Phylogenetic Trees and Their Analysis

Determining the best possible evolutionary history, the lowest-cost phylogenetic tree, to fit a given set of taxa and character sequences using maximum parsimony is an active area of research due to its underlying importance in understanding biological processes. As several steps in this process are NP-Hard when using popular, biologically-motivated optimality criteria, significant amounts of resources are dedicated to both both heuristics and to making exact methods more computationally tractable. We examine both phylogenetic data and the structure of the search space in order to suggest methods to reduce the number of possible trees that must be examined to find an exact solution for any given set of taxa and associated character data. Our work on four related problems combines theoretical insight with empirical study to improve searching of the tree space. First, we show that there is a Hamiltonian path through tree space for the most common tree metrics, answering Bryant\u27s Challenge for the minimal such path. We next examine the topology of the search space under various metrics, showing that some metrics have local maxima and minima even with perfect data, while some others do not. We further characterize conditions for which sequences simulated under the Jukes-Cantor model of evolution yield well-behaved search spaces. Next, we reduce the search space needed for an exact solution by splitting the set of characters into mutually-incompatible subsets of compatible characters, building trees based on the perfect phylogenies implied by these sets, and then searching in the neighborhoods of these trees. We validate this work empirically. Finally, we compare two approaches to the generalized tree alignment problem, or GTAP: Sequence alignment followed by tree search vs. Direct Optimization, on both biological and simulated data

The development and application of metaheuristics for problems in graph theory: A computational study

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.It is known that graph theoretic models have extensive application to real-life discrete optimization problems. Many of these models are NP-hard and, as a result, exact methods may be impractical for large scale problem instances. Consequently, there is a great interest in developing e±cient approximate methods that yield near-optimal solutions in acceptable computational times. A class of such methods, known as metaheuristics, have been proposed with success. This thesis considers some recently proposed NP-hard combinatorial optimization problems formulated on graphs. In particular, the min- imum labelling spanning tree problem, the minimum labelling Steiner tree problem, and the minimum quartet tree cost problem, are inves- tigated. Several metaheuristics are proposed for each problem, from classical approximation algorithms to novel approaches. A compre- hensive computational investigation in which the proposed methods are compared with other algorithms recommended in the literature is reported. The results show that the proposed metaheuristics outper- form the algorithms recommended in the literature, obtaining optimal or near-optimal solutions in short computational running times. In addition, a thorough analysis of the implementation of these methods provide insights for the implementation of metaheuristic strategies for other graph theoretic problems

ALGORITHMS FOR MASSIVE, EXPENSIVE, OR OTHERWISE INCONVENIENT GRAPHS

A long-standing assumption common in algorithm design is that any part of the input is accessible at any time for unit cost. However, as we work with increasingly large data sets, or as we build smaller devices, we must revisit this assumption. In this thesis, I present some of my work on graph algorithms designed for circumstances where traditional assumptions about inputs do not apply. 1. Classical graph algorithms require direct access to the input graph and this is not feasible when the graph is too large to fit in memory. For computation on massive graphs we consider the dynamic streaming graph model. Given an input graph defined by as a stream of edge insertions and deletions, our goal is to approximate properties of this graph using space that is sublinear in the size of the stream. In this thesis, I present algorithms for approximating vertex connectivity, hypergraph edge connectivity, maximum coverage, unique coverage, and temporal connectivity in graph streams. 2. In certain applications the input graph is not explicitly represented, but its edges may be discovered via queries which require costly computation or measurement. I present two open-source systems which solve real-world problems via graph algorithms which may access their inputs only through costly edge queries. M ESH is a memory manager which compacts memory efficiently by finding an approximate graph matching subject to stringent time and edge query restrictions. PathCache is an efficiently scalable network measurement platform that outperforms the current state of the art

Building Information Filtering Networks with Topological Constraints: Algorithms and Applications

We propose a new methodology for learning the structure of sparse networks from data; in doing so we adopt a dual perspective where we consider networks both as weighted graphs and as simplicial complexes. The proposed learning methodology belongs to the family of preferential attachment algorithms, where a network is extended by iteratively adding new vertices. In the conventional preferential attachment algorithm a new vertex is added to the network by adding a single edge to another existing vertex; in our approach a new vertex is added to a set of vertices by adding one or more new simplices to the simplicial complex. We propose the use of a score function to quantify the strength of the association between the new vertex and the attachment points. The methodology performs a greedy optimisation of the total score by selecting, at each step, the new vertex and the attachment points that maximise the gain in the score. Sparsity is enforced by restricting the space of the feasible configurations through the imposition of topological constraints on the candidate networks; the constraint is fulfilled by allowing only topological operations that are invariant with respect to the required property. For instance, if the topological constraint requires the constructed network to be be planar, then only planarity-invariant operations are allowed; if the constraint is that the network must be a clique forest, then only simplicial vertices can be added. At each step of the algorithm, the vertex to be added and the attachment points are those that provide the maximum increase in score while maintaining the topological constraints. As a concrete but general realisation we propose the clique forest as a possible topological structure for the representation of sparse networks, and we allow to specify further constraints such as the allowed range of clique sizes and the saturation of the attachment points. In this thesis we originally introduce the Maximally Filtered Clique Forest (MFCF) algorithm: the MFCF builds a clique forest by repeated application of a suitably invariant operation that we call Clique Expansion operator and adds vertices according to a strategy that greedily maximises the gain in a local score function. The gains produced by the Clique Expansion operator can be validated in a number of ways, including statistical testing, cross-validation or value thresholding. The algorithm does not prescribe a specific form for the gain function, but allows the use of any number of gain functions as long as they are consistent with the Clique Expansion operator. We describe several examples of gain functions suited to different problems. As a specific practical realisation we study the extraction of planar networks with the Triangulated Maximally Filtered Graph (TMFG). The TMFG, in its simplest form, is a specialised version of the MFCF, but it can be made more powerful by allowing the use of specialised planarity invariant operators that are not based on the Clique Expansion operator. We provide applications to two well known applied problems: the Maximum Weight Planar Subgraph Problem (MWPSP) and the Covariance Selection problem. With regards to the Covariance Selection problem we compare our results to the state of the art solution (the Graphical Lasso) and we highlight the benefits of our methodology. Finally, we study the geometry of clique trees as simplicial complexes and note how the statistics based on cliques and separators provides information equivalent to the one that can be achieved by means of homological methods, such as the analysis of Betti numbers, however with our approach being computationally more efficient and intuitively simpler. Finally, we use the geometric tools developed to provide a possible methodology for inferring the size of a dataset generated by a factor model. As an example we show that our tools provide a solution for inferring the size of a dataset generated by a factor model

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

IST Austria Thesis

Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications. For the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries

Reconstrução de filogenias para imagens e vídeos

Orientadores: Anderson de Rezende Rocha, Zanoni DiasTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Com o advento das redes sociais, documentos digitais (e.g., imagens e vídeos) se tornaram poderosas ferramentas de comunicação. Dada esta nova realidade, é comum esses documentos serem publicados, compartilhados, modificados e republicados por vários usuários em diferentes canais da Web. Além disso, com a popularização de programas de edição de imagens e vídeos, muitas vezes não somente cópias exatas de documentos estão disponíveis, mas, também, versões modificadas das fontes originais (duplicatas próximas). Entretanto, o compartilhamento de documentos facilita a disseminação de conteúdo abusivo (e.g., pornografia infantil), que não respeitam direitos autorais e, em alguns casos, conteúdo difamatório, afetando negativamente a imagem pública de pessoas ou corporações (e.g., imagens difamatórias de políticos ou celebridades, pessoas em situações constrangedoras, etc.). Muitos pesquisadores têm desenvolvido, com sucesso, abordagens para detecção de duplicatas de documentos com o intuito de identificar cópias semelhantes de um dado documento multimídia (e.g., imagem, vídeo, etc.) publicado na Internet. Entretanto, somente recentemente têm se desenvolvido as primeiras pesquisas para ir além da detecção de duplicatas e encontrar a estrutura de evolução de um conjunto de documentos relacionados e modificados ao longo do tempo. Para isso, é necessário o desenvolvimento de abordagens que calculem a dissimilaridade entre duplicatas e as separem corretamente em estruturas que representem a relação entre elas de forma automática. Este problema é denominado na literatura como Reconstrução de Filogenia de Documentos Multimídia. Pesquisas na área de filogenia de documentos multimídia são importantes para auxiliar na resolução de problemas como, por exemplo, análise forense, recuperação de imagens por conteúdo e rastreamento de conteúdo ilegal. Nesta tese de doutorado, apresentamos abordagens desenvolvidas para solucionar o problema de filogenias para imagens e vídeos digitais. Considerando imagens, propomos novas abordagens para tratar o problema de filogenia considerando dois pontos principais: (i) a reconstrução de florestas, importante em cenários onde se tem um conjunto de imagens semanticamente semelhantes, mas geradas por fontes ou em momentos diferentes no tempo; e (ii) novas medidas para o cálculo de dissimilaridade entre as duplicatas, uma vez que esse cálculo afeta diretamente a qualidade de reconstrução da filogenia. Os resultados obtidos com as soluções para filogenia de imagens apresentadas neste trabalho confirmam a efetividade das abordagens propostas, identificando corretamente as raízes das florestas (imagens originais de uma sequencia de evolução) com até 95% de acurácia. Para filogenia de vídeos, propomos novas abordagens que realizam alinhamento temporal nos vídeos antes de se calcular a dissimilaridade, uma vez que, em cenários reais, os vídeos podem estar desalinhados temporalmente, terem sofrido recorte temporal ou serem comprimidos, por exemplo. Nesse contexto, nossas abordagens conseguem identificar a raiz das árvores com acurácia de até 87%Abstract: Digital documents (e.g., images and videos) have become powerful tools of communication with the advent of social networks. Within this new reality, it is very common these documents to be published, shared, modified and often republished by multiple users on different web channels. Additionally, with the popularization of image editing software and online editor tools, in most of the cases, not only their exact duplicates will be available, but also manipulated versions of the original source (near duplicates). Nevertheless, this document sharing facilitates the spread of abusive content (e.g., child pornography), copyright infringement and, in some cases, defamatory content, adversely affecting the public image of people or corporations (e.g., defamatory images of politicians and celebrities, people in embarrassing situations, etc.). Several researchers have successfully developed approaches for the detection and recognition of near-duplicate documents, aiming at identifying similar copies of a given multimedia document (e.g., image, video, etc.) published on the Internet. Notwithstanding, only recently some researches have developed approaches that go beyond the near-duplicate detection task and aim at finding the ancestral relationship between the near duplicates and the original source of a document. For this, the development of approaches for calculating the dissimilarity between near duplicates and correctly reconstruct structures that represent the relationship between them automatically is required. This problem is referred to in the literature as Multimedia Phylogeny. Solutions for multimedia phylogeny can help researchers to solve problems in forensics, content-based document retrieval and illegal-content document tracking, for instance. In this thesis, we designed and developed approaches to solve the phylogeny reconstruction problem for digital images and videos. Considering images, we proposed approaches to deal with the phylogeny problem considering two main points: (i) the forest reconstruction, an important task when we consider scenarios in which there is a set of semantically similar images, but generated by different sources or at different times; and (ii) new measures for dissimilarity calculation between near-duplicates, given that the dissimilarity calculation directly impacts the quality of the phylogeny reconstruction. The results obtained with our approaches for image phylogeny showed effective, identifying the root of the forests (original images of an evolution sequence) with accuracy up to 95%. For video phylogeny, we developed a new approach for temporal alignment in the video sequences before calculating the dissimilarity between them, once that, in real-world conditions, a pair of videos can be temporally misaligned, one video can have some frames removed and video compression can be applied, for example. For such problem, the proposed methods yield up to 87% correct of accuracy for finding the roots of the treesDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação2013/05815-2FAPESPCAPE