Trinets encode tree-child and level-2 phylogenetic networks

Phylogenetic networks generalize evolutionary trees, and are commonly used to represent evolutionary histories of species that undergo reticulate evolutionary processes such as hybridization, recombination and lateral gene transfer. Recently, there has been great interest in trying to develop methods to construct rooted phylogenetic networks from triplets, that is rooted trees on three species. However, although triplets determine or encode rooted phylogenetic trees, they do not in general encode rooted phylogenetic networks, which is a potential issue for any such method. Motivated by this fact, Huber and Moulton recently introduced trinets as a natural extension of rooted triplets to networks. In particular, they showed that level-1 level-1 phylogenetic networks are encoded by their trinets, and also conjectured that all “recoverable” rooted phylogenetic networks are encoded by their trinets. Here we prove that recoverable binary level-2 networks and binary tree-child networks are also encoded by their trinets. To do this we prove two decomposition theorems based on trinets which hold for all recoverable binary rooted phylogenetic networks. Our results provide some additional evidence in support of the conjecture that trinets encode all recoverable rooted phylogenetic networks, and could also lead to new approaches to construct phylogenetic networks from trinets

Fully dynamic maintenance of k-connectivity in parallel

©2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.Given a graph G=(V, E) with n vertices and m edges, the k-connectivity of G denotes either the k-edge connectivity or the k-vertex connectivity of G. In this paper, we deal with the fully dynamic maintenance of k-connectivity of G in the parallel setting for k=2, 3. We study the problem of maintaining k-edge/vertex connected components of a graph undergoing repeatedly dynamic updates, such as edge insertions and deletions, and answering the query of whether two vertices are included in the same k-edge/vertex connected component. Our major results are the following: (1) An NC algorithm for the 2-edge connectivity problem is proposed, which runs in O(log n log(m/n)) time using O(n3/4) processors per update and query. (2) It is shown that the biconnectivity problem can be solved in O(log2 n ) time using O(nα(2n, n)/logn) processors per update and O(1) time with a single processor per query or in O(log n logn/m) time using O(nα(2n, n)/log n) processors per update and O(logn) time using O(nα(2n, n)/logn) processors per query, where α(.,.) is the inverse of Ackermann's function. (3) An NC algorithm for the triconnectivity problem is also derived, which takes O(log n logn/m+logn log log n/α(3n, n)) time using O(nα(3n, n)/log n) processors per update and O(1) time with a single processor per query. (4) An NC algorithm for the 3-edge connectivity problem is obtained, which has the same time and processor complexities as the algorithm for the triconnectivity problem. To the best of our knowledge, the proposed algorithms are the first NC algorithms for the problems using O(n) processors in contrast to Ω(m) processors for solving them from scratch. In particular, the proposed NC algorithm for the 2-edge connectivity problem uses only O(n3/4) processors. All the proposed algorithms run on a CRCW PRAMWeifa Liang, Brent, R.P., Hong She

Paradigm and paradox in power networks

Well known in the theory of network flows, Braess paradox states that adding path(s) to a congested road network may increase overall journey time. In transportation networks, the phenomenon results from selfish routing. In power systems, an analogous increase in congestion can arise as a consequence of Kirchhoff's laws, suggesting opportunities to optimize grid topology. The thesis starts with the discussion of Braess-like congestion phenomena in linear circuits. We prove that adding electrical path(s) always increases congestion in networks powered by voltage sources, while the opposite in networks driven by current sources. Although such predictability is not present in networks controlled by a mixture of voltage and current sources, our results offer a clean decomposition that completely separates the effect of current sources and voltage sources on total loss. The culmination of this research is a set of four equivalent methods of computing I^2R loss in mixed-source networks. We go on to explore network decomposition in combination with greedy sequential line switching heuristics to address the NP-hardness of power grid topology control. By means of some low order examples, it is shown that within a reasonably large class of greedy heuristics, none can be found that perform better than the others across all grid topologies. Despite this cautionary tale, statistical evidence indicates that, among three most representative heuristics, the global greedy heuristic is most computationally intensive but has the best chance of reducing generation cost while enforcing connectivity. The final part of the thesis presents a new approach to grid decomposition using vertex cut sets. We show that each vertex cut set and corresponding grid decomposition establishes a natural upper bound on the interactions between subgrids as nodal injections are regulated within each. Using such decomposition, it becomes possible to isolate congestion effects to a relatively small subgrid. A fast grid decomposition heuristic based on vertex cut sets and locational marginal prices is then proposed and studied through simulations on IEEE 118-bus system. On average, the computational cost is significantly reduced and the generation cost saving is similar to what is obtained with a global greedy algorithm

Upward planar drawings with two slopes

In an upward planar 2-slope drawing of a digraph, edges are drawn as straight-line segments in the upward direction without crossings using only two different slopes. We investigate whether a given upward planar digraph admits such a drawing and, if so, how to construct it. For the fixed embedding scenario, we give a simple characterisation and a linear-time construction by adopting algorithms from orthogonal drawings. For the variable embedding scenario, we describe a linear-time algorithm for single-source digraphs, a quartic-time algorithm for series-parallel digraphs, and a fixed-parameter tractable algorithm for general digraphs. For the latter two classes, we make use of SPQR-trees and the notion of upward spirality. As an application of this drawing style, we show how to draw an upward planar phylogenetic network with two slopes such that all leaves lie on a horizontal line

Topology Control Multi-Objective Optimisation in Wireless Sensor Networks: Connectivity-Based Range Assignment and Node Deployment

The distinguishing characteristic that sets topology control apart from other methods, whose motivation is to achieve effects of energy minimisation and an increased network capacity, is its network-wide perspective. In other words, local choices made at the node-level always have the goal in mind of achieving a certain global, network-wide property, while not excluding the possibility for consideration of more localised factors. As such, our approach is marked by being a centralised computation of the available location-based data and its reduction to a set of non-homogeneous transmitting range assignments, which elicit a certain network-wide property constituted as a whole, namely, strong connectedness and/or biconnectedness. As a means to effect, we propose a variety of GA which by design is multi-morphic, where dependent upon model parameters that can be dynamically set by the user, the algorithm, acting accordingly upon either single or multiple objective functions in response. In either case, leveraging the unique faculty of GAs for finding multiple optimal solutions in a single pass. Wherefore it is up to the designer to select the singular solution which best meets requirements. By means of simulation, we endeavour to establish its relative performance against an optimisation typifying a standard topology control technique in the literature in terms of the proportion of time the network exhibited the property of strong connectedness. As to which, an analysis of the results indicates that such is highly sensitive to factors of: the effective maximum transmitting range, node density, and mobility scenario under observation. We derive an estimate of the optimal constitution thereof taking into account the specific conditions within the domain of application in that of a WSN, thereby concluding that only GA optimising for the biconnected components in a network achieves the stated objective of a sustained connected status throughout the duration.fi=Opinnäytetyö kokotekstinä PDF-muodossa.|en=Thesis fulltext in PDF format.|sv=Lärdomsprov tillgängligt som fulltext i PDF-format