A shortest-path based clustering algorithm for joint human-machine analysis of complex datasets

Clustering is a technique for the analysis of datasets obtained by empirical studies in several disciplines with a major application for biomedical research. Essentially, clustering algorithms are executed by machines aiming at finding groups of related points in a dataset. However, the result of grouping depends on both metrics for point-to-point similarity and rules for point-to-group association. Indeed, non-appropriate metrics and rules can lead to undesirable clustering artifacts. This is especially relevant for datasets, where groups with heterogeneous structures co-exist. In this work, we propose an algorithm that achieves clustering by exploring the paths between points. This allows both, to evaluate the properties of the path (such as gaps, density variations, etc.), and expressing the preference for certain paths. Moreover, our algorithm supports the integration of existing knowledge about admissible and non-admissible clusters by training a path classifier. We demonstrate the accuracy of the proposed method on challenging datasets including points from synthetic shapes in publicly available benchmarks and microscopy data

Towards a Coherent Theory of Physics and Mathematics

As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently strong, and it must maximally describe its own validity and sufficient strength. The mathematical logical definition of validity is used, and sufficient strength is seen to be a necessary and useful concept. The requirement of maximal description of its own validity and sufficient strength may be useful to reject candidate coherent theories for which the description is less than maximal. Other aspects of a coherent theory discussed include universal applicability, the relation to the anthropic principle, and possible uniqueness. It is suggested that the basic properties of the physical and mathematical universes are entwined with and emerge with a coherent theory. Support for this includes the indirect reality status of properties of very small or very large far away systems compared to moderate sized nearby systems. Discussion of the necessary physical nature of language includes physical models of language and a proof that the meaning content of expressions of any axiomatizable theory seems to be independent of the algorithmic complexity of the theory. G\"{o}del maps seem to be less useful for a coherent theory than for purely mathematical theories because all symbols and words of any language musthave representations as states of physical systems already in the domain of a coherent theory.Comment: 38 pages, earlier version extensively revised and clarified. Accepted for publication in Foundations of Physic

Conflict Detection for Edits on Extended Feature Models using Symbolic Graph Transformation

Feature models are used to specify variability of user-configurable systems as appearing, e.g., in software product lines. Software product lines are supposed to be long-living and, therefore, have to continuously evolve over time to meet ever-changing requirements. Evolution imposes changes to feature models in terms of edit operations. Ensuring consistency of concurrent edits requires appropriate conflict detection techniques. However, recent approaches fail to handle crucial subtleties of extended feature models, namely constraints mixing feature-tree patterns with first-order logic formulas over non-Boolean feature attributes with potentially infinite value domains. In this paper, we propose a novel conflict detection approach based on symbolic graph transformation to facilitate concurrent edits on extended feature models. We describe extended feature models formally with symbolic graphs and edit operations with symbolic graph transformation rules combining graph patterns with first-order logic formulas. The approach is implemented by combining eMoflon with an SMT solver, and evaluated with respect to applicability.Comment: In Proceedings FMSPLE 2016, arXiv:1603.0857

Relatedness Measures to Aid the Transfer of Building Blocks among Multiple Tasks

Multitask Learning is a learning paradigm that deals with multiple different tasks in parallel and transfers knowledge among them. XOF, a Learning Classifier System using tree-based programs to encode building blocks (meta-features), constructs and collects features with rich discriminative information for classification tasks in an observed list. This paper seeks to facilitate the automation of feature transferring in between tasks by utilising the observed list. We hypothesise that the best discriminative features of a classification task carry its characteristics. Therefore, the relatedness between any two tasks can be estimated by comparing their most appropriate patterns. We propose a multiple-XOF system, called mXOF, that can dynamically adapt feature transfer among XOFs. This system utilises the observed list to estimate the task relatedness. This method enables the automation of transferring features. In terms of knowledge discovery, the resemblance estimation provides insightful relations among multiple data. We experimented mXOF on various scenarios, e.g. representative Hierarchical Boolean problems, classification of distinct classes in the UCI Zoo dataset, and unrelated tasks, to validate its abilities of automatic knowledge-transfer and estimating task relatedness. Results show that mXOF can estimate the relatedness reasonably between multiple tasks to aid the learning performance with the dynamic feature transferring.Comment: accepted by The Genetic and Evolutionary Computation Conference (GECCO 2020

Incompleteness of relational simulations in the blocking paradigm

Refinement is the notion of development between formal specifications For specifications given in a relational formalism downward and upward simulations are the standard method to verify that a refinement holds their usefulness based upon their soundness and joint completeness This is known to be true for total relational specifications and has been claimed to hold for partial relational specifications in both the non-blocking and blocking interpretations In this paper we show that downward and upward simulations in the blocking interpretation where domains are guards are not Jointly complete This contradicts earlier claims in the literature We illustrate this with an example (based on one recently constructed by Reeves and Streader) and then construct a proof to show why Joint completeness fails in general (C) 2010 Elsevier B V All rights reserve