28870218
An algorithm for optimal difference systems of sets
Abstract
Difference Systems of Sets (DSS) are combinatorial structures that generalize cyclic difference sets and are used in code synchronization. A DSS is optimal if the associated code has minimum redundancy for the given block length n, alphabet size q, and error-correcting capacity ρ. An algorithm for finding optimal DSS is presented together with tables of optimal solutions found by this algorithm.

46526063
Optimal Difference Systems of Sets with Multipliers
Difference Systems of Sets (DSS) are combinatorial structures that are used in code synchronization. A DSS is optimal if the associated code has minimum redundancy for the given block length n, alphabet size q, and error-correcting capacity ρ. An algorithm is described for finding optimal DSS that admit prescribed symmetries defined by automorphisms of the cyclic group of order n, together with optimal DSS found by this algorithm.
11024065
An algorithm for optimal comma free codes with isomorphism rejection
A general algorithm for finding optimal comma-free codes and deriving upper bounds on the minimum redundancy of comma-free codes that implements the idea of isomorphism rejection is presented, together with tables with bounds on the minimum redundancy computed by using this algorithm.
38679232
Short Definitions of the Ordinals
In this paper, a simple inductive characterization of the ordinal numbers is stated and developed. The characterization forms the basis for a set of axioms for ordinal theory and also for several short explicit definitions of the ordinals. The axioms are shown to be sufficient for ordinal theory, and, subject to suitable existence assumptions, each of the definitions is shown to imply the axioms. The present results apply to the familiar von Neumann version of the ordinals, but the methods used are easily adapted to other versions. ? 1. Axioms for ordinal theory. According to the usual interpretation, each ordinal is the set of all lesser ordinals. Thus zero is the empty set A, a successor ordinal x' is x U {x} for some ordinal x, and a limit ordinal is a set w of ordinals that is equal to its own sum set Zw. In fact, the class On of all ordinals might be characterized informally as the smallest class Z such that (1) AEZ, (2) (y) (yEZ D y'EZ), and (3) (w) (1w = w c Z D wEZ). More simply, On can be characterized as the smallest Z such that
18365285
An automated approach to specification animation for validation
Formal specification has been increasingly adopted for the development of software systems of the highest integrity. However, the readability of specifications for large-scale and complex systems can be so poor that even the developers may not easily understand whether their specifications define the ''intended behaviors''. In this paper, we describe a software tool that supports the animation of specifications by simulating their functional scenarios using the Message Sequence Chart (MSC). The tool extracts automatically functional scenarios from a specification and generates a message sequence chart for each of them for a syntactic level analysis. The tool can also execute a functional scenario with test cases for a semantic level analysis if all the processes involved in the scenario are defined using explicit specifications. With the tool support the animation of a specification can be carried out incrementally to assist its user to review the adequacy of the specification. We present a case study applying the tool to animate a formal specification for a library system and evaluate its result.
16346838
Ant-MST: An Ant-Based Minimum Spanning Tree for Gene Expression Data Clustering
We have proposed an ant-based clustering algorithm for document clustering based on the travelling salesperson scenario. In this paper, we presented an approach called Ant-MST for gene expression data clustering based on both ant-based clustering and minimum spanning trees (MST). The ant-based clustering algorithm is firstly used to construct a fully connected network of nodes. Each node represents one gene, and every edge is associated with a certain level of pheromone intensity describing the co-expression level between two genes. Then MST is used to break the linkages in order to generate clusters. Comparing to other MST-based clustering approaches, our proposed method uses pheromone intensity to measure the similarity between two genes instead of using Euclidean distance or correlation distance. Pheromone intensities associated with every edge in a fully-connected network records the collective memory of the ants. Self-organizing behavior could be easily discovered through pheromone intensities. Experimental results on three gene expression datasets show that our approach in general outperforms the classical clustering methods such as K-means and agglomerate hierarchical clustering.
9889663
Feature Similarity Based Redundancy Reduction for Gene Selection
this paper we propose a feature similarity based redundancy reduction (FSRR) algorithm for high-dimensional gene expression data analysis. FSRR has two steps. First, the relevance of each feature is evaluated. Second, based on the relevance, the redundant features are removed by feature similarity. The efficiency and effectiveness of our algorithm is established through an experimental study using gene expression data. Four state-of-art feature ranking algorithms and three feature similarity measures are compared and discussed in our work. The results indicate that our algorithm has the capability of finding a well-suited feature set and improving the classification accuracy.
18424476
Proving theorems by pattern recognition I
Certain preliminary results on doing mathematics by machines (“mechanical mathematics”) were reported in an earlier paper [20]. The writer suggested developing inferential analysis as a branch of applied logic and as a sister discipline of numerical analysis. This analogy rests on the basic distinction of pure existence proofs, elegant procedures which in theory always terminate, and efficient procedures which are more complex to describe but can more feasibly be carried out in practice. In contrast with pure logic, the chief emphasis of inferential analysis is on the efficiency of algorithms, which is usually attained by paying a great deal more attention to the detailed structures of the problems and their solutions, to take advantage of possible systematic short cuts. The possibilities of much more elaborate calculations by machines provide an incentive to studying a group of rather minute questions which were formerly regarded as of small theoretical interest. When the range of actual human computation was narrow, there seemed little point in obtaining faster procedures which were still far beyond what was feasible. Furthermore, on account of the versatility of machines, it now appears that as more progress is made, strategies in the search for proofs, or what are often called heuristic methods, will also gradually become part of the subject matter of inferential analysis. An analogous situation in numerical analysis would be, for example, to make the machine choose to apply different tricks such as taking the Fourier transform to obtain a solution of some differential equation.