Solving the maximum agreement subtree and the maximum compatible tree problems on many bounded degree trees

Given a set of leaf-labeled trees with identical leaf sets, the well-known Maximum Agreement SubTree problem (MAST) consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. Its variant called Maximum Compatible Tree (MCT) is less stringent, as it allows the input trees to be refined. Both problems are of particular interest in computational biology, where trees encountered have often small degrees. In this paper, we study the parameterized complexity of MAST and MCT with respect to the maximum degree, denoted by D, of the input trees. Although MAST is polynomial for bounded D [1, 6, 3], we show that the problem is W[1]-hard with respect to parameter D. Moreover, relying on recent advances in parameterized complexity we obtain a tight lower bound: while MAST can be solved in O(N O(D)) time where N denotes the input length, we show that an O(N o(D) ) bound is not achievable, unless SNP ⊆ SE. We also show that MCT is W[1]-hard with respect to D, and that MCT cannot be solved in O(N o(2D/2)) time, unless SNP ⊆ SE.

Den fysiska aktivitetens inverkan på småbarn : En kvalitativ studie av den fysiska aktivitetens betydelse för barn och daghemspersonalens roll i skapandet av ett fysisk aktivt daghem

Examensarbetes syfte är att ta reda på vilken inverkan den fysiska aktiviteten har på dagens småbarn, samt vilken roll daghemspersonalen har när det kommer till att skapa en fysiskt aktiv miljö på daghemmet. Examensarbetets undersökning är kvalitativ och har syftet att undersöka daghemspersonalens roll i skapandet av ett fysiskt aktivt daghem. Respondenterna arbetar med barn i åldrarna 3 till 6. Teoridelen fokuserar mer på att ta reda på hur den fysiska aktiviteten påverkar barn, detta genom litteratur och vetenskapliga artiklar. Teoridelen tar upp hur fysisk aktivitet påverkar barn i olika områden av livet, rekommendationer som finns och hur inaktivitet påverkar barnen. Jag kom fram till att fysisk aktivitet har stor positiv inverkan på barn och bidrar med fördelar för barnet i många områden av livet. Samt att inaktivitet och stillasittande har motsatt effekt. Utifrån de kvalitativa intervjuerna framkom det att dagvårdspersonal är väldigt involverade när det kommer till barnens fysiska aktivitet och hur fysisk aktivitet syns i verksamheten. Dagvårdspersonalen har en positiv inverkan på barns fysiska aktivitet.Opinnäytetyön tarkoitus on selvittää fyysisen aktiivisuuden vaikutus nykypäivän pieniin lapsiin, sekä päiväkotihenkilökunnan rooli fyysisesti aktiivisen ympäristön luomisessa päiväkodissa. Opinnäytetyön tutkimus on kvalitatiivinen jonka tarkoitus on tutkia päiväkotihenkilökunnan rooli fyysisesti aktiivisen päiväkodin luomisessa. Vastaajat työskentelevät lasten kanssa iältään 3-6 vuotiaita. Teoriaosa keskittyy enemmän siihen kuinka fyysinen aktiivisuus vaikuttaa lapsiin, kirjallisuuden sekä tieteellisten artikkelien kautta. Teoriaosa käsittelee kuinka fyysinen aktiivisuus vaikuttaa lapsiin eri alueilla elämässä, voimassaolevat suositukset ja kuinka inaktiivisuus vaikuttaa lapsiin. Tulin siihen tulokseen että fyysisellä aktiivisuudella on iso positiivinen vaikutus lapsiin ja antaa lapselle etuja elämän monilla eri alueilla. Sekä että inaktiivisuudella ja paikallaistumisella on päinvastainen vaikutus. Kvalitatiivisissa haastatteluissa ilmeni että päiväkotihenkilökunta on tärkeässä roolissa kun tulee lasten fyysiseen aktiivisuuteen ja kuinka fyysinen aktiivisuus näkyy toiminnassa. Päiväkotihenkilökunnalla on positiivinen vaikutus lasten fyysiseen aktiivisuuteen.The purpose of the bachelor’s thesis is to examine the affects of physical activity on today's children, and what role the nursing staff have when it comes to creating a physically active environment in the day care center. The survey is done by using qualitative interviews and aims to investigate the role that day care staff has in the creation of a physically active day care center. The respondents work with children between the ages of 3-6. The theory part of the bachelor’s thesis focuses more on finding out how physical activity affects children, this is achieved through literature and scientific articles. The theory discusses how physical activity affects children in different areas of life, which recommendations there are and how inactivity affects the children. I concluded that physical activity has a big positive impact on children and contributes to benefits for the child in many areas of its life. In addition, inactivity and sedentary seduction have the opposite effect. Based on the qualitative interviews it emerged that the day care staff are very involved when it comes to children's physical activity and how physical activity is seen in the function. Day care staff has a positive impact on children's physical activity

Pattern Identification in Biogeography

We develop and study two distance metrics for area cladograms (leaf-labeled trees where many leaves can share the same label): the edge contract-and-refine metric and the MAAC distance metric. We demonstrate that in contrast to phylogenies, the contract-and-refine distance between two area cladograms is not identical to the character encoding distance, and the latter is not a metric. We present a polynomial time algorithm to compute the MAAC distance, based on a polynomial-time algorithm for computing the largest common pruned subtree of two area cladograms. We also describe a linear time algorithm to decide if two area cladograms are identical

Pattern Identification in Biogeography

Identifying common patterns among area cladograms that arise in historical biogeography is an important tool for biogeographical inference. We develop the first rigorous formalization of these pattern-identification problems. We develop metrics to compare area cladograms. We define the maximum agreement area cladogram (MAAC) and we develop efficient algorithms for finding the MAAC of two area cladograms, while showing that it is NP-hard to find the MAAC of several binary area cladograms. We also describe a linear-time algorithm to identify if two area cladograms are identical

Online Consensus and Agreement of Phylogenetic Trees

Abstract. Computational heuristics are the primary methods for reconstruction of phylogenetic trees on large datasets. Most large-scale phylogenetic analyses produce numerous trees that are equivalent for some optimization criteria. Even using the best heuristics, it takes significant amount of time to obtain optimal trees in simulation experiments. When biological data are used, the score of the optimal tree is not known. As a result, the heuristics are either run for a fixed (long) period of time, or until some measure of a lack of improvement is achieved. It is unclear, though, what is a good criterion for measuring this lack of improvement. However, often it is useful to represent the collection of best trees so far in a compact way to allow scientists to monitor the reconstruction progress. Consensus and agreement trees are common such representations. Using existing static algorithms to produce these trees increases an already lengthy computational time substantially. In this paper we present efficient online algorithms for computing strict and majority consensi and the maximum agreement subtree.