A note on the packing of two copies of some trees into their third power

AbstractIt is proved in [1] that if a tree T of order n is not a star, then there exists an edge-disjoint placement of two copies of this tree into its fourth power.In this paper, we prove the packing of some trees into their third power

Real-time tracking and mining of users’ actions over social media

© 2020, ComSIS Consortium. All rights reserved. With the advent of Web 2.0 technologies and social media, companies are actively looking for ways to know and understand what users think and say about their products and services. Indeed, it has become the practice that users go online using social media like Facebook to raise concerns, make comments, and share recommendations. All these actions can be tracked in real-time and then mined using advanced techniques like data analytics and sentiment analysis. This paper discusses such tracking and mining through a system called Social Miner that allows companies to make decisions about what, when, and how to respond to users’ actions over social media. Questions that Social Miner allows to answer include what actions were frequently executed and why certain actions were executed more than others

On circular disarranged strings of sequences

Two sequences (a1, a2, ... , an) and (b1, b2, ..., bn), sharing n-1 elements, are said disarranged if for every non-empty subset Q of [n], the sets {ai : i in Q} and {bi : i in Q} are different. In this paper we investigate properties of these pairs of sequences. Moreover we extend the definition of disarranged pairs to a circular string of n-sequences and prove that, for every positive integer m, except some initials values for n even, there exists a similar structure of length m

Ciliopathies: an expanding disease spectrum

Ciliopathies comprise a group of disorders associated with genetic mutations encoding defective proteins, which result in either abnormal formation or function of cilia. As cilia are a component of almost all vertebrate cells, cilia dysfunction can manifest as a constellation of features that include characteristically, retinal degeneration, renal disease and cerebral anomalies. Additional manifestations include congenital fibrocystic diseases of the liver, diabetes, obesity and skeletal dysplasias. Ciliopathic features have been associated with mutations in over 40 genes to date. However, with over 1,000 polypeptides currently identified within the ciliary proteome, several other disorders associated with this constellation of clinical features will likely be ascribed to mutations in other ciliary genes. The mechanisms underlying many of the disease phenotypes associated with ciliary dysfunction have yet to be fully elucidated. Several elegant studies have crucially demonstrated the dynamic ciliary localisation of components of the Hedgehog and Wnt signalling pathways during signal transduction. Given the critical role of the cilium in transducing “outside-in” signals, it is not surprising therefore, that the disease phenotypes consequent to ciliary dysfunction are a manifestation of aberrant signal transduction. Further investigation is now needed to explore the developmental and physiological roles of aberrant signal transduction in the manifestation of ciliopathy phenotypes. Utilisation of conditional and inducible murine models to delete or overexpress individual ciliary genes in a spatiotemporal and organ/cell-specific manner should help clarify some of the functional roles of ciliary proteins in the manifestation of phenotypic features

Polycystic kidney diseases: From molecular discoveries to targeted therapeutic strategies

Polycystic kidney diseases (PKDs) represent a large group of progressive renal disorders characterized by the development of renal cysts leading to end-stage renal disease. Enormous strides have been made in understanding the pathogenesis of PKDs and the development of new therapies. Studies of autosomal dominant and recessive polycystic kidney diseases converge on molecular mechanisms of cystogenesis, including ciliary abnormalities and intracellular calcium dysregulation, ultimately leading to increased proliferation, apoptosis and dedifferentiation. Here we review the pathobiology of PKD, highlighting recent progress in elucidating common molecular pathways of cystogenesis. We discuss available models and challenges for therapeutic discovery as well as summarize the results from preclinical experimental treatments targeting key disease-specific pathways

Partially Square Graphs, Hamiltonicity and Circumference II

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Distance-2 Self-stabilizing Algorithm for a b-Coloring of Graphs

International audienceA b-coloring of a graph G is a proper $k$-coloring of G such that for each color $i$, $1 \leq i\leq k$, at least one vertex colored with $i$ is adjacent to every color $j$, with $1\leq j\neq i\leq k$. This kind of coloring is useful to decompose any system into communities, where each community contains a vertex adjacent to all the other communities. This kind of organization can provide improving in many fields, especially in the data clustering. In this paper we propose a new self-stabilizing algorithm for finding a b-coloring of arbitrary undirected connected graphs. Because the characteristics of the b-coloring problem, the proposed self-stabilizing algorithm use a distance-2 knowledge

Exact values for the b-chromatic number of a power complete k-ary tree

International audienceLet G be a graph on vertices x1, x2, . . . , xn. The b-chromatic number of G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i ≤ k, has at least one representant xi adjacent to a vertex of every color j, 1 ≤ j != i ≤ k. In this paper, we give the exact value for the b-chromatic number of power graphs of a complete binary tree