FUTURETEK: 2007

Liu, Liping

1. with Thomas and Dowell, Higher order harmonic balance analysis for limit cycle oscillations in an airfoil with cubic restoring forces, Journal of Fluids and Structures, vol. 23 no. 3 (2007) .
2. with Dowell and Hall, A novel harmonic balance analysis for the Van der Pol oscillator, Special Issue of International Journal of Nonlinear Mechanics (September, 2006) .
3. with Mei and Wong, Asymptotic behavior of solutions to Rosenau-Burgers equation with periodic boundary, Journal of Nonlinear Analysis (August, 2006) .
4. with Mei and Wong, Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (II) Convergence (June, 2006) .
5. with Mei and Wong, Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (I) Existence and uniform boundedness, Journal of Discrete and Continuous Dynamical Systems (June, 2006) .
6. with Lee, Bifurcation of an airfoil in subsonic flow with coupled cubic restoring forces, Journal of Aircraft, vol. 43 no. 3 (2006), pp. 652-659 .
7. with Dowell, Thomas, Attar and Hall, A comparison of two harmonic balance approaches for Duffing’s oscillators: classical and high dimensional, Journal of Computational Physics, vol. 215 no. 1 (2006), pp. 298-320 .

Lucas, Timothy

1. T. Lucas, Operator Splitting for an Immunology Model Using Reaction-Diffusion Equations with Stochastic Source Terms (Fall, 2007) (Submitted.) [abs] [author's comments].

Maggioni, Mauro

1. James C Bremer and Ronald R Coifman and Mauro Maggioni and Arthur D Szlam, Diffusion Wavelet Packets, Tech. Rep. YALE/DCS/TR-1304, Yale Univ. 2004, Appl. Comp. Harm. Anal., vol. 21 no. 1 (2006), pp. 95--112 .
2. Ronald R Coifman and Mauro Maggioni, Diffusion Wavelets, Appl. Comp. Harm. Anal., vol. 21 no. 1 (2006), pp. 53--94 .
3. Ronald R. Coifman and Stephane Lafon and Mauro Maggioni and Yosi Keller and Arthur D. Szlam and Frederick J. Warner and Steven W. Zucker, Geometries of sensor outputs, inference, and information processing, in Proc. SPIE, edited by Intelligent Integrated Microsystems; Ravindra A. Athale, John C. Zolper; Eds., vol. 6232 (2006), pp. 623209 .
4. Arthur D. Szlam and Mauro Maggioni and Ronald R. Coifman, A General Framework for Adaptive Regularization Based on Diffusion Processes On Graphs no. YALE/DCS/TR1365 (2006) .
5. Sridhar Mahadevan and Kimberly Ferguson and Sarah Osentoski and Mauro Maggioni, Simultaneous Learning of Representation and Control In Continuous Domains, in submitted, Proc. AAAI 2006 (2006) .
6. Mauro Maggioni and Gustave L. Davis and Frederick J. Warner and Frank B. Geshwind and Andreas C. Coppi and Richard A. DeVerse and Ronald R. Coifman, Hyperspectral microscopic analysis of normal, benign and carcinoma microarray tissue sections, edited by Robert R. Alfano and Alvin Katz, Optical Biopsy VI, vol. 6091 no. 1 (2006), pp. 60910I, SPIE [1] .
7. Sridhar Mahadevan and Mauro Maggioni, Proto-value Functions: A Spectral Framework for Solving Markov Decision Processes, submitted (2006) .
8. Michael W Mahoney and Mauro Maggioni and Petros Drineas,, Tensor-CUR Decompositions For Tensor-Based Data, in Proc 12-th Annual SIGKDD, to appear in SIAM Journal on Matrix Analysis and Applications (2006) .
9. Mauro Maggioni and Ronald R Coifman, Multiscale Spectral Analysis on Data Sets with Diffusion Wavelets, in submitted (2006) .
10. Mauro Maggioni and Sridhar Mahadevan, Multiscale Diffusion Bases for Policy Iteration in Markov Decision Processes, submitted (2006) .
11. Ronald Raphel Coifman and Mauro Maggioni, Multiscale Analysis of Document Corpora (2006) .
12. Arthur D. Szlam and Mauro Maggioni and Ronald R. Coifman, A General Framework for Adaptive Regularization Based on Diffusion Processes On Graphs no. YALE/DCS/TR1365 (2006) .
13. E Causevic and R~R Coifman and R Isenhart and A Jacquin and E~R John and M Maggioni and L~S Prichep and F~J Warner, QEEG-based classification with wavelet packets and microstate features for triage applications in the ER (2005) .
14. Ronald R Coifman and Mauro Maggioni, Multiscale Data Analysis with Diffusion Wavelets no. YALE/DCS/TR-1335 (2005) .
15. S. Ferrari and M. Maggioni and N. A. Borghese, Multi-Scale Approximation with Hierarchical Radial Basis Functions Networks,, IEEE Trans. on Neural Networks, vol. 15 no. 1 (2004), pp. 178--188 .
16. GL Davis and Mauro Maggioni and FJ Warner and FB Geshwind and AC Coppi and RA DeVerse and RR Coifman, Hyper-spectral Analysis of normal and malignant colon tissue microarray sections using a novel DMD system (2004) (Poster, Optical Imaging NIH workshop, to app. in proc..) .
17. Ronald R Coifman and Mauro Maggioni, Multiresolution Analysis associated to diffusion semigroups: construction and fast algorithms no. YALE/DCS/TR-1289 (2004) .

Mattingly, Jonathan C.

1. Jonathan C. Mattingly, Etienne Pardoux, Malliavin calculus for the Stochastic 2D Navier Stokes Equation, Communications on Pure and Applied Mathematics, vol. 59 no. 12 (December, 2006), pp. 1742 - 1790 [math.PR/0407215] [abs].
2. Martin Hairer, J.C. Mattingly, Ergodicity of the 2D Navier-Stokes Equations with Degenerate Stochastic Forcing, Annals of Mathematics, vol. 164 no. 3 (November, 2006) [math.PR/0406087] [abs].
3. with Yuri Bakhtin, Malliavin Calculus for Infinite-Dimensional Systems with Additive Noise (October, 2006) [math.PR/0610754] [abs].
4. with Toufic M. Suidan, Eric Vanden-Eijnden, Anomalous Dissipation in a Stochastically Forced Infinite-Dimensional System of Coupled Oscillators (October, 2006) [math-ph/0610066] [abs].
5. with Toufic Suidan, Eric Vanden-Eijnden, Simple Systems with Anomalous Dissipation and Energy Cascade (Summer, 2006) [math-ph/0607047] [abs].
6. with David F. Anderson, Propagation of Fluctuations in Biochemical Reaction Systems, II: Nonlinear Chains (2006) .
7. with David F. Anderson, ropagation of Fluctuations in Biochemical Systems, I: Linear SSC Networks (2006) .
8. H. Frederik Nijhout, Michael C. Reed, David F. Anderson, Jonathan C. Mattingly, S. Jill james, and Cornelia M. Ulrich, Long-Range Allosteric Interactions between the Folate and Methionine Cycles Stabilize DNA Methylation Reaction Rate, Epigenetics, Epigenetics, vol. 1 no. 2 (April/May 2006), pp. 81-87 .
9. with Martin Hairer, Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations (2006) [math.PR/0602479] [abs].

Mihalcea, Leonardo Constantin

1. L. Mihalcea, Sums of binomial determinants, non-intersecting lattice paths and positivity of Chern-Schwartz-MacPherson classes (2007) [math.CO/0702566] .
2. Leonardo C. Mihalcea, Equivariant quantum cohomology of homogeneous spaces, accepted in Duke Math. J. (2006) [math.AG/0501213] .
3. with Paolo Aluffi, Chern classes of Schubert cells and varieties, to appear in Journal of Algebraic Geometry; Max Planck Institute fur Mathematik preprint series (2006) [math.AG/0607752] .

Morrison, David R

1. D. Green, A. Lawrence, J. McGreevy, D. R. Morrison, and E. Silverstein, Dimensional duality (2007) [arXiv:0705.0550 [hep-th]] .
2. M. Buican, D. Malyshev, D. R. Morrison, H. Verlinde, and M. Wijnholt, D-branes at singularities, compactification, and hypercharge, J. High Energy Phys. 01 (2007) 107 (2007) [hep-th/0610007] .
3. C. Curto and D. R. Morrison, Threefold flops via matrix factorization (November, 2006) [math.AG/0611014] .
4. D. S. Freed, D. R. Morrison, and I. Singer, eds., Quantum Field Theory, Supersymmetry, and Enumerative Geometry, IAS/Park City Mathematics Series, vol. 11 (2006), American Mathematical Society, Providence .

Ng, Lenhard

1. L. Ng, Framed knot contact homology, Duke Math. J. (2007) (to appear.) [math.GT/0407071] .
2. L. Ng, On arc index and maximal Thurston-Bennequin number (2007) [math.GT/0612356] .
3. L. Ng, P. Ozsvath, and D. Thurston, Transverse knots distinguished by knot Floer homology (2007) [math.GT/0703446] .
4. L. Ng, Conormal bundles, contact homology, and knot invariants, in The interaction of finite type and Gromov–Witten invariants at the Banff International Research Station (2003), Geom. Topol. Monogr., vol. 8 (2006), pp. 129-144 [math.GT/0412330] .
5. L. Ng & J. Sabloff, The correspondence between augmentations and rulings for Legendrian knots, Pacific J. Math., vol. 224 no. 1 (2006), pp. 141-150 [math.SG/0503168] .
6. L. Ng, Plane curves and contact geometry, in Proceedings of 12th Gokova Geometry–Topology Conference (2006), pp. 162-171 [math.GT/0503162] .

Petters, Arlie O

1. A. O. Petters, Gravitational Lensing by Black Holes (December, 2007), in preparation .
2. X. Dong and A. O. Petters, Mathematical Finance II (November, 2007), in preparation .
3. X. Dong and A.O. Petters, Mathematical Finance I (November, 2007), in preparation .
4. A.O. Petters, Algebra, Geometry, and Trigonometry: Teacher Edition (August, 2007), BRC, Benque-Belize .
5. A.O. Petters, Algebra, Geometry, and Trigonometry: Student Edition (August, 2007), BRC, Benque-Belize .
6. M. C. Werner and A.O. Petters, Magnification Relations for Kerr Lensing and Testing Cosmic Censorship, Phys. Rev. D (in press) (August, 2007) .
7. A.O. Petters, Scientific Reasoning: Student Edition (July, 2007), BRC, Benque-Belize .
8. A.O. Petters, Scientific Reasoning: Teacher Edition (July, 2007), BRC, Benque-Belize .
9. A.O. Petters, PSE Mathematics: Teacher Edition (February, 2007), BRC, Benque-Belize .
10. A.O. Petters, PSE Mathematics: Student Edition (February, 2007), BRC, Benque-Belize .
11. I. V. Iyer and A. O. Petters, Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity, Gen. Rel. and Grav. (in press); gr-qc/0611086 (July, 2007) .
12. C. Keeton and A.O. Petters, Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. III. Braneworld Gravity, Phys. Rev. D, vol. 73 (2006), pp. 104032 [0603061] .
13. C. Keeton and A.O. Petters, Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. II. Probing Post-Post-Newtonian Metrics, Phys. Rev. D, vol. 73 (2006), pp. 044024 [0601053] .

Reed, Michael C

1. M.C. Reed, Mathematical Biology, in The Princeton Companion to Mathematics (2007), Princeton University Press, Princeton .
2. Nijhout, H. F., Reed, M., Anderson, D., Mattingly, J., James, S. J., and Ulrich, C. M., Long-range allosteric interactions between the folate and methionine cycles stabilize DNA methylation rate, Epigenetics, vol. 1 (2006), pp. 81-87 .
3. Ulrich , C.M., Nijhout , H.F. and Reed, M.C., Mathematical modeling: epidemiology meets systems biology, Cancer Epidemiol. Biomarkers Prev., vol. 15 (2006), pp. 827-829 .
4. Reed, M.C., Nijhout, H.F., Neuhouser, M.L., Gregory J.F. III., Shane, B., James, S.J., Boynton, A. and Ulrich, C.M., A mathematical model gives insights into nutritional and genetic aspects of folate-mediated one-carbon metabolism, J. Nutrition, vol. 136 (2006), pp. 2653-2661 .
5. Boyles, A.L. Billups, A.V., Deak, K.L., Siegel, D.G., Mehltretter, L., Slifer, S.H. Bassuk, A.G., Kessler, J.A., Reed, M.C. Nijhout, H.F. George, T.M., Enterline, D.S., Gilbert, J.R., Speer, M.C., Neural tube defects and folate pathway genes: family-based association tests of gene-gene and gene-environment interactions, Environ. Health Perspect., vol. 114 (2006), pp. 1547-1552 .
6. Laurent, T, Rider, B. and M. Reed, Parabolic Behavior of a Hyberbolic Delay Equation, SIAM J. Mathematical Analysis, vol. 38 (2006), pp. 1-15 .
7. Nijhout, H. F., Reed, M. C., Shane, B., Gregory, J. F., Ulrich, C. M., In Silico experimentation with a model of hepatic mitochondrial folate metabolism, Theoretical Biology and Medical Modeling (2006) .
8. Mitchell, C., and M.C. Reed, Neural Timing in Highly Convergent Systems, SIAM J. Applied Math. (2006) (under revision.) .
9. D. Anderson, J. Mattingly, F. Nijhout, M.C. Reed, Propagation of Fluctuations in Biochemical Systems, I: Linear SSC Networks (2006) (under revision.) .

Schaeffer, David G

1. D.G. Schaeffer, X. Zhao, Alternate pacing of border-collision period-doubling bifurcations, Nonlinear Dynamics (2006) .
2. D.G. Schaeffer, C. Berger, D. Gauthier, X. Zhao, Small-signal amplification of period-doubling bifurcations in smooth iterated mappings, Nonlinear Dynamics (2006) .
3. D.G. Schaeffer, C. Berger, D. Gauthier, H. Dobrovolny, W. Krassowska, X. Zhao, Smooth and border-collision characteristics of the bifurcation to alternans in paced cardiac tissue, Phys. Rev. Lett (2006) .
4. D.G. Schaeffer, A. Catlla, A. Lin, E. Monson, T. Witelski, On spiking models for synaptic activity and impulsive differential equations, SIAM Review (2006) .
5. D.G. Schaeffer, J. Cain, Shortening of action potential duraction near an insulating boundary, Math Medicine and Biology (2006) .
6. D.G. Schaeffer, M Shearer, and T. Witelski, Boundary-value problems for hyperbolic partial differential equations related to steady granular flow, Math. and Mech. of Solids, vol. 11 (2006) .
7. D.G. Schaeffer, M. Matthews, P. Gremaud, On the computation of steady hopper flows III: Comparison of von Mises and Matsuoka-Nakai materials", J Comp. Phy., vol. 219 (2006), pp. 443-454 .
8. D.G. Schaeffer, W. Ying, X. Zhao, Asymptotic spproximation of an ionic model for cardiac restitution, Nonlinear Dynamics (2006) .
9. D.G. Schaeffer, J. Cain, D. Gauthier,S. Kalb, W. Krassowska, R. Oliver, E. Tolkacheva, W. Ying, An ionically based mapping model with memory for cardiac restitution, Bull Math Bio (2006) .

Schoen, Chad

1. C. Schoen, A family of surfaces constructed from genus 2 curves, International Journal of Mathematics, vol. 18 no. 5 (May, 2007), pp. 585-612 .
2. C. Schoen, Fermat covers, Fermat hypersurfaces, and abelian varieties of Fermat type,, Quarterly Journal of Mathematics, vol. 57 no. 4 (2007), pp. 539-554 .
3. C. Schoen and J. Top, Drinfeld modules and torsion in the Chow groups of certain threefolds, Proceedings London Mathematical Society (June 21, 2007) (Published online 2007; doi: 10.1112/plms/pdm013.) .
4. C. Schoen, Albanese standard and albanese exotic varieties, J. London Math. Soc., vol. 74 (2006), pp. 304-320 .
5. C. Schoen, Specialization of the torsion subgroup of the Chow group, Mathematische Zeitschrift,, vol. 252 (2006), pp. 11-17 .

Schwartz, Fernando A.

1. F.A. Schwartz, Existence of outermost apparent horizons with product of spheres topology (2007) [arXiv:0704.2403v1] .
2. F.A. Schwartz, The zero scalar curvature Yamabe problem on manifolds with boundary, Indiana Univ. Math. J. no. 55 (2006), pp. 1449-1460 [arXiv:math/0605650] .

Smith, David A

1. Lang Moore and David A. Smith, Changing Technology Implies Changing Pedagogy, in A Fresh Start for Collegiate Mathematics: Rethinking the Courses below Calculus, MAA Notes, edited by J. Narayan, et al., vol. 69 (March, 2006), Mathematical Association of America [pdf] .

Stern, Mark A

1. M.A. Stern, Fixed point theorems from a de Rham perspective, math.DG (2006) .

Streets, Jeffrey D.

1. J.D. Streets, The Gradient Flow of $\int_M | \Rm|^2$, Journal of Geometric Analysis (2006) [pdf] .
2. J.D. Streets, Quasi-Local Mass Functionals and Generalized Inverse Mean Curvature Flow, Communications in Analysis and Geometry (2006) [pdf] .

Trangenstein, John

1. J. Trangenstein, Numerical Solution of Hyperbolic Conservation Laws (Spring, 2007), Cambridge University Press [abs].
2. Trangenstein, J.A. and Bell, J.B., Mathematical structure of compositional reservoir simulation, SIAM J. Sci. Stat. Comput. (USA), vol. 10 no. 5 , pp. 817 - 45 [abs].

Wang, Jin

1. Computation of 2D Navier-Stokes equations with moving interfaces by using GMRES, Internat. J. Numer. Methods Fluids, vol. 54 (2007), pp. 333-352 .
2. On the accuracy of a numerical method for linear interfacial motion, Appl. Math. Comput., vol. 188 (2007), pp. 1733-1741 .
3. with A. T. Layton, Numerical simulation of fiber sedimentation in Navier-Stokes flows (2007) .
4. with A. Friedman, J. P. Tian, G. Fulci, and A. E. Chiocca, Glioma virotherapy: the effects of innate immune suppression and increased viral replication capacity, Cancer Research, vol. 66 (2006), pp. 2314-2319 .
5. with J. P. Tian, Numerical study for a model of tumor virotherapy (2006) .
6. Highly accurate difference methods for linear Burgers' equation (2006) .
7. On the study of multilevel finite difference methods (2006) .
8. with G. R. Baker, A numerical approach for simulating two-dimensional viscous incompressible flows with interfaces (2006) .

Witelski, Thomas P

1. L. B. Smolka and T. P. Witelski, On the extensional motion of a falling liquid sheet, Physics of Fluids (August, 2007) .
2. M.B. Gratton and T.P. Witelski, Coarsening of dewetting thin films subject to gravity, Physical Review E (July, 2007) .
3. David G. Schaeffer, Michael Shearer and T.P. Witelski, Boundary-value problems for hyperbolic PDE related to steady granular flow, Mathematics and Mechanics of Solids, vol. 11 (August, 2006) (DOI: 10.1177/1081286506067325.) .
4. T.P. Witelski, R. Levy and M. Shearer, Growing surfactant waves in thin liquid films driven by gravity, Applied Mathematics Research Express, vol. 2006 no. 15487 (2006), pp. 1-21 .
5. Mark Bowen and Thomas P. Witelski, The linear limit of the dipole problem for the thin film equation, SIAM journal on applied mathematics, vol. 66 no. 5 (2006), pp. 1727--1748 .

Yoshida, Ruriko (search)

1. A. Takemura and R. Yoshida, Saturation Points on Faces of a Rational Polyhedral Cone, Proceedings of Integer Points In Polyhedra Geometry, Number Theory, Representation Theory Algebra, Optimization, Statistics, Joint Summer Research Conferences (September, 2006) [math.CO/0605479] .
2. R. Hemmecke, A. Takemura, and R. Yoshida, Computing holes in semi-groups, Journal on Discrete and Computational Geometry (July, 2006) [math.CO/0607599] .
3. M. B\'ona, H. Ju, and R. Yoshida, Enumerations of Weighted Graphs, Discrete Applied Math (June, 2006) [math.CO/0606163] .
4. D. Levy, R. Yoshida and L. Pachter, Beyond Pairwise Distances: Neighbor Joining with Phylogenetic Diversity Estimates, the Molecular Biology and Evolution, vol. 23 no. 3 (March, 2006), pp. 491-498 [q-bio.QM/0508001], [491] .
5. A. Takemura and R. Yoshida, A generalization of the integer linear infeasibility problem, Discrete Optimization (2006) [math.ST/0603108] [abs].

Zhou, Xin

1. with A. Tovbis, S. Venakides, On the long time limit of semiclassical (zero dispersion limit) solutions of the focusing Nonlinear Schroedinger Equation: Pure radiation case.,, Comm. Pure Appl. Math. (2006) .
2. with K. T.-R. McLaughlin, A. H. Vartanian, Asymptotics of Orthogonal Laurent Polynomials of Even Degree with Respect to Varying Exponential Weights, IMRP (2006) .
3. with K. McLaughlin , A.H. Vartanian, Asymptotics of Orthogonal Laurent Polynomials of Odd Degree with Respect to Varying Exponential Weights, Constructive Approximation (2006) .
4. with P. Deift, A. Its, I. Krasovsky, The Widpm-Dyson constant for the gap probability in random matrix theory, a special edition of the Journal of Computational and Applied Mathematics (2006) .
5. with K. T.-R. McLaughlin, A. H. Vartanian, Asymptotics of Coefficients of Recurrence Relations, Hankel Determinants Ratios, and Root Products Associated with Orthogonal Laurent Polynomials with Respect to Varying Exponential Weights, journal Acta Applicandae Mathematicae (2006) .
6. with A. Tovbis and S. Venakides, Semiclassical focusing nonlinear Schroedinger equation I: Inverse scattering map and its evolution for radiative initial data, completed (2006) .
7. B. Rider and X. Zhou, Janossy densities for unitary ensembles at the spectral edge (2006) .

I am just, for fun, looking through different mathematical patterns and bio-mechanical workings of the true fabric of evolution..here is where I begin..

(I CUT AND PASTE THIS TEXT)
Molecules and phylogenies

Back in the mid-1980s we started hearing a lot about "African Eve." As we note on this weblog, there were two parts of this:

1) A caution not to overread the results into imagining a single foremother.
2) The popular press basically ignoring this caution.

But here are a few "fun facts."

1) The probability of fixation of a new mutation is 1/2N, where N is the population size.
2) The time until fixation is usually 4N, where N is the population size.
3) 1/2N X 2NÎ¼, where Î¼ is the mutation rate, reflects the reality that the probability of mutation times the rate of mutation results in the substitution, the turnover of alleles, on loci being a function just of mutation rate (Î¼).
4) Time until extinction of an allele is usually 2Ne/N X ln(2N).
5) The long term effective population is 1/t(1/N0 + ... + 1/Nt - 1).

You can do some "plug & chug" in Excel if you want to check out the long term effective population, but trust me when I tell you that it is far closer to the low bound as a function of time than the high bound as far as what your intuition would tell you.

http://www.gnxp.com/blog/2005/11/8th-grade-math-for-rest-of-us.php