Anael VerdugoPhD Student 657 Rhodes Hall, Ithaca, NY 14953 607-255-3399 |
| Biography | Research | Publications | Teaching | CV |
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Academic Bio |
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| Ph.D. | 2009 Cornell University : Applied Mathematics [expected] |
| M.S. | 2007 Cornell University : Applied Mathematics |
| B.S. | 2003 California Institute of Technology : Mathematics |
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Research I am working with Dr. Richard H. Rand from the Theoretical and Applied Mechanics Department at Cornell. My research work involves using mathematical methods, such as perturbation and bifurcation theory, to study the dynamics of differential-delay equations (DDEs). These DDEs arise in many areas such as engineering and biology. One of the applications and purposes of my research is the dynamical study of biological models of gene expression. |
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Publications |
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| Refereed Journal Publications | |
| 5. | Bridge J., Mendelowitz L., Rand R., Sah S., Verdugo A., "Dynamics of a Ring of Three Coupled Relaxation Oscillators." Communications in Nonlinear Science and Numerical Simulation, doi:10.1016/j.cnsns.2008.05.012 (In Press) |
| 4. | Mendelowitz, L., Verdugo, A., and Rand, R. "Dynamics of Three Coupled Limit Cycle Oscillators with Application to Artificial Intelligence." Commun Nonlinear Sci Numer Simulat, doi:10.1016/j.cnsns.2007.08.009 (In Press) |
| 3. | Verdugo, A. and Rand, R. "Center Manifold Analysis of a DDE Model of Gene Expression." Comm Nonlinear Sci Numer Simulat, 13:1112-1120 (2008). |
| 2. | Verdugo, A. and Rand, R. "Hopf Bifurcation in a DDE Model of Gene Expression." Commun Nonlinear Sci Numer Simulat, 13:235-242 (2008). |
| 1. | Rand, R. and Verdugo, A. "Hopf Bifurcation Formula for First Order Differential-Delay Equations." Comm Nonlin Sci Numer Simul, 12:859-864 (2007) |
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Refereed Conference Proceedings |
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| 2. | Verdugo A. and Rand R. "DDE Model of Gene Expression: A Continuum Approach." Proceedings of the 2008 IMECE-ASME International Mechanical Engineering Congress, paper no. IMECE2008-66321 |
| 1. | Verdugo, A. and Rand, R. "Delay Differential Equations in the Dynamics of Gene Copying." Proceedings of the 2007 ASME International Design Engineering Technical Conferences, paper no. DETC2007-34214 (2007) |
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Papers Submitted |
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| Papers in Preparation | |
| * | Verdugo A. and Rand R. "Nonlinear Analysis of a Continuous Model of Gene Expression." In preparation |
| * | Verdugo A. and Rompala K. "Bifurcation Analysis of Two Repressilator Networks Coupled through Quorum-Sensing." In preparation |
| * | Ohlsson H., Wahi P., Kalmar-Nagy T., and Verdugo A. "Confirmation of Aschoff's Rule in a Delay Equation Model for Circadian Rhythm." In preparation |
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Teaching |
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| Fa 2008 |
Department of Mathematics, Cornell University |
| Head TA: Math 293 (Differential Equations) | |
| Sp 2008 |
Department of Mathematics, Cornell University |
| Teaching assistant: Math 293 (Differential Equations) | |
| Fa 2005 |
Department of Mathematics, Cornell University |
| Teaching assistant: Math 111 (Calculus I) and Math 112 (Calculus II) | |
| Fa 2004 |
Benjamin Franklyn High School |
| Instructor: Physics III & Physics IV | |
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Jose Vasconcelos High School |
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| Instructor: Calculus I & Calculus II | |
| Sp 2004 |
Department of Theoretical and Applied Mechanics, Cornell University |
| Grader: TAM 311 (Advanced Engineering Analysis II) | |
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CV
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Last revised: 08/25/08 |
