Bounded repairability for regular tree languages

We study the problem of bounded repairability of a given restriction tree language R into a target tree language T. More precisely, we say that R is bounded repairable w.r.t. T if there exists a bound on the number of standard tree editing operations necessary to apply to any tree in R in order to obtain a tree in T. We consider a number of possible specifications for tree languages: bottom-up tree automata (on curry encoding of unranked trees) that capture the class of XML Schemas and DTDs. We also consider a special case when the restriction language R is universal, i.e., contains all trees over a given alphabet. We give an effective characterization of bounded repairability between pairs of tree languages represented with automata. This characterization introduces two tools, synopsis trees and a coverage relation between them, allowing one to reason about tree languages that undergo a bounded number of editing operations. We then employ this characterization to provide upper bounds to the complexity of deciding bounded repairability and we show that these bounds are tight. In particular, when the input tree languages are specified with arbitrary bottom-up automata, the problem is coNEXPTIME-complete. The problem remains coNEXPTIME-complete even if we use deterministic non-recursive DTDs to specify the input languages. The complexity of the problem can be reduced if we assume that the alphabet, the set of node labels, is fixed: the problem becomes PSPACE-complete for non-recursive DTDs and coNP-complete for deterministic non-recursive DTDs. Finally, when the restriction tree language R is universal, we show that the bounded repairability problem becomes EXPTIME-complete if the target language is specified by an arbitrary bottom-up tree automaton and becomes tractable (PTIME-complete, in fact) when a deterministic bottom-up automaton is used

Tree-Structured Shading Decomposition

We study inferring a tree-structured representation from a single image for object shading. Prior work typically uses the parametric or measured representation to model shading, which is neither interpretable nor easily editable. We propose using the shade tree representation, which combines basic shading nodes and compositing methods to factorize object surface shading. The shade tree representation enables novice users who are unfamiliar with the physical shading process to edit object shading in an efficient and intuitive manner. A main challenge in inferring the shade tree is that the inference problem involves both the discrete tree structure and the continuous parameters of the tree nodes. We propose a hybrid approach to address this issue. We introduce an auto-regressive inference model to generate a rough estimation of the tree structure and node parameters, and then we fine-tune the inferred shade tree through an optimization algorithm. We show experiments on synthetic images, captured reflectance, real images, and non-realistic vector drawings, allowing downstream applications such as material editing, vectorized shading, and relighting. Project website: https://chen-geng.com/inv-shade-treesComment: Accepted at ICCV 2023. Project website: https://chen-geng.com/inv-shade-tree

Going weighted: Parameterized algorithms for cluster editing

AbstractThe goal of the Cluster Editing problem is to make the fewest changes to the edge set of an input graph such that the resulting graph is a disjoint union of cliques. This problem is NP-complete but recently, several parameterized algorithms have been proposed. In this paper, we present a number of surprisingly simple search tree algorithms for Weighted Cluster Editing assuming that edge insertion and deletion costs are positive integers. We show that the smallest search tree has size O(1.82k) for edit cost k, resulting in the currently fastest parameterized algorithm, both for this problem and its unweighted counterpart. We have implemented and compared our algorithms, and achieved promising results.11This is an extended version of two articles published in: Proc. of the 6th Asia Pacific Bioinformatics Conference, APBC 2008, in: Series on Advances in Bioinformatics and Computational Biology, vol. 5, Imperial College Press, pp. 211–220; and in: Proc. of the 2nd Conference on Combinatorial Optimization and Applications, COCOA 2008, in: LNCS, vol. 5038, Springer, pp. 289–302

TreeGraph 2: Combining and visualizing evidence from different phylogenetic analyses

<p>Abstract</p> <p>Background</p> <p>Today it is common to apply multiple potentially conflicting data sources to a given phylogenetic problem. At the same time, several different inference techniques are routinely employed instead of relying on just one. In view of both trends it is becoming increasingly important to be able to efficiently compare different sets of statistical values supporting (or conflicting with) the nodes of a given tree topology, and merging this into a meaningful representation. A tree editor supporting this should also allow for flexible editing operations and be able to produce ready-to-publish figures.</p> <p>Results</p> <p>We developed TreeGraph 2, a GUI-based graphical editor for phylogenetic trees (available from <url>http://treegraph.bioinfweb.info</url>). It allows automatically combining information from different phylogenetic analyses of a given dataset (or from different subsets of the dataset), and helps to identify and graphically present incongruences. The program features versatile editing and formatting options, such as automatically setting line widths or colors according to the value of any of the unlimited number of variables that can be assigned to each node or branch. These node/branch data can be imported from spread sheets or other trees, be calculated from each other by specified mathematical expressions, filtered, copied from and to other internal variables, be kept invisible or set visible and then be freely formatted (individually or across the whole tree). Beyond typical editing operations such as tree rerooting and ladderizing or moving and collapsing of nodes, whole clades can be copied from other files and be inserted (along with all node/branch data and legends), but can also be manually added and, thus, whole trees can quickly be manually constructed de novo. TreeGraph 2 outputs various graphic formats such as SVG, PDF, or PNG, useful for tree figures in both publications and presentations.</p> <p>Conclusion</p> <p>TreeGraph 2 is a user-friendly, fully documented application to produce ready-to-publish trees. It can display any number of annotations in several ways, and permits easily importing and combining them. Additionally, a great number of editing- and formatting-operations is available.</p

Minimisation of Multiplicity Tree Automata

We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a polynomial bound in the standard Turing model would require a breakthrough in the complexity of polynomial identity testing by proving that the latter problem is logspace equivalent to the decision version of minimisation. The developed techniques also improve the state of the art in multiplicity word automata: we give an NC algorithm for minimising multiplicity word automata. Finally, we consider the minimal consistency problem: does there exist an automaton with $n$ states that is consistent with a given finite sample of weight-labelled words or trees? We show that this decision problem is complete for the existential theory of the rationals, both for words and for trees of a fixed alphabet rank.Comment: Paper to be published in Logical Methods in Computer Science. Minor editing changes from previous versio

iSAM2 : incremental smoothing and mapping using the Bayes tree

Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Sage for personal use, not for redistribution. The definitive version was published in International Journal of Robotics Research 31 (2012): 216-235, doi:10.1177/0278364911430419.We present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root information matrix of the simultaneous localization and mapping (SLAM) problem. In this paper, we highlight three insights provided by our new data structure. First, the Bayes tree provides a better understanding of the matrix factorization in terms of probability densities. Second, we show how the fairly abstract updates to a matrix factorization translate to a simple editing of the Bayes tree and its conditional densities. Third, we apply the Bayes tree to obtain a completely novel algorithm for sparse nonlinear incremental optimization, named iSAM2, which achieves improvements in efficiency through incremental variable re-ordering and fluid relinearization, eliminating the need for periodic batch steps. We analyze various properties of iSAM2 in detail, and show on a range of real and simulated datasets that our algorithm compares favorably with other recent mapping algorithms in both quality and efficiency.M. Kaess, H. Johannsson and J. Leonard were partially supported by ONR grants N00014-06-1-0043 and N00014-10-1-0936. F. Dellaert and R. Roberts were partially supported by NSF, award number 0713162, “RI: Inference in Large-Scale Graphical Models”. V. Ila has been partially supported by the Spanish MICINN under the Programa Nacional de Movilidad de Recursos Humanos de Investigación

Mistranslation and its control by tRNA synthetases

Aminoacyl tRNA synthetases are ancient proteins that interpret the genetic material in all life forms. They are thought to have appeared during the transition from the RNA world to the theatre of proteins. During translation, they establish the rules of the genetic code, whereby each amino acid is attached to a tRNA that is cognate to the amino acid. Mistranslation occurs when an amino acid is attached to the wrong tRNA and subsequently is misplaced in a nascent protein. Mistranslation can be toxic to bacteria and mammalian cells, and can lead to heritable mutations. The great challenge for nature appears to be serine-for-alanine mistranslation, where even small amounts of this mistranslation cause severe neuropathologies in the mouse. To minimize serine-for-alanine mistranslation, powerful selective pressures developed to prevent mistranslation through a special editing activity imbedded within alanyl-tRNA synthetases (AlaRSs). However, serine-for-alanine mistranslation is so challenging that a separate, genome-encoded fragment of the editing domain of AlaRS is distributed throughout the Tree of Life to redundantly prevent serine-to-alanine mistranslation. Detailed X-ray structural and functional analysis shed light on why serine-for-alanine mistranslation is a universal problem, and on the selective pressures that engendered the appearance of AlaXps at the base of the Tree of Life

Phylogenetics from paralogs

Motivation: Sequence-based phylogenetic approaches heavily rely on initial data sets to be composed of orthologous sequences only. Paralogs are treated as a dangerous nuisance that has to be detected and removed. Recent advances in mathematical phylogenetics, however, have indicated that gene duplications can also convey meaningful phylogenetic information provided orthologs and paralogs can be distinguished with a degree of certainty. Results: We demonstrate that plausible phylogenetic trees can be inferred from paralogy information only. To this end, tree-free estimates of orthology, the complement of paralogy, are first corrected to conform cographs and then translated into equivalent event-labeled gene phylogenies. A certain subset of the triples displayed by these trees translates into constraints on the species trees. While the resolution is very poor for individual gene families, we observe that genome-wide data sets are sufficient to generate fully resolved phylogenetic trees of several groups of eubacteria. The novel method introduced here relies on solving three intertwined NP-hard optimization problems: the cograph editing problem, the maximum consistent triple set problem, and the least resolved tree problem. Implemented as Integer Linear Program, paralogy-based phylogenies can be computed exactly for up to some twenty species and their complete protein complements. Availability:The ILP formulation is implemented in the Software ParaPhylo using IBM ILOG CPLEX (TM) Optimizer 12.6 and is freely available from http://pacosy.informatik.uni-leipzig.de/paraphyl

Fast Parallel Fixed-Parameter Algorithms via Color Coding

Fixed-parameter algorithms have been successfully applied to solve numerous difficult problems within acceptable time bounds on large inputs. However, most fixed-parameter algorithms are inherently \emph{sequential} and, thus, make no use of the parallel hardware present in modern computers. We show that parallel fixed-parameter algorithms do not only exist for numerous parameterized problems from the literature -- including vertex cover, packing problems, cluster editing, cutting vertices, finding embeddings, or finding matchings -- but that there are parallel algorithms working in \emph{constant} time or at least in time \emph{depending only on the parameter} (and not on the size of the input) for these problems. Phrased in terms of complexity classes, we place numerous natural parameterized problems in parameterized versions of AC$^0$. On a more technical level, we show how the \emph{color coding} method can be implemented in constant time and apply it to embedding problems for graphs of bounded tree-width or tree-depth and to model checking first-order formulas in graphs of bounded degree