Brown University | Division of Applied Mathematics

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Division of Applied Mathematics Papers & Technical Reports on
Applied Probability, Pattern Theory, and Statistics



  1. Ulf Grenander. Rules of Thought. Click here to download the postscript file.
  2. Ulf Grenander. MATLAB code for LEGACY. Click here to download the zip archive. Extract the files into "C:\" to obtain directories "C:\mind06a\", "C:\mind07\", and file "C:\mind_data06". Then start MATLAB and do "cd c:\mind07" and say "legacy".


  1. Yuri Tarnopolsky, Ulf Grenander. History as Points and Lines. [ pdf ]
  2. Sahar Pirmoradian. Seminar on Patterns of Thought [ ppt ]
  3. Ulf Grenander, Anuj Srivastava, and Sanjay Saini. A Pattern-Theoretic Characterization of Biological Growth. Click here to download the PDF file.
  4. Nataliya Portman. Estimation of growth parameters for the Drosophila wing disc from the sequence of its micrographs using the Growth as Random Iterated Di eomorphisms Model. Click here to download the PDF file.


  1. Ulf Grenander. On the Road to Nowhere. 2006. [pdf]
  2. Ulf Grenander. Mathematics in Biology. 2006. [PowerPoint]
  3. A. Amarasingham, T.-L. Chen, S. Geman, M. Harrison, and D. Sheinberg. Spike count reliability and the Poisson Hypothesis. Journal of Neuroscience, 2006, 26(3):801-809. [pdf]
  4. Y. Jin and S. Geman. Context and hierarchy in a probabilistic image model. CVPR, 2006. [pdf]
  5. S. Geman. Invariance and selectivity in the ventral visual pathway. Journal of Physiology - Paris, 2006 (in press). [pdf]
  6. E. Cinquemani and M. Micheli. State Estimation in Stochastic Hybrid Systems with Sparse Observations. IEEE Transactions on Automatic Control, 51(8):1337-1342, August 2006. [pdf]
  7. I. Kontoyiannis and M. Madiman. Measure Concentration for Compound Poisson Distributions. Electronic Communications in Probability, Vol. 11, May 2006. [pdf]
  8. P. W. Michor and D. Mumford. Riemannian geometries on spaces of plane curves. Journal of the European Mathematical Society, Vol. 8, No. 1, 2006. [pdf]
  9. P. W. Michor and D. Mumford. An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach. To appear in: Applied and Computational Harmonic Analysis (ACHA). arXiv:math.DG/0605009. [pdf]
  10. E. Sharon and D. Mumford. 2D-Shape Analysis using Conformal Mapping. International Journal of Computer Vision (IJCV), Vol. 70, No. 1, October 2006. [pdf]


  1. Asohan Amarasingham, Ting-Li Chen, Stuart Geman, Matthew Harrison, David Sheinberg. Spike Count Reliability and the Poisson Hypothesis. April 2005. [View]

  2. P. W. Michor and D. Mumford. Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Documenta Mathematica, Vol. 10, 2005. [pdf]


  1. Matthew Harrison, Stuart Geman, Elie Bienenstock. Using Statistics of Natural Images to Facilitate Automatic Receptive Field Analysis. APPTS Report #04-2, March 2004. [pdf]

  2. Matthew Harrison and Stuart Geman. An Exact Jitter Method using Dynamic Programming. APPTS Report #04-3, March 2004. [pdf]

  3. Ulf Grenander. A Stochastic Partial Differential Equation for Biological Growth with Genetically Controlled Cells. [pdf]

  4. Ulf Grenander. MODALITIES. Supplement to Patterns of Thought. [zip] and [PowerPoint] (Warning: with a slow connection the audio will be delayed considerably).
  5. Mokshay Madiman and Ioannis Kontoyiannis. Second Order Properties of Lossy Likelihoods and the MLE/MDL Dichotomy in Lossy Compression. APPTS Report #04-5, May 2004. [pdf]

  6. Asohan Amarasingham. Statistical methods for the assessment of temporal structure in the activity of the nervous system. Doctoral Dissertation, Brown University, May 2004. [pdf]


  1. Ulf Grenander. Towards a Theory of Natural Scenes, [ps] and [pdf].
  2. Yuri Tarnopolsky. Molecules and Thoughts: Pattern Complexity and Evolution in Chemical Systems and the Mind, [pdf].

  3. Matthew Harrison. The First Order Asymptotics of Waiting Times between Stationary Processes under Nonstandard Conditions. APPTS Report #03-3, April 2003. [ps] [pdf]

  4. Matthew Harrison. Epi-Convergence of Lossy Likelihoods. APPTS Report #03-4, April 2003. [ps] [pdf]

  5. Matthew Harrison. The Convergence of Lossy Maximum Likelihood Estimators. APPTS Report #03-5, July 2003. [ps] [pdf]

  6. Wei Wu, Ann B. Lee and David Mumford. A Hierarchical Model for Minimum Entropy Data Partitioning. APPTS Report #03-6, October 2003. [pdf]

  7. Asohan Amarasingham, Ting-Li Chen, Stuart Geman, and Matthew Harrison. Notes on a Spike Count Variability Test. APPTS Report #03-8, September 2003. [pdf]


  1. Kim S. Pedersen and Ann B. Lee. Toward a Full Probability Model of Edges in Natural Images. APPTS Report #02-1, January 2002. [ps] [pdf]

  2. Ulf Grenander. A Useful Hint? Tech. Rep. D.A.M., Brown University. [doc]

  3. Ulf Grenander. Computer Understanding of Natural Scenes. [ps] [pdf]

  4. Ulf Grenander. Clutter17. Non-Diffeomorphic Background Deformations. [ps] [pdf]

  5. Ulf Grenander. Heuristic Inference in Sensory Perception with an Application to Computer Vision. [ps] [pdf]

  6. V. Castelli and I. Kontoyiannis. An Efficient Recursive Partitioning Algorithm for Classification, Using Wavelets. APPTS Report #02-7, September 2002. [ps] [pdf]

  7. M. Micheli and M. I. Jordan Random Sampling of a Continiuous-time Stochastic Dynamical System. APPTS Report #02-8, October 2002. [pdf]

  8. Tai Sing Lee and David Mumford. Hierarchical Bayesian Inference in the Visual Cortex. APPTS Report #02-9, November 2002. [pdf]

  9. D. Mumford. Pattern Theory: the Mathematics of Perception. APPTS Report #02-10, August 2002. [pdf]

  10. C. Lu, Y. Cao and D. Mumford. Surface Evolution under Curvature Flows. Journal of Visual Communication and Image Representation, Vol. 13, 65-81, 2002. [pdf]


  1. I. Kontoyiannis and J. Zhang. Arbitrary source models and Bayesian codebooks in rate-distortion theory. APPTS Report #01-1, April 2001. [ps] [pdf]

  2. A. Dembo and I. Kontoyiannis. Source coding, large deviations, and approximate pattern matching. APPTS Report #01-2, April 2001. [ps] [pdf]

  3. Ann B. Lee, Kim S. Pedersen and David Mumford. The Nonlinear Statistics of High-Contrast Patches in Natural Images. APPTS Report #01-3, June 2001 (Revised Dec 2001). [ps] [pdf]

  4. Anuj Srivastava, Xiuwen Liu and Ulf Grenander. Universal analytical forms for modeling image probabilities. APPTS Report #01-4, November 2001. [ps] [pdf]

  5. I. Kontoyiannis and A.D. Sezer. A remark on unified error exponents: Hypothesis testing, data compression and measure concentration. APPTS Report #01-5, November 2001. [ps] [pdf]

  6. I. Kontoyiannis. Pattern matching and lossy data compression on random fields. APPTS Report #01-6, November 2001. [ps] [pdf]

  7. I. Kontoyiannis and P. Harremoes. Entropy and the law of small numbers. APPTS Report #01-7, December 2001. [ps] [pdf]

  8. Oddvar Husby and Ulf Grenander. A Model for Recognition of 3D Non-dense Objects in Range images. [ps] [pdf]


  1. U. Grenander, Clutter 5, Tech. Rep., March 1999. [ps]

  2. U. Grenander, Clutter 6, Tech. Rep., April 1999. [ps]


Some more publications from 1998-99 can be found here.

Earlier publications:

Can be obtained from the web pages of the individual members of the group.


The following CD-ROMs can be obtained without cost by writing to
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