List circular backbone colouring

Graph TheoryInternational audienceA natural generalization of graph colouring involves taking colours from a metric space and insisting that the endpoints of an edge receive colours separated by a minimum distance dictated by properties of the edge. In the q-backbone colouring problem, these minimum distances are either q or 1, depending on whether or not the edge is in the backbone. In this paper we consider the list version of this problem, with particular focus on colours in ℤp - this problem is closely related to the problem of circular choosability. We first prove that the list circular q-backbone chromatic number of a graph is bounded by a function of the list chromatic number. We then consider the more general problem in which each edge is assigned an individual distance between its endpoints, and provide bounds using the Combinatorial Nullstellensatz. Through this result and through structural approaches, we achieve good bounds when both the graph and the backbone belong to restricted families of graphs

Backbone Colouring of Graphs

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H). It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j∈{6,7,8} planar graph without adjacent triangles. In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method. In the second part of this thesis we further improve these results by proving that for any graph G with χ(G) ≥ 4, BBC(G,T) = χ(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ∀ uv ∈ T, |f(u)-f(v)|=2 or |f(u)-f(v)| ≥ k-2, k = χ(G). For the case that G is a planar graph, according to Four Colour Theorem, χ(G) = 4; so, BBC(G,T) = 4

Solving problems on generalized convex graphs via mim-width

A bipartite graph G = (A, B, E) is H-convex, for some family of graphs H, if there exists a graph H ∈ H with V (H) = A such that the set of neighbours in A of each b ∈ B induces a connected subgraph of H. Many NP-complete problems become polynomial-time solvable for H-convex graphs when H is the set of paths. In this case, the class of H-convex graphs is known as the class of convex graphs. The underlying reason is that this class has bounded mim-width. We extend the latter result to families of H-convex graphs where (i) H is the set of cycles, or (ii) H is the set of trees with bounded maximum degree and a bounded number of vertices of degree at least 3. As a consequence, we can reprove and strengthen a large number of results on generalized convex graphs known in the literature. To complement result (ii), we show that the mim-width of H-convex graphs is unbounded if H is the set of trees with arbitrarily large maximum degree or an arbitrarily large number of vertices of degree at least 3. In this way we are able to determine complexity dichotomies for the aforementioned graph problems. Afterwards we perform a more refined width-parameter analysis, which shows even more clearly which width parameters are bounded for classes of H-convex graphs

A proposed mechanism for IS607-family serine transposases

Background The transposases encoded by the IS607 family of mobile elements are unusual serine recombinases with an inverted domain order and minimal specificity for target DNA.<p></p> Results Structural genomics groups have determined three crystal structures of the catalytic domains of IS607 family transposases. The dimers formed by these catalytic domains are very different from those seen for other serine recombinases and include interactions that usually only occur upon formation of a synaptic tetramer.<p></p> Conclusions Based on these structures, we propose a model for how IS607-family transposases could form a synaptic tetramer. The model suggests that, unlike other serine recombinases, these enzymes carry out sequence-specific DNA binding and catalysis in trans: the DNA binding and catalytic domains of each subunit are proposed to interact with different DNA duplexes. The model also suggests an explanation for the minimal target DNA specificity.<p></p&gt

An interference-aware virtual clustering paradigm for resource management in cognitive femtocell networks

Femtocells represent a promising alternative solution for high quality wireless access in indoor scenarios where conventional cellular system coverage can be poor. They are randomly deployed by the end user, so only post deployment network planning is possible. Furthermore, this uncoordinated deployment creates severe interference to co-located femtocells, especially in dense deployments. This paper presents a new architecture using a generalised virtual cluster femtocell (GVCF) paradigm, which groups together FAP into logical clusters. It guarantees severely interfering and overlapping femtocells are assigned to different clusters. Since each cluster operates on different band of frequencies, the corresponding virtual cluster controller only has to manage its own FAPs, so the overall system complexity is low. The performance of the GVCF algorithm is analysed from both a resource availability and cluster number perspective. Simulation results conclusively corroborate the superior performance of the GVCF model in interference mitigation, particularly in high density FAP scenarios

Complex network analysis and nonlinear dynamics

This chapter aims at reviewing complex network and nonlinear dynamical models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the field of complex networks, the present summary introduces some applications of complex networks to economics, finance, epidemic spreading of innovations, and regional trade and developments. The chapter also reviews results involving applications of complex networks to other relevant socioeconomic issue

Proteins analysed as virtual knots

Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or disappear rapidly under manipulation and interaction. Knotting has been previously identified in protein backbone chains, for which these mechanical constraints are of fundamental importance to their molecular functionality, despite their being open curves in which the knots are not mathematically well defined; knotting can only be identified by closing the termini of the chain somehow. We introduce a new method for resolving knotting in open curves using virtual knots, which are a wider class of topological objects that do not require a classical closure and so naturally capture the topological ambiguity inherent in open curves. We describe the results of analysing proteins in the Protein Data Bank by this new scheme, recovering and extending previous knotting results, and identifying topological interest in some new cases. The statistics of virtual knots in protein chains are compared with those of open random walks and Hamiltonian subchains on cubic lattices, identifying a regime of open curves in which the virtual knotting description is likely to be important

An Implementation of Cardiovascular Disease Prediction in Ultrasonography Images using AWMYOLOv4 Deep Learning Mode

Cardiovascular diseases are one of the most important issues facing the people and their origins also death is contained all over the world the facing issues in past 25 years. Every country’s inversing large amount in health care researches and it’s related to enhanced predict the diseases. Cardio issues are not even physicians can easily be predicted and it is a very challenging task that requires high knowledge and expertise. To identify to create machine language models used to efficiently predict the earliest stage of cardiovascular disease. In this work, we recommend AWMF filter for the pre-process the Input Image after the input move to YOLOv4 neural network method for classification and segmentation to the heart affected areas by using ultrasonic Images with the help of a machine learning algorithm. The proposed algorithm uses ultrasonic picture classification and segmentation to detect cardiovascular disease earlier. This model shows the more accurate result on 96% of training and 98% testing data. And this method shows better results and providing while compared to the existing method