3,751 research outputs found
Attribute Value Reordering For Efficient Hybrid OLAP
The normalization of a data cube is the ordering of the attribute values. For
large multidimensional arrays where dense and sparse chunks are stored
differently, proper normalization can lead to improved storage efficiency. We
show that it is NP-hard to compute an optimal normalization even for 1x3
chunks, although we find an exact algorithm for 1x2 chunks. When dimensions are
nearly statistically independent, we show that dimension-wise attribute
frequency sorting is an optimal normalization and takes time O(d n log(n)) for
data cubes of size n^d. When dimensions are not independent, we propose and
evaluate several heuristics. The hybrid OLAP (HOLAP) storage mechanism is
already 19%-30% more efficient than ROLAP, but normalization can improve it
further by 9%-13% for a total gain of 29%-44% over ROLAP
Knowing Values and Public Inspection
We present a basic dynamic epistemic logic of "knowing the value". Analogous
to public announcement in standard DEL, we study "public inspection", a new
dynamic operator which updates the agents' knowledge about the values of
constants. We provide a sound and strongly complete axiomatization for the
single and multi-agent case, making use of the well-known Armstrong axioms for
dependencies in databases
Overview of Business-Facing Arts Audience Research
This report is a review of public-domain research conducted specifically in order to inform arts organisations about their audiences. The research covered is driven by the demands of the arts industry to understand its audiences and to develop and broaden audiences for the arts. The report includes links to key publications and research organisations, and an overview of the key offerings
Logical reduction of relations: from relational databases to Peirce's reduction thesis
We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them, and introduce a new characteristic of relations, ternarity, that measures their `complexity of relating' and allows to refine reduction results. In particular, we refine Peirce's controversial reduction thesis, and show that reducibility behavior is dramatically different on finite and infinite domains
A new interpretation for null values in the weak instance model
AbstractA new definition of the weak instance model for relational databases is presented, which does not consider the missing values as existent though unknown, but just assumes that no information is available about them. It is possible to associate with the new definition logical theories that do not contain existentially quantified variables. The new model enjoys various desirable properties of the classic weak instance model, with respect to dependency satisfaction, query answering, and associated logical theories
Twists of X(7) and primitive solutions to x^2+y^3=z^7
We find the primitive integer solutions to x^2+y^3=z^7. A nonabelian descent
argument involving the simple group of order 168 reduces the problem to the
determination of the set of rational points on a finite set of twists of the
Klein quartic curve X. To restrict the set of relevant twists, we exploit the
isomorphism between X and the modular curve X(7), and use modularity of
elliptic curves and level lowering. This leaves 10 genus-3 curves, whose
rational points are found by a combination of methods.Comment: 47 page
- …