Magic: The Gathering (MTG, or Magic) is the oldest and most popular trading card game played today, due in part to the complex interplay of thousands of cards. In two-player games, each player constructs a "main" deck (referred to as simply 'deck' hereafter) which consists of 60 cards, allowing players to pursue an enormous number of strategies and card combinations. When experienced Magic play...

Magic state distillation is an important primitive in fault-tolerant quantum computation. The magic states are pure nonstabilizer states which can be distilled from certain mixed nonstabilizer states via Clifford group operations alone. Because of the Gottesman-Knill theorem, mixtures of Pauli eigenstates are not expected to be magic state distillable, but it has been an open question whether a...

Using a virtual probe method in molecular dynamics approach, we have explored the growing process of atomic clusters by adding atoms in a one-by-one manner to a tetrahedron up to 50 atoms and found that the growing path repeats a process of split-then-merge chaining. The sequential chains merge in the vicinity of the ones with atoms of magic number and then diverge, meaning that, in the cluster...

A graph G is called edge-magic if there exists a bijective function φ : V (G)∪E(G) → {1, 2,. .. , |V (G)|+ |E(G)|} such that φ(x)+φ(xy)+φ(y) is a constant c(φ) for every edge xy ∈ E(G); here c(φ) is called the valence of φ. A graph G is said to be super edge-magic if φ(V (G)) = {1, 2,. .. , |V (G)|}. The super edge-magic deficiency, denoted by μ s (G), is the minimum nonnegative integer n such ...

Let G = (V,E) be a finite (non-empty) graph, where V and E are the sets of vertices and edges of G. An edge magic total labeling is a bijection α from V ∪E to the integers 1,2, . . . , n+e, with the property that for every xy ∈E, α(x)+α(y)+α(xy)= k, for some constant k. Such a labeling is called an a-vertex consecutive edge magic total labeling if α(V )= {a + 1, . . . , a + n} and a b-edge cons...

BACKGROUND Hepatocyte Growth Factor (HGF) is a pleiotropic cytokine of mesenchymal origin that mediates a characteristic array of biological activities including cell proliferation, survival, motility and morphogenesis. Its high affinity receptor, the tyrosine kinase Met, is expressed by a wide range of tissues and can be activated by either paracrine or autocrine stimulation. Adult myogenic pr...

Work for this essay began with a problem that will sound all too familiar to most of us in higher education: It has recently dawned upon administrators and faculty in many departments across our university's curriculum that our students can't write. Or more accurately, enough of our students write poorly enough that we have cause for concern. This concern is usually expressed in the unequivocal...

During its Cycle I, the MAGIC telescope targeted about 250 hours several galactic sources sought to be, or detected previously by other experiments in the same energy domain, γ-ray emitters. This paper reviews some results of such MAGIC observations covering, among others, supernova remnants, the Galactic Center and microquasars. We will concentrate on the recent discovery at very high energy γ...

We present an infinite family of protocols to distill magic states for T -gates that has a low space overhead and uses an asymptotic number of input magic states to achieve a given target error that is conjectured to be optimal. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input ma...

For any positive integer k, a graph G = (V, E) is said to be ZZ k-magic if there exists a labeling l : E(G) −→ ZZ k − {0} such that the induced vertex set labeling l : V (G) −→ ZZ k defined by l(v) = ∑ { l(uv) : uv ∈ E(G) } is a constant map. For a given graph G, the set of all h ∈ ZZ + for which G is ZZ h-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper, w...