian mtDNA phylogeny. The majority of 'novel' mutations suspected of being pathogenic are in actual fact known (and presumably neutral) polymorphisms (although unknown to MITOMAP), and this becomes glaringly evident when proper database searches and straightforward Internet queries are carried out.Instituto Multidisciplinario de Biología Celula

Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count

We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter $D=\Omega(\sqrt n)$, and at most $\min\bigl(2n-\Omega(\sqrt n),2n-D-2\bigr)$ edges.Comment: 10 pages, 2 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017