In this paper we present a phenomenological approach to describe a complex system: scientific research impact through Citation Mining. The novel concept of Citation Mining, a combination of citation bibliometrics and text mining, is used for the phenomenological description. Citation Mining starts with a group of core papers whose impact is to be examined , retrieves the papers that cite these ...

A brief historical perspective is first given concerning financial crashes, from the 17th till the 20th century. In modern times, it seems that log periodic oscillations are found before crashes in several financial indices. The same is found in sand pile avalanches on Sierpinski gaskets. A discussion pertains to the after shock period with illustrations from the DAX index. The factual financia...

We study the steady state of the abelian sandpile models with stochastic toppling rules. The particle addition operators commute with each other, but in general these operators need not be diagonalizable. We use their abelian algebra to determine their eigenvalues, and the Jordan block structure. These are then used to determine the probability of different configurations in the steady state. W...

Non-Fellerian processes show phenomena that are unseen in standard interacting particle systems. We consider freezing transitions in one-dimensional non-Fellerian processes which are built from the abelian sandpile additions to which in one case, spin flips are added, and in another case, the so called anti-sandpile subtractions. In the first case and as a function of the sandpile addition rate...

Abstract. We perform a statistical analysis of two onedimensional avalanching models: the bi-directional sandpile and the burning model (described in detail in the companion paper by Gedalin et al. (2005) “Dynamics of the burning model”). Such a comparison helps understand whether very limited measurements done by a remote observer may provide sufficient information to distinguish between the t...

A polynomial ideal encoding topplings in the abelian sandpile model on a graph is introduced. A Gröbner basis of this ideal is interpreted combinatorially in terms of well-connected subgraphs. This gives rise to algorithms to determine the identity and the operation in the group of recurrent configurations.

In this paper we prove that the general avalanche problem AP is in NC for the Kadanoff sandpile model in one dimension, answering an open problem of [2]. Thus adding one more item to the (slowly) growing list of dimension sensitive problems since in higher dimensions the problem is P-complete (for monotone sandpiles).

Proof: (R ⊂ κ(G, s)). Let I ⊂ M(G, s) be a nonempty ideal. Fix ψ ∈ I. Given σ ∈ R, there exists a sandpile φ such that σ = (φ + ψ)◦ by defintion. Since I is an ideal, this implies that σ ∈ I. Hence R ⊂ I. We conclude that R ⊂ ⋂ I ideal of M(G,s) I = κ(G, s). (κ(G, s) ⊂ R). Recall that R 6= ∅. Since κ(G, s) is the minimal ideal of M(G, s), it is enough to show that R is an ideal. Consider σ ∈ R ...

We consider a variation of the chip-firing game in an induced subgraph S of a graph G. Starting from a given chip configuration, if a vertex v has at least as many chips as its degree, we can fire v by sending one chip along each edge from v to its neighbors. Chips are removed at the boundary δS. The game continues until no vertex can be fired. We will give an upper bound, in terms of Dirichlet...

We regard the limit as p ! 1 of the ow governed by the p-Laplacian as providing a simplistic model for the \collapse of an initially unstable sandpile." Upon rescaling to stretch out the initial layer we obtain some simple dynamics and provide fairly explicit solutions in certain cases. In particular we note that such models entail \instanta-neous" mass transfer governed by Monge-Kantorovich th...