52
Automatic Construction of Synthetic Musical Instruments and Performers Ning Hu Ph.D. Thesis Proposal Carnegie Mellon University December 2004

Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

  • Upload
    halien

  • View
    217

  • Download
    1

Embed Size (px)

Citation preview

Page 1: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

Automatic Construction of Synthetic Musical Instruments and Performers

Ning Hu

Ph.D. Thesis Proposal

Carnegie Mellon UniversityDecember 2004

Page 2: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Thesis Committee• Roger B. Dannenberg, Chair• Michael S. Lewicki• Richard M. Stern• David Wessel (UC Berkeley)

Page 3: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Roadmap• Introduction• System Structure• Main Modules

• Audio Alignment and Segmentation• Instrument Model• Performance Model

• Schedule• Conclusion

Page 4: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Introduction• Define thesis topic• Thesis statement• Start with modeling the trumpet for

classical music• Contributions of the thesis• Criteria for success

Page 5: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Topic Definition• Title

Automatic Construction of Synthetic Musical Instruments and Performers

• Meaning• Framework that builds music synthesis

Page 6: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Topic Definition• Title

Automatic Construction of Synthetic Musical Instruments and Performers

• Meaning• Framework that builds music synthesis• Automatic construction

Page 7: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Topic Definition• Title

Automatic Construction of Synthetic Musical Instruments and Performers

• Meaning• Framework that builds music synthesis• Automatic construction• Instrument model

Page 8: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Topic Definition• Title

Automatic Construction of Synthetic Musical Instruments and Performers

• Meaning• Framework that builds music synthesis• Automatic construction• Instrument model• Performance model

Page 9: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Topic Definition• Title

Automatic Construction of Synthetic Musical Instruments and Performers

• Meaning• Framework that builds music synthesis

• High quality• High performance• Capable of modeling different instruments • Capable of modeling different music styles

Page 10: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Topic Definition• Title

Automatic Construction of Synthetic Musical Instruments and Performers

• Meaning• Automatic construction

• Use machine learningmachine learning techniques• Learn from performance examples• Constructs instrument model and

performance model

Page 11: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Topic Definition• Title

Automatic Construction of Synthetic Musical Instruments and Performers

• Meaning• Instrument model

• Similar to traditional concept of synthesis• Input: control signals• Output: synthesized sound samples

Page 12: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Topic Definition• Title

Automatic Construction of Synthetic Musical Instruments and Performers

• Meaning• Performance model

• Generating appropriate control signals from music context is crucial

• Drives instrument model• Input: digital score (music notation)• Output: control signals

Page 13: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Topic Definition• Title

Automatic Construction of Synthetic Musical Instruments and Performers

• Meaning• Framework that builds music synthesis• Automatic construction• Instrument model• Performance model

Page 14: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Thesis Statement• To create a system framework that

can automatically create high-quality musical instrument synthesis by using machine-learning techniques to construct the instrument model and the performance model by learning from the performance examples (acoustic recordings and their corresponding scores).

Page 15: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Start with Modeling…• Musical Instrument:

• Trumpet• Music Style:

• Classical Music

Page 16: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Reasons for Modeling the Trumpet (1)• Most wind instrument synthesizers

do not sound realistic• Conflict between:

• Working mechanisms of wind instruments• Driven by continuous energy exerted by player• Continuous control drives sound production

• Basic structure of synthesizers• Mostly sampling-based• Based on single, isolated notes• Do not offer a wide range of control

Page 17: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Reasons for Modeling the Trumpet (2)• Previous research

• By Dannenberg and Derenyi (1998)• Similar scheme• Produces convincing trumpet sound

Page 18: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Reasons for Modeling Classical Music• Characteristics of classical music

• “Purer” playing style• More faithful to the score• Fewer articulation effects

• Characteristics of non-classical music• Significant inharmonic & transient sounds• Need to model noise with a residual model

Page 19: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Contributions of the thesis• Use machine learning techniques • Automatically create high-quality

synthesis• The problem of control

• Problems of note-oriented synthesis• Problems of physical models• This approach simplifies the problem

Page 20: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Criteria for success• Minimum requirement

• Design, implement & test basic framework• Being able to synthesize realistic trumpet

performance for classical music• Automated modeling process• Tested on one or two wind instruments.

• Extra tasks• Extend system framework

• Model different musical instruments• Model different music styles

• Future work

Page 21: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Roadmap• Introduction• System Structure• Main Modules

• Audio Alignment and Segmentation• Instrument Model• Performance Model

• Schedule• Conclusion

Page 22: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

System Structure• Synthesis process• Pre-processing training data• Training process for instrument model• Training process for performance model

Page 23: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Synthesis Process

Performance Model

Instrument Model

Control Signals

Page 24: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Pre-processing training data

AutomaticAlignment &

Segmentation

Segmented Score

Segmented Audio

Page 25: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Training the Performance ModelSegmented

Score

Control Signals

Segmented Audio

Control Signals

Error

Compare

Parameter Extraction

Performance Model

Correspond

Page 26: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Training the Instrument Model

Spectra

Segmented Score

Control Signals

Segmented Audio

Parameter Extraction

Spectral Analysis

Correspond

Supervised Learning

Instrument Model

Page 27: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Roadmap• Introduction• System Structure• Main Modules

• Audio Alignment and Segmentation• Instrument Model• Performance Model

• Schedule• Conclusion

Page 28: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Audio Alignment• Find recording score• Polyphonic audio alignment

• Extract feature sequences from …• Acoustic recording• Score

• Find optimal alignment• Dynamic programming (DP) or Hidden

Markov Model (HMM)• Satisfactory results

Correspondence

Page 29: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Audio Segmentation (1)• Dannenberg, et. al., (1999) early work

• Define rules & thresholds• Use features: power; #peaks/period; #zero-

crossings/period• Not reliable and accurate enough

• Precise alignment = reliable segmentation• Require higher accuracy• Need further modification

Page 30: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Audio Segmentation (2)•Kapanci & Pfeffer’s (2004) work

•Segmentation problem Classification problem•Hierarchical machine-learning framework•Detect soft onset: compare frames separated by increasingly longer distances

Classification Modules

Page 31: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Roadmap• Introduction• System Structure• Main Modules

• Audio Alignment and Segmentation• Instrument Model• Performance Model

• Schedule• Conclusion

√√

Page 32: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Instrument Model

•Harmonic Model + Residual model

Instrument Model

Control Signal

Page 33: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Harmonic Model

• Control signals Spectra• Spectra Wavetables• Wavetables Sound samples

Interpo-lation

Spectrum Generation

Waveform Construction

Table 2

Table 1

Phase

×

×

×+Amplitude Control

Frequency Control

Page 34: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Control Signals Spectra• Spectral interpolation (Dannenberg, et. al., 1998)

• Memory-based approach (Wessel, et. al., 1998)

• Neural network (Wessel, et. al., 1998)

Page 35: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Spectral interpolation (Dannenberg, et. al., 1998)

• Generate Spectral lookup table• Record a set of sounds• Obtain a spectrogram for each sound• Retain specific spectra at thresholds

Amplitude

Frequency SyntheticSpectra

2D Interpolated Spectral Lookup Actual

Spectra

Page 36: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Memory-based approach (Wessel, et. al., 1998)

• Index spectra in a n dim. space• Interpolate among k nearest

neighbors• Special case

• Spectral interpolation technique• n=2 (frequency & amplitude)• k=4• Linear interpolation

Page 37: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Neural network (Wessel, et. al., 1998)•A feed-forward neural network with multiples layers•Input: frequency, amplitude•Output: info of sinusoidal components•Back-propagation learning method•Advantage: very compact & generalize well

Page 38: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Interpo-lation

Spectrum Generation

Waveform Construction

Table 2

Table 1

Phase

×

×

×+Amplitude Control

Frequency Control

Harmonic Model

•Control signals Spectra•Spectra Wavetables•Wavetables Sound samples

Page 39: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Residual Model• Modeling attacks

• Use recorded attacks• Phase matching

• For other instruments

Page 40: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Roadmap• Introduction• System Structure• Main Modules

• Audio Alignment and Segmentation• Instrument Model• Performance Model

• Schedule• Conclusion

√√√√

Page 41: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Performance Model

•Control signals•Amplitude envelope•Frequency envelope

•Error metrics•Envelope representation•Mapping scheme

Performance Model

Control Signal

Page 42: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Amplitude Envelope

•A tongued note

•A slurred note

*Figures borrowed from (Dannenberg, et. al., 1998)

Page 43: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Error Metrics

• Typical metric: RMS error• Recent work by (Horner et. al., 2004)

• Measure perceptual difference• Useful reference for error metrics

Acoustic and Synthetic Envelopes

Page 44: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Envelope Representation•Envelope representation

•Characteristics of amplitude envelope•Specific duration•Specific shape•Specific properties of each part

Page 45: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Ways to Represent Envelopes• Collection of general parameters

• Candidates: center of mass, global/local maximum/minimum, etc.

• Manual vs. automatic selection• Wavelets

• Hierarchical decomposing functions• Very powerful and popular

Page 46: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Mapping Scheme• Non-linear regression

• Find music context actual envelopes• Examples:

• Neural network• Kalman filters Xk = AXk-1 + Wk-1

• Function approximation

• Pattern clustering• Classify envelopes into clusters• For each input data point:

• Use corresponding representative envelope• Stretch, scale & interpolate accordingly

• Considered as a form of case-based reasoning

Page 47: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Roadmap• Introduction• System Structure• Main Modules

• Audio Alignment and Segmentation• Instrument Model• Performance Model

• Schedule• Conclusion

√√√√√√

Page 48: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Schedule (1)

Dec 2004 ~ May 2005 System Development

System integration and testingMay 2005

Design and implement performance modelMar 2005 ~ Apr 2005

Develop and compare instrument modelsFeb 2005

Incorporate SNDAN package to training data pre-processing stage

Jan 2005

Implement Audio Alignment & Segmentation module

Dec 2004 ~ Jan 2005

•Collect performance examples for initial experiments•Get familiar with SNDAN package•Read the original code by Dannenberg & Derenyi•Propose thesis topic

Oct 2004 ~ Nov 2004 (past) Thesis Proposal

Page 49: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Schedule (2)

Sep ~ Nov 2005 Writing Thesis

Jun ~ Aug 2005 System Evaluation & Tuning

Thesis defenseNov 2005

Thesis write-up and revisionsSep 2005 ~ Nov 2005

System and model evaluation and fine tuningAug 2005Synthesize other types of music Jul 2005Model other instrumentsJun 2005

Page 50: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Conclusion• Propose a scheme:

• automatically construct• high-quality instrument synthesis• by learning from performance examples

• Machine learning a crucial role. • Future work

• Modeling different instruments• Modeling different music styles• Make it work in real-time

Page 51: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Roadmap• Introduction• System Structure• Main Modules

• Audio Alignment and Segmentation• Instrument Model• Performance Model

• Schedule• Conclusion

√√√√√√

Page 52: Automatic Construction of Synthetic Musical …rbd/music/ninghu/thesis/ProposalSlides.pdfAutomatic Construction of Synthetic Musical Instruments and Performers NingHu Ph.D. Thesis

December 2004 Ning Hu’s Ph.D. Thesis Proposal

Thank You• Acknowledgements

• Roger B. Dannenberg• Istvan Derenyi• James Beauchamp (SNDAN)

• ContactNing Hu ([email protected])