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A Musical Mnemonic for Logarithms of Small Integers
, 2004
"... When solving problems on the back of a napkin it is often useful to know approximate logarithms of small integers. Here we indicate a trick for working these out that requires only a little bit of musical knowledge. The overtone series is familiar to anyone who plays a musical instrument. In particu ..."
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When solving problems on the back of a napkin it is often useful to know approximate logarithms of small integers. Here we indicate a trick for working these out that requires only a little bit of musical knowledge. The overtone series is familiar to anyone who plays a musical instrument
A New Algorithm for Sorting Small Integers
, 2008
"... Abstract: This paper presents a new sorting algorithm called RAMISort algorithm. The RAMISort algorithm enhanced the time complexity of the best, average, and worst cases of many standard sorting algorithms, such as Quicksort, Cocktail sort, and Shell sort, when dealing with a large size of the in ..."
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of the input array especially when the integer values of the elements were small and distinct. The proposed algorithm and many standard sorting algorithms have been applied in a realworld case study simulation and compared. Keywords: RAMISort, enhanced sorting, small integers sorting, distinct elements
On comparing sums of square roots of small integers ∗ of
"... Let k and n be positive integers, n> k. Define r(n, k) to be the minimum positive value  √ a1 + · · · + √ ak − � b1 − · · · − � bk where a1, a2, · · · , ak, b1, b2, · · · , bk are positive integers no larger than n. It is an important problem in computational geometry to determin ..."
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Cited by 3 (1 self)
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Let k and n be positive integers, n> k. Define r(n, k) to be the minimum positive value  √ a1 + · · · + √ ak − � b1 − · · · − � bk where a1, a2, · · · , ak, b1, b2, · · · , bk are positive integers no larger than n. It is an important problem in computational geometry
Interval stabbing problems in small integer ranges
 in: Proc. 20th ISAAC, 2009
"... Given a set I of n intervals, a stabbing query consists of a point q and asks for all intervals in I that contain q. The Interval Stabbing Problem is to find a data structure that can handle stabbing queries efficiently. We propose a new, simple and optimal approach for different kinds of interval s ..."
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Cited by 4 (0 self)
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Given a set I of n intervals, a stabbing query consists of a point q and asks for all intervals in I that contain q. The Interval Stabbing Problem is to find a data structure that can handle stabbing queries efficiently. We propose a new, simple and optimal approach for different kinds of interval stabbing problems in a static setting where the query points and interval ends are in {1,..., O(n)}.
REPRESENTATION OF NUMBERS WITH NEGATIVE DIGITS AND MULTIPLICATION OF SMALL INTEGERS
, 1999
"... The usual way to multiply numbers in binary representation runs as follows: To compute mn, copy n to x. Multiply x by two. If the last digit of m is 1, then add n to x. Now delete the last digit of m. Repeat until m = 1, then x = mn. Since multiplication by 2 needs almost no time, the running time ..."
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that these algorithms have no meaning for most computations. Thus, faster multiplication of small numbers might speed up
Guide to Elliptic Curve Cryptography
, 2004
"... Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves ..."
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Cited by 596 (18 self)
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also figured prominently in the recent proof of Fermat's Last Theorem by Andrew Wiles. Originally pursued for purely aesthetic reasons, elliptic curves have recently been utilized in devising algorithms for factoring integers, primality proving, and in publickey cryptography. In this article, we
A comparison of event models for Naive Bayes text classification
, 1998
"... Recent work in text classification has used two different firstorder probabilistic models for classification, both of which make the naive Bayes assumption. Some use a multivariate Bernoulli model, that is, a Bayesian Network with no dependencies between words and binary word features (e.g. Larkey ..."
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Cited by 1007 (26 self)
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.g. Larkey and Croft 1996; Koller and Sahami 1997). Others use a multinomial model, that is, a unigram language model with integer word counts (e.g. Lewis and Gale 1994; Mitchell 1997). This paper aims to clarify the confusion by describing the differences and details of these two models, and by empirically
Distribution of inverses and multiples of small integers and the Sato–Tate conjecture on average
 Michigan Math. J
"... We show that, for sufficiently large integers m and X, for almost all a = 1,...,m the ratios a/x and the products ax, where x  � X, are very uniformly distributed in the residue ring modulo m. This extends some recent results of Garaev and Karatsuba. We apply this result to show that on average o ..."
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Cited by 10 (7 self)
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We show that, for sufficiently large integers m and X, for almost all a = 1,...,m the ratios a/x and the products ax, where x  � X, are very uniformly distributed in the residue ring modulo m. This extends some recent results of Garaev and Karatsuba. We apply this result to show that on average
On the minimum gap between sums of square roots of small integers I
"... Let k and n be positive integers, n> k. Define r(n, k) to be the minimum positive value of √a1 + · · ·+√ak − b1 − · · · − bk where a1, a2, · · · , ak, b1, b2, · · · , bk are positive integers no larger than n. Define R(n, k) to be − log r(n, k). It is important to find tight bounds fo ..."
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Let k and n be positive integers, n> k. Define r(n, k) to be the minimum positive value of √a1 + · · ·+√ak − b1 − · · · − bk where a1, a2, · · · , ak, b1, b2, · · · , bk are positive integers no larger than n. Define R(n, k) to be − log r(n, k). It is important to find tight bounds
Results 1  10
of
530,981