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The fundamental properties of natural numbers
 Journal of Formalized Mathematics
, 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
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Cited by 682 (76 self)
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.html The articles [4], [6], [1], [2], [5], and [3] provide the notation and terminology for this paper. A natural number is an element of N. For simplicity, we use the following convention: x is a real number, k, l, m, n are natural numbers, h, i, j are natural numbers, and X is a subset of R
Construction of Escherichia coli K12 inframe, singlegene knockout mutants: the Keio collection. Mol. Syst. Biol 2:2006.0008
, 2006
"... We have systematically made a set of precisely defined, singlegene deletions of all nonessential genes in Escherichia coli K12. Openreading frame coding regions were replaced with a kanamycin cassette flanked by FLP recognition target sites by using a onestep method for inactivation of chromosom ..."
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Cited by 701 (7 self)
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We have systematically made a set of precisely defined, singlegene deletions of all nonessential genes in Escherichia coli K12. Openreading frame coding regions were replaced with a kanamycin cassette flanked by FLP recognition target sites by using a onestep method for inactivation
The Viterbi algorithm
 Proceedings of the IEEE
, 1973
"... vol. 6, no. 8, pp. 211220, 1951. [7] J. L. Anderson and J. W..Ryon, “Electromagnetic radiation in accelerated systems, ” Phys. Rev., vol. 181, pp. 17651775, 1969. [8] C. V. Heer, “Resonant frequencies of an electromagnetic cavity in an accelerated system of reference, ” Phys. Reu., vol. 134, pp. A ..."
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Cited by 985 (3 self)
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vol. 6, no. 8, pp. 211220, 1951. [7] J. L. Anderson and J. W..Ryon, “Electromagnetic radiation in accelerated systems, ” Phys. Rev., vol. 181, pp. 17651775, 1969. [8] C. V. Heer, “Resonant frequencies of an electromagnetic cavity in an accelerated system of reference, ” Phys. Reu., vol. 134, pp
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k
Directional Statistics and Shape Analysis
, 1995
"... There have been various developments in shape analysis in the last decade. We describe here some relationships of shape analysis with directional statistics. For shape, rotations are to be integrated out or to be optimized over whilst they are the basis for directional statistics. However, various c ..."
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Cited by 775 (31 self)
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to shape analysis. Note that the idea of using tangent space for analysis is common to both manifold as well. 1 Introduction Consider shapes of configurations of points in Euclidean space. There are various contexts in which k labelled points (or "landmarks") x 1 ; :::; x k in IR m are given
A Framework for Uplink Power Control in Cellular Radio Systems
 IEEE Journal on Selected Areas in Communications
, 1996
"... In cellular wireless communication systems, transmitted power is regulated to provide each user an acceptable connection by limiting the interference caused by other users. Several models have been considered including: (1) fixed base station assignment where the assignment of users to base stations ..."
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Cited by 636 (18 self)
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power control problem can be reduced to finding a vector p of users' transmitter powers satisfying p I(p) where the jth constraint p j I j (p) describes the interference that user j must overcome to achieve an acceptable connection. This work unifies results found for these systems
The ratedistortion function for source coding with side information at the decoder
 IEEE Trans. Inform. Theory
, 1976
"... AbstractLet {(X,, Y,J}r = 1 be a sequence of independent drawings of a pair of dependent random variables X, Y. Let us say that X takes values in the finite set 6. It is desired to encode the sequence {X,} in blocks of length n into a binary stream*of rate R, which can in turn be decoded as a seque ..."
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Cited by 1055 (1 self)
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sequence { 2k}, where zk E %, the reproduction alphabet. The average distorjion level is (l/n) cl = 1 E[D(X,,z&, where D(x, $ 2 0, x E I, 2 E J, is a preassigned distortion measure. The special assumption made here is that the decoder has access to the side information {Yk}. In this paper we determine
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
Protecting respondents’ identities in microdata release
 In IEEE Transactions on Knowledge and Data Engineering (TKDE
, 2001
"... Today’s globally networked society places great demand on the dissemination and sharing of information. While in the past released information was mostly in tabular and statistical form, many situations call today for the release of specific data (microdata). In order to protect the anonymity of the ..."
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Cited by 503 (32 self)
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. The approach is based on the definition of kanonymity. A table provides kanonymity if attempts to link explicitly identifying information to its content map the information to at least k entities. We illustrate how kanonymity can be provided without compromising the integrity (or truthfulness
Lag length selection and the construction of unit root tests with good size and power
 Econometrica
, 2001
"... It is widely known that when there are errors with a movingaverage root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We conside ..."
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Cited by 534 (14 self)
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It is widely known that when there are errors with a movingaverage root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We
Results 1  10
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3,534,685