At the interface, we pioneered both matrix4,5,6 and tensor7,8 modeling of large-scale molecular biological data, which, as we demonstrated, can be used to correctly predict previously unknown physical,9,10,11 cellular,12,13,14,15,16 and evolutionary17,18 mechanisms that govern the activity of DNA and RNA.19,20,21
In mathematics, we developed the only framework that can create a single coherent model from multiple two-dimensional datasets, by extending the generalized singular value decomposition (GSVD) from two to more than two matrices.22,23,24
In genetics, our recent GSVD and tensor GSVD comparisons of the genomes of tumor and normal cells from the same sets of glioblastoma and lower-grade astrocytoma brain25,26,27 and, separately, ovarian28,29,30,31,32,33,34 cancer patients uncovered patterns of DNA copy-number alterations that were found to be correlated with a patient's survival and response to chemotherapy. For three decades prior, the best predictor of ovarian cancer survival was the tumor's stage; more than a quarter of ovarian tumors are resistant to the platinum-based chemotherapy, the first-line treatment, yet no diagnostic existed to distinguish resistant from sensitive tumors before the treatment. For five decades prior, the best prognostic indicator of glioblastoma was the patient's age at diagnosis. The ovarian and brain cancer data were published, but the patterns remained unknown until we applied our mathematical frameworks.
Currently, our work is supported by a five-year, three million-dollar National Cancer Institute (NCI) Physical Sciences in Oncology U01 project grant.35,36 Additional support for our work comes from the Utah Science, Technology, and Research (USTAR) Initiative.
- English, fluent.
- Hebrew, fluent.
- K. A. Aiello and O. Alter, "Platform-Independent Genome-Wide Pattern of DNA Copy-Number Alterations Predicting Astrocytoma Survival and Response to Treatment Revealed by the GSVD Formulated as a Comparative Spectral Decomposition," Public Library of Science (PLoS) One 11 (10), article e0164546 (October 2016); doi: 10.1371/journal.pone.0164546. Published, 10/2016.
- O. Alter, "DNA Copy-Number Alterations in Primary Ovarian Serous Cystadenocarcinoma Encoding for Cell Transformation and Predicting Survival and Response to Platinum Therapy Throughout the Course of the Disease," American Association for Cancer Research (AACR) Special Conference on Advances in Ovarian Cancer Research: Exploiting Vulnerabilities (Orlando, FL, October 17–20, 2015). Philadelphia, PA: AACR (January 2016); doi: 10.1158/1557-3265.OVCA15-A60. Published, 01/2016.
- P. Sankaranarayanan,* T. E. Schomay,* K. A. Aiello and O. Alter, "Tensor GSVD of Patient- and Platform-Matched Tumor and Normal DNA Copy-Number Profiles Uncovers Chromosome Arm-Wide Patterns of Tumor-Exclusive Platform-Consistent Alterations Encoding for Cell Transformation and Predicting Ovarian Cancer Survival," Public Library of Science (PLoS) One 10 (4), article e0121396 (April 2015); doi: 10.1371/journal.pone.0121396. Press Release: J. Kiefer, "New Method Increases Accuracy of Ovarian Cancer Prognosis and Diagnosis," American Association for the Advancement of Science (AAAS) EurekAlert! (April 15, 2015). Feature: R. Atkins, "Calculating Cancer Cures," National Academy of Engineering (NAE) Innovation Podcast and Radio Series (April 19, 2015).1 Feature: F. Pavlou, "Big Data, Hidden Knowledge," The Pathologist (June 15, 2015).2. Published, 04/2015.
- N. M. Bertagnolli, J. A. Drake, J. M. Tennessen and O. Alter, "SVD Identifies Transcript Length Distribution Functions from DNA Microarray Data and Reveals Evolutionary Forces Globally Affecting GBM Metabolism," Public Library of Science (PLoS) One 8 (11), article e78913 (November 2013); doi: 10.1371/journal.pone.0078913. Highlight. Published, 11/2013.
- C. H. Lee,* B. O. Alpert,* P. Sankaranarayanan and O. Alter, "GSVD Comparison of Patient-Matched Normal and Tumor aCGH Profiles Reveals Global Copy-Number Alterations Predicting Glioblastoma Multiforme Survival," Public Library of Science (PLoS) One 7 (1), article e30098 (January 2012); doi: 10.1371/journal.pone.0030098. Highlight. Published, 01/2012.
- S. P. Ponnapalli, M. A. Saunders, C. F. Van Loan and O. Alter, "A Higher-Order Generalized Singular Value Decomposition for Comparison of Global mRNA Expression from Multiple Organisms," Public Library of Science (PLoS) One 6 (12), article e28072 (December 2011); doi: 10.1371/journal.pone.0028072. Highlight. Published, 12/2011.
- C. Muralidhara, A. M. Gross, R. R. Gutell and O. Alter, "Tensor Decomposition Reveals Concurrent Evolutionary Convergences and Divergences and Correlations with Structural Motifs in Ribosomal RNA," Public Library of Science (PLoS) One 6 (4), article e18768 (April 2011); doi: 10.1371/journal.pone.0018768. Highlight. Published, 04/2011.
- L. Omberg, J. R. Meyerson, K. Kobayashi, L. S. Drury, J. F. X. Diffley and O. Alter, "Global Effects of DNA Replication and DNA Replication Origin Activity on Eukaryotic Gene Expression," Molecular Systems Biology (MSB) 5, article 312 (October 2009); doi: 10.1038/msb.2009.70. Review: M. Méchali, Faculty of 1000 recommendation 1728974 (February 2010). Highlight. Published, 10/2009.
- L. Omberg, G. H. Golub and O. Alter, "A Tensor Higher-Order Singular Value Decomposition for Integrative Analysis of DNA Microarray Data from Different Studies," Proceedings of the National Academy of Sciences (PNAS) USA104 (47), pp. 18371–18376 (November 2007); doi: 10.1073/pnas.0709146104. Published, 11/2007.
- O. Alter, "Genomic Signal Processing: From Matrix Algebra to Genetic Networks." In: M. J. Korenberg, editor, Microarray Data Analysis: Methods and Applications. Totowa, NJ: Humana Press, Methods in Molecular Biology, vol. 377, pp. 17–59 (May 2007); doi: 10.1007/978-1-59745-390-5_2. Published, 05/2007.
- O. Alter, "Discovery of Principles of Nature from Mathematical Modeling of DNA Microarray Data," Proceedings of the National Academy of Sciences (PNAS) USA 103 (44), pp. 16063–16064 (October 2006); doi: 10.1073/pnas.0607650103. Published, 10/2006.
- O. Alter and G. H. Golub, "Singular Value Decomposition of Genome-Scale mRNA Lengths Distribution Reveals Asymmetry in RNA Gel Electrophoresis Band Broadening," Proceedings of the National Academy of Sciences (PNAS) USA 103 (32), pp. 11828–11833 (August 2006); doi: 10.1073/pnas.0604756103. Published, 08/2006.
- S. P. Ponnapalli, G. H. Golub and O. Alter, "A Novel Higher-Order Generalized Singular Value Decomposition for Comparative Analysis of Multiple Genome-Scale Datasets," Workshop on Algorithms for Modern Massive Datasets (MMDS). Stanford, CA: Stanford University and Yahoo! Research (June 21–24, 2006). Published, 06/2006.
- O. Alter and G. H. Golub, "Reconstructing the Pathways of a Cellular System from Genome-Scale Signals by Using Matrix and Tensor Computations," Proceedings of the National Academy of Sciences (PNAS) USA 102 (49), pp. 17559–17564 (December 2005); doi: 10.1073/pnas.0509033102. Published, 12/2005.
- O. Alter and G. H. Golub, "Integrative Analysis of Genome-Scale Data by Using Pseudoinverse Projection Predicts Novel Correlation between DNA Replication and RNA Transcription," Proceedings of the National Academy of Sciences (PNAS) USA 101 (47), pp. 16577–16582 (November 2004); doi: 10.1073/pnas.0406767101. Published, 11/2004.
- O. Alter, G. H. Golub, P. O. Brown and D. Botstein, "Novel Genome-Scale Correlation between DNA Replication and RNA Transcription During the Cell Cycle in Yeast is Predicted by Data-Driven Models." In: M. P. Deutscher, S. Black, P. E. Boehmer, G. D'Urso, T. Fletcher, F. Huijing, A. Marshall, B. Pulverer, B. Renault, J. D. Rosenblatt, J. M. Slingerland and W. J. Whelan, editors, Miami Nature Biotechnology Winter Symposium: Cell Cycle, Chromosomes and Cancer. Miami Beach, FL: University of Miami School of Medicine, vol. 15 (January 31 – February 4, 2004).
- O. Alter, P. O. Brown and D. Botstein, "Generalized Singular Value Decomposition for Comparative Analysis of Genome-Scale Expression Datasets of Two Different Organisms," Proceedings of the National Academy of Sciences (PNAS) USA 100 (6), pp. 3351–3356 (March 2003); doi: 10.1073/pnas.0530258100. Feature: M. E. Kilmer and C. D. Moravitz Martin, "Decomposing a Tensor," SIAM News 37 (9), (November 2004). Feature: J. Wixon and J. Ashurst, "Genome Informatics," Computational Functional Genomics 4 (5), pp. 509–514 (October 2003). Published, 03/2003.
- T. Nielsen, R. B. West, S. C. Linn, O. Alter, M. A. Knowling, J. O'Connell, S. Zhu, M. Fero, G. Sherlock, J. R. Pollack, P. O. Brown, D. Botstein and M. van de Rijn, "Molecular Characterisation of Soft Tissue Tumours: a Gene Expression Study," Lancet 359 (9314), pp. 1301–1307 (April 2002); doi: 10.1016/S0140-6736(02)08270-3. Invited Commentary: L. Y. Dirix and A. T. van Oosterom, "Gene-Expression Profiling to Classify Soft-Tissue Sarcomas," Lancet 359 (9314), pp. 1263–1264 (April 2002). Published, 04/2002.
- O. Alter and Y. Yamamoto, Quantum Measurement of a Single System. New York, NY: Wiley-Interscience (May 2001), 136 pp.; doi: 10.1002/9783527617128. Ph.D. Dissertation Slides. Published, 05/2001.
- O. Alter, P. O. Brown and D. Botstein, "Processing and Modeling Genome-Wide Expression Data Using Singular Value Decomposition." In: M. L. Bittner, Y. Chen, A. N. Dorsel and E. R. Dougherty, editors, Microarrays: Optical Technologies and Informatics. Bellingham, WA: International Society for Optics and Photonics (SPIE), vol. 4266, pp. 171–186 (January 21, 2001); doi: 10.1117/12.427986. Published, 01/21/2001.
- O. Alter, P. O. Brown and D. Botstein, "Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling," Proceedings of the National Academy of Sciences (PNAS) USA 97 (18), pp. 10101–10106 (August 2000); doi: 10.1073/pnas.97.18.10101. Published, 08/2000.
- O. Alter and Y. Yamamoto, "Fundamental Quantum Limit to External Force Detection via Monitoring a Single Harmonic Oscillator or Free Mass," Physics Letters A 263 (4–6), pp. 226–231 (December 1999); doi: 10.1016/S0375-9601(99)00743-4. Published, 12/1999.
- O. Alter and Y. Yamamoto, "Impossibility of Determining the Unknown Wavefunction of a Single Quantum System: Quantum Non-Demolition Measurements, Measurements without Entanglement and Adiabatic Measurements," Fortschritte der Physik 46 (6–8), pp. 817–827 (November 1998). Published, 11/1998.
- O. Alter and Y. Yamamoto, "Reply to the Comment on 'Protective Measurement of the Wave Function of a Single Squeezed Harmonic Oscillator State,' " Physical Review A 56 (1), pp. 1057–1059 (July 1997); doi: 10.1103/PhysRevA.56.1057. Published, 07/1997.
- O. Alter and Y. Yamamoto, "Quantum Zeno Effect and the Impossibility of Determining the Quantum State of a Single System," Physical Review A Rapid Communications 55 (4), pp. R2499–R2502 (April 1997); doi: 10.1103/PhysRevA.55.R2499. Published, 04/1997.
- O. Alter and Y. Yamamoto, "Inhibition of the Measurement of the Wavefunction of a Single Quantum System and the Projection Postulate." In: M. Namiki, I. Ohba, K. Maeda and Y. Aizawa, editors, Quantum Physics, Chaos Theory and Cosmology. New York, NY: American Institute of Physics, pp. 151–172 (October 1996). Published, 10/1996.
- O. Alter and Y. Yamamoto, "The Quantum Zeno Effect of a Single System is Equivalent to the Indetermination of the Quantum State of a Single System. In: F. De Martini, G. Denardo and Y. Shih, editors, Quantum Interferometry. Weinheim, Germany: Wiley-VCH, pp. 539–544 (October 1996). Published, 10/1996.
- O. Alter and Y. Yamamoto, "Protective Measurement of the Wave Function of a Single Squeezed Harmonic Oscillator State," Physical Review A Rapid Communications 53 (5), R2911–R2914 (May 1996); doi: 10.1103/PhysRevA.53.R2911. Published, 05/1996.
- O. Alter and Y. Yamamoto, "The Unknown Wavefunction of a Single System Cannot Be Inferred Using Repeated Quantum Measurements." In: K. Fujikawa and Y. A. Ono, editors, Quantum Coherence and Decoherence. Amsterdam, Netherlands: Elsevier Science, pp. 31–34 (May 1996). Published, 05/1996.
- O. Alter and Y. Yamamoto, "Inhibition of the Measurement of the Wave Function of a Single Quantum System in Repeated Weak Quantum Nondemolition Measurements," Physical Review Letters 74 (21), pp. 4106–4109 (May 1995); doi: 10.1103/PhysRevLett.74.4106. Published, 05/1995.
- O. Alter and Y. Yamamoto, "Can We Measure the Wave Function of a Single Wave Packet of Light?: Brownian Motion and Continuous Wave Packet Collapse in Repeated Weak Quantum Non-Demolition Measurements." In: D. M. Greenberger and A. Zeilinger, editors, Fundamental Problems in Quantum Theory. New York, NY: New York Academy of Sciences, vol. 755, pp. 103–109 (April 1995). Published, 04/1995.