Given a finite point set P ⊂ R, we call a multiset A a one-sided weak ε-approximant for P (with respect to convex sets), if |P ∩ C|/|P | − |A ∩C|/|A| ≤ ε for every convex set C. We show that, in contrast with the usual (two-sided) weak ε-approximants, for every set P ⊂ R there exists a one-sided weak ε-approximant of size bounded by a function of ε and d.

When is an argument to be called one-sided? When is putting forward such an argument fallacious? How can we develop a model for critical discussion, such that a fallaciously one-sided argument corresponds to a violation of a discussion rule? These issues are dealt with within ‘the limits of the dialogue model of argument’ by specifying a type of persuasion dialogue in which an arguer can offer ...

In this paper, we study the problem of privacy-preserving data sharing, wherein only a subset of the records in a database are sensitive, possibly based on predefined privacy policies. Existing solutions, viz, differential privacy (DP), are over-pessimistic and treat all information as sensitive. Alternatively, techniques, like access control and personalized differential privacy, reveal all no...

It is shown that a previously unknown class of magneti" zation patterns exists in planar structures which have the unique property that all the flux escapes from one surface with none leaving the other side. A simple case is a constant amplitude rotating vector magnetization where the sense of rotation dictates which surface has no flux. More complicated magnetization patterns are elucidated. T...

We give an alternative treatment and extension of some results of Itoh and Mahmoud on one-sided interval trees. The proofs are based on renewal theory, including a case with mixed multiplicative and additive renewals.

This paper considers the main positions of one-sided and two-sided problems. For onesided problems only the method of solution “the distance to the ideal point” is discussed in the actual version. For two-sided problems a distinction is made between games with rational behaviour and games against nature. The main strategic principles are as follows: simple min-max principle, extended min-max pr...