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ASYMPTOTIC DENSITY AND THE COARSE COMPUTABILITY BOUND
"... Abstract. For r ∈ [0, 1] we say that a set A ⊆ ω is coarsely computable at density r if there is a computable set C such that {n: C(n) = A(n)} has lower density at least r. Let γ(A) = sup{r: A is coarsely computable at density r}. We study the interactions of these concepts with Turing reducibilit ..."
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Cited by 2 (2 self)
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Abstract. For r ∈ [0, 1] we say that a set A ⊆ ω is coarsely computable at density r if there is a computable set C such that {n: C(n) = A(n)} has lower density at least r. Let γ(A) = sup{r: A is coarsely computable at density r}. We study the interactions of these concepts with Turing
December,1991 ASYMPTOTIC DENSITY OF STATES
"... The asymptotic form of the density of states for a pbrane is computed (using the semiclassical approximation for the expression of the mass formula), and a value is found which only resembles the exponential growth of black holes in the formal limit p → ∞. Some physical consequences for the therm ..."
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The asymptotic form of the density of states for a pbrane is computed (using the semiclassical approximation for the expression of the mass formula), and a value is found which only resembles the exponential growth of black holes in the formal limit p → ∞. Some physical consequences
Asymptotic density for kalmost primes
, 2014
"... Landau’s well known asymptotic formula Nk(x): =  {n ≤ x: Ω(n) = k}  ∼ x log x (log log x)k−1 ..."
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Landau’s well known asymptotic formula Nk(x): =  {n ≤ x: Ω(n) = k}  ∼ x log x (log log x)k−1
Design of capacityapproaching irregular lowdensity paritycheck codes
 IEEE TRANS. INFORM. THEORY
, 2001
"... We design lowdensity paritycheck (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the unde ..."
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Cited by 588 (6 self)
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We design lowdensity paritycheck (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming
On the asymptotic densities of certain subsets of N k
 Concerned with sequences A000010, A001221, A005361, A008683, A018804, A047994, and A145388.) Received April 24 2009; revised version received June 22 2009. Published in Journal of Integer Sequences
"... We determine the asymptotic density δk of the set of ordered ktuples (n1,..., nk) ∈ N k, k ≥ 2, such that there exists no prime power p a, a ≥ 1, appearing in the canonical factorization of each ni, 1 ≤ i ≤ k, and deduce asymptotic formulae with error terms regarding this problem and analogous ones ..."
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Cited by 1 (1 self)
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We determine the asymptotic density δk of the set of ordered ktuples (n1,..., nk) ∈ N k, k ≥ 2, such that there exists no prime power p a, a ≥ 1, appearing in the canonical factorization of each ni, 1 ≤ i ≤ k, and deduce asymptotic formulae with error terms regarding this problem and analogous
THE ASYMPTOTIC DENSITY OF FINITEORDER ELEMENTS IN VIRTUALLY NILPOTENT GROUPS
, 2006
"... Abstract. Let Γ be a finitely generated group with a given word metric. The asymptotic density of elements in Γ that have a particular property P is the limit, as r → ∞, of the proportion of elements in the ball of radius r which have the property P. We obtain a formula to compute the asymptotic den ..."
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Cited by 1 (0 self)
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Abstract. Let Γ be a finitely generated group with a given word metric. The asymptotic density of elements in Γ that have a particular property P is the limit, as r → ∞, of the proportion of elements in the ball of radius r which have the property P. We obtain a formula to compute the asymptotic
On the Asymptotic Density of Tautologies in Logic of Implication and Negation
, 2003
"... The paper solves the problem of finding the asymptotic probability of the set of tautologies of classical logic with one propositional variable, implication and negation. We investigate the proportion of tautologies of the given length n among the number of all formulas of length n. We are espec ..."
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Cited by 15 (6 self)
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The paper solves the problem of finding the asymptotic probability of the set of tautologies of classical logic with one propositional variable, implication and negation. We investigate the proportion of tautologies of the given length n among the number of all formulas of length n. We
Least squares quantization in pcm.
 Bell Telephone Laboratories Paper
, 1982
"... AbstractIt has long been realized that in pulsecode modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as t ..."
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Cited by 1362 (0 self)
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as the number of quanta becomes infinite, the asymptotic fractional density of quanta per unit voltage should vary as the onethird power of the probability density per unit voltage of signal amplitudes. In this paper the corresponding result for any finite number of quanta is derived; that is, necessary
Asymptotic Density in a Coalescing Random Walk Model
, 1998
"... . We consider a system of particles, each of which performs a continuous time random walk on Z d . The particles interact only at times when a particle jumps to a site at which there are a number of other particles present. If there are j particles present, then the particle which just jumped is ..."
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Cited by 9 (2 self)
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. We consider a system of particles, each of which performs a continuous time random walk on Z d . The particles interact only at times when a particle jumps to a site at which there are a number of other particles present. If there are j particles present, then the particle which just jumped is removed from the system with probability p j . We show that if p j is increasing in j and if the dimension d is at least 6 and if we start with one particle at each site of Z d , then p(t) := P{there is at least one particle at the origin at time t} # C(d)/t. The constant C(d) is explicitly identified. We think the result holds for every dimension d # 3 and we briefly discuss which steps in our proof need to be sharpened to weaken our assumption d # 6. The proof is based on a justification of a certain mean field approximation for dp(t)/dt. The method seems applicable to many more models of coalescing and annihilating particles. 1991 Mathematics Subject Classification: 60K35, 82C22 ...
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