In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution D over [n]. More precisely, we define both the dual and cumulative dual access models, in which the algorithm A can both sample from D and respectively, for an...

Given a k-graph Λ and an element p of N, we define the dual k-graph, pΛ. We show that when Λ is row-finite and has no sources, the C∗-algebras C∗(Λ) and C∗(pΛ) coincide. We use this isomorphism to apply Robertson and Steger’s results to calculate the K-theory of C∗(Λ) when Λ is finite and strongly connected and satisfies the aperiodicity condition.

We present M-theory compactifications on K3 × K3 with membranes near the An or Dn singularities of the K3 spaces. By realizing each of these compactifications in two different ways as type I’ models with 2and 6-branes, we explain the three-dimensional duality between gauge theories recently found by Intriligator and Seiberg. We also find new pairs of dual gauge theories, which we briefly descri...

We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...

Intellectual synergy is a major source of high competitive power for an organization. Through our research project, we have been developing an environment, Kfarm, to support creating/inheriting organizational intellect. Characteristic features of Kfarm include a Dual Loop Model which represents ideal processes of knowledge-level communication among personnel to create/inherit organizational kno...

In this paper, we focus on the organization of activities that produce graphical representations on the shared whiteboard of a CSCL system with dual interaction spaces called VMT Chat, and the ways those representations are used as interactional resources by small groups during their collaborative math problem solving work. In particular, we will investigate how actions performed in one medium ...

In this work, we consider matroid theory. After presenting three different (but equivalent) definitions of matroids, we mention some of the most important theorems of such theory. In particular, we note that every matroid has a dual matroid and that a matroid is regular if and only if it is binary and includes no Fano matroid or its dual. We show a connection between this last theorem and octon...

IT devices such as computers, tablets, smartphones as well as Internet are playing extremely important role in both work and non-work fields. Meanwhile, IT facilities also blurred the boundary between work and non-work. With the ubiquity of IT devices and Internet at workplace, organizational employees nowadays increasingly engage in online activities for personal purposes, which are not relate...