Alex Barnett: publications, talks, notes

You can access my arxiv preprints here, which is a subset of the complete list given on this page. Also see my google scholar page.


40. Efficient numerical solution of electromagnetic scattering from doubly-periodic arrays of axisymmetric objects, Y. Liu and A. H. Barnett, in preparation.

39. Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues, Alex Barnett, Andrew Hassell, and Melissa Tacy, submitted, Duke Math. J., 40 pages (2015). (math.NA:1512.04165)

38. Unimodal clustering using isotonic regression: ISO-SPLIT, Jeremy Magland and Alex Barnett, submitted, J. Comput. Graph. Stat., 31 pages (2015). (arxiv)

Publications - refereed

37. A fully automated approach to spike sorting, J. E. Chung, J. F. Magland, A. H. Barnett, V. M. Tolosa, A. C. Tooker, K. Y. Lee, K. G. Shah, S. H. Felix, L. M. Frank, L. F. Greengard. NEURON 95(6) 1381-1394 (2017).

36. Ubiquitous evaluation of layer potentials using quadrature by kernel-independent expansion, Abtin Rahimian, Alex Barnett, and Denis Zorin, appeared online, BIT Numer. Math., 22 pages (2017). (original submission PDF 4MB, arxiv)

35. A unified integral equation scheme for doubly-periodic Laplace and Stokes boundary value problems in two dimensions, A. H. Barnett, G. Marple, S. Veerapaneni, and L. Zhao, in press, Comm. Pure Appl. Math., 41 pages (2017). (arxiv, revised, PDF 7MB)

34. Rapid solution of the cryo-EM reconstruction problem by frequency marching, Alex Barnett, Leslie Greengard, Andras Pataki, and Marina Spivak, SIAM J. Imaging Sci., vol 10 (3); 20 pages (2017). (math.NA:1610.00404;PDF 7MB)

33. A fast algorithm for simulating multiphase flows through periodic geometries of arbitrary shape, Gary Marple, Alex Barnett, Adrianna Gillman, and Shravan Veerapaneni, SIAM J. Sci. Comput., 38(5), B740-B772 (2016). (PDF 2MB)

32. Efficient numerical solution of acoustic scattering from doubly-periodic arrays of axisymmetric objects, Y. Liu and A. H. Barnett, J. Comput. Phys., 324, 226-245 (2016). (PDF 2MB)

31. Validation of neural spike sorting algorithms without ground-truth information, Alex Barnett, Jeremy Magland, and Leslie Greengard, J. Neurosci. Meth., 264, 65-77 (2016). (PDF 1.3MB, arxiv, codes)

30. A fast and robust solver for the scattering from a layered periodic structure containing multi-particle inclusions, J. Lai, M. Kobayashi, and A. H. Barnett, J. Comput. Phys. 298, 194-208 (2015). (PDF 800kB)

29. Spectrally-accurate quadratures for evaluation of layer potentials close to the boundary for the 2D Stokes and Laplace equations, A. H. Barnett, B. Wu, and S. Veerapaneni, SIAM J. Sci. Comput., 37(4), B519-B542 (2015). (preprint PDF 1.8 MB, code)

28. High-order boundary integral equation solution of high frequency wave scattering from obstacles in an unbounded linearly stratified medium, A. H. Barnett, B. J. Nelson, and J. M. Mahoney, J. Comput. Phys. 297, 407-426 (2015). (PDF 1.7 MB, code)

27. Robust and efficient solution of the drum problem via Nyström approximation of the Fredholm determinant, L. Zhao and A. H. Barnett, SIAM J. Numer. Anal., 53 (4) 1984--2007 (2015). (PDF 0.8MB, arxiv)

26. Robust fast direct integral equation solver for quasi-periodic scattering problems with a large number of layers, M. H. Cho and A. H. Barnett, Optics Express, 23(2), 1775-1799 (2015). (PDF 6.2MB, code)

25. A spectrally accurate direct solution technique for frequency-domain scattering problems with variable media, A. Gillman, A. H. Barnett, and P.G. Martinsson, BIT Numer. Math., 55(1), 141-170 (2015). math.NA 1308.5998

24. Evaluation of layer potentials close to the boundary for Laplace and Helmholtz problems on analytic planar domains, Alex Barnett, SIAM J. Sci. Comput. 36 (2), A427-A451 (2014). (revised version PDF 3.4MB; also see codes)

23. High-order accurate Nyström discretization of integral equations with weakly singular kernels on smooth curves in the plane , S. Hao, A. H. Barnett, P.G. Martinsson, and P. Young, Adv. Comput. Math. 40(1), 245-272 (2014). (PDF 0.7MB)

22. Fast computation of high frequency Dirichlet eigenmodes via the spectral flow of the interior Neumann-to-Dirichlet map, Alex Barnett and Andrew Hassell, Comm. Pure Appl. Math., 67(3) 351-407 (2014). (math.NA 1112.5665)

21. A fast direct solver for quasiperiodic scattering problems, Adrianna Gillman and Alex Barnett, J. Comput. Phys. 248, 309-322 (2013). (preprint PDF 0.7MB)

20. Quadrature by expansion: A new method for the evaluation of layer potentials, Andreas Kloeckner, Alex Barnett, Leslie Greengard, and Michael O'Neil, J. Comput. Phys. 252, 332-349 (2013). (PDF 2MB)

19. Boundary quasi-orthogonality and sharp inclusion bounds for large Dirichlet eigenvalues, Alex Barnett and Andrew Hassell, SIAM J. Numer. Anal. 49, 1046-1063 (2011) (preprint PDF 0.6MB)

18. A new integral representation for quasi-periodic scattering problems in two dimensions, Alex Barnett and Leslie Greengard, BIT Numer. Math. 51, 67-90 (2011) (preprint PDF 1MB)

17. A few more words about James Tenney: dissonant counterpoint and statistical feedback, Larry Polansky, Alex Barnett, and Mike Winter, J. Math. Music, 5 (2), 63-82 (2011) (preprint PDF 0.9MB)

16. A new integral representation for quasi-periodic fields and its application to two-dimensional band structure calculations, Alex Barnett and Leslie Greengard, J. Comput. Phys., 229 (19), 6898-6914 (2010). (math.NA 1001.5464)

15. An exponentially convergent nonpolynomial finite element method for time-harmonic scattering from polygons, Alex H. Barnett and Timo Betcke, SIAM J. Sci. Comp., 32 (3), 1417-1441 (2010). (preprint PDF 0.6MB)

14. Perturbative analysis of the Method of Particular Solutions for improved inclusion of high-lying Dirichlet eigenvalues, Alex H. Barnett, SIAM J. Num. Anal. 47 1952-1970 (2009). (PDF 1.8MB)

13. Stability and convergence of the Method of Fundamental Solutions for Helmholtz problems on analytic domains, A. H. Barnett and T. Betcke, J. Comput. Phys. 227 (14) 7003-7026 (2008). (0708.3533 [math.NA])

12. Analytic steady-state space use patterns and rapid computations in mechanistic home range analysis, A. H. Barnett and P. R. Moorcroft, J. Math. Biol., 57 (1) 139-159 (July 2008). (q-bio.QM/0705.3473)

11. Quantum mushroom billiards, A. H. Barnett and T. Betcke, CHAOS, 17, 043123 (2007). (13 pages) (nlin.CD/0611059)

10. Mechanistic home range models and resource selection analysis: a reconciliation and unification, P. R. Moorcroft and A. H. Barnett, Ecology, 89 (4), 1112-1119 (2008). (q-bio.PE/0612008)

9. Asymptotic rate of quantum ergodicity in chaotic Euclidean billiards, Alex. H. Barnett, Comm. Pure Appl. Math., 59 (10), 1457-1488 (2006). math-ph/0512030

8. Effective scattering coefficient of the cerebral spinal fluid in adult head models for Diffuse Optical Imaging, A. Custo, W. M. Wells III, A. H. Barnett, E. M. C. Hillman, and D. A. Boas, Applied Optics, 45, 4747--55 (2006) (preprint PDF 233kB)

7. A fast numerical method for time-resolved photon diffusion in general stratified turbid media, Alex H. Barnett, Journal of Computational Physics, 201 771-797 (2004) (preprint PDF 590kB)

6. Robust inference of baseline optical properties of the human head with 3D segmentation from magnetic resonance imaging, Alex H. Barnett, Joseph P. Culver, A. Gregory Sorensen, Anders Dale, and David A. Boas, Applied Optics 42, 3095-3108 (2003). (preprint version PDF 464kB)

5. Parametric evolution for a deformed cavity, D. Cohen, A. H. Barnett, and E. J. Heller, Phys. Rev. E 63, 46207 (2001),(nlin/0008040)

4. Mesoscopic scattering in the half-plane: squeezing conductance through a small hole, A. H. Barnett, M. Blaauboer, A. Mody, and E. J. Heller, Phys. Rev. B 63, 245312/1 (2001),(cond-mat/0008279)

3. Rate of energy absorption for a driven chaotic cavity, A. H. Barnett, D. Cohen, and E. J. Heller, J. Phys. A 34, 413-437 (2001), (nlin.CD/0006041)

2. Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions, A. H. Barnett, D. Cohen, and E. J. Heller, Phys. Rev. Lett.85, 1412 (2000) (nlin/0003018)

1. Substrate-based atom waveguide using guided two-color evanescent light fields, A. H. Barnett, S. P. Smith, M. Olshanii, K. S. Johnson, A. W. Adams, M. Prentiss, Phys. Rev. A. 61, 023608 (2000) (physics/9907014)

Publications - conference proceedings, unrefereed reports and theses

Boundary integral equations for BVPs, and their high-order Nyström quadratures: a tutorial, A. H. Barnett, CBMS Conference on Fast Direct Solvers (June 2014). (PDF 354kB, code, notes)

Robust high-order numerical scattering from multi-layer dielectric gratings using a new integral representation for quasi-periodic fields, A. H. Barnett and L. Greengard, Proceedings of WAVES2011: The 10th International Conference on Mathematical and Numerical Aspects of Waves Propagation (July 2011). (PDF 144kB)

Estimates on Neumann eigenfunctions at the boundary, and the "Method of Particular Solutions" for computing them, A. Hassell and A. H. Barnett, P.S.P.M. proceedings of the International Conference on Spectral Geometry, July 2010, Dartmouth College, 14 pages (2011). (preprint 1.6MB). Please note that results in this report have been superceded by our Duke Math J. submission numbered 35 above.

Accurate and Robust Computation of Photonic Crystal Band Structure using Second-Kind Integral Equations, A. H. Barnett and L. Greengard, Proceedings of WAVES2009: The 9th International Conference on Mathematical and Numerical Aspects of Waves Propagation (June 2009). (PDF 158kB)

Quasi-orthogonality on the boundary for Euclidean Laplace eigenfunctions, Alex. H. Barnett, technical report, math-ph/0601006

Bayesian estimation of optical properties of the human head via 3D structural MRI, A. H. Barnett, J. P. Culver, A. G. Sorensen, A. M. Dale, and D. A. Boas, Proc. SPIE 5138 (2003). (PS 0.7MB)

Fast computation of the time domain diffusion forward model for optical tomography in the Born approximation, Jonathan S. Stott, Quan Zhang, Alex H. Barnett, and David A. Boas, (2003). Technical report (preprint PDF 275kB)

PhD thesis: Dissipation in Deforming Chaotic Billiards, A. H. Barnett (2000). (.ps.gz 2.6MB)

Undergrad thesis: Bayesian Comparison of Models for Images, A. H. Barnett and D. J. C. MacKay, in Maximum Entropy and Bayesian Methods (Kluwer, 1996) p.239--248 (.ps.gz 421kB) (PDF 582kB)

Publications - education, outreach and media

Snapshots of modern mathematics from Oberwolfach: Fast solvers for highly oscillatory problems, A. H. Barnett, 9 pages (2017). (PDF 0.7MB). This is aimed at advanced high school or first-year university students.

Computed eigenmodes of billiards that I produced, Sept 2009, feature in Peter Sarnak's review article, Recent Progress on QUE, and Dana Mackenzie, What's Happening in the Mathematical Sciences, Volume 8 (AMS, to appear, Jan 2011), and Shin-ya Koyama, "Arithmetic quantum chaos and zeta functions", Suurikagaku, vol. 571 (2011) Saiensu-sha, and Shin-ya Koyama, "From primes and zetas to arithmetic quantum chaos" Nihon Hyoronsha (December 2010).

convolution: son et lumiere, for issue 01 of Convolution. A Journal for Experimental Criticism, (October 2009), (preprint PDF 0.5MB)

Cover image for Notices of the AMS, January 2008. Computed eigenmodes numbered 1, 10, 102, 103, 104, 105 of a uniformly hyperbolic billiard, with background of random waves. (Accompanying article by Z. Rudnick)

Talks and workshops (invited, unless otherwise stated)

Modern Advances in Computational and Applied Mathematics, Yale, June 2017. (co-organizer)

SIAM meeting on Computational Science and Engineering, Atlanta, Mar 2017.

Workshop on Numerical and mathematical modeling in optics, IMA, Minneapolis, Dec 2016.

Math/ICES numerical analysis seminar, UT Austin, Dec 2016.

Oberwolfach Workshop on fast solvers for oscillatory problems, Nov 2016.

SIAM Annual Meeting, Boston, July 2016.

SIAM meeting on Computational Science and Engineering, Salt Lake City, Mar 2015.

Applied Mathematics Colloquium, Princeton, Feb 2, 2015. (PDF)

SCDA Journal Club, Simons Foundation, Nov 20, 2014.

CBMS-NSF conference on fast direct solvers for elliptic PDE, Dartmouth College, NH, Jun 23, 2014. (guest lecture)

Numerical Analysis and Scientific Computing Seminar, Courant Institute, NYU, Mar 7, 2014. (PDF)

Workshop on fast algorithms and integral equations, Banff, Canada, Dec 9-13, 2013. (PDF)

Numerical analysis and PDE seminar, U. of Delaware, Nov 21, 2013.

Colloquium, U. of Arizona, Tuscon, AZ, Nov 7, 2013.

Colloquium, Mathematics Dept, Tufts University, Sep 27, 2013.

Physics Colloquium, UMASS Boston, Apr 24, 2013.

Mathematics Research Seminar, Middlebury College, VT, Apr 16, 2013.

Applied Mathematics Seminar, NJIT, NJ, Mar 13, 2013.

SIAM meeting on Computational Science and Engineering, minisymposium on integral equations, Boston, Feb 25 - Mar 1, 2013.

Numerical Analysis and Scientific Computing Seminar, Courant Institute, NYU, Feb 15, 2013. (PDF 6MB)

Widely Applied Math Seminar, SEAS, Harvard, Jan 29, 2013.

Oberwolfach Workshop on Computational Electromagnetism and Acoustics. MFO, Germany, Jan 20-26, 2013.

Applied Math Seminar, U Michigan, Nov 30, 2012.

Integrated Applied Mathematics Seminar, UNH, Durham, NH, Nov 16, 2012.

SIAM Annual Meeting, Minneapolis, Jul 9-13, 2012.

Workshop on Geometry of eigenvalues and eigenfunctions, CRM, Montreal, Jun 4-8, 2012.

Challenges in Geometry, Analysis, and Computation. (in honor of Coifman-Jones-Rokhlin), Yale, Jun 3-6, 2012. (poster)

Frontiers in Computational and Applied Mathematics, NJIT, Newark, NJ, May 18-20, 2012

Analysis/PDE Seminar, UNC Chapel Hill, Apr 4, 2012

Mathematical Physics and Harmonic Analysis Seminar, Texas A&M, Feb 10, 2012

"The Fast Fourier Transform: an algorithm that has changed your life", Applied and Computational Mathematics Seminar, Jan 2012; and Dartmouth Mathematics Society, Oct 2011. (demo codes: test_fft.m which calls cooleytukey.m)

"New Integral Representations for Scattering from Multi-layer Dielectric Gratings", WAVES 2011, Vancouver, BC, Jul 2011. (contributed talk)

ICIAM 2011, Vancouver, BC, Jul 2011. (one talk on periodic integral-equation solvers; co-organized 2 minisymposia)

"The Mathematical Overtones of Music," lecture with demonstrations, JHU Center for Talented Youth, Odyssey Series, May 2011

"How integral equations help you solve PDEs," (PDF 6MB), Applied and Computational Mathematics Seminar, Dartmouth College, May 2011

"Diffraction gratings and photonic crystals: new integral representations for periodic scattering and eigenvalue problems", New England Numerical Analysis Day, UMass Dartmouth, Apr 2011

"Diffraction gratings and photonic crystals: numerical analysis of waves," (PDF 1.5MB), Graduate Open House, Mathematics Dept, Dartmouth College, Apr 2011

NIST DLMF Conference Special functions in the 21st century: theory and applications, Washington DC, Mar, 2011. (not a speaker)

CSC Seminar, SFU, Vancouver, BC, Mar 2011

Numerical Analysis and Scientific Computing Seminar, Courant Institute, NYU, Jan 2011

Applied Mathematics and Computational Science Colloquium, U. Penn, Jan 2011

Conference in honor of 65th birthday of Eric Heller, Harvard, October 2010

Integral Equation Methods, Fast Algorithms and Applications, IMA Hot Topics Workshop, Minnesota, Aug 2010

"A new integral representation of quasi-periodic fields and its application to scattering and Bloch eigenvalue problems", (PDF 5MB, with movies: moving contour and scattered field), Frontiers in Computational and Applied Mathematics, NJIT, Newark, NJ, May 2010

Numerical Solutions of the Painleve Equations, International Centre for Mathematical Sciences, Edinburgh, UK, May 2010

"Robust and efficient computation of two-dimensional photonic crystal band structure using second-kind integral equations", (PDF 3.6MB, movie of band structure), Applied Analysis Seminar, Lousiana State University, Mar 2010

Dartmouth Mathematics Colloquium, Nov 2009

MIT Applied Math Colloquium, Nov 2009

Dartmouth Math Society, introductory talk for undergraduates, Oct 2009

Computational Optical Sensing and Imaging (COSI) graduate program seminar series, UC Boulder, Sep 2009. (PDF 9MB)

Topological Complexity of Random Sets, AIM workshop, Palo Alto, Aug 2009, (including results on random plane waves)

WAVES2009, Pau, France, Jun 2009. (contributed talk)

Colloquium and PDE/Analysis Seminar (two talks, and 3-week visiting fellowship), ANU, Canberra, Australia, Feb 2009

"Computing eigenmodes on the torus: photonic crystals using second-kind integral equations" (PDF 7MB), Laplacian Eigenvalues and Eigenfunctions: Theory, Application, IPAM, UCLA, Feb 2009.

Workshop on Numerical and Analytical Methods for Wave Scattering, Manchester, UK, June 2008

Mathematical Aspects of Quantum Chaos, CRM (Univ. de Montreal), June 2008

Frontiers in Computational and Applied Mathematics (FACM08), NJIT, Newark, NJ; submitted poster, May 2008

"Eigenmodes and quantum chaos: Lost on the frequency axis? Check your Dirichlet-to-Neumann map!" (PDF 17MB), McGill Applied Math Seminar, Montreal, Mar 2008

Applied Math Seminar, U. Delaware, Nov 2007

Numerical analysis seminar, Manchester, UK, July 2007

Three inivited minisymposia talks at ICIAM 2007 meeting, Zurich, Switzerland, Jul 2007.

UMass Amherst, Applied Mathematics Seminar, Nov 2006. (PDF 14MB).

"Quantum mushrooms and scars: what is the high frequency limit of cavity eigenmodes?", Dartmouth Physics Colloquium, Oct 2006. (PDF 11MB, streaming video)

"High-frequency cavity modes: fast methods and quantum chaos", SIAM Annual Meeting, Boston, Jul 2006. (PDF 5MB)

"Numerical study of the asymptotic rate of quantum ergodicity in chaotic billiards", Joint MIT/Harvard Analysis Seminar, Mar 2006. (PDF 7.6MB).

Three lectures on quantum ergodicity and quantum chaos to Dartmouth Geometry Topology Seminar, Feb 2006.

"High-frequency cavity modes: efficient algorithms, and quantum chaos", Computations in Science Seminar, Mathematics/Physics, U. Chicago, Nov 2005. (PDF 14MB).

"High-frequency cavity modes: efficient computation and applications", Oxford U. Computing Laboratory, June 2005. (PDF 11MB).

Institute of Sound and Vibration Research, U. Southampton, UK, June 2005.

"High-frequency cavity modes: efficient computation and applications", New Jersey Institute of Technology, Feb 2005. (PDF 9.5MB).

"Eigenfunctions of the Laplacian: quantum ergodicity, chaos, and fast numerical methods", invited talk, Applied Mathematics Colloquium, Columbia University, Oct 2004. (PDF 11MB).

"Quantum ergodicity and billiards", Courant Instructor Day, CIMS, Sept 2004. (PDF 4.3MB)

"Asymptotic ergodicity of eigenfunctions in a uniformly hyperbolic billiard", invited presentation, Workshop on Semi-classical Theory of Eigenfunctions and PDEs, CRM (Univ. de Montréal) and Fields Institute (Toronto), June 2004. (PDF 5.1MB)

"Ergodicity of quantum eigenfunctions in classically chaotic systems", invited talk, Applied Math Seminar, Yale, Mar 2004. (PDF 4.3MB)

"Ergodicity of quantum eigenfunctions in classically chaotic systems", Applied Math Lab Seminar, CIMS, Feb 2004. (PDF 4.2MB)

"Bayesian estimation of optical properties of the human head via 3D structural MRI", European Conference on Biomedical Optics, Munich, June 2003. (PDF 1.4MB)

"Forward models and Bayesian inference in diffuse optical brain imaging", invited talk, Theoretical & Computational Biology Seminar Series, Mount Sinai School of Medicine, May 2003. (PDF 2.1MB)

"Noninvasive imaging of the brain with diffusing light pulses", invited talk, Applied Math Seminar, CIMS, Nov 2002. (PDF 1.2MB)

"Forward and inverse wave problems: Quantum billiards and brain imaging", Instructors' Day, CIMS, Sept 2002. (PDF 3.2MB)

"Inferring baseline optical properties of the human head", Photon Migration Imaging group talk, MGH, May 2002. (PDF 646kB)

"How can quantum-classical correspondence help you find the modes of a drum?" (poster), Dynamics Days, Baltimore, January 2002.

"How can quantum-classical correspondence help you find the modes of a drum?", invited talk, Courant Institute of Mathematical Sciences, New York University, December 2001.

"Application of Statistical Methods to Wind Forecasting for Wind Power Generation", invited talk. Radford Neal, Dept of Statistics, University of Toronto, September 2001. (PDF 9.7MB)

"Deformations of Chaotic Billiards and a New `Wall Formula' for Heating Rate", Pan-American Advanced Study Institute, Ushuaia, Argentina, October 2000 (PDF 361kB) (.ps.gz 227kB)

"Dielectric Waveguides for 1D Atom Traps" (poster presentation), Cambridge Area Atomic and Molecular Physics 3rd Open House, Harvard-Smithsonian Center for Astrophysics, May 1998. (.ps 350kB)

"Bayesian Comparison of Models for Images", MAXENT94 (14th Maximum Entropy Workshop), Cambridge, England, June 1994.

Unpublished notes

Tutorials, notes, and resources on boundary integral equations, 2014.

Using the impedance-to-impedance map for frequency-domain scattering problems, November 2012. (187kB PDF).

1D band structure of single periodic scatterer in Schrodinger equation, June 2008. (0.5MB PDF).

Linearizing the photonic band structure eigenvalue problem using the Dirichlet-to-Neumann map, May 2008. (87kB PDF).

Greens functions for the wave equation, December 2006, (140kB PDF).

Notes on Method of Fundamental Solutions convergence in the disc (and other domains), June 2006. (2MB PDF).

Spring Break Puzzler on stochastic processes, March 2005, (30kB PDF), with insightful answer from Jonathan Goodman.

Ill-posed inference and sampling from a high-dimensional sheet-like distribution. (ps 116kB). Introducing Bayesian inference, and presenting a mixed Gaussian-approximation/MCMC method (originally notes for David Boas, June 2002).

Embryonic research proposal for statistical methods in wind forecasting, 2001. (ps 113kB).