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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 ...
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.
A physicist considers whether artificial intelligence can fix science, regulation, and innovation.
An undirected hypergraph (,) is an undirected graph whose edges connect not just two vertices, but an arbitrary number. [2] An undirected ...
Wolfram states several phenomena are normally computationally irreducible [1]. Computational irreducibility explains why many natural systems are hard to predict or simulate. The Principle of Computational Equivalence implies these systems are as computationally powerful as any designed computer.
On May 14, 2007, Wolfram announced a $25,000 prize to be won by the first person to prove or disprove the universality of the (2,3) Turing machine. [2] On 24 October 2007, it was announced that the prize had been won by Alex Smith, a student in electronics and computing at the University of Birmingham , for his proof that it was universal.
Very informally, the hypergraph regularity lemma decomposes any given -uniform hypergraph into a random-like object with bounded parts (with an appropriate boundedness and randomness notions) that is usually easier to work with. On the other hand, the hypergraph counting lemma estimates the number of hypergraphs of a given isomorphism class in ...