To a large extent the present work is far from being conclusive, instead, new directions of research in combinatorial extremal theory are started. Also questions concerning generalizations are immediately noticeable. The incentive came from problems in several fields such as Algebra, Geometry, Probability, Information and Complexity Theory. Like several basic combinatorial problems they may pla...

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Using ε-bias spaces over F2, we show that the Remote Point Problem (RPP), introduced by Alon et al [APY09], has an NC algorithm (achieving the same parameters as [APY09]). We study a generalization of the Remote Point Problem to groups: we replace F2 by G n for an arbitrary fixed group G. When G is Abelian we give an NC algorithm for RPP, again using ε-bias spaces. For nonabelian G, we give a d...

At the beginning of every course, it can be expected that several students have some syllabus knowledge. For efficiency in learning systems, and to combat student frustration and boredom, it is important to quickly uncover this latent knowledge. This enables students to begin new learning immediately. In this paper we compare two algorithms used to achieve this goal, both based on the theory of...

We discuss a membrane-based calculus for the combination of conceptual spaces during runtime. Since our goal is to support emergent properties of behavior (and due to the fact that it is not possible to define a complete calculus for all situations) we introduce the notion of self-modification. Terms from situational description can evolve according to simple rules thus providing various possib...

We propose a framework for learning new target tasks by leveraging existing heterogeneous knowledge sources. Unlike the traditional transfer learning, we do not require explicit relations between source and target tasks, and instead let the learner actively mine transferable knowledge from a source dataset. To this end, we develop (1) a transfer learning method for source datasets with heteroge...

It is shown that the existence of a closed convex set all of whose points are properly supported in a Banach space is equivalent to the existence of a certain type of uncountable ordered one-sided biorthogonal system. Under the continuum hypothesis, we deduce that this notion is weaker than the existence of an uncountable biorthogonal system. Introduction. We will say a closed convex set C in a...

We describe an abstract framework in which the notion of fundamental category can be defined. The structures matching this framework are categories endowed with some additional structure. Provided we have a suitable adjunction between two of them, the fundamental categories defined in both cases can be easily compared. Each of these structures has a “natural” functor to the category of d-spaces...

Some useful topological properties of the moment space of the family of distributions with increasing failure rates are established. These results are exploited to obtain tight inequalities for moments of such distributions and also to derive some interesting facts concerning weak convergence within this family.

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson (2006) present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, r...