Results 1  10
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4,467
Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 961 (11 self)
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polynomials feZ[X] into irreducible factors in Z[X]. Here we call f ~ Z[X] primitive if the greatest common divisor of its coefficients (the content of f) is 1. Our algorithm performs well in practice, cf. [8]. Its running time, measured in bit operations, is O(nl2+n9(log[fD3). Here f~Tl[X] is the polynomial
On the bursty evolution of Blogspace
, 2003
"... O)( 1 #$ #+&PQ+&,0,/RP 2 ":9:0/ +%&P &.F0, )& ;)S O)( 1 #$ #+&PQ+&,0,/RP 2 ":9:0/ +% # O,<&7& =1 P &7"U;(Z ;>A@CB;D,[\D]K,D?^_ B`Bba]@C>Ac >AG8H$^2d)@C]E 9='0,*+82 &e " & Q (T0 U;Ub%&7*',#$ %& :3 Q ..."
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Cited by 365 (8 self)
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O)( 1 #$ #+&PQ+&,0,/RP 2 ":9:0/ +%&P &.F0, )& ;)S O)( 1 #$ #+&PQ+&,0,/RP 2 ":9:0/ +% # O,<&7& =1 P &7"U;(Z ;>A@CB;D,[\D]K,D?^_ B`Bba]@C>Ac >AG8H$^2d)@C]E 9='0,*+82 &e " & Q (T0 U;Ub%&7*',#$ %& :3
Improved Localization of Cortical Activity by Combining EEG and MEG with MRI Cortical Surface Reconstruction: A Linear Approach
 J. Cogn. Neurosci
, 1993
"... We describe a comprehensive linear approach to the prob lem of imaging brain activity with high temporal as well as spatial resolution based on combining EEG and MEG data with anatomical constraints derived from MRI images. The "inverse problem" of estimating the distribution of dipole st ..."
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Cited by 263 (19 self)
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is recursively fiood4illed ,o determine the topology of the gray.white matter border, and (3) the resulting continuous surface is refinc by relaxing it against the original 3D grayscale image using a deformable template method, which is also used to computationally flatten the cortex for k'asier vic
Generalization Of An Inequality By Talagrand, And Links With The Logarithmic Sobolev Inequality
 J. Funct. Anal
, 2000
"... . We show that transport inequalities, similar to the one derived by Talagrand [30] for the Gaussian measure, are implied by logarithmic Sobolev inequalities. Conversely, Talagrand's inequality implies a logarithmic Sobolev inequality if the density of the measure is approximately logconcave, ..."
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Cited by 244 (12 self)
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distance d(x; y) = inf 8 < : s Z 1 0 j _ w(t)j 2 dt; w 2 C 1 ((0; 1); M); w(0) = x; w(1) = y 9 ...
RNA polymerase III transcribes human microRNAs.
 Nature Struct. Mol. Biol.
, 2006
"... Prior work demonstrates that mammalian microRNA (miRNA or miR) expression requires RNA polymerase II (Pol II). However, the transcriptional requirements of many miRNAs remain untested. Our genomic analysis of miRNAs in the human chromosome 19 miRNA cluster (C19MC) revealed that they are intersperse ..."
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Cited by 201 (3 self)
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how the C19MC miRNAs are expressed, we used one of these miRNAs, miR517a, and sequences immediately upstream, which consist of an Alu We next made reporter constructs to test whether the hairpins expressed from the miR517a 5¢ Alu had silencing activity. These reporters (517AS and LacZAS) produced
Adaptive Optimization in the Jalapeno JVM
 In ACM SIGPLAN Conference on ObjectOriented Programming Systems, Languages, and Applications (OOPSLA
, 2000
"... (*58()9$"2#$:0/,;58(03<10/2,>=?33@">"29 #A:0*/,B58(*C2"258/052,D3*>#$,,6*0'/ 58@F,058*,+HG?!"*0"I"252J58K0/ ,6*0'/ 030"6N*IO40"58DP)"58QF,058SRUT6252,D<0!2T6252,V52!8("9 "W5X3,06*9E,'Y58(*03C:0'/ X3,06 ..."
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Cited by 181 (14 self)
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(*58()9$"2#$:0/,;58(03<10/2,>=?33@">"29 #A:0*/,B58(*C2"258/052,D3*>#$,,6*0'/ 58@F,058*,+HG?!"*0"I"252J58K0/ ,6*0'/ 030"6N*IO40"58DP)"58QF,058SRUT6252,D<0!2T6252,V52!8("9 "W5X3,06*9E,'Y58(*03C:0'/ X3,06*9
The eigenvalues of random symmetric matrices
 Combinatorica
, 1981
"... Let A:(at;) be an zxn matrix whose entries for i=j are independent random variables and ai;:aii. Suppose that every a;; is bounded and for eveÍy i>j we have Eaii:!, D2ai,:62 and Eaiiv. E. P. Wigner determined the asymptotic behavior of the eigenvalues of I (semicircle law). In particular, for a ..."
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Cited by 179 (0 self)
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, for any c>2a with probability I o (1) all eigenvalues except for at most o (n) lie in the interval t:(_,Íi ' ci). We show that with probability 1o(1) a/ / eigenvalues belong to the above interval 1if p:0, while in case p=0 only the largest eigenvalue,lt is outside /, and n,: , Zl.iaii &apos
Abyssal recipes
 DeepSea Res
, 1966
"... AbstractVertical distributions in the interior Pacific (excluding tbe top and bottom kilometer) are not inzonsistent with a simple model involving aconstant upward vertical velozity w ~ 12 cm clu yt and eddy diffusivity, ¢ ~ 1.3 cm ~ sec1. Thus temperature and salinity can be fitted by expone ..."
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Cited by 175 (0 self)
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consumption is computed at 0004 (ml/I) yearL The vertical distributions of7', S, t4C and O: are consistent with the corresponding southnorth gradients in the deep Pacific, provided there is an average northward rift of at least a few millimetres per second. How can one meaningfully interpret
FILTERED HIRSCH ALGEBRAS
, 707
"... Abstract. Motivated by the cohomology theory of loop spaces we consider a concept of a special class of higher order homotopy commutative differential graded algebras. For such algebras the socalled filtered Hirsch model is constructed. As an application we converse a theorem of Borel by proving th ..."
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Cited by 1 (1 self)
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Abstract. Motivated by the cohomology theory of loop spaces we consider a concept of a special class of higher order homotopy commutative differential graded algebras. For such algebras the socalled filtered Hirsch model is constructed. As an application we converse a theorem of Borel by proving
Beyond Hirsch conjecture: Walks on random polytopes and smoothed complexity of the simplex method
 In Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
, 2006
"... Abstract. The smoothed analysis of algorithms is concerned with the expected running time of an algorithm under slight random perturbations of arbitrary inputs. Spielman and Teng proved that the shadowvertex simplex method has polynomial smoothed complexity. On a slight random perturbation of an ar ..."
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Cited by 24 (2 self)
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polylogarithmic in the number of constraints n. SpielmanTeng’s bound on the walk was O ∗ (n 86 d 55 σ −30), up to logarithmic factors. We improve this to O(log 7 n(d 9 + d 3 σ −4)). This shows that the tight Hirsch conjecture n − d on the length of walk on polytopes is not a limitation for the smoothed Linear
Results 1  10
of
4,467