This paper shows that with B = {1, 2, . . . , n}, the smallest k such that (B ×B)− {(j, j) | j ∈ B} = k ⋃ i=1 (Ci ×Di) is s(n), where s(n) is the smallest integer k such that n 6 ( k b k 2 c ) . This provides a simple set-based formulation and a new proof of a result for boolean ranks [2] and biclique covering of bipartite graphs [1, 5], making these intricate results more accessible.

now a third. We confess not to be great believers in drugs, whether ' simples' or very compound?but no one can read or glance through this book without great interest. It is wiitten iu Dr. Fernie's best style, full of apt quotations and gentle humour, while at the same time conveying a vast amount of information, traditional and experimental, on the therapeutic use of innumerable common and rar...

In this paper, we find explicit formulas or generating functions for the cardinalities of the sets Sn(T, τ) of all permutations in Sn that avoid a pattern τ ∈ Sk and a set T , |T | ≥ 2, of patterns from S3. The main body of the paper is divided into three sections corresponding to the cases |T | = 2, 3 and |T | ≥ 4. As an example, in the fifth section, we obtain the complete classification of a...

In this paper, we find explicit formulas or generating functions for the cardinalities of the sets Sn(T, τ ) of all permutations in Sn that avoid a pattern τ ∈ Sk and a set T , |T | ≥ 2, of patterns from S3. The main body of the paper is divided into three sections corresponding to the cases |T | = 2, 3 and |T | ≥ 4. As an example, in the fifth section, we obtain the complete classification of ...

15 Parametric Curves And Surfaces 15.1 Parametric Curves Designing Curves • We don’t want only polygons. • Curves are used for design. Users require a simple set of controls to allow them to edit and design curves easily. • Curves should have infinite resolution, so we can zoom in and still see a smooth curve. • We want to have a compact representation. Parametric functions are of the form x(t)...

State-of-the-art statistical approaches to the Coreference Resolution task rely on sophisticated modeling, but very few (10-20) simple features. In this paper we propose to extend the standard feature set substantially, incorporating more linguistic knowledge. To investigate the usability of linguistically motivated features, we evaluate our system for a variety of machine learners on the stand...

We introduce a game in preference form, which consists of a game form and a preference structure, and define preference rationalizability that allows for each player’s ex-post preferences over outcomes to depend on opponents’ actions. We show that preference rationalizability is invariant to redundant types and states as long as all players have simplex restrictions on their ex-post preferences...

This paper discusses experience gained while implementing Vince, a publicly available software package for the development of protocols in ATM networks. Vince provides a simple set of general abstractions which are extremely useful for protocol development and experimentation.