On Partition Metric Space, Index Function, and Data Compression

We discuss a metric structure on the set of partitions of a finite set induced by the Gini index and two applications of this metric: the identification of determining sets for index functions using techniques that originate in machine learning, and a data compression algorithm

AFIT School of Engineering Contributions to Air Force Research and Technology. Calendar Year 1971

This report contains abstracts of Master of Science theses and Doctoral Dissertations completed during the 1971 calendar year at the School of Engineering, Air Force Institute of Technology

Four Lessons in Versatility or How Query Languages Adapt to the Web

Exposing not only human-centered information, but machine-processable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the Web into islands of data, each in different Web formats: Some providers choose XML, others RDF, again others JSON or OWL, for their data, even in similar domains. This fracturing stifles innovation as application builders have to cope not only with one Web stack (e.g., XML technology) but with several ones, each of considerable complexity. With Xcerpt we have developed a rule- and pattern based query language that aims to give shield application builders from much of this complexity: In a single query language XML and RDF data can be accessed, processed, combined, and re-published. Though the need for combined access to XML and RDF data has been recognized in previous work (including the W3C’s GRDDL), our approach differs in four main aspects: (1) We provide a single language (rather than two separate or embedded languages), thus minimizing the conceptual overhead of dealing with disparate data formats. (2) Both the declarative (logic-based) and the operational semantics are unified in that they apply for querying XML and RDF in the same way. (3) We show that the resulting query language can be implemented reusing traditional database technology, if desirable. Nevertheless, we also give a unified evaluation approach based on interval labelings of graphs that is at least as fast as existing approaches for tree-shaped XML data, yet provides linear time and space querying also for many RDF graphs. We believe that Web query languages are the right tool for declarative data access in Web applications and that Xcerpt is a significant step towards a more convenient, yet highly efficient data access in a “Web of Data”

Ternary Max-Min algebra with application to reversible logic synthesis

Ternary reversible circuits are 0.63 times more compact than equivalent binary reversible circuits and are suitable for low-power implementations. Two notable previous works on ternary reversible circuit synthesis are the ternary Galois field sum of products (TGFSOP) expression-based method and the ternary Max-Min algebra-based method. These methods require high quantum cost and large number of ancilla inputs. To address these problems we develop an alternative ternary Max-Min algebra-based method, where ternary logic functions are represented as Max-Min expressions and realized using our proposed multiple-controlled unary gates. We also show realizations of multiple-controlled unary gates using elementary quantum gates. We develop a method for minimization of ternary Max-Min expressions of up to four variables using ternary K-maps. Finally, we develop a hybrid Genetic Algorithm (HGA)-based method for the synthesis of ternary reversible circuits. The HGA has been tested with 24 ternary benchmark functions with up to five variables. On average our method reduces quantum cost by 41.36% and requires 35.72% fewer ancilla inputs than the TGFSOP-based method. Our method also requires 74.39% fewer ancilla inputs than the previous ternary Max-Min algebra-based method

Prescriptive formalism for constructing domain-specific evolutionary algorithms

It has been widely recognised in the computational intelligence and machine learning communities that the key to understanding the behaviour of learning algorithms is to understand what representation is employed to capture and manipulate knowledge acquired during the learning process. However, traditional evolutionary algorithms have tended to employ a fixed representation space (binary strings), in order to allow the use of standardised genetic operators. This approach leads to complications for many problem domains, as it forces a somewhat artificial mapping between the problem variables and the canonical binary representation, especially when there are dependencies between problem variables (e.g. problems naturally defined over permutations). This often obscures the relationship between genetic structure and problem features, making it difficult to understand the actions of the standard genetic operators with reference to problem-specific structures. This thesis instead advocates m..

Sparse random graphs with clustering

In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results about this extension. The basic idea is to construct the random graph by adding not only edges but also other small graphs. In other words, we first construct an inhomogeneous random hypergraph with independent hyperedges, and then replace each hyperedge by a (perhaps complete) graph. Although flexible enough to produce graphs with significant dependence between edges, this model is nonetheless mathematically tractable. Indeed, we find the critical point where a giant component emerges in full generality, in terms of the norm of a certain integral operator, and relate the size of the giant component to the survival probability of a certain (non-Poisson) multi-type branching process. While our main focus is the phase transition, we also study the degree distribution and the numbers of small subgraphs. We illustrate the model with a simple special case that produces graphs with power-law degree sequences with a wide range of degree exponents and clustering coefficients.Comment: 62 pages; minor revisio

Integrated testing and verification system for research flight software design document

The NASA Langley Research Center is developing the MUST (Multipurpose User-oriented Software Technology) program to cut the cost of producing research flight software through a system of software support tools. The HAL/S language is the primary subject of the design. Boeing Computer Services Company (BCS) has designed an integrated verification and testing capability as part of MUST. Documentation, verification and test options are provided with special attention on real time, multiprocessing issues. The needs of the entire software production cycle have been considered, with effective management and reduced lifecycle costs as foremost goals. Capabilities have been included in the design for static detection of data flow anomalies involving communicating concurrent processes. Some types of ill formed process synchronization and deadlock also are detected statically