Topology construction and topology maintenance are significant sub-problems of topology control. Spanning tree based algorithms for topology control are basically transmission range based type construction algorithms. The construction of an effective backbone, however, is indirectly related to the placement of nodes. Also, the dependence of network reliability on the communication path undertak...

In this paper we consider composition operators on locally convex spaces of functions defined R . We prove results concerning supercyclicity, power boundedness, mean ergodicity and convergence the iterates in strong operator topology.

The prevalent strategy in the topology optimization phase is to select a subset of members existing in an excessively connected truss, called Ground Structure, such that the overall weight or cost is minimized. Although finding a good topology significantly reduces the overall cost, excessive growth of the size of topology space combined with existence of varied types of design variables challe...

motivated by the recent study on categorical properties of latticevalued topology, the paper considers a generalization of the notion of topological system introduced by s. vickers, providing an algebraic and a coalgebraic category of the new structures. as a result, the nature of the category   topsys   of s. vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalu...

for each * in X. For any Banach space X and any element * of Xt J(x) is a nonempty closed convex subset of the sphere of radius ||x|| about zero in X*. If X* is strictly convex, J is a singlevalued mapping of X into X* and is continuous from the strong topology of X to the weak* topology of X*. J is continuous in the strong topologies if and only if the norm in X is C on the complement of the o...

This report is a companion to another technical report [3] to present the formal proofs that could not fit into the conference proceedings of this article [4] due to space limitations. In this report we revisit the problem of Byzantine-robust topology discovery. We formally state the weak and strong versions of the problem. We focus on non-cryptographic solutions to these problems and explore t...

Starting with Grothendieck’s proof of the local version of the Lefschetz hyperplane theorems [Gro68], it has been understood that there are strong parallels between the topology of smooth projective varieties and the topology of links of isolated singularities. This relationship was formulated as one of the guiding principles in the monograph [GM88, p. 26]: “Philosophically, any statement about...

Social networks often provide only a binary perspective on social ties: two individuals are either connected or not. While sometimes external information can be used to infer the strength of social ties, access to such information may be restricted or impractical. Sintos and Tsaparas (KDD 2014) first suggested to infer the strength of social ties from the topology of the network alone, by lever...