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Fast and precise independent component analysis for high field fMRI time series tailored using prior information on spatiotemporal structure

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HUMAN BRAIN MAPPING 2002年第1期15卷 54-66页

作者： Suzuki, K Kiryu, T Nakada, T Niigata Univ Brain Res Inst Dept Integrated Neurosci Niigata 9518585 Japan Niigata Univ Grad Sch Sci & Technol Niigata 95021 Japan Univ Calif Davis Dept Neurol Davis CA 95616 USA

Independent component analysis (ICA) has been shown as a promising tool for the analysis of functional magnetic resonance imaging (fMRI) time series. Each of these studies, however, used a general-purpose algorithm for performing ICA and the computational efficiency and accuracy of elicited neuronal activations have not been discussed in much detail. We have previously proposed a direct search method for improving computational efficiency. The method, which is based on independent component-cross correlation-sequential epoch (ICS) analysis, utilizes a form of the fixed-point ICA algorithm and considerably reduces the time required for extracting desired components. At the same time, it is shown that the accuracy of detecting physiologically meaningful components is much improved by tailoring the contrast function used in the algorithm. In this study, further improvement was made to this direct search method by integrating an optimal contrast function. Functional resolution of activation maps could be controlled with a suitable selection of the contrast function derived from prior knowledge of the spatial patterns of physiologically desired components. A simple skewness-weighted contrast function was verified to extract sufficiently precise activation maps from the fMRI time series acquired using a 3.0 Tesla MRI system. (C) 2001 Wiley-Liss, Inc.

关键词： fMRI independent component analysis fixed-point algorithm contrast function sequential epoch analysis overcomplete representation

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Optimal inclusion probabilities for balanced sampling

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2011年第2期141卷 984-994页

作者： Chauvet, G. Bonnery, D. Deville, J. -C. Ecole Natl Stat & Anal Informat F-35170 Bruz France

When auxiliary information is available at the design stage, samples may be selected by means of balanced sampling. The variance of the Horvitz-Thompson estimator is then reduced, since it is approximately given by that of the residuals of the variable of interest on the balancing variables. In this paper, a method for computing optimal inclusion probabilities for balanced sampling on given auxiliary variables is studied. We show that the method formerly suggested by Title and Favre (2005) enables the computation of inclusion probabilities that lead to a decrease in variance under some conditions on the set of balancing variables. A disadvantage is that the target optimal inclusion probabilities depend on the variable of interest. If the needed quantities are unknown at the design stage, we propose to use estimates instead (e.g., arising from a previous wave of the survey). A limited simulation study suggests that, under some conditions, our method performs better than the method of Title and Favre (2005). (C) 2010 Elsevier B.V. All rights reserved.

关键词： Balanced sampling Calibration Cube method fixed-point algorithm Variance approximation

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An Invitation to Pharmacostatics

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BULLETIN OF MATHEMATICAL BIOLOGY 2019年第9期81卷 3642-3654页

作者： Gnacadja, Gilles Amgen Inc San Francisco CA 94080 USA

Pharmacology, the study of interactions between biological processes and therapeutic agents, is traditionally presented as consisting of two subdisciplines: pharmacokinetics, which is about the distribution and metabolism of drugs in organisms, and pharmacodynamics, which is about the organisms' response to drugs. In discovery-stage pharmacology however, one primary concern is what we call pharmacostatics, the characterization of equilibrium parameters and states of core interactions of physiologic and therapeutic interest. This usually takes the form of studying dose-response curves, without consideration for the relevant qualitative properties of the underlying reaction networks, e.g., the existence, multiplicity and asymptotic stability of steady states. Furthermore, steady-state calculations customarily employ manually derived closed-form expressions based on approximating assumptions. While these formulas may seem adequate most of the time, the assumptions need not apply, and there are genuine though seemingly uncommon cases where this approach is not feasible and/or fails to explain non-monotone dose-response curves. It is this paper's aim to stimulate interest in mathematical problems arising in pharmacostatics. We specifically pose two problems about a particular relevant class of networks of reversible binding reactions. The first problem is to exploit a certain fixed-point formulation of the equilibrium equation to devise an algorithmic method that would be compellingly preferable to current practice in the pharmacostatics context. The second problem is to explicitly anticipate the possibility of non-monotone dose-response curves from network topology. Addressing these problems would positively impact biopharmaceutical research, and they have inherent mathematical interest.

关键词： Pharmacostatics Receptor pharmacology Non-monotone dose-response curve Equilibrium calculation Polynomial system solving fixed-point algorithm

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Compositions and convex combinations of averaged nonexpansive operators

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2015年第1期425卷 55-70页

作者： Combettes, Patrick L. Yamada, Isao Univ Paris 06 Sorbonne Univ Lab Jacques Louis Lions UMR 7598 F-75005 Paris France Tokyo Inst Technol Dept Commun & Comp Engn Tokyo 1528550 Japan

Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward backward splitting algorithm for finding a zero of the sum of two monotone operators is obtained. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Averaged operator fixed-point algorithm Forward-backward splitting Monotone operator Nonexpansive operator

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Real-time independent component analysis of fMRI time-series

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NEUROIMAGE 2003年第4期20卷 2209-2224页

作者： Esposito, F Seifritz, E Formisano, E Morrone, R Scarabino, T Tedeschi, G Cirillo, S Goebel, R Di Salle, F Univ Naples Federico II Dept Neurol Sci Poliklin Nouvo Policlin 2 I-80131 Naples Italy Univ Naples 2 Div Neurol 2 I-80138 Naples Italy Univ Basel Dept Psychiat CH-4025 Basel Switzerland Maastricht Univ Dept Cognit Neurosci NL-6200 MD Maastricht Netherlands Morrone Diagnost Ctr I-81100 Caserta Italy IRCCS Casa Sollievo Sofferenza Dept Neuroradiol I-71013 San Giovanni Rotondo Italy Univ Naples 2 Dept Neuroradiol I-80138 Naples Italy

Real-time functional magnetic resonance imaging fMRI) enables one to monitor a subject's brain activity during an ongoing session. The availability of online information about brain activity is essential for developing and refining interactive fMRI paradigms in research and clinical trials and for neurofeedback applications. Data analysis for real-time fMRI has traditionally been based on hypothesis-driven processing methods. Off-line data analysis, conversely, may be usefully complemented by data-driven approaches, such as independent component analysis (ICA), which can identify brain activity without a priori temporal assumptions on brain activity. However, ICA is commonly considered a time-consuming procedure and thus unsuitable to process the high flux of fMRI data while they are acquired. Here, by specific choices regarding the implementation, we exported the ICA framework and implemented it into real-time fMRI data analysis. We show that, reducing the ICA input to a few points within a time-series in a sliding-window approach, computational times become compatible with real-time settings. Our technique produced accurate dynamic readouts of brain activity as well as a precise spatiotemporal history of quasistationary patterns in the form of cumulative activation maps and time courses. Results from real and simulated motor activation data show comparable performances for the proposed ICA implementation and standard linear regression analysis applied either in a sliding-window or in a cumulative mode. Furthermore, we demonstrate the possibility of monitoring transient or unexpected neural activities and suggest that real-time ICA may provide the fMRI researcher with a better understanding and control of subjects' behaviors and performances. (C) 2003 Elsevier Inc. All rights reserved.

关键词： functional magnetic resonance imaging fMRI real-time analysis exploratory data-driven analysis descriptive statistics sliding-window analysis independent component analysis fixed-point algorithm receiver operating characteristics

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On the Hicksian laws of comparative statics for the Hicksian case: the path-following approach using an alternative homotopy

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Computational Economics 1998年第1期12卷 25-33页

作者： Shiomura, Takashi Faculty of Informatics Kansai University Takatsuki Osaka 569-11 Japan

The paper discusses an approach to comparative statics in the large by making use of a homotopy continuation method. This is based on the path-following approach presented by the author which is in turn due to the fixed-point algorithm explored by Garcia and Zangwill. We investigate from a global viewpoint the Hicksian laws of comparative statics for the Hicksian case which is a key to the first Hicksian law at least locally, and obtain the first Hicksian law in the large. Global results for the dominant diagonal case and the G1-Metzlerian case are also obtained.

关键词： comparative statics fixed-point algorithm homotopy.

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Interpretation and improvement of an iterative wavelet-based denoising method

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IEEE SIGNAL PROCESSING LETTERS 2003年第8期10卷 239-241页

作者： Ranta, R Heinrich, C Louis-Dorr, V Wolf, D CRAN UMR CNRS INPL 7039 F-54516 Vandoeuvre Les Nancy France Univ Strasbourg 1 UMR CNRS 7005 LSIIT F-67400 Illkirch Graffenstaden France

The goal of this letter is to shed new light on a wavelet-based denoising method developed by Hadjileontiadis et al, which is derived from an iterative denoising algorithm by Coifman and Wickerhauser. The underlying algorithm is revisited and interpreted as a fixed-point algorithm. This allows to derive a new version of the algorithm largely increasing computational efficiency.

关键词： denoising fixed-point algorithm orthogonal wavelet transform

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INFINITE RETROGRESSION IN THE EAVES-SAIGAL algorithm

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MATHEMATICAL PROGRAMMING 1980年第3期19卷 313-327页

作者： BROOKS, PS Stanford University Stanford CA USA

For certain functionsf fromRn toRn, the Eaves—Saigal algorithm computes a path inRn × (0, 1] which converges to a zero off. In this case, it is shown that even whenf is of classC∞ and has a unique zero, the con... 详细信息

关键词： Retrogressing Paths Homotopy Method fixed-point algorithm

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Improved fixed-point seismic inversion constrained by instantaneous phase

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2022年第PartB期215卷

作者： Pei, Song Yin, Xingyao Li, Kun China Univ Petr East China Sch Geosci Qingdao 266580 Peoples R China Pilot Natl Lab Marine Sci & Technol Qingdao Qingdao 266580 Peoples R China Shandong Prov Key Lab Deep Oil & Gas Qingdao 266580 Peoples R China

Some subtle reservoirs are hidden in the weak reflection areas and thin layers in seismic profiles, and they cannot be identified easily. Thus, the thin layer interpretation and the subtle reservoir prediction are the essential in reservoir management plan while field development and production stage. To improve the recognition capability in the weak reflection areas and resolution, the fixed-point (FP) algorithm is employed to obtain the inversion results since the conventional FP seismic inversion (CFPSI) is sensitive to the weak changes in seismic signals. However, the CFPSI suffers from low convergence. Therefore, the new iterative equations of pre-and post-stack FP seismic inversion are designed to improve the computational efficiency and convergence. Besides, a new constraint, which is derived from the instantaneous phase of the seismic trace, is also sensitive to the weak changes of the seismic signal. The instantaneous phase constraint is then involved in the objective function, contributing to a significant improvement of identification capability in weak reflection areas and the resolution of inversion. Additionally, the initial model constraint is introduced into the objective function to weaken the multi-solution and noise sensitivity. The synthetic examples demonstrate that the computational efficiency, recognition capability in the weak reflection areas and resolution of the proposed approach are higher than those of the CFPSI. The field examples suggest that the subtle reservoirs and thin layers, which are hidden in the weak reflection areas in the field data, are accurately identified using our method. Thus, the proposed method is useful for improving the recognition capability in weak reflection areas and resolution of the inversion results.

关键词： Seismic inversion fixed-point algorithm Instantaneous phase Resolution

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A method to build non-scattering perturbations of two-dimensional acoustic waveguides

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2017年第2期40卷 335-349页

作者： Bonnet-Ben Dhia, A. S. Luneville, E. Mbeutchaa, Y. Nazarov, S. A. CNRS INRIA ENSTA UMR 7231 POEMS 828 Blvd Marechaux F-91762 Palaiseau France St Petersburg State Univ Univ Pr 28 St Petersburg 198504 Russia St Petersburg State Polytechn Univ Polytechnicheskaya Ul 29 St Petersburg Russia

We are interested in finding deformations of the rigid wall of a two-dimensional acoustic waveguide, which are not detectable in the far field, as they produce neither reflection nor conversion of propagative modes. A proof of existence of such invisible deformations has been presented in a previous paper. It combines elements of the asymptotic analysis for small deformations and a fixed-point argument. In the present paper, we give a systematic presentation of the method, and we prove that it works for all frequencies except a discrete set. A particular attention is devoted to the practical implementation of the method. The main difficulty concerns the building of a dual family to given oscillating functions. Advantages and limits of the method are illustrated by several numerical results. Copyright (C) 2015 JohnWiley & Sons, Ltd.

关键词： waveguide modal analysis scattering matrix asymptotic analysis cloaking fixed-point algorithm

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