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Big Omega Versus the Wild Functions*
"... The question of the desirable properties and proper definitions of the OrderofMagnitude symbols, in particular 0 and e, is addressed once more. The definitions proposed are chosen for complementary mathematical properties, rather than for similarity of form. L brmoDuCTioN The old order changeth, ..."
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The question of the desirable properties and proper definitions of the OrderofMagnitude symbols, in particular 0 and e, is addressed once more. The definitions proposed are chosen for complementary mathematical properties, rather than for similarity of form. L brmoDuCTioN The old order changeth, yielding place to new, And God Urals himself in many ways, Lest owe good custom should corrupt thc worldTennyson, The 14 Ih i f t h e K i n g. The issue of the proper definitions for the OrderofMagnitude symbols would appear to have been settled once and for all by Knuth in 111. At the end of an exhaustive discussion the subject is, the author feels, about "beaten to death". The purpose of this communication is to point out that there is life in the old dog yeti ' The dehlerations below Were prompted by surprise that, while proving a lower bound where the precise definitions mattered, matters % P ere n o t a s d e a r c u t a s o n e m i g h t a s s u m e t h
Big Oh, Big Omega, and Big Theta
"... We consider sequences f: N − → R or f: N − → N or sometimes functions f: R+ − → R. Here N denotes the positive integers, R the real numbers, and R+ the positive real numbers. For asymptotics, we are interested only in the behavior of f(n) for large values of n, so we need only that f be defined for ..."
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We consider sequences f: N − → R or f: N − → N or sometimes functions f: R+ − → R. Here N denotes the positive integers, R the real numbers, and R+ the positive real numbers. For asymptotics, we are interested only in the behavior of f(n) for large values of n, so we need only that f be defined for n> k for some k. Asymptotic Relations Often, but not always, we use the following relations in comparing functions f(n) and g(n) that both approach infinity as n approaches infinity. Here are two equivalent notations that say that f(n) grows more slowly than g(n): f(n) ≺ g(n) if and only if f(n) = o(g(n)) if and only if lim n→∞ f(n) g(n) = 0. The second notation, o(g(n)), is Landau’s “little oh ” notation. For example, if 0 < p < q and b> 1, log n ≺ np ≺ nq ≺ bn. Here is how we denote that f(n) and g(n) have the same rate of growth: f(n) ≍ g(n) if and only if f(n)  ≤ Cg(n)  and g(n)  ≤ Cf(n) for some C and all n> some k. A stronger relation says that “f(n) is asymptotic to g(n)”: f(n) ∼ g(n) if and only if lim n→∞ f(n) g(n) = 1. For example, n3 ≍ n3 and n3 ∼ n3
SIGACT News 18 Apr.June 1976 BIG OMICRON AND BIG OMEGA AND BIG THETA
"... Most of us have gotten accustomed to the idea of using the notation O(f(n)) to stand for any function whose magnitude is upperbounded by a constant times f(n) , for all large n. Sometimes we also need a corresponding notation for lowerbounded functions, i.e., those functions which are at least as ..."
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Most of us have gotten accustomed to the idea of using the notation O(f(n)) to stand for any function whose magnitude is upperbounded by a constant times f(n) , for all large n. Sometimes we also need a corresponding notation for lowerbounded functions, i.e., those functions which are at least as large as a constant times f(n) for all large n. Unfortunately ~ people have occasionally been using the Onotation for lower bounds, for example when they reject a particular sorting method "because its running time is O(n 2) " I have seen instances of this in print quite of tent and finally it has prompted me to sit down and write a Letter to the Editor about the situation. The classical literature does have a notation for functions that are bounded below, namely ~(f(n)). The most prominent appearance of this notation is in Titchmarsh's magnum opus on Riemann's zeta function [8], where he defines ~(f(n)) on p. 152 and devotes his entire Chapter 8 to " ~theorems". See also Karl Prachar's Primzahlverteilung [7], P. 245.
Personality in scientific and artistic creativity
 In R.J.Sternerg (Ed.), Handbook of human creativity
, 1999
"... Theory and research in both personality psychology and creativity share an essential commonality: emphasis on the uniqueness of the individual. Both disciplines also share an emphasis on temporal consistency and have a 50year history, and yet no quantitative review of the literature on the creative ..."
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Cited by 117 (0 self)
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and creativity have in common, and to show how the topic ofcreativity has been important to personality psychologists and can be to social psychologists. A common system of personality description was obtained by classifying trait terms or scales onto one of the FiveFactor Model (or Big Five) dimensions
Littleoh and Littleomega
"... g that any constant factor will eventually be overcome. Similarly, if h = !(f ), then h grows faster than f . We say that g is "littleoh" of f , and h is "littleomega" of f . Unlike BigOh and BigOmega, these two sets can be defined exactly in terms of limits. In particular, ..."
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g that any constant factor will eventually be overcome. Similarly, if h = !(f ), then h grows faster than f . We say that g is "littleoh" of f , and h is "littleomega" of f . Unlike BigOh and BigOmega, these two sets can be defined exactly in terms of limits. In particular
Big versus Little: Who will trip?
"... Abstract—Since the marginal cost of operating powerful monolithic single core systems has become prohibitive, horizontal scaling has become the defacto method for expanding computational power and maintaining acceptable levels of energy efficiency. While horizontal scaling is now the accepted mean ..."
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means, there is still a debate as to whether this should be done with ”big ” or ”little ” architectures. While this subject has typically been approached from the perspective of performance or power, we choose to analyze it in the light of reliability. In recent years reliability has joined performance
Simple Extractors for All MinEntropies and a New PseudoRandom Generator
"... We present a simple, selfcontained extractor construction that produces good extractors for all minentropies (minentropy measures the amount of randomness contained in a weak random source). Our construction is algebraic and builds on a new polynomialbased approach introduced by TaShma, Zuckerm ..."
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Cited by 111 (27 self)
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set generator with optimal seed length that outputs s\Omega (1) bits when given a function that requires circuits of size s (for any s). This implies a hardness versus randomness tradeoff for RP and BP P that is optimal (up to polynomial factors), solving an open problem raised by [14]. Our generators
Levels of personal agency: Individual variation in action identification
 Journal of Personality and Social Psychology
, 1989
"... This research examined individual differences in action identification level as measured by the Behavior Identification Form. Action identification theory holds that any action can be identified in many ways, ranging from lowlevel identities that specify how the action is performed to highlevel id ..."
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Cited by 104 (4 self)
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for the individual's overall competence in action, for the individual's inclination toward planful versus impulsive action and for the degree to which the individual's actions are organized by and reflected in the selfconcept. Some people think they can do big things. They set out to write a book
Mass Boom versus Big Bang: Einstein was right
 International Symposium n o V ”Frontiers in Fundamental Physics”. Hyderabad, India 2003. arXiv:physics 0302058
"... When considering possible time variations of fundamental physical constants one has to keep firm well established principles. Following this approach we keep firm the Action Principle, General Relativity (the Equivalence Principle), and Mach’s Principle. Also we introduce a new principle under the n ..."
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Cited by 1 (0 self)
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with time too. This is the cause of the red shift (it is an alternative to the expansion of the Universe interpretation, and explains the BIG BANG model approach as an apparent interpretation of the observers). The speed of light turns out to be decreasing also with time. An “absolute ” cosmological model
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