This paper formalizes the stepping stone problem introduced Ladoucer and Rebenstock [G] to setting of simple graphs. considers set functions from vertices our graph N, which assign a fixed number 1’s some higher numbers other by adding up their neighbors’ assignments. The solution is defined as an element obtained argmax maxima these functions, its growth. work organized into on bounded unbound...

In this paper we consider a stepping-stone model on a circle with circular Brownian migration. We first point out a connection between Arratia flow and the marginal distribution of this model. We then give a new representation for the stepping-stone model using Arratia flow and circular coalescing Brownian motion. Such a representation enables us to carry out some explicit computation. In parti...

Somatic cells can be reprogrammed into pluripotent stem cells via either expression of transcription factors or addition of small molecule chemicals only. Zhao et al. reveal a unique intermediate state during chemical reprogramming allowing a significant improvement in its efficiency and kinetics.

Intruders on the Internet often prefer to launch network intrusions indirectly, i.e., using a chain of hosts on the Internet as relay machines using protocols such as Telnet or SSH. This type of attack is called a stepping-stone attack. In this paper, we propose and analyze algorithms for stepping-stone detection using ideas from Computational Learning Theory and the analysis of random walks. O...

Anonymity is important to perpetrators of network-based attacks. One of the simplest ways to remain anonymous is to hide the source of an attack by chaining together multiple connections into an extended connection. This is typically done by logging into a remote host, then from there logging into a third and fourth and so on until, at the final host, an attack is launched. These intermediate h...