) programs are required to be self-delimiting, i.e. no program is a prefix of another, and (2) instead of being given C and D directly, one is given a program for calculating them that is minimal in size. Unlike previous definitions, this one has precisely the formal 2 G. J. Chaitin properties of the entropy

states of this system and shows how to construct entanglement-minimizing pure-state decompositions. PACS numbers: 03.65.Bz, 89.70.+c 1 Entanglement is the peculiar feature of quantum mechanics that allows, in principle, feats such as teleportation [1] and dense coding [2] and is what Schrödinger called

Abstract- A new measure of string complexity [3] for finite strings is presented based on a specific recursive hierarchical string production process (c.f. [2] ). From the maximal bound we deduce a relationship between complexity and total infor-mation content. Given an alphabet A and prefix

Abstract not found

. We present a method for accurately computing the metric entropy (or, equivalently, the Lyapunov exponent) of the absolutely continuous invariant measure for a piecewise analytic expanding Markov map of the interval. We construct atomic measures M supported on periodic orbits up to period M

In this paper we are interested in the maximisation problem for the quantum or non-quantum entropy functional (1.1) H(g):=

(1/g). Alternatively we can build a data structure of size Õ(n1/(1−ρ)) to answer queries in Õ(d) time. By applying this analysis to the locality pre-serving hash functions in [17, 21, 6] and adjusting the parameters we show that the c nearest neighbor can be computed in time Õ(nρ) and near linear

rmodynamically stable (LTS) if no local modi cation of it yields a state with lower speci c free energy. It can be shown that any GTS state is also LTS, but the converse is generally false. States that are LTS but not GTS are referred to as metastable states. An apt example comes from laser

Introduction One of the most promising directions in Knowledge Discovery in Databases (KDD) [4] is induction of decision rules. During the last two decades many methods e.g. AQ-family [9], CN2 [1] or C4.5 [10] were proposed. The advantages of the rule-based approach to KDD include natural

if f i (c) c: The initial word e 1 : : : e n of the kneading invariant will be denoted by K n (f ). Dene the cutting times [Bruin, 1995] as S 0 = 1 and S k = minfn > S k 1 ; e n 6= e n S k 1 g: Next let M(n) = (m i;j ) n i;j=2 be the n 1 n 1matrix given by m i;j = 8 > > >