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Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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an imaging experiment using an array of n C receiver coils. Fourier encoding is described by a set of n K sampling positions in kspace. Let the whole object be within the volume of interest (VOI). Then a sample value m obtained from the ␥th coil at the th position in kspace is given by where r denotes 3D
Polynomials
"... cos(φ − µ) ≈ 1 − (φ − µ) 2 /2 The circular Gaussian could be approximated by: g c 2(cos(x − µ) − 1) (φ; µ,λ) = exp[ λ 2 ≈ exp[− (φ − µ)2 λ 2] = g(φ; µ,λ) This means a circular Gaussian can be well approximated by a Gaussian. When φ ∈ [µ − π, µ + π] and λ < π/6, the relative error of this appr ..."
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Cited by 1 (0 self)
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cos(φ − µ) ≈ 1 − (φ − µ) 2 /2 The circular Gaussian could be approximated by: g c 2(cos(x − µ) − 1) (φ; µ,λ) = exp[ λ 2 ≈ exp[− (φ − µ)2 λ 2] = g(φ; µ,λ) This means a circular Gaussian can be well approximated by a Gaussian. When φ ∈ [µ − π, µ + π] and λ < π/6, the relative error
Subresultants and reduced polynomial remainder sequences
 J. ACM
, 1967
"... ABSTRACT. Let 9 be an integral domain, (9(9) the integral domain of polynomials over 9. L~ P, Q E (P(9) with m = deg (P) _> n = deg (Q)> 0. Let M be the matrix whose determina~ defines the resultant of P and Q. Let M~j be the submatrix of M obtained by deleting the la~ j rows of P coefficients ..."
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Cited by 86 (0 self)
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, P~, ' " " , P~, for k> _ 3, is called a reduced polynomial remainder sequence Some of the main results are: (1) P ~ 6 (P(9) for 1 < i < k; (2) P ~ ~ ±AkR,~_~~, whet A ~ =.t~,~,'Il~:L'~'~~(~~) ", (3) c~~lP ~ = ~A~+~R,~. ~, &
Target atmospheric CO2: where should humanity aim?
 Open Atmospheric Science Journal,
, 2008
"... Paleoclimate data show that climate sensitivity is ~3°C for doubled CO 2 , including only fast feedback processes. Equilibrium sensitivity, including slower surface albedo feedbacks, is ~6°C for doubled CO 2 for the range of climate states between glacial conditions and icefree Antarctica. Decreasi ..."
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Cited by 148 (6 self)
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made warming (4). Hansen et al. (5) argued for a limit of 1°C global warming (relative to 2000, 1.7°C relative to preindustrial time), aiming to avoid practically irreversible ice sheet and species loss. This 1°C limit, with nominal climate sensitivity of ¾°C per W/m 2 and plausible control of other GHGs (6
PolynomialTime Membership Comparable Sets
, 1994
"... This paper studies a notion called polynomialtime membership comparable sets. For a function g, a set A is polynomialtime gmembership comparable if there is a polynomialtime computable function f such that for any x 1 ; \Delta \Delta \Delta ; xm with m g(maxfjx 1 j; \Delta \Delta \Delta ; jx m j ..."
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Cited by 32 (5 self)
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jg), outputs b 2 f0; 1g m such that (A(x 1 ); \Delta \Delta \Delta ; A(xm )) 6= b. The following is a list of major results proven in the paper. 1. Polynomialtime membership comparable sets construct a proper hierarchy according to the bound on the number of arguments. 2. Polynomial
Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows
 SIAM J. Sci. Comput
"... this paper is to discuss the a posteriori error analysis and adaptive mesh design for discontinuous Galerkin finite element approximations to systems of conservation laws. In Section 2, we introduce the model problem and formulate its discontinuous Galerkin finite element approximation. Section 3 is ..."
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Cited by 122 (17 self)
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initial/boundary conditions. For example, assuming that B(u, y) := EiL1 biVu'(u) has m real eigenvalues and a complete set of linearly independent eigenvectors for all y = (yl,, Yn) C n; then at inflow/outflow boundaries, we require that B(u, n)(u g) = 0, where n denotes the unit outward normal
Chromatic Polynomials and Rings in Species
"... Abstract. We present a generalization of the chromatic polynomial, and chromatic symmetric function, arising in the study of combinatorial species. These invariants are defined for modules over lattice rings in species. The primary examples are graphs and set partitions. For these new invariants, we ..."
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Abstract. We present a generalization of the chromatic polynomial, and chromatic symmetric function, arising in the study of combinatorial species. These invariants are defined for modules over lattice rings in species. The primary examples are graphs and set partitions. For these new invariants
Two Strikes Against Perfect Phylogeny
 PROC. OF 19TH INTERNATIONAL COLLOQUIUM ON AUTOMATA LANGUAGES AND PROGRAMMING
, 1992
"... One of the major efforts in molecular biology is the computation of phylo genies for species sets. A longstanding open problem in this area is called the Perfect Phylogeny problem. For almost two decades the complexity of this problem remained open, with progress limited to polynomial time algor ..."
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Cited by 123 (28 self)
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One of the major efforts in molecular biology is the computation of phylo genies for species sets. A longstanding open problem in this area is called the Perfect Phylogeny problem. For almost two decades the complexity of this problem remained open, with progress limited to polynomial time
Biochemical limitations to carbon assimilation in C3 plants—A retrospective analysis of the A/Ci curves from 109 species
, 1993
"... Speciesspecific differences in the assimilation of atmospheric CO2 depends upon differences in the capacities for the biochemical reactions that regulate the gasexchange process. Quantifying these differences for more than a few species, however, has proven difficult. Therefore, to understand bett ..."
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Cited by 97 (3 self)
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utilization was used to analyse 164 previously published A/C, curves for 109 C3 plant species. Based on this analysis, the maximum rate of carboxylation, Vcmax, ranged from 6/umol m~2 s"1 for the coniferous species Picea abies to 194jj,mol m " 2 s"1 for the agricultural species Beta vulgaris
Results 1  10
of
3,590