837 research outputs found

    The vanishing ideal of a finite set of points with multiplicity structures

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    Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method discloses the essential geometric connection between the relative position of the points with multiplicity structures and the quotient basis of the vanishing ideal, so we will explicitly know the set of leading terms of elements of I. We split the problem into several smaller ones which can be solved by induction over variables and then use our new algorithm for intersection of ideals to compute the result of the original problem. The new algorithm for intersection of ideals is mainly based on the Extended Euclidean Algorithm.Comment: 12 pages,12 figures,ASCM 201

    Critical Susceptibility Exponent Measured from Fe/W(110) Bilayers

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    The critical phase transition in ferromagnetic ultrathin Fe/W(110) films has been studied using the magnetic ac susceptibility. A statistically objective, unconstrained fitting of the susceptibility is used to extract values for the critical exponent (gamma), the critical temperature Tc, the critical amplitude (chi_o) and the range of temperature that exhibits power-law behaviour. A fitting algorithm was used to simultaneously minimize the statistical variance of a power law fit to individual experimental measurements of chi(T). This avoids systematic errors and generates objective fitting results. An ensemble of 25 measurements on many different films are analyzed. Those which permit an extended fitting range in reduced temperature lower than approximately .00475 give an average value gamma=1.76+-0.01. Bilayer films give a weighted average value of gamma = 1.75+-0.02. These results are in agreement with the -dimensional Ising exponent gamma= 7/4. Measurements that do not exhibit power-law scaling as close to Tc (especially films of thickness 1.75ML) show a value of gamma higher than the Ising value. Several possibilities are considered to account for this behaviour.Comment: -Submitted to Phys. Rev. B -Revtex4 Format -6 postscript figure

    Health knowledge among the millennial generation

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    The Millennial Generation, also known as Generation Y, is the demographic cohort following Generation X, and is generally regarded to be composed of those individuals born between 1980 and 2000. They are the first to grow up in an environment where health-related information is widely available by internet, TV and other electronic media, yet we know very little about the scope of their health knowledge. This study was undertaken to quantify two domains of clinically relevant health knowledge: factual content and ability to solve health related questions (application) in nine clinically related medical areas. Study subjects correctly answered, on average, 75% of health application questions but only 54% of health content questions. Since students were better able to correctly answer questions dealing with applications compared to those on factual content contemporary US high school students may not use traditional hierarchical learning models in acquisition of their health knowledge

    Knowledge-based gene expression classification via matrix factorization

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    Motivation: Modern machine learning methods based on matrix decomposition techniques, like independent component analysis (ICA) or non-negative matrix factorization (NMF), provide new and efficient analysis tools which are currently explored to analyze gene expression profiles. These exploratory feature extraction techniques yield expression modes (ICA) or metagenes (NMF). These extracted features are considered indicative of underlying regulatory processes. They can as well be applied to the classification of gene expression datasets by grouping samples into different categories for diagnostic purposes or group genes into functional categories for further investigation of related metabolic pathways and regulatory networks. Results: In this study we focus on unsupervised matrix factorization techniques and apply ICA and sparse NMF to microarray datasets. The latter monitor the gene expression levels of human peripheral blood cells during differentiation from monocytes to macrophages. We show that these tools are able to identify relevant signatures in the deduced component matrices and extract informative sets of marker genes from these gene expression profiles. The methods rely on the joint discriminative power of a set of marker genes rather than on single marker genes. With these sets of marker genes, corroborated by leave-one-out or random forest cross-validation, the datasets could easily be classified into related diagnostic categories. The latter correspond to either monocytes versus macrophages or healthy vs Niemann Pick C disease patients.Siemens AG, MunichDFG (Graduate College 638)DAAD (PPP Luso - Alem˜a and PPP Hispano - Alemanas

    Semidefinite Characterization and Computation of Real Radical Ideals

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    For an ideal IR[x]I\subseteq\mathbb{R}[x] given by a set of generators, a new semidefinite characterization of its real radical I(VR(I))I(V_\mathbb{R}(I)) is presented, provided it is zero-dimensional (even if II is not). Moreover we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety VR(I)V_\mathbb{R}(I) as well as a set of generators of the real radical ideal. The latter is obtained in the form of a border or Gr\"obner basis. The algorithm is based on moment relaxations and, in contrast to other existing methods, it exploits the real algebraic nature of the problem right from the beginning and avoids the computation of complex components.Comment: 41 page

    Interweaving PFASST and Parallel Multigrid

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    The parallel full approximation scheme in space and time (PFASST) introduced by Emmett and Minion in 2012 is an iterative strategy for the temporal parallelization of ODEs and discretized PDEs. As the name suggests, PFASST is similar in spirit to a space-time full approximation scheme multigrid method performed over multiple time steps in parallel. However, since the original focus of PFASST was on the performance of the method in terms of time parallelism, the solution of any spatial system arising from the use of implicit or semi-implicit temporal methods within PFASST have simply been assumed to be solved to some desired accuracy completely at each substep and each iteration by some unspecified procedure. It hence is natural to investigate how iterative solvers in the spatial dimensions can be interwoven with the PFASST iterations and whether this strategy leads to a more efficient overall approach. This paper presents an initial investigation on the relative performance of different strategies for coupling PFASST iterations with multigrid methods for the implicit treatment of diffusion terms in PDEs. In particular, we compare full accuracy multigrid solves at each substep with a small fixed number of multigrid V-cycles. This reduces the cost of each PFASST iteration at the possible expense of a corresponding increase in the number of PFASST iterations needed for convergence. Parallel efficiency of the resulting methods is explored through numerical examples