We generalize the notion of saturated orders to infinite partial orders and give both a set-theoretic and an algebraic characterization of such orders. We then study the proof theoretic strength of the equivalence of these characterizations in the context of reverse mathematics, showing that depending on one’s choice of definitions, this equivalence is either provable in RCA0 or equivalent to A...

The search for an adequate avalanche RPC working model evidenced that the simple exponential growth can describe the electron multiplication phenomena in the gas with acceptable accuracy until the external electric field is not perturbed by the growing avalanche. We present here a model in which the saturated growth induced by the space charge effects is explained in a natural way by a constant...

In this paper, we revise two commonly used saturated functions, the logistic sigmoid and the hyperbolic tangent (tanh). We point out that, besides the well-known non-zero centered property, slope of the activation function near the origin is another possible reason making training deep networks with the logistic function difficult to train. We demonstrate that, with proper rescaling, the logist...

For a hereditary property P let kP(G) denote the number of forbidden subgraphs contained in G. A graph G is said to be weakly Psaturated, if G has the property P and there is a sequence of edges of G, say e1, e2, . . . , el, such that the chain of graphs G = G0 ⊂ G0+e1 ⊂ G1 + e2 ⊂ . . . ⊂ Gl−1 + el = Gl = Kn (Gi+1 = Gi + ei+1) has the following property: kP(Gi+1) > kP(Gi), 0 ≤ i ≤ l − 1. In thi...

Stephan-Yl ~n Solomon Let L be a lan~'uage over m vocmb~Ja~y V ~nd let de~ot~. by E (V) the s,t of ml! enuSv~lence relmtlon~ (partitions) on V. If ~ ~ E (V) and x ~ V then we sb~ll denote by ~(v) the cell of ~ containing the elmment 7. Defini%ion I. A p~rtition ~GE(V) is s~id to be smturated ev~-VY i (I ~imn) there exlst such elements x~ Our purpose i.,~ to find (in the cese of m finite vocebu-...

Hyperoperations are mappings that assign a non-void subset of a set to each n-tuple of elements from the set. They present a fundamental notion for modeling non deterministic processes. Even though for each non deterministic automaton there is a language equivalent deterministic automaton, they do not have the same behavior. As behavior of concurrent processes took place in emerging fields of t...

Among shellable complexes a certain class has maximal modular homology, and these are the so-called saturated complexes. We extend the notion of saturation to arbitrary pure complexes and give a survey of their properties. It is shown that saturated complexes can be characterized via the p -rank of incidence matrices and via the structure of links. We show that rank-selected subcomplexes of sat...

We say that a hypergraph H is hamiltonian path (cycle) saturated if H does not contain an open (closed) hamiltonian chain but by adding any new edge we create an open (closed) hamiltonian chain in H. In this paper we ask about the smallest size of an r-uniform hamiltonian path (cycle) saturated hypergraph, mainly for r = 3. We present a construction of a family of 3-uniform path (cycle) saturat...

We prove the following: (1) If κ is weakly inaccessible then NSκ is not κ+-saturated. (2) If κ is weakly inaccessible and θ < κ is regular then NSθ κ is not κ +saturated. (3) If κ is singular then NS κ+ is not κ++-saturated. Combining this with previous results of Shelah, one obtains the following: (A) If κ > א1 then NSκ is not κ+-saturated. (B) If θ+ < κ then NSθ κ is not κ +-saturated.