Participatory Data Analytics: Collaborative interfaces for data composition and visualisation

This research proposes the development of interfaces to support collaborative, community-driven inquiry into data, which we refer to as Participatory Data Analytics. Since the investigation is led by local communities, it is not possible to anticipate which data will be relevant and what questions are going to be asked. Therefore, users have to be able to construct and tailor visualisations to their own needs. The poster presents early work towards defining a suitable compositional model, which will allow users to mix, match, and manipulate data sets to obtain visual representations with little-to-no programming knowledge. Following a user-centred design process, we are subsequently planning to identify appropriate interaction techniques and metaphors for generating such visual specifications on wall-sized, multi-touch displays.

A treatise of algebra, in three parts : containing I. The fundamental rules and operations. II. The composition and resolution of equations of all degrees; and the different affections of their roots. III. The application of algebra and geometry to each other : to which is added, an appendix, concerning the general properties of geometrical lines /

Mode of access: Internet.

A treatise of algebra, in three parts. Containing I. The fundamental rules and operations; II. The composition and resolution of equations of all degrees, and the different affections of their roots; III. The application of algebra and geometry to each other. To which is added an appendix concerning the general properties of geometrical lines.

Appendix in Latin.

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a simpler version of the algebra G,(Ω). Although this subalgebra does not contain, in canonical way, the space D′(Ω) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

Class Notes for Math 901/902: Abstract Algebra, Instructor Tom Marley

Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures; Separable algebraic extensions, the Primitive Element Theorem; Inseparability, purely inseparable extensions; Finite fields; Cyclotomic field extensions; Galois theory; Norm and trace maps of an algebraic field extension; Solvability by radicals, Galois' theorem; Transcendence degree; Rings and modules: Examples and basic properties; Exact sequences, split short exact sequences; Free modules, projective modules; Localization of (commutative) rings and modules; The prime spectrum of a ring; Nakayama's lemma; Basic category theory; The Hom functors; Tensor products, adjointness; Left/right Noetherian and Artinian modules; Composition series, the Jordan-Holder Theorem; Semisimple rings; The Artin-Wedderburn Theorem; The Density Theorem; The Jacobson radical; Artinian rings; von Neumann regular rings; Wedderburn's theorem on finite division rings; Group representations, character theory; Integral ring extensions; Burnside's paqb Theorem; Injective modules.

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).