Finding the ℓ-core of a tree

AbstractAn ℓ-core of a tree T=(V,E) with |V|=n, is a path P with length at most ℓ that is central with respect to the property of minimizing the sum of the distances from the vertices in P to all the vertices of T not in P. The distance between two vertices is the length of the shortest path joining them. In this paper we present efficient algorithms for finding the ℓ-core of a tree. For unweighted trees we present an O(nℓ) time algorithm, while for weighted trees we give a procedure with time complexity of O(nlog2n). The algorithms use two different types of recursive principle in their operation

Recombination and Population Mosaic of a Multifunctional Viral Gene, Adeno-Associated Virus cap

Homologous recombination is a dominant force in evolution and results in genetic mosaics. To detect evidence of recombination events and assess the biological significance of genetic mosaics, genome sequences for various viral populations of reasonably large size are now available in the GenBank. We studied a multi-functional viral gene, the adeno-associated virus (AAV) cap gene, which codes for three capsid proteins, VP1, VP2 and VP3. VP1-3 share a common C-terminal domain corresponding to VP3, which forms the viral core structure, while the VP1 unique N-terminal part contains an enzymatic domain with phospholipase A2 activity. Our recombinant detection program (RecI) revealed five novel recombination events, four of which have their cross-over points in the N-terminal, VP1 and VP2 unique region. Comparison of phylogenetic trees for different cap gene regions confirmed discordant phylogenies for the recombinant sequences. Furthermore, differences in the phylogenetic tree structures for the VP1 unique (VP1u) region and the rest of cap highlighted the mosaic nature of cap gene in the AAV population: two dominant forms of VP1u sequences were identified and these forms are linked to diverse sequences in the rest of cap gene. This observation together with the finding of frequent recombination in the VP1 and 2 unique regions suggests that this region is a recombination hot spot. Recombination events in this region preserve protein blocks of distinctive functions and contribute to convergence in VP1u and divergence of the rest of cap. Additionally the possible biological significance of two dominant VP1u forms is inferred

Molecular Phylogeny Implemented in an Introductory Plant Classification Course

Plant classification is one of the core components in undergraduate programs related to plant sciences. Traditionally plant classification courses primarily introduce morphology-based taxonomy because of practical needs in the field. However, the publication of new plant classification systems by Angiosperm Phylogeny Group (APG) using molecular phylogeny methods leads to the trends of using molecular evidence (DNA barcode) for plant identification. In our introductory plant classification course, we included a two-week module (lectures and labs) to introduce key concepts and fundamental skills in molecular phylogeny. Week 1 included concepts of evolutionary tree thinking, data mining in NCBI using BLAST search, and phylogenetic tree building. Week 2 introduced concepts of DNA sequencing and barcoding for plant identification. Student selected their own plants to sequence the DNA barcodes, which were then used in the final exam for practice and summative assessments. One challenge we are constantly dealing with is the increasing difficulty in finding diverse sequence using BLAST because of the fast-growing number of angiosperm genomes sequenced

Combining multiple isotopes and metagenomic to delineate the role of tree canopy nitrification in European forests along nitrogen deposition and climate gradients

Forest canopies influence our climate through carbon, water and energy exchanges with the atmosphere. However, less investigated is whether and how tree canopies change the chemical composition of precipitation, with important implications on forest nutrient cycling. Recently, we provided for the first time isotopic evidence that biological nitrification in tree canopies was responsible for significant changes in the amount of nitrate from rainfall to throughfall across two UK forests at high nitrogen (N) deposition [1]. This finding strongly suggested that bacteria and/or Archaea species of the phyllosphere are responsible for transforming atmospheric N before it reaches the soil. Despite microbial epiphytes representing an important component of tree canopies, attention has been mostly directed to their role as pathogens, while we still do not know whether and how they affect nutrient cycling. Our study aims to 1) characterize microbial communities harboured in tree canopies for two of the most dominant species in Europe (Fagus sylvatica L. and Pinus sylvestris L.) using metagenomic techniques, 2) quantify the functional genes related to nitrification but also to denitrification and N fixation, and 3) estimate the contribution of NO3 derived from biological canopy nitrification vs. atmospheric NO3 input by using \u3b415N, \u3b418O and \u3b417O of NO3in forest water. We considered i) twelve sites included in the EU ICP long term intensive forest monitoring network, chosen along a climate and nitrogen deposition gradient, spanning from Fennoscandia to the Mediterranean and ii) a manipulation experiment where N mist treatments were carried out either to the soil or over tree canopies. We will present preliminary results regarding microbial diversity in the phyllosphere, water (rainfall and throughfall) and soil samples over the gradient. Furthermore, we will report differences between the two investigated tree species for the phyllosphere core microbiome in terms of relative abundance of bacterial and Archaea classes and those species related to N cycling. Finally we will assess whether there are differences among tree species and sites in the number of functional genes related to N cycling and how they are related to the N deposition and/or climate. [1] Guerrieri et al. 2015 Global Change and Biology 21 (12): 4613-4626

ShallowForest: Optimizing All-to-All Data Transmission in WANs

All-to-all data transmission is a typical data transmission pattern in both consensus protocols and blockchain systems. Developing an optimization scheme that provides high throughput and low latency data transmission can significantly benefit the performance of those systems. This thesis investigates the problem of optimizing all-to-all data transmission in a wide area network (WAN) using overlay multicast. I first prove that in a congestion-free core network model, using shallow tree overlays with height up to two is sufficient for all-to-all data transmission to achieve the optimal throughput allowed by the available network resources. Based on this finding, I build ShallowForest, a data plane optimization for consensus protocols and blockchain systems. The goal of ShallowForest is to improve consensus protocols' resilience to skewed client load distribution. Experiments with skewed client load across replicas in the Amazon cloud demonstrate that ShallowForest can improve the commit throughput of the EPaxos consensus protocol by up to 100% with up to 60% reduction in commit latenc

Caminos Pareto-eficientes en redes: aplicaciones

The problem of finding the path in a network connecting two given nodes, source and sink, with minimum possible cost is known in the literature as the shortest path problem (SPP) and it is a core model that lies at the heart of network optimization. The reason is the wide range of its practical applications and the large amount of interesting generalizations that can be considered, among them, the analysis of the multiobjective shortest path problem. This last model allows us to find how to send a given product between two specified nodes of a network as quickly, as cheaply and as reliable as possible taking into account the so-called Pareto optimal paths. The text presented here consists of two chapters. The first one is devoted to the introduction of some notation and properties related to networks where each arc is associated to just one cost value. The formulation of the SPP as a Mathematical Programming model is considered as well as its corresponding dual problem. The complementary slackness theorem provides us with a characterization of any basic feasible solution as a spanning tree in the original network. A sufficient optimality condition is also derived from this relation. Finally, the Dijkstra algorithm is studied as well as other specific algorithms that use special properties on acyclic networks. The second chapter extends the hypotheses considered in the previous one to a multiobjective context. The continuous formulation of the problem of finding the Pareto optimal paths is compared with its discrete version and some properties are stated. A generalization of the Dijkstra algorithm is proposed in order to find the whole set of Pareto optimal solutions. This procedure allows us to determine that the optimal set of paths corresponds with a set of adjacent trees. This property is very important in order to generate the Pareto optimal set of solutions and is the basis of a new improved algorithm that, starting with a given optimal tree, explores its adjacent trees and finds those Pareto optimal ones by using the duality conditions of the complementary slackness theorem presented in the chapter one.Universidad de Sevilla. Grado en Matemática

Distributed Computing on Core-Periphery Networks: Axiom-based Design

Inspired by social networks and complex systems, we propose a core-periphery network architecture that supports fast computation for many distributed algorithms and is robust and efficient in number of links. Rather than providing a concrete network model, we take an axiom-based design approach. We provide three intuitive (and independent) algorithmic axioms and prove that any network that satisfies all axioms enjoys an efficient algorithm for a range of tasks (e.g., MST, sparse matrix multiplication, etc.). We also show the minimality of our axiom set: for networks that satisfy any subset of the axioms, the same efficiency cannot be guaranteed for any deterministic algorithm