Constraint Satisfaction Problems over Numeric Domains

We present a survey of complexity results for constraint satisfaction problems (CSPs) over the integers, the rationals, the reals, and the complex numbers. Examples of such problems are feasibility of linear programs, integer linear programming, the max-atoms problem, Hilbert\u27s tenth problem, and many more. Our particular focus is to identify those CSPs that can be solved in polynomial time, and to distinguish them from CSPs that are NP-hard. A very helpful tool for obtaining complexity classifications in this context is the concept of a polymorphism from universal algebra

Model Theory: Around Valued Fields and Dependent Theories

The general topic of the meeting was “Valued fields and related structures”. It included both applications of model theory, as well as so-called “pure” model theory: the classification of first order structures using new techniques extending those developed in stable theories

Complexity Classification Transfer for CSPs via Algebraic Products

We study the complexity of infinite-domain constraint satisfaction problems: our basic setting is that a complexity classification for the CSPs of first-order expansions of a structure $\mathfrak A$ can be transferred to a classification of the CSPs of first-order expansions of another structure $\mathfrak B$. We exploit a product of structures (the algebraic product) that corresponds to the product of the respective polymorphism clones and present a complete complexity classification of the CSPs for first-order expansions of the $n$-fold algebraic power of $(\mathbb{Q};<)$. This is proved by various algebraic and logical methods in combination with knowledge of the polymorphisms of the tractable first-order expansions of $(\mathbb{Q};<)$ and explicit descriptions of the expressible relations in terms of syntactically restricted first-order formulas. By combining our classification result with general classification transfer techniques, we obtain surprisingly strong new classification results for highly relevant formalisms such as Allen's Interval Algebra, the $n$-dimensional Block Algebra, and the Cardinal Direction Calculus, even if higher-arity relations are allowed. Our results confirm the infinite-domain tractability conjecture for classes of structures that have been difficult to analyse with older methods. For the special case of structures with binary signatures, the results can be substantially strengthened and tightly connected to Ord-Horn formulas; this solves several longstanding open problems from the AI literature.Comment: 61 pages, 1 figur

Feature Selection Inspired Classifier Ensemble Reduction

Classifier ensembles constitute one of the main research directions in machine learning and data mining. The use of multiple classifiers generally allows better predictive performance than that achievable with a single model. Several approaches exist in the literature that provide means to construct and aggregate such ensembles. However, these ensemble systems contain redundant members that, if removed, may further increase group diversity and produce better results. Smaller ensembles also relax the memory and storage requirements, reducing system's run-time overhead while improving overall efficiency. This paper extends the ideas developed for feature selection problems to support classifier ensemble reduction, by transforming ensemble predictions into training samples, and treating classifiers as features. Also, the global heuristic harmony search is used to select a reduced subset of such artificial features, while attempting to maximize the feature subset evaluation. The resulting technique is systematically evaluated using high dimensional and large sized benchmark datasets, showing a superior classification performance against both original, unreduced ensembles, and randomly formed subsets. ? 2013 IEEE

Internet-based solutions to support distributed manufacturing

With the globalisation and constant changes in the marketplace, enterprises are adapting themselves to face new challenges. Therefore, strategic corporate alliances to share knowledge, expertise and resources represent an advantage in an increasing competitive world. This has led the integration of companies, customers, suppliers and partners using networked environments. This thesis presents three novel solutions in the tooling area, developed for Seco tools Ltd, UK. These approaches implement a proposed distributed computing architecture using Internet technologies to assist geographically dispersed tooling engineers in process planning tasks. The systems are summarised as follows. TTS is a Web-based system to support engineers and technical staff in the task of providing technical advice to clients. Seco sales engineers access the system from remote machining sites and submit/retrieve/update the required tooling data located in databases at the company headquarters. The communication platform used for this system provides an effective mechanism to share information nationwide. This system implements efficient methods, such as data relaxation techniques, confidence score and importance levels of attributes, to help the user in finding the closest solutions when specific requirements are not fully matched In the database. Cluster-F has been developed to assist engineers and clients in the assessment of cutting parameters for the tooling process. In this approach the Internet acts as a vehicle to transport the data between users and the database. Cluster-F is a KD approach that makes use of clustering and fuzzy set techniques. The novel proposal In this system is the implementation of fuzzy set concepts to obtain the proximity matrix that will lead the classification of the data. Then hierarchical clustering methods are applied on these data to link the closest objects. A general KD methodology applying rough set concepts Is proposed In this research. This covers aspects of data redundancy, Identification of relevant attributes, detection of data inconsistency, and generation of knowledge rules. R-sets, the third proposed solution, has been developed using this KD methodology. This system evaluates the variables of the tooling database to analyse known and unknown relationships in the data generated after the execution of technical trials. The aim is to discover cause-effect patterns from selected attributes contained In the database. A fourth system was also developed. It is called DBManager and was conceived to administrate the systems users accounts, sales engineers’ accounts and tool trial monitoring process of the data. This supports the implementation of the proposed distributed architecture and the maintenance of the users' accounts for the access restrictions to the system running under this architecture