In this chapter, we present a survey of algorithms for dense subgraph discovery. The problem of dense subgraph discovery is closely related to clustering though the two problems also have a number of differences. For example, the problem of clustering is largely concerned with that of finding a fixed partition in the data, whereas the problem of dense subgraph discovery defines these dense comp...

‎let $pa$ be a commutative banach algebra and $ex$ be a left banach $pa$-module‎. ‎we study the set‎ ‎$dec_{pa}(ex)$ of all elements in $pa$ which induce a decomposable multiplication operator on $ex$‎. ‎in the case $ex=pa$‎, ‎$dec_{pa}(pa)$ is the well-known apostol algebra of $pa$‎. ‎we show that $dec_{pa}(ex)$ is intimately related with the largest spectrally separable subalgebra of $pa$ and...

We discuss residual finiteness and several related separability conditions for the class of monoid acts, namely weak subact separability, strong complete separability. For each these four conditions, we investigate which monoids have property that all their (finitely generated) acts satisfy condition. In particular, prove that: over a finite are completely separable (and hence other three condi...

This paper describes an approach to system design called the dialectical. In this approach, the design and its environment, including the people involved, are assumed to form an inseparable whole. The whole and its parts are subject to interaction and change throughout the entire design process. Using this approach, a number of aspects of system design are covered, and a model for design proces...

Recent research has to a limited extent explored the nature of collaborative knowledge construction in 3D environments. In this paper we describe this issue by identifying two collaboration patterns that are manifested in the students’ dialogues and actions in a particular 3D learning environment. The theoretical framework is found within socio-cultural perspectives that view learning as social...

While demands for large scale improvements in education systems increase worldwide, education system structures continuously fail to meet, or even make notable advancements, toward these demands. Inseparable from this problem is the very similar way in which education systems are managed. Educational managerial structures have become so universal, perpetual, and therefore, deeply ingrained in s...

For a finite cyclic Galois extension of fields K/k of degree n and a separable polynomial of degree dn or dn−1, we construct an explicit smooth compactification X → Pk of the affine normic bundle X0 given by NK/k(~z) = P (x) 6= 0, extending the map X0 → Ak, where (~z, x) 7→ x. The construction makes no assumption of the characteristic of k, making it a suitable departure point for studying the ...

But this picture of a ”block universe”, composed of a timeless web of ”world-lines”in a four-dimensional space, however strongly suggested by the theory of relativity, is a piece of gratuitous metaphysics. Since the concept of change, of something happening, is an inseparable component of the common-sense concept of time and a necessary component of the scientist’s view of reality, it is quite ...