This article examines how imaginaries of security in the Anthropocene function at Svalbard Global Seed Vault (SGSV), otherwise known as ‘Doomsday Vault’. Recent explorations by scholars have suggested that different ways seeing, understanding, acting in, and imagining world are necessary to adequately respond complex crises Anthropocene. The dissolution nature/culture divide existential risk fr...

Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to move per attack, whereas more than one guard may move per attack in the m-eternal domination model. Inequality chains consisting of the domination, eternal domination, m-eternal domination, independence, and clique c...

In recent literature on eternal inflation, a number of measures have been introduced which attempt to assign probabilities to different pocket universes by counting the number of each type of pocket according to a specific procedure. We give an overview of the existing measures, pointing out some interesting connections and generic predictions. For example, pairs of vacua that undergo fast tran...

Mobile guards on the vertices of a graph are used to defend the graph against an infinite sequence of attacks on vertices. A guard must move from a neighboring vertex to an attacked vertex (we assume attacks happen only at vertices containing no guard and that each vertex contains at most one guard). More than one guard is allowed to move in response to an attack. The m-eternal domination numbe...

Eternal domination is a problem that asks the following question: Can we eternally defend graph ? The principle to against an attacked vertex, changes every turn, by moving guards along edges of graph. In classical version game (Burger et al., 2004), only one guard can move at time, but in m-eternal (Goddard 2005), any number single turn. This led introduction two parameters: eternal and number...

Abstract. Eternal solutions of parabolic equations (those which are defined for all time) are typically rather rare. For example, the heat equation has exactly one eternal solution – the trivial solution. While solutions to the heat equation exist for all forward time, they cannot be extended backwards in time. Nonlinearities exasperate the situation somewhat, in that solutions may form singula...

A vertex u of a graph “t-dominates” a vertex v if there are at most t vertices different from u, v that are adjacent to v and not to u; and a graph is “t-dominating” if for every pair of distinct vertices, one of them t-dominates the other. Our main result says that if a graph is t-dominating, then it is close (in an appropriate sense) to being 0-dominating. It was already known that every t-do...