Multiscale methods and analysis for highly oscillatory differential equations
Multiscale methods and analysis for highly oscillatory differential equations
... MULTISCALE METHODS AND ANALYSIS FOR HIGHLY OSCILLATORY DIFFERENTIAL EQUATIONS ZHAO XIAOFEI (B.Sc., Beijing Normal University, China) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR ... that z− (s) = z+ (s) for ≤ s ≤ τ in (2.4.2) from (2.4.5) and (2.4.10), and (2.4.16) and (2.4.18) for MDF and MDFA, respectively Thus the multiscale decompositions MDF and MDFA and their numerical ... n), h and ε, such that |A| ≤ CB Chapter For highly oscillatory second order differential equations 2.1 Introduction This chapter considers the highly oscillatory second order differential equations...
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Báo cáo hóa học: "TERMINAL VALUE PROBLEM FOR SINGULAR ORDINARY DIFFERENTIAL EQUATIONS: THEORETICAL ANALYSIS AND NUMERICAL SIMULATIONS OF GROUND STATES" pdf
... Proof By the continuation of solutions and the singularity of at the point P0 , the set (P0 ) = ∅ Taking into account the nature of the vector field and the definition of the singularity of ... ,ρ0 ) ∈ E ⊆ ∂ω and the family ᐄ(P0 ) of all noncontinuable solutions of the initial value problem (2.6) By the continuity of the nonlinearity and the nature of the vector field (sign of f ), we have ... boundary value problems for higher-order linear differential equations with strong singularities, Boundary Value Problems 2006 (2006), Article ID 83910, 32 pages [2] J V Baxley, Boundary value problems...
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Advanced Methods and Tools for ECG Data Analysis - Part 1 ppt
... CHAPTER 11 Probabilistic Approaches to ECG Segmentation and Feature Extraction 2 91 11. 1 11 .2 11 .3 11 .4 11 .5 11 .6 11 .7 11 .8 Introduction The Electrocardiogram 11 .2 .1 The ECG Waveform 11 .2.2 ECG Interval ... References 10 6 10 8 10 9 11 0 11 1 11 3 11 4 11 5 11 6 11 7 12 6 12 7 CHAPTER Linear Filtering Methods 13 5 5 .1 Introduction 5.2 Wiener Filtering 5.3 Wavelet Filtering 5.3 .1 The Continuous Wavelet Transform 5.3.2 ... Component Analysis for Source Separation and Filtering 5.5 Summary and Conclusions References 13 5 13 6 14 0 14 1 14 2 14 4 14 8 14 9 15 1 15 7 16 7 16 7 CHAPTER Nonlinear Filtering Techniques 17 1 6 .1 Introduction...
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Advanced Methods and Tools for ECG Data Analysis - Part 2 doc
... Through 22 2 Omitted) Record Nn Vn Fn On Nv Vv Fv Ov No Vo Fo Q Se Q+P 100 101 103 105 106 108 22 3 22 8 23 0 23 1 23 2 23 3 23 4 Sum Gross Average 1901 1 521 1 725 21 17 123 6 1461 1736 122 5 1858 127 8 ... Chest, Vol 124 , No 6, 20 03, pp 20 57 20 63 P1: Shashi August 24 , 20 06 11:36 Chan-Horizon 2. 6 Summary [11] [ 12] [13] [14] [15] [16] [17] [18] [19] [20 ] [21 ] [22 ] [23 ] [24 ] [25 ] [26 ] [27 ] [28 ] Azuaje˙Book ... becoming the standard for ECGs); HL7 [26 , 27 ] (an XML-based format for the exchange of data in hospitals); and WaveForm DataBase (WFDB), a set of libraries developed at MIT [28 , 29 ] HL7 is by...
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Advanced Methods and Tools for ECG Data Analysis - Part 3 docx
... 24, 2006 11 :39 94 Chan-Horizon Azuaje˙Book ECG Statistics, Noise, Artifacts, and Missing Data [20] [21] [22] [ 23] [24] [25] [26] [27] [28] [29] [30 ] [31 ] [32 ] [33 ] [34 ] [35 ] [36 ] [37 ] Malik, M., ... Chan-Horizon Azuaje˙Book 3. 7 Heart Rate Variability 71 Figure 3. 8 Zero-mean unit-variance clean ECG with additive brown, pink, and white noise (also zero-mean and unit-variance, and hence SNR = in ... account for the increased dimensionality of the input feature space See Chapters 12 and 13 for further discussions of training, test, and validation data sets 3. 6 Noise and Artifact in the ECG 3. 6.1...
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Advanced Methods and Tools for ECG Data Analysis - Part 4 ppsx
... [32] [33] [ 34] [35] [36] [37] [38] [39] [40 ] [41 ] [42 ] [43 ] [44 ] [45 ] [46 ] [47 ] [48 ] [49 ] [50] [51] Azuaje˙Book 129 Mateo, J., and P Laguna, “Improved Heart Rate Variability Signal Analysis from ... http://www.physionet.org/physiotools/ecgsyn/ P1: Shashi August 24, 2006 11 :42 Chan-Horizon Azuaje˙Book 4. 3 ECG Models Figure 4. 5 119 Spectral characteristics of (4. 9), the RR interval generator for ECGSYN two Gaussian ... Shashi August 24, 2006 11 :42 Chan-Horizon 4. 3 ECG Models Azuaje˙Book 123 Figure 4. 8 Synthetic ECG signals for different mean heart rates: (a) 30 bpm, (b) 60 bpm, and (c) 120 bpm Table 4. 1 ensure...
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Advanced Methods and Tools for ECG Data Analysis - Part 5 pdf
... Azuaje˙Book 147 Figure 5. 6 Raw ECG with 50 Hz mains noise, IIR 50 -Hz notch filtered ECG, 0. 1- to 4 5- Hz bandpass filtered ECG and bior3.3 wavelet filtered ECG The left-most arrow indicates the low ... where s > α i=1 si and α is some fraction ≈ 0. 95 i=1 i P1: Shashi August 30, 2006 11 :5 Chan-Horizon Azuaje˙Book 150 Linear Filtering Methods Figure 5. 7 SVD of 20 R-peak-aligned P-QRS-T complexes: ... Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis, ” Proc R Soc Lond A, Vol 454 , 1998, pp 903–9 95 Huang, N E., and S S Shen, The Hilbert-Huang Transform and Its...
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Advanced Methods and Tools for ECG Data Analysis - Part 6 docx
... 20 06 11: 46 1 96 Chan-Horizon Azuaje˙Book Nonlinear Filtering Techniques [45] [ 46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [ 56] [57] [58] [59] [60 ] [61 ] [62 ] [63 ] [64 ] [65 ] Lehnertz, K., and ... 20 06 11: 46 Chan-Horizon 6. 5 Model-Based Filtering Azuaje˙Book 187 Figure 6. 6 Demonstration of ICA noise reduction for γ = 10: (a) original noise-free ECG signal, x(t); (b) χ -optimized noise-reduced ... 2003, pp 61 6 62 7 Pincus, S M., and A L Goldberger, “Physiological Time-Series Analysis: What Does Regularity Quantify?” Am J Physio Heart Circ Physiol., Vol 266 , 1994, pp H 164 3–H 165 6 Costa, M.,...
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Advanced Methods and Tools for ECG Data Analysis - Part 7 ppt
... r ( N) [%] [%] [%] 74 77 47 54 27 37 10 14 27 13 21 14 ⇑ 19 14 18 14 16 12 ST Segment Patterns, Human Annotator: r c ( N) r n ( N) r ( N) [%] [%] [%] 74 74 47 48 27 29 14 21 7 15 ⇑ 12 11 10 coefficients ... feature-vector time series in long-term ECGs for the purpose of ST segment analysis may involve following phases: Preprocessing; Derivation of time-domain and OFM transform-based diagnostic and ... which are visually informative and accessible for analysis at any time instant Therefore, a technique which converts such point event series into a form suitable for standard analysis techniques...
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Advanced Methods and Tools for ECG Data Analysis - Part 8 docx
... [ 18] , Neural net, KLT [g] [a] [g] [a] [g] [a] [g] [a] [g] [a] [g] [a] [g] [a] ESC DB S E [%] Se +P 81 76 84 81 – – 84 .7 86 .1 79.2 81 .4 81 .5 82 .5 85 .2 86 .2 87 .1 87 .7 77.2 86 .3 81 .3 89 .2 85 .0 68. 7 ... Chan-Horizon Azuaje˙Book 284 ST Analysis The open-source tool EVAL ST [45] provides first (record-by-record) and secondorder (aggregate gross and average) performance statistics for evaluation and ... Se +P Se +P – – – – – – – – – – – – – – – – – – – – – – – – 77.0 58. 8 48. 5 47 .8 74.0 61.4 54 .8 58. 4 79.6 78. 3 68. 4 67.3 78. 9 80 .7 73.1 74.9 – – – – – – – – – – – – – – – – The system from [7]...
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Advanced Methods and Tools for ECG Data Analysis - Part 9 ppsx
... 0.74E-2 1.46E-2 1.49E-2 1.47E-2 1.64E-2 1.72E-2 0.59E-2 Second-Order Cumulants 0.31E-2 0.60E-2 0 .94 E-2 0.67E-2 0.68E-2 0.52E-2 0.42E-2 Third-Order Cumulants 0.28E-2 1.03E-2 1.06E-2 0.85E-2 0.71E-2 ... 0.85E-2 0.71E-2 0.34E-2 0.40E-2 Fourth-Order Cumulants 0.24E-2 0.51E-2 0.55E-2 0.38E-2 0.54E-2 0.24E-2 0.60E-2 We have chosen the values of the cumulants of the second, third, and fourth orders ... to were used to form a seven-dimensional encoding for each ECG signal Table 11.2 shows the five-fold cross-validation results for HMMs trained on ECG waveforms from leads II and V2 which had...
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Advanced Methods and Tools for ECG Data Analysis - Part 10 pps
... and 13.15 The SOM Toolbox automatically selects the map size for each data set In this example: 23 × 16 neurons for the ECG beat data set, and 28 × neurons for the sleep apnea data set The U-matrices ... Learning for ECG Classification healthcare environment, ECG data are commonly stored and analyzed using different formats and software tools Thus, there is a need to develop cross-platform solutions ... support data analysis tasks and applications [64] A relevant solution consists of applying eXtensible Markup Language (XML) for representing ECG information ecgML [65], a markup language for ECG data...
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Báo cáo sinh học: "Analysis of the real EADGENE data set: Comparison of methods and guidelines for data normalisation and selection of differentially expressed genes (Open Access publication)" potx
... estimate of the background intensity, and therefore no further background correction was possible on these data Detection of differentially expressed genes 637 2.2 Normalisation of the data 2.2.1 Data ... Various comparisons of lists of differentially expressed genes found by the EADGENE teams were performed We focussed mainly on the comparison of the differentially expressed genes found between time and ... will be discussed: data quality control, normalisation and statistical methods for the detection of differentially expressed genes For each of these steps, the techniques used by the workshop participants...
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Báo cáo y học: "Statistical methods and software for the analysis of highthroughput reverse genetic assays using flow cytometry readouts" pps
... (99%) of the data from a negative control The gradual nature of these types of responses supports the use of regression analysis Because the effect may deviate from linearity in the range of perturbations ... cleaning up of the data, removal of systematic biases and drifts (a process often referred to as 'normalization'), and transformation to a format and scale that is suitable for the following analysis ... with the technical aspects of data import and management, and refer the interested reader to the documentation of the software package prada for a thorough discussion of these [19] Selection of...
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Báo cáo sinh học: "Assessment of methods and analysis of outcomes for comprehensive optimization of nucleofection" pptx
... first standardized by subtracting the mean of the data set from each data point and then dividing by the standard deviation of the data set Standardized and raw data for the secondary optimization ... assay Secondary Nucleofection Optimization A second nucleofection optimization was performed using SE reagent, which allowed the further evaluation of Page of (page number not for citation purposes) ... the 96-well shuttle system for any cell line Methods Initial Nucleofection Optimization Nucleofection was carried out using the Cell Line Optimization 96-well Nucleofector Kit from Amaxa http://...
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