Manual mapping of drumlins in synthetic landscapes to assess operator effectiveness

Mapped topographic features are important for understanding processes that sculpt the Earth’s surface. This paper presents maps that are the primary product of an exercise that brought together 27 researchers with an interest in landform mapping wherein the efficacy and causes of variation in mapping were tested using novel synthetic DEMs containing drumlins. The variation between interpreters (e.g. mapping philosophy, experience) and across the study region (e.g. woodland prevalence) opens these factors up to assessment. A priori known answers in the synthetics increase the number and strength of conclusions that may be drawn with respect to a traditional comparative study. Initial results suggest that overall detection rates are relatively low (34–40%), but reliability of mapping is higher (72–86%). The maps form a reference dataset.

Computational approaches to finding and measuring inconsistency in arbitrary knowledge bases

There is extensive theoretical work on measures of inconsistency for arbitrary formulae in knowledge bases. Many of these are defined in terms of the set of minimal inconsistent subsets (MISes) of the base. However, few have been implemented or experimentally evaluated to support their viability, since computing all MISes is intractable in the worst case. Fortunately, recent work on a related problem of minimal unsatisfiable sets of clauses (MUSes) offers a viable solution in many cases. In this paper, we begin by drawing connections between MISes and MUSes through algorithms based on a MUS generalization approach and a new optimized MUS transformation approach to finding MISes. We implement these algorithms, along with a selection of existing measures for flat and stratified knowledge bases, in a tool called mimus. We then carry out an extensive experimental evaluation of mimus using randomly generated arbitrary knowledge bases. We conclude that these measures are viable for many large and complex random instances. Moreover, they represent a practical and intuitive tool for inconsistency handling.

Operator Synthesis and Tensor Products

We show that Kraus' property $ S_{\sigma }$ is preserved under taking weak* closed sums with masa-bimodules of finite width and establish an intersection formula for weak* closed spans of tensor products, one of whose terms is a masa-bimodule of finite width. We initiate the study of the question of when operator synthesis is preserved under the formation of products and prove that the union of finitely many sets of the form $ \kappa \times \lambda $, where $ \kappa $ is a set of finite width while $ \lambda $ is operator synthetic, is, under a necessary restriction on the sets $ \lambda $, again operator synthetic. We show that property $ S_{\sigma }$ is preserved under spatial Morita subordinance.

Operator systems from discrete groups

We express various sets of quantum correlations studied in the theoretical physics literature in terms of different tensor products of operator systems of discrete groups. We thus recover earlier results of Tsirelson and formulate a new approach for the study of quantum correlations. To do this we formulate a general framework for the study of operator systems arising from discrete groups. We study in detail the operator system of the free group Fn on n generators, as well as the operator systems of the free products of finitely many copies of the two-element group Z2. We examine various tensor products of group operator systems, including the minimal, the maximal, and the commuting tensor products. We introduce a new tensor product in the category of operator systems and formulate necessary and sufficient conditions for its equality to the commuting tensor product in the case of group operator systems.

Local operator multipliers and positivity

We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators. We apply these results to study positivity for Schur multipliers. We characterise positive local Schur multipliers, and provide a description of positive local Schur multipliers of Toeplitz type. We introduce local operator multipliers as a non-commutative analogue of local Schur multipliers, and characterise them extending both the characterisation of operator multipliers from [16] and that of local Schur multipliers from [27]. We provide a description of the positive local operator multipliers in terms of approximation by elements of canonical positive cones.

On the Merit of Selecting Different Belief Merging Operators

Belief merging operators combine multiple belief bases (a profile) into a collective one. When the conjunction of belief bases is consistent, all the operators agree on the result. However, if the conjunction of belief bases is inconsistent, the results vary between operators. There is no formal manner to measure the results and decide on which operator to select. So, in this paper we propose to evaluate the result of merging operators by using three ordering relations (fairness, satisfaction and strength) over operators for a given profile. Moreover, a relation of conformity over operators is introduced in order to classify how well the operator conforms to the definition of a merging operator. By using the four proposed relations we provide a comparison of some classical merging operators and evaluate the results for some specific profiles.

A Characteristic Function Approach to Inconsistency Measures for Knowledge Bases.

Knowledge is an important component in many intelligent systems.
Since items of knowledge in a knowledge base can be conflicting, especially if
there are multiple sources contributing to the knowledge in this base, significant
research efforts have been made on developing inconsistency measures for
knowledge bases and on developing merging approaches. Most of these efforts
start with flat knowledge bases. However, in many real-world applications, items
of knowledge are not perceived with equal importance, rather, weights (which
can be used to indicate the importance or priority) are associated with items of
knowledge. Therefore, measuring the inconsistency of a knowledge base with
weighted formulae as well as their merging is an important but difficult task. In
this paper, we derive a numerical characteristic function from each knowledge
base with weighted formulae, based on the Dempster-Shafer theory of evidence.
Using these functions, we are able to measure the inconsistency of the knowledge
base in a convenient and rational way, and are able to merge multiple knowledge
bases with weighted formulae, even if knowledge in these bases may be
inconsistent. Furthermore, by examining whether multiple knowledge bases are
dependent or independent, they can be combined in different ways using their
characteristic functions, which cannot be handled (or at least have never been
considered) in classic knowledge based merging approaches in the literature.