Cristina Ciampelli, Grazia Galleri, Manuela Galioto
et al.
Parkinson’s disease (PD) is a fatal neurodegenerative disease for which there are no still effective treatments able to stop or slow down neurodegeneration. To date, pathological mutations in the leucine-rich repeat kinase 2 (LRRK2) gene have been identified as the major genetic cause of PD, although the molecular mechanism responsible for the loss of dopaminergic neurons is still cryptic. In this review, we explore the contribution of Drosophila models to the elucidation of LRRK2 function in different cellular pathways in either neurons or glial cells. Importantly, recent studies have shown that LRRK2 is highly expressed in immunocompetent cells, including astrocytes and microglia in the brain, compared to neuronal expression. LRRK2 mutations are also strongly associated with the development of inflammatory diseases and the production of inflammatory molecules. Using Drosophila models, this paper shows that a genetic reduction of the inflammatory response protects flies from the neurodegeneration induced by LRRK2 pathological mutant expression.
In a recent work, Bensmail, Blanc, Cohen, Havet and Rocha, motivated by applications for TDMA scheduling problems, have introduced the notion of BMRN*-colouring of digraphs, which is a type of arc-colouring with particular colouring constraints. In particular, they gave a special focus to planar digraphs. They notably proved that every planar digraph can be 8-BMRN*-coloured, while there exist planar digraphs for which 7 colours are needed in a BMRN*-colouring. They also proved that the problem of deciding whether a planar digraph can be 3-BMRN*-coloured is NP-hard. In this work, we pursue these investigations on planar digraphs, in particular by answering some of the questions left open by the authors in that seminal work. We exhibit planar digraphs needing 8 colours to be BMRN*-coloured, thus showing that the upper bound of Bensmail, Blanc, Cohen, Havet and Rocha cannot be decreased in general. We also generalize their complexity result by showing that the problem of deciding whether a planar digraph can be k-BMRN*-coloured is NP-hard for every k ∈ {3,...,6}. Finally, we investigate the connection between the girth of a planar digraphs and the least number of colours in its BMRN*-colourings.
SUMMARY In mammals, females generally live longer than males. Nevertheless, the mechanisms underpinning sex-dependent longevity are currently unclear. Epigenetic clocks are powerful biological biomarkers capable of precisely estimating chronological age using only DNA methylation data. These clocks have been used to identify novel factors influencing the aging rate, but few studies have examined the performance of epigenetic clocks in divergent mammalian species. In this study, we developed the first epigenetic clock for domesticated sheep ( Ovis aries ), and using 185 CpG sites can predict chronological age with a median absolute error of 5.1 months from ear punch and blood samples. We have discovered that castrated male sheep have a decelerated aging rate compared to intact males, mediated at least in part by the removal of androgens. Furthermore, we identified several androgen-sensitive CpG dinucleotides that become progressively hypomethylated with age in intact males, but remain stable in castrated males and females. Many of these androgen sensitive demethylating sites are regulatory in nature and located in genes with known androgen-dependent regulation, such as MKLN1, LMO4 and FN1 . Comparable sex-specific methylation differences in MKLN1 also exist in mouse muscle (p=0.003) but not blood, indicating that androgen dependent demethylation exists in multiple mammalian groups, in a tissue-specific manner. In characterising these sites, we identify biologically plausible mechanisms explaining how androgens drive male-accelerated aging.
Let $G$ be a graph and $\mathcal{S}$ be a subset of $Z$. A vertex-coloring $\mathcal{S}$-edge-weighting of $G$ is an assignment of weights by the elements of $\mathcal{S}$ to each edge of $G$ so that adjacent vertices have different sums of incident edges weights. It was proved that every 3-connected bipartite graph admits a vertex-coloring $\mathcal{S}$-edge-weighting for $\mathcal{S} = \{1,2 \}$ (H. Lu, Q. Yu and C. Zhang, Vertex-coloring 2-edge-weighting of graphs, European J. Combin., 32 (2011), 22-27). In this paper, we show that every 2-connected and 3-edge-connected bipartite graph admits a vertex-coloring $\mathcal{S}$-edge-weighting for $\mathcal{S} \in \{ \{ 0,1 \} , \{1,2 \} \}$. These bounds we obtain are tight, since there exists a family of infinite bipartite graphs which are 2-connected and do not admit vertex-coloring $\mathcal{S}$-edge-weightings for $\mathcal{S} \in \{ \{ 0,1 \} , \{1,2 \} \}$.
A graph $G$ is said to be ISK4-free if it does not contain any subdivision of $K_4$ as an induced subgraph. In this paper, we propose new upper bounds for chromatic number of ISK4-free graphs and $\{$ISK4, triangle$\}$-free graphs.
In this article, we introduce the notion of the double competition multigraph of a digraph. We give characterizations of the double competition multigraphs of arbitrary digraphs, loopless digraphs, reflexive digraphs, and acyclic digraphs in terms of edge clique partitions of the multigraphs.
We give a statistic preserving bijection from rigged configurations to a tensor product of Kirillov–Reshetikhin crystals $\otimes_{i=1}^{N}B^{1,s_i}$ in type $D_4^{(3)}$ by using virtualization into type $D_4^{(1)}$. We consider a special case of this bijection with $B=B^{1,s}$, and we obtain the so-called Kirillov–Reshetikhin tableaux model for the Kirillov–Reshetikhin crystal.
For any finite path $v$ on the square lattice consisting of north and east unit steps, we construct a poset Tam$(v)$ that consists of all the paths lying weakly above $v$ with the same endpoints as $v$. For particular choices of $v$, we recover the traditional Tamari lattice and the $m$-Tamari lattice. In particular this solves the problem of extending the $m$-Tamari lattice to any pair $(a; b)$ of relatively prime numbers in the context of the so-called rational Catalan combinatorics.For that purpose we introduce the notion of canopy of a binary tree and explicit a bijection between pairs $(u; v)$ of paths in Tam$(v)$ and binary trees with canopy $v$. Let $(\overleftarrow{v})$ be the path obtained from $v$ by reading the unit steps of $v$ in reverse order and exchanging east and north steps. We show that the poset Tam$(v)$ is isomorphic to the dual of the poset Tam$(\overleftarrow{v})$ and that Tam$(v)$ is isomorphic to the set of binary trees having the canopy $v$, which is an interval of the ordinary Tamari lattice. Thus the usual Tamari lattice is partitioned into (smaller) lattices Tam$(v)$, where the $v$’s are all the paths of length $n-1$ on the square lattice.We explain possible connections between the poset Tam$(v)$ and (the combinatorics of) the generalized diagonal coinvariant spaces of the symmetric group.
We completely determine the complexity status of the dominating set problem for hereditary graph classes defined by forbidden induced subgraphs with at most five vertices.
This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated graphs, indicates that the multidimensional generalization is more difficult to solve than the original problem.
We use a recently introduced combinatorial object, the $\textit{interval-poset}$, to describe two bijections on intervals of the Tamari lattice. Both bijections give a combinatorial proof of some previously known results. The first one is an inner bijection between Tamari intervals that exchanges the $\textit{initial rise}$ and $\textit{lower contacts}$ statistics. Those were introduced by Bousquet-Mélou, Fusy, and Préville-Ratelle who proved they were symmetrically distributed but had no combinatorial explanation. The second bijection sends a Tamari interval to a closed flow of an ordered forest. These combinatorial objects were studied by Chapoton in the context of the Pre-Lie operad and the connection with the Tamari order was still unclear.
This article present a application of Block Korkin---Zolotarev lattice reduction method for Lattice Reduction---Aided decoding under MIMO---channel. We give a upper bound estimate on the lattice reduced by block Korkin---Zolotarev method (BKZ) for different value of the block size and detecting by SIC.
We prove that edge contractions do not preserve the property that a set of graphs has bounded clique-width. This property is preserved by contractions of edges, one end of which is a vertex of degree 2.
A chromatic root is a zero of the chromatic polynomial of a graph. At a Newton Institute workshop on Combinatorics and Statistical Mechanics in 2008, two conjectures were proposed on the subject of which algebraic integers can be chromatic roots, known as the ``$α +n$ conjecture'' and the ``$nα$ conjecture''. These say, respectively, that given any algebraic integer α there is a natural number $n$ such that $α +n$ is a chromatic root, and that any positive integer multiple of a chromatic root is also a chromatic root. By computing the chromatic polynomials of two large families of graphs, we prove the $α +n$ conjecture for quadratic and cubic integers, and show that the set of chromatic roots satisfying the nα conjecture is dense in the complex plane.
A 4-wheel is a graph formed by a cycle C and a vertex not in C that has at least four neighbors in C. We prove that a graph G that does not contain a 4-wheel as a subgraph is 4-colorable and we describe some structural properties of such a graph.
The aim of this paper is to derive on the basis of the Euler's formula several analytical relations which hold for certain classes of planar graphs and which can be useful in algorithmic graph theory.