The Covariant Approach to LRS Perfect Fluid Spacetime Geometries

The dynamics of perfect fluid spacetime geometries which exhibit {\em Local Rotational Symmetry} (LRS) are reformulated in the language of a $1+\,3$ "threading" decomposition of the spacetime manifold, where covariant fluid and curvature variables are used. This approach presents a neat alternative to the orthonormal frame formalism. The dynamical equations reduce to a set of differential relations between purely scalar quantities. The consistency conditions are worked out in a transparent way. We discuss their various subcases in detail and focus in particular on models with higher symmetries within the class of expanding spatially inhomogeneous LRS models, via a consideration of functional dependencies between the dynamical variables.Comment: 25 pages, uuencoded/compressed postscript fil

Lattices with non-Shannon Inequalities

We study the existence or absence of non-Shannon inequalities for variables that are related by functional dependencies. Although the power-set on four variables is the smallest Boolean lattice with non-Shannon inequalities there exist lattices with many more variables without non-Shannon inequalities. We search for conditions that ensures that no non-Shannon inequalities exist. It is demonstrated that 3-dimensional distributive lattices cannot have non-Shannon inequalities and planar modular lattices cannot have non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group.Comment: Ten pages. Submitted to ISIT 2015. The appendix will not appear in the proceeding

Learning Models over Relational Data using Sparse Tensors and Functional Dependencies

Integrated solutions for analytics over relational databases are of great practical importance as they avoid the costly repeated loop data scientists have to deal with on a daily basis: select features from data residing in relational databases using feature extraction queries involving joins, projections, and aggregations; export the training dataset defined by such queries; convert this dataset into the format of an external learning tool; and train the desired model using this tool. These integrated solutions are also a fertile ground of theoretically fundamental and challenging problems at the intersection of relational and statistical data models. This article introduces a unified framework for training and evaluating a class of statistical learning models over relational databases. This class includes ridge linear regression, polynomial regression, factorization machines, and principal component analysis. We show that, by synergizing key tools from database theory such as schema information, query structure, functional dependencies, recent advances in query evaluation algorithms, and from linear algebra such as tensor and matrix operations, one can formulate relational analytics problems and design efficient (query and data) structure-aware algorithms to solve them. This theoretical development informed the design and implementation of the AC/DC system for structure-aware learning. We benchmark the performance of AC/DC against R, MADlib, libFM, and TensorFlow. For typical retail forecasting and advertisement planning applications, AC/DC can learn polynomial regression models and factorization machines with at least the same accuracy as its competitors and up to three orders of magnitude faster than its competitors whenever they do not run out of memory, exceed 24-hour timeout, or encounter internal design limitations.Comment: 61 pages, 9 figures, 2 table

CML: the commonKADS conceptual modelling language

We present a structured language for the specification of knowledge models according to the CommonKADS methodology. This language is called CML (Conceptual Modelling Language) and provides both a structured textual notation and a diagrammatic notation for expertise models. The use of our CML is illustrated by a variety of examples taken from the VT elevator design system

Supporting 'design for reuse' with modular design

Engineering design reuse refers to the utilization of any knowledge gained from the design activity to support future design. As such, engineering design reuse approaches are concerned with the support, exploration, and enhancement of design knowledge prior, during, and after a design activity. Modular design is a product structuring principle whereby products are developed with distinct modules for rapid product development, efficient upgrades, and possible reuse (of the physical modules). The benefits of modular design center on a greater capacity for structuring component parts to better manage the relation between market requirements and the designed product. This study explores the capabilities of modular design principles to provide improved support for the engineering design reuse concept. The correlations between modular design and 'reuse' are highlighted, with the aim of identifying its potential to aid the little-supported process of design for reuse. In fulfilment of this objective the authors not only identify the requirements of design for reuse, but also propose how modular design principles can be extended to support design for reuse