The mechanisms of temporal inference

The properties of a temporal language are determined by its constituent elements: the temporal objects which it can represent, the attributes of those objects, the relationships between them, the axioms which define the default relationships, and the rules which define the statements that can be formulated. The methods of inference which can be applied to a temporal language are derived in part from a small number of axioms which define the meaning of equality and order and how those relationships can be propagated. More complex inferences involve detailed analysis of the stated relationships. Perhaps the most challenging area of temporal inference is reasoning over disjunctive temporal constraints. Simple forms of disjunction do not sufficiently increase the expressive power of a language while unrestricted use of disjunction makes the analysis NP-hard. In many cases a set of disjunctive constraints can be converted to disjunctive normal form and familiar methods of inference can be applied to the conjunctive sub-expressions. This process itself is NP-hard but it is made more tractable by careful expansion of a tree-structured search space

Stochastic Tree Models for Macroevolution: Development, Validation and Application

Phylogenetic trees capture the relationships between species and can be investigated by morphological and/or molecular data. When focusing on macroevolution, one considers the large-scale history of life with evolutionary changes affecting a single species of the entire clade leading to the enormous diversity of species obtained today. One major problem of biology is the explanation of this biodiversity. Therefore, one may ask which kind of macroevolutionary processes have given rise to observable tree shapes or patterns of species distribution which refers to the appearance of branching orders and time periods. Thus, with an increasing number of known species in the context of phylogenetic studies, testing hypotheses about evolution by analyzing the tree shape of the resulting phylogenetic trees became matter of particular interest. The attention of using those reconstructed phylogenies for studying evolutionary processes increased during the last decades. Many paleontologists (Raup et al., 1973; Gould et al., 1977; Gilinsky and Good, 1989; Nee, 2004) tried to describe such patterns of macroevolution by using models for growing trees. Those models describe stochastic processes to generate phylogenetic trees. Yule (1925) was the first who introduced such a model, the Equal Rate Markov (ERM) model, in the context of biological branching based on a continuous-time, uneven branching process. In the last decades, further dynamical models were proposed (Yule, 1925; Aldous, 1996; Nee, 2006; Rosen, 1978; Ford, 2005; Hernández-García et al., 2010) to address the investigation of tree shapes and hence, capture the rules of macroevolutionary forces. A common model, is the Aldous\\\'' Branching (AB) model, which is known for generating trees with a similar structure of \\\"real\\\" trees. To infer those macroevolutionary forces structures, estimated trees are analyzed and compared to simulated trees generated by models. There are a few drawbacks on recent models such as a missing biological motivation or the generated tree shape does not fit well to one observed in empirical trees. The central aim of this thesis is the development and study of new biologically motivated approaches which might help to better understand or even discover biological forces which lead to the huge diversity of organisms. The first approach, called age model, can be defined as a stochastic procedure which describes the growth of binary trees by an iterative stochastic attachment of leaves, similar to the ERM model. At difference with the latter, the branching rate at each clade is no longer constant, but decreasing in time, i.e., with the age. Thus, species involved in recent speciation events have a tendency to speciate again. The second introduced model, is a branching process which mimics the evolution of species driven by innovations. The process involves a separation of time scales. Rare innovation events trigger rapid cascades of diversification where a feature combines with previously existing features. The model is called innovation model. Three data sets of estimated phylogenetic trees are used to analyze and compare the produced tree shape of the new growth models. A tree shape statistic considering a variety of imbalance measurements is performed. Results show that simulated trees of both growth models fit well to the tree shape observed in real trees. In a further study, a likelihood analysis is performed in order to rank models with respect to their ability to explain observed tree shapes. Results show that the likelihoods of the age model and the AB model are clearly correlated under the trees in the databases when considering small and medium-sized trees with up to 19 leaves. For a data set, representing of phylogenetic trees of protein families, the age model outperforms the AB model. But for another data set, representing phylogenetic trees of species, the AB model performs slightly better. To support this observation a further analysis using larger trees is necessary. But an exact computation of likelihoods for large trees implies a huge computational effort. Therefore, an efficient method for likelihood estimation is proposed and compared to the estimation using a naive sampling strategy. Nevertheless, both models describe the tree generation process in a way which is easy to interpret biologically. Another interesting field of research in biology is the coevolution between species. This is the interaction of species across groups such that the evolution of a species from one group can be triggered by a species from another group. Most prominent examples are systems of host species and their associated parasites. One problem is the reconciliation of the common history of both groups of species and to predict the associations between ancestral hosts and their parasites. To solve this problem some algorithmic methods have been developed in recent years. But only a few host parasite systems have been analyzed in sufficient detail which makes an evaluation of these methods complex. Within the scope of coevolution, the proposed age model is applied to the generation of cophylogenies to evaluate such host parasite reconciliation methods. The presented age model as well as the innovation model produce tree shapes which are similar to obtained tree structures of estimated trees. Both models describe an evolutionary dynamics and might provide a further opportunity to infer macroevolutionary processes which lead to the biodiversity which can be obtained today. Furthermore with the application of the age model in the context of coevolution by generating a useful benchmark set of cophylogenies is a first step towards systematic studies on evaluating reconciliation methods

Lysine Residue 185 of Rad1 Is a Topological but Not a Functional Counterpart of Lysine Residue 164 of PCNA

Monoubiquitylation of the homotrimeric DNA sliding clamp PCNA at lysine residue 164 (PCNAK164) is a highly conserved, DNA damage-inducible process that is mediated by the E2/E3 complex Rad6/Rad18. This ubiquitylation event recruits translesion synthesis (TLS) polymerases capable of replicating across damaged DNA templates. Besides PCNA, the Rad6/Rad18 complex was recently shown in yeast to ubiquitylate also 9-1-1, a heterotrimeric DNA sliding clamp composed of Rad9, Rad1, and Hus1 in a DNA damage-inducible manner. Based on the highly similar crystal structures of PCNA and 9-1-1, K185 of Rad1 (Rad1K185) was identified as the only topological equivalent of PCNAK164. To investigate a potential role of posttranslational modifications of Rad1K185 in DNA damage management, we here generated a mouse model with a conditional deletable Rad1K185R allele. The Rad1K185 residue was found to be dispensable for Chk1 activation, DNA damage survival, and class switch recombination of immunoglobulin genes as well as recruitment of TLS polymerases during somatic hypermutation of immunoglobulin genes. Our data indicate that Rad1K185 is not a functional counterpart of PCNAK164

Efficient Time and Space Representation of Uncertain Event Data

Process mining is a discipline which concerns the analysis of execution data of operational processes, the extraction of models from event data, the measurement of the conformance between event data and normative models, and the enhancement of all aspects of processes. Most approaches assume that event data is accurately capture behavior. However, this is not realistic in many applications: data can contain uncertainty, generated from errors in recording, imprecise measurements, and other factors. Recently, new methods have been developed to analyze event data containing uncertainty; these techniques prominently rely on representing uncertain event data by means of graph-based models explicitly capturing uncertainty. In this paper, we introduce a new approach to efficiently calculate a graph representation of the behavior contained in an uncertain process trace. We present our novel algorithm, prove its asymptotic time complexity, and show experimental results that highlight order-of-magnitude performance improvements for the behavior graph construction.Comment: 34 pages, 16 figures, 5 table

Optimizing Code Generation from SSA Form: A Comparison Between Two Formal Correctness Proofs in Isabelle/HOL

AbstractCorrectness of compilers is a vital precondition for the correctness of the software translated by them. In this paper, we present two approaches for the formalization of static single assignment (SSA) form together with two corresponding formal proofs in the Isabelle/HOL system, each showing the correctness of code generation. Our comparison between the two proofs shows that it is very important to find adequate formalizations in formal proofs since they can simplify the verification task considerably. Our formal correctness proofs do not only verify the correctness of a certain class of code generation algorithms but also give us sufficient, easily checkable correctness criteria characterizing correct compilation results obtained from implementations (compilers) of these algorithms. These correctness criteria can be used in a compiler result checker

Compact union of disjoint boxes: An efficient decomposition model for binary volumes

This paper presents in detail the CompactUnion of Disjoint Boxes (CUDB), a decomposition modelfor binary volumes that has been recently but brieflyintroduced. This model is an improved version of aprevious model called Ordered Union of Disjoint Boxes(OUDB). We show here, several desirable features thatthis model has versus OUDB, such as less unitary basicelements (boxes) and thus, a better efficiency in someneighborhood operations. We present algorithms forconversion to and from other models, and for basiccomputations as area (2D) or volume (3D). We alsopresent an efficient algorithm for connected-componentlabeling (CCL) that does not follow the classical two-passstrategy. Finally we present an algorithm for collision (oradjacency) detection in static environments. We test theefficiency of CUDB versus existing models with severaldatasets.Peer ReviewedPostprint (published version

A segment-swapping approach for executing trapped computations

We consider the problem of supporting goal-level, independent andparallelism (IAP) in the presence of non-determinism. IAP is exploited when two or more goals which will not interfere at run time are scheduled for simultaneous execution. Backtracking over non-deterministic parallel goals runs into the wellknown trapped goal and garbage slot problems. The proposed solutions for these problems generally require complex low-level machinery which makes systems difficult to maintain and extend, and in some cases can even affect sequential execution performance. In this paper we propose a novel solution to the problem of trapped nondeterministic goals and garbage slots which is based on a single stack reordering operation and offers several advantages over previous proposals. While the implementation of this operation itself is not simple, in return it does not impose constraints on the scheduler. As a result, the scheduler and the rest of the run-time machinery can safely ignore the trapped goal and garbage slot problems and their implementation is greatly simplified. Also, standard sequential execution remains unaffected. In addition to describing the solution we report on an implementation and provide performance results. We also suggest other possible applications of the proposed approach beyond parallel execution