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Stephen Wolfram was born in London in 1959 to Hugo and Sybil Wolfram, both German Jewish refugees to the United Kingdom. [10] His maternal grandmother was British psychoanalyst Kate Friedlander . Wolfram's father, Hugo Wolfram , was a textile manufacturer and served as managing director of the Lurex Company—makers of the fabric Lurex . [ 11 ]
The basic subject of Wolfram's "new kind of science" is the study of simple abstract rules—essentially, elementary computer programs.In almost any class of a computational system, one very quickly finds instances of great complexity among its simplest cases (after a time series of multiple iterative loops, applying the same simple set of rules on itself, similar to a self-reinforcing cycle ...
In another style of hypergraph visualization, the subdivision model of hypergraph drawing, [25] the plane is subdivided into regions, each of which represents a single vertex of the hypergraph. The hyperedges of the hypergraph are represented by contiguous subsets of these regions, which may be indicated by coloring, by drawing outlines around ...
For instance, a hypergraph whose edges all have size k is called k-uniform. (A 2-uniform hypergraph is a graph). In hypergraph theory, it is often natural to require that hypergraphs be k-uniform. Every graph is the line graph of some hypergraph, but, given a fixed edge size k, not every graph is a line graph of some k-uniform hypergraph.
The idea demonstrates that there are occurrences where theory's predictions are effectively not possible. Wolfram states several phenomena are normally computationally irreducible [1]. Computational irreducibility explains why many natural systems are hard to predict or simulate.
A physicist considers whether artificial intelligence can fix science, regulation, and innovation.
Recall that a hypergraph H is a pair (V, E), where V is a set of vertices and E is a set of subsets of V called hyperedges.Each hyperedge may contain one or more vertices. A matching in H is a subset M of E, such that every two hyperedges e 1 and e 2 in M have an empty intersection (have no vertex in common).
The following results pertain to tripartite hypergraphs in which each of the 3 parts contains exactly n vertices, the degree of each vertex is exactly n, and the set of neighbors of every vertex is a matching (henceforth "n-tripartite-hypergraph"): Every n-tripartite-hypergraph has a matching of size 2n ⁄ 3. [16]