36095353
Extremal Regular Graphs with Prescribed Odd Girth
The odd girth of a graph G gives the length of a shortest odd cycle in G. Let ?(k, g) denote the smallest n such that there exists a k-regular graph of order n and odd girth g. It is known that ?(k, g) ? kg/2 and that ?(k, g) = kg/2 if k is even. The exact values of ?(k, g) are also known if k = 3 or g = 5. Let ?x?e denote the smallest even integer no less than x, ?(g) = (?1)g ? 1/2, and s(k) = min {p + q | k = pq, where p and q are both positive integers}. It is proved that if k ? 5 and g ? 7 are both odd, then formula] with the exception that ?(5, 7) = 20.
38503566
Pseudo-one-factorizations of regular graphs of odd order - II. products of graphs
Abstract We study the pseudo-one-factorization of regular graphs of odd order. It is shown that some classes of products (including composition and cartesian product) of graphs are pseudo-one- factorizable. In particular, we prove that a complete regular t -partite graph of odd order has this property.
37771428
Some New Bounds on Single-Change Covering Designs
A single-change covering design SCD(v, k, b) on a c-set V is a sequence of b k-sets (blocks) on V that together cover every pair of elements of V at least once, such that two successive blocks have k-1 elements in common. Let f(v,k) denote the smallest b for which there exists an SCD(v, k, b). Some new upper and lower bounds for f(v,k) are given.
7172030
Information-theoretic inequalities for contoured probability distributions
We show that for a special class of probability distributions that we call contoured distributions, information-theoretic invariants and inequalities are equivalent to geometric invariants and inequalities of bodies in Euclidean space associated with the distributions. Using this, we obtain characterizations of contoured distributions with extremal Shannon and Renyi entropy. We also obtain a new reverse information-theoretic inequality for contoured distributions.
2346481
The End of Pumping?
14387948
Axiomatic Aspects of Default Inference
This paper studies axioms for nonmonotonic consequences from a semantics-based point of view, focusing on a class of mathematical structures for reasoning about partial information without a predefined syntax/logic. This structure is called a default structure. We study axioms for the nonmonotonic consequence relation derived from extensions as in Reiter's default logic, using skeptical reasoning, but extensions are now used for the construction of possible worlds in a default information structure. 
In previous work we showed that skeptical reasoning arising from default-extensions obeys a well-behaved set of axioms including the axiom of cautious cut. We show here that, remarkably, the converse is also true: any consequence relation obeying this set of axioms can be represented as one constructed from skeptical reasoning. We provide representation theorems to relate axioms for nonmonotonic consequence relation and properties about extensions, and provide one-to-one correspondence between nonmonotonic systems which satisfies the law of cautious monotony and default structures with unique extensions. Our results give a theoretical justification for a set of basic rules governing the update of nonmonotonic knowledge bases, demonstrating the derivation of them from the more concrete and primitive construction of extensions. It is also striking to note that proofs of the representation theorems show that only shallow extensions are necessary, in the sense that the number of iterations needed to achieve an extension is at most three. All of these developments are made possible by taking a more liberal view of consistency: consistency is a user defined predicate, satisfying some basic properties.
7607437
A representation of stably compact spaces, and patch topology
This note presents a concrete representation of stably compact spaces. This is used to give a simple, and predicative, description of the patch topology of a stably compact space (J. Pure Appl. Algebra, to appear).
13992541
Enhancing relevance scoring with chronological term rank
We introduce a new relevance scoring technique that enhances existing relevance scoring schemes with term position information. This technique uses chronological term rank (CTR) which captures the positions of terms as they occur in the sequence of words in a document. CTR is both conceptually and computationally simple when compared to other approaches that use document structure information, such as term proximity, term order and document features. CTR works well when paired with Okapi BM25. We evaluate the performance of various combinations of CTR with Okapi BM25 in order to identify the most effective formula. We then compare the performance of the selected approach against the performance of existing methods such as Okapi BM25, pivoted length normalization and language models. Significant improvements are seen consistently across a variety of TREC data and topic sets, measured by the major retrieval performance metrics. This seems to be the first use of this statistic for relevance scoring. There is likely to be greater retrieval improvements possible using chronological term rank enhanced methods in future work.