THE FORMALIZED MATHEMATICAL CONTENT COGNITIVE MANAGEMENT

Problem of the formalized mathematical content management for any given subject domain is considered. The content represented by domain ontology as the unified variety of elementary knowledge classes and relations for such classes as subject domain content. The ontology includes variety different types of entities and relations between them analogous to categories and structures of mathematical language. Such knowledge is formal that allows developing correct algorithms for the tasks’ solution searching processes at abstract and applied knowledge domains based on ontologies. The content management consists in modeling the processes of realization the cognitive goals adapted to the professional activity domain. The considered system of cognitive goals classes based on the weakly formalized cognitive goals hierarchy of classes introduced by B. Blum's and corresponding cognitive operations realized as result of the thinking processes versatile analysis. The cognitive goal realization makes algebraic structures for the complex semantic representations synthesized by application of ontology elements. Simulating the synthesis processes defined by regular structures of abstract knowledge processing operations extracted from hierarchy of such operations classes, analogous of fundamental types of morphisms at fundamental mathematical systems. Achieving the exact definitions in work realized at this work by narrowing the formal goals interpretation for considered system of Blum’s cognitive goals classification. The independence of goals and operations based on applying the different classes of objects as goals and operations domains and ranges, different classes of mathematical operations and scenarios of simulating the cognitive goals realization processes. The resulted table of mathematical associations for B. Blum goals classification includes information about integrated mathematical specifications and abstract knowledge processing operations for knowledge representation formalisms, added by domains and ranges for such operations. Formal descriptions provided for regular formats of knowledge neighborhoods and series, examples of scenarios for formal operations combinations that realize the cognitive goals of understanding and estimation made by special language constructs

Unstructured spline spaces for isogeometric analysis based on spline manifolds

Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces that have a tensor-product structure locally, but not globally. This includes configurations such as B-splines over multi-patch domains with extraordinary points, analysis-suitable unstructured T-splines, or more general constructions. Within this framework, we generalize the concept of dual-compatible B-splines, which was originally developed for structured T-splines. This allows us to prove the key properties that are needed for isogeometric analysis, such as linear independence and optimal approximation properties for $h$-refined meshes

A counterexample to Thiagarajan's conjecture on regular event structures

We provide a counterexample to a conjecture by Thiagarajan (1996 and 2002) that regular event structures correspond exactly to event structures obtained as unfoldings of finite 1-safe Petri nets. The same counterexample is used to disprove a closely related conjecture by Badouel, Darondeau, and Raoult (1999) that domains of regular event structures with bounded $\natural$-cliques are recognizable by finite trace automata. Event structures, trace automata, and Petri nets are fundamental models in concurrency theory. There exist nice interpretations of these structures as combinatorial and geometric objects. Namely, from a graph theoretical point of view, the domains of prime event structures correspond exactly to median graphs; from a geometric point of view, these domains are in bijection with CAT(0) cube complexes. A necessary condition for both conjectures to be true is that domains of regular event structures (with bounded $\natural$-cliques) admit a regular nice labeling. To disprove these conjectures, we describe a regular event domain (with bounded $\natural$-cliques) that does not admit a regular nice labeling. Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex whose universal cover is a CAT(0) square complex containing a particular plane with an aperiodic tiling. We prove that other counterexamples to Thiagarajan's conjecture arise from aperiodic 4-way deterministic tile sets of Kari and Papasoglu (1999) and Lukkarila (2009). On the positive side, using breakthrough results by Agol (2013) and Haglund and Wise (2008, 2012) from geometric group theory, we prove that Thiagarajan's conjecture is true for regular event structures whose domains occur as principal filters of hyperbolic CAT(0) cube complexes which are universal covers of finite nonpositively curved cube complexes

A Practical Type Analysis for Verification of Modular Prolog Programs

Regular types are a powerful tool for computing very precise descriptive types for logic programs. However, in the context of real life, modular Prolog programs, the accurate results obtained by regular types often come at the price of efficiency. In this paper we propose a combination of techniques aimed at improving analysis efficiency in this context. As a first technique we allow optionally reducing the accuracy of inferred types by using only the types defined by the user or present in the libraries. We claim that, for the purpose of verifying type signatures given in the form of assertions the precision obtained using this approach is sufficient, and show that analysis times can be reduced significantly. Our second technique is aimed at dealing with situations where we would like to limit the amount of reanalysis performed, especially for library modules. Borrowing some ideas from polymorphic type systems, we show how to solve the problem by admitting parameters in type specifications. This allows us to compose new call patterns with some pre computed analysis info without losing any information. We argue that together these two techniques contribute to the practical and scalable analysis and verification of types in Prolog programs

Leveraging Semantic Web Technologies for Managing Resources in a Multi-Domain Infrastructure-as-a-Service Environment

This paper reports on experience with using semantically-enabled network resource models to construct an operational multi-domain networked infrastructure-as-a-service (NIaaS) testbed called ExoGENI, recently funded through NSF's GENI project. A defining property of NIaaS is the deep integration of network provisioning functions alongside the more common storage and computation provisioning functions. Resource provider topologies and user requests can be described using network resource models with common base classes for fundamental cyber-resources (links, nodes, interfaces) specialized via virtualization and adaptations between networking layers to specific technologies. This problem space gives rise to a number of application areas where semantic web technologies become highly useful - common information models and resource class hierarchies simplify resource descriptions from multiple providers, pathfinding and topology embedding algorithms rely on query abstractions as building blocks. The paper describes how the semantic resource description models enable ExoGENI to autonomously instantiate on-demand virtual topologies of virtual machines provisioned from cloud providers and are linked by on-demand virtual connections acquired from multiple autonomous network providers to serve a variety of applications ranging from distributed system experiments to high-performance computing