We study the positive Bergman complex B(M) of an oriented matroid M , which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid M . The positive Bergman complex is defined so that given a linear ideal I with associated oriented matroid MI , the positive tropical variety associated to I is equal to the fan over B(MI). Our main result is that a certain “fine” ...

The quest for the identification of fruitless branch has been an enduring theological battleground between Calvinists and Arminians who argue as to whether or not removal indicates loss eternal salvation. Using a qualitative approach, this study sought examine various interpretations on security believer with focus three phrases in passage namely; ἐν ἐμοὶ, (in me) airō (cut off) μείνατε ἐμοί (a...

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...

We present the gravitational action and Hamiltonian for a spatially bounded region of an eternal black hole. The Hamiltonian is of the general form H = H+ − H−, where H+ and H− are respectively the Hamiltonian for the regions M+ and M− located in the left and right wedges of the spacetime. We construct explicitly the quasilocal energy for the system and discuss its dependence on the time direct...

The volume enclosed by subdivision surfaces, such as Doo-Sabin, Catmull-Clark, and Loop has recently been derived. Moments of higher degree d are more challenging because of the growing number of coefficients in the d + 3-linear forms. We derive the intrinsic symmetries of the tensors, and thereby reduce the complexity of the problem. Our framework allows to compute the 4-linear forms that de...

For any k ∈ N, the k-subdivision of a graph G is a simple graph G 1 k , which is constructed by replacing each edge of G with a path of length k. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the mth power of the n-subdivision of G has been introduced as a fractional power of G, denoted by G m n . In this regard, we investig...

In 1985, Mader conjectured the existence of a function f such that every digraph with minimum out-degree at least f(k) contains a subdivision of the transitive tournament of order k. This conjecture is still completely open, as the existence of f(5) remains unknown. In this paper, we show that if D is an oriented path, or an in-arborescence (i.e., a tree with all edges oriented towards the root...

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...