Individual Faculty Information

Lawrence Shepp

Address:
Department of Statistics
Hill Center, Busch Campus,
Piscataway NJ 08854
Phone: (732) 445-1143
FAX: (732) 445-3428

Home:
48 Castle Pointe Blvd,
Piscataway, NJ 08854
Phone: (732) 463-8042

EDUCATION:
1960 - 1961PhD, Mathematics, Princeton University
1958 - 1960 MA, Mathematics, Princeton University
1954 - 1958 BS Appl Math, Polytechnic Institute of Brooklyn

EXPERIENCE:
1996 - 1997 Professor Columbia U, Statistics and Operations Research
1986 - 1996 Distinguished Member of Technical Staff} Bell Laboratories Research areas: Tomography, probability, combinatorics
1983 - 1984 Member of Scientific Board Resonex Inc, MRI scanners
1978 - 1992 Professor of Statistics (1/4 time) Stanford University
1974 - 1975 Member of Scientific Board American Science and Engineering Inc, X-ray CT scanners
1974 - 1996 Mathematician in Radiology Service Columbia Presbyterian Hospital
1973-1996 Professor of Radiology Columbia University

CURRENT INTERESTS:
Probabilistic, combinatorial, and statistical analysis of models for problems arising in physics, engineering, or communications: Computed tomography; Automatic pattern recognition; Probabilistic models for phase transitions; Connectedness of random graphs; Mathematics of finance; Genetics

HONORS:
1989 - present Member, National Academy of Science (NAS)
1992 - present Member, Institute of Medicine (IOM)
1993 - present Member, Academy of Arts and Science (AAS)

PRIZES:
1958 Winner William Lowell Putnam Intercollegiate Mathematics competition
1966 Paul Levy Prize
1979 IEEE Distinguished Scientist Award

VISITING POSITIONS:
Extended leaves in: Moscow, USSR (1965), Stanford University (1968-1992)
Mittag-Leffler Institute, Sweden (1973), MIT (1975), Simon Bolivar University Venezuela (1982), Australia (U. New South Wales, 1986, ANU, 1997)

PERSONAL:
Born: September 9, 1936; US Citizen
Married to: Britt-Louise Shepp; 3 Children

EDITORIAL ACTIVITIES:
Co-Editor: Int. Jour. Imaging Systems and Technology
Editor: Jour. Computer Assisted Tomography
PhD Advisor and Postdoctoral mentor:
PhD Adviser: Prof William Feller (deceased);
Mentor: Dr David Slepian
Collaborators within the past 48 months:
D Daley C Mallows R Calderbank L Dubins P Fishburn R Graham
S Gutmann J Kemperman B Logan J Reeds T Richardson A Shiryaev
Y Vardi O Zeitouni Xin Gu

PUBLICATIONS `The Double Dixie Cup Problem,'' (with D. J. Newman) Amer. Math. Monthly 67, (1960), 58-61.

``Symmetric Random Walk,'' Trans. Amer. Math. Soc. 104, (1962), 144-153.

``A Limit Law Concerning Moving Averages,'' Ann. Math. Statist. 35, (1964), 424-428.

``A Local Limit Theorem,'' Ann. Math. Statist. 35, (1964), 419-423.

``Recurrent Random Walks With Arbitrarily Large Steps,'' Bull. Amer. Math. Soc. 70, (1964), 540-542.

``The Singularity of Gaussian Measures in Function Space,'' Proc. National Academy of Sciences, USA 52, (1964), 430-433.

``An Application of Group Random Walk Theory to Random Walks in Euclidean Space,'' (with K. Hinderer) Archives Math. 16, (1965), 75-80.

``The Estimation of Some Determinants of Toeplitz-Type,'' (with H.O.Pollak) Proc. Amer. Math. Soc. 16, (1965), 919-922.

``Distinguishing a Sequence of Random Variables From a Translate of Itself,'' Ann. Math. Statist. 36, (1965), 1107-1112.

``Gaussian Measures in Function Space,'' Pacific J. Math. 17, (1966), 167-173.

``Radon-Nikodym Derivatives of Gaussian Measures,'' Ann. Math. Statist. 37, (1966), 321-354.

``Ordered Cycle Length in a Random Permutation,'' (with S. P. Lloyd) Trans. Amer. Math. Soc. 121, (1966), 340-357.

``Appendix to Stochastic Point Processes: Limit Theorems by J. R. Goldman,'' Ann. Math. Statist. 38, (1967), 771-779.

``A First Passage Problem for the Wiener Process,'' Ann. Math. Statist. 38, (1967), 1912-1914.

``On the Best Finite set of Linear Observables for Discriminating Two Gaussian Signals,'' (with T. T. Kadota) IEEE Trans. on Information Theory 13, (1967), 278-284.

``Wiener Integrals Associated with Diffusion Processes,'' (with V. E. Benes) Theory of Probability 13, (1968), 498-501.

``Real Zeros of Random Polynomials,'' (with B. F. Logan) Proc. London Math. Soc. 18, (1968), 29-35.

``Real Zeros of Random Polynomials II,'' (with B. F. Logan) Proc. London Math. Soc. 18, (1968), 308-314.

``Explicit Solutions to Some Problems of Optimal Stopping,'' Ann. Math. Statist. 40, (1969), 993-1010.

``Binary Communication Over the Gaussian Channel Using Feedback with a Peak Energy Constraint,'' (with J. K. Wolf A. D. Wyner J. Ziv) IEEE Trans. on Information Theory 15, (1969), 476-478.

``Conditions for Absolute Continuity Between a Certain Pair of Probability Measures,'' (with T. T. Kadota) Z. Wahrscheinlichkeitstheorie Verwandte Geb. 16, (1970) 250-260.

``On the Supremum of a Gaussian Process,'' (with H. J. Landau) Sankhya A 32, (1970), 369-378.

``Continuity of Gaussian Processes,'' (with M. B. Marcus) Trans. Amer. Math. Soc. 151, (1970), 377-391.

``On the Supremum of S(N)/N,'' (with B. J. McCabe) Ann. Math. Statist. 41, (1970), 2166-2168.

``Problem 68-17 (An Integral),'' (with B. F. Logan C. L. Mallows) SIAM Review 12, (1970), 153-154.

``First Passage Time for a Particular Gaussian Process,'' Ann. Math. Statist. 42, (1971), 946-951.

``Covering the Circle With Random Arcs,'' Israel J. Math. 11, (1972), 328-345.

``Covering the Line With Random Intervals,'' Z. Wahrscheinlichkeitstheorie Verwandte Geb. 23, (1972), 163-170.

``Sample Behavior of Gaussian Processes,'' (with M. B. Marcus) Proc of 6th. Berkeley Symp. (1972), 423-442.

``Supremum of an Integral, Problem 71-18,'' (with B. F. Logan) SIAM Rev. 14, (1972), 500-501.

``Inability of Humans to Discriminate Between Visual Textures That Differ Only in Third-Order Statistics (Revisited),'' (with B. Julesz H. L. Frisch E. N. Gilbert) Perception 2, (1973), 391-405.

``Limit Distributions of Self-Normalized Sums,'' (with B. F. Logan C. L. Mallows S. O. Rice) Ann. Prob. 1, (1973), 788-809.

``A Birth and Death Model of Neuron Firing,'' (with B. F. Logan) J. Appl. Prob. 11, (1973), 369-373.

``Error Rates on a Data Link With Nonlinear Regeneration,'' (with J. E. Mazo J. Salz) IEEE Trans. on Communications 21, (1973), 671-679.

``A Path Space Picture for Feynman-Kac Averages,'' (with H. Ezawa J. R. Klauder) Ann. Phys. 88, (1974), 588.

``On the Divergence of Certain Integrals of the Wiener Process,'' (with J. R. Klauder H. Ezawa) Ann. Inst. Fourier 24, (1974), 189-193.

``The Fourier Reconstruction of a Head Section,'' (with B. F. Logan) IEEE Trans. on Nuclear Science 21, (1974), 21-43.

``Reconstructing Interior Head Tissue From X-ray Transmissions,'' (with B. F. Logan) IEEE Trans. on Nuclear Science 21, (1974), 228-236.

``Vestigial Effects of Singular Potentials in Diffusion Theory and Quantum Mechanics,'' (with H. Ezawa J. R. Klauder) J. Math. Phys. 16, (1975), 783-799.

``Optimal Reconstruction of a Function from its Projections,'' (with B. F. Logan) Duke Math. J. 42, (1975), 645-659.

``Correction to ``Random-Nikodym Derivatives of Gaussian Measures,'' Ann. Prob. 5, (1976), 315-317.

``First-Passage Time for a Particular Stationary Periodic Gaussian Process,'' (with D. Slepian) J. Appl. Prob. 13, (1976), 27-38.

``Simulated Artifacts in Computerized Tomography,'' (with J. A. Stein) Reconstructive Tomography in Diagnostics Radiology and Nuclear Medicine (editor M. M. Ter-Pogossian), 1976 ``A Variational Problem for Random Young Tableaux,'' (with B. F. Logan) J. Advances in Math. 26, (1977), 206-222.

``Orthogonal Bases for Two Subspaces With All Mutual Angles Acute,'' (with S. Gutmann) Indiana J. Math. 27, (1978), 79-90.

``Computerized Tomography: The New Medical X-Ray Technology,'' (with J. B. Kruskal) Amer. Math. Monthly 85, (1978), 420-439.

``Problem 78-16 for SIAM Review,'' (with A. M. Odlyzko) SIAM Review 20, (1978) ``Two-Dimensional Remote Air-Pollution Monitoring via Tomography,'' (with R. L. Byer) Optics Letters 4, (1979), 75-77.

``On the Lower Tail of Gaussian Seminorms,'' (with J. Hoffmann-Jorgensen R. M. Dudley) Ann. Prob. 7, (1979), 319-342.

``A New Design for High Speed Computerized Tomography,'' (with D. Maydan Z.H. Cho) IEEE Trans. on Nuclear Science 26, (1979), 2870-2871.

``The Joint Density of the Maximum and Its Location for a Wiener Process with Drift,'' J. Appl. Prob. 16, (1979), 423-427.

``The Tuning Fork Artifact in Computerized Tomography,'' (with S. K. Hilal R. A. Schulz) Computer Graphics and Image Processing 10, (1979), 246-255.

``On Contingent Claims that Insure Ex-Post Optimal Stock Market Timing,'' (with H. B. Sosin M. B. Goldman) J. Finance 34, (1979), 401-413.

``Some Solvable Stochastic Control Problems,'' (with V. E. Benes H. S. Witsenhausen) Stochastics 4, (1980), 39-83.

``Computerized Tomography and Nuclear Magnetic Resonance,'' J. Computerized Tomography 4, (1980), 94-107.

``The FKG Inequality and Some Monotonicity Properties of Partial Orders,'' SIAM J. Algebraic and Discrete Methods 1, (1980), 295-299.

``On Prediction of Moving-Average Processes,'' (with D. Slepian A. D. Wyner) Bell Sys. Tech. J. 59, (1980), 367-415.

``Distribution Functions Invariant Under Residual-Lifetime and Length-Biased Sampling,'' (with Y. Vardi B. F. Logan) Z. Wahrscheinlichkeitstheorie Verwandte Geb. 56, (1981), 13-38.

``On Skew Brownian Motion,'' (with J. M. Harrison) Ann. Prob. 9, (1981), 309-313.

``Entropy of the Sum of Independent Bernoulli Random Variables and,'' of the Multinomial Distribution (with I. Olkin) Contributions to Probability (editor J. Gani V. K. Rohatgi) Academic Press, 1981, New York, 201-206.

``On the Integral of the Absolute Value of the Pinned Wiener Process,'' Ann. Prob. 10, (1982), 234-239.

``A Variational Problem for Random Young Tableaux,'' (with B. F. Logan) Young Tableaux in Combinatorics, Invariant Theory, and Algebra (editor Joseph P. S. Kung) Academic Press New York, (1982), 63-79.

``A Poisson Process Whose Rate is a Hidden Markov Process,'' (with D. S. Freed) Adv. Appl. Prob. 14, (1982), 21-36.

``The XYZ Conjecture and the FKG Inequality,'' Ann. Prob. 10, (1982), 824-827.

``Maximum Likelihood Reconstruction for Emission Tomography,'' (with Y. Vardi) IEEE Trans. on Medical Imaging 1, (1982), 113-122.

``An explicit solution to a problem in nonlinear stochastic control,'' Nonlinear Stochastic Problems (editor R.S.Bucy J.M.F.Moura) D.Reidel Dordrecht, Holland, (1982), 229-232.

``Scope of Pure and Applied Tomography,'' Computed Tomography (editor L. A. Shepp) American Mathematical Society, Providence, R.I. 27, (1983), 1-6.

``On the Sum of Symmetric Random Variables,'' (with R. Chen) The Amer. Statistician 37, (1983), 237.

``On the Average Product of Gauss-Markov Variables,'' (with B. F. Logan J. E. Mazo A. M. Odlyzko) The Bell System Tech. Jour. 62, (1983), 2993-3006.

``A Tandem Storage System and Its Diffusion Limit,'' (with J. Michael Harrison) Stoc. Proc. and their Appl. 16, (1984), 257-274.

``Maximum Likelihood PET with Real Data,'' (with Y. Vardi J. B. Ra S. K. Hilal Z. H. Cho) IEEE Trans. Nucl. Sci. 31, (1984), 910-913.

``Optimal Sequential Selection of N Random Variables under a Constraint,'' (with R. W. Chen V. N. Nair A. M. Odlyzko Y. Vardi) J. Appl. Prob. 21, (1984), 537-547.

``Diffusion, Cell Mobility, and Bandlimited Functions,'' (with N. Bauman H. J. Landau B. F. Logan) SIAM J. Math. 44, (1984), 1232-1245.

``Remarks and open problems in the area of the FKG inequality,'' (with J.-D. Kumar R. A. Vitale) Inequalities in Statistics and Probability (editor Y.L.Tong) Institute of Mathematical Statistics, Hayward, Cal. 5, !984), 121-126.

``The Set of Real Numbers Left Uncovered by Random Covering Intervals,'' (with P. J. Fitzsimmons B. Fristedt) Z. Wahrscheinlichkeitstheorie verw. Gebiete 70, (1985), 175-189.

``A Stochastic Model of Fragmentation in Dynamic Storage Allocation,'' (with E. G. Coffman T. T. Kadota) SIAM J. on Computing 14, (1985), 416-425.

``A Statistical Model for Positron Emission Tomography,'' (with Y. Vardi L. Kaufman) J. of the Amer. Stat. Assoc. 80, (1985), 8-37.

``The Stationary Distribution of Reflected Brownian Motion in a Planar Region,'' (with J. M. Harrison H. J. Landau) Ann. Prob. 13, (1985), 744-757.

``Enumerating Pairs of Permutations with the Same Up-Down Form,'' (with C. L. Mallows) Discrete Math 54, (1985), 301-311.

``On the Asymptotic Optimality of First-Fit Storage Allocation,'' (with E. G. Coffman T. T. Kadota) IEEE Trans. on Software Engineering 11, (1985), 235-239.

``Optimal Sequential Selection of Secretaries,'' (with E. G. Coffman C. L. Mallows V. N. Nair Y. Vardi) Math. of O.R. 10, (1985), 709-715.

``Component-Level Redundancy is Better than System Level Redundancy for Channel Graphs,'' (with F. K. Hwang) Networks (1985), 449-453.

``An inequality conjectured by Hajela and Seymour in combinatorial geometry,'' (with H. J. Landau B. F. Logan) Combinatorica 5, (1985), 337-342.

``A Probabilistic Analysis of Dynamic Storage Allocation,'' (with E. G. Coffman T. T. Kadota F. T. Leighton) Proc. Int. Seminar on Teletraffic Theory and Computer Performance Evaluation North Holland (1986), 275-295.

``Computed Tomography of PKM \& AKM Exit Cones,'' (with S. Srivastava) ATT Tech. J. 65, (1986), 78-83.

``A View of Reconstruction Tomography: XCT, ECT, NMRCT,'' SPIE 671, (1986), 1-5.

``On the Number of Crossings of Empirical Distribution Functions,'' (with V. N. Nair M. J. Klass) The Annals of Probability 14, (1986), 877-890.

``Some Inequalities Concerning Random Subsets of a Set,'' (with F. K. Hwang) IEEE Trans. Inf. Th. 33, (1987), 596-598.

``On the Probability of Covering the Circle by Random Arcs,'' (with F. W. Huffer) J. Appl. Prob. 24, (1987), 422-429.

``Admissibility as a Touchstone,'' (with A. Mandelbaum) The Annals of Statistics 15, (1987), 252-268.

``A Queueing Analysis of Hashing with Lazy Deletion,'' (with J. A. Morrison C. J. VanWyk) SIAM J. Comput. 16, (1987), 1155-1164.

``Limited angle reconstruction in tomography via squashing,'' (with J. A. Reeds) IEEE Trans. Med. Imaging 2, (1987), 89-97.

``On the number of leaves of a Euclidean minimal spanning tree,'' (with J. M. Steele W. F. Eddy) J. Appl. Prob. 24, (1987), 806-826.

``A counterexample to localization for multiple Fourier series,'' (with J. Price) Proc. of Centre for Math. Anal. of the Australian National University 15, (1987), 201-207.

``The Least Variable Phase Type Distribution is Erlang,'' (with David Aldous) Commun. Statist.-Stochastic Models 3, (1987), 467-473.

``Electrical Tomography,'' (with E. N. Gilbert) Open Problems in Communication and Computation (editor T. Cover B. Gopinath), (1987), 164-170 ``The Match Set of a Random Permutation has the FKG Property,'' (with P. C. Fishburn P. G. Doyle) Annals of Probability 16, (1988), 1194-1214.

``A Probabilistic Model for the Time to Unravel a Strand of DNA,'' (with R. J. Vanderbei) Stochastic Models 4, (1988), 229-314.

``New Insights into Emission Tomography via Linear Programming ,'' (with R. J. Vanderbei) NATO Advanced Study Institute International Conference on the Formation, Processing, and Evaluation of Medical Images (1988).

``Self-Avoiding Random Loops,'' (with Lester. E. Dubins Alon Orlitsky Jim A. Reeds) IEEE Trans. Inf Theory 34, (1988), 1509-1516.

``On the Evolution of Islands,'' (with P. G. Doyle C. Mallows A. Orlitsky) Israel Journal of Mathematics 67, (1989), 34-42.

``Connectedness of Certain Random Graphs,'' Israel Journal of Mathematics 67, (1989), 23-33.

``Tracking a Wiener Process with a Proces of Finite Energy,'' (with P. G. Doyle) Commun. Statist.-Stochastic Models 5, (1989), 327-334.

``Embedding Nonnegative Definite Toeplitz Matrices in Nonnegative Definite Circulant Matrices, with Application to Covariance Estimation,'' (with A. Dembo C. L. Mallows) IEEE Transactions on Information Theory 35, (1989), 1206-1212.

``A Convolution Inequality,'' (with Gavin Brown) Contributions to Prob and Stat; Essays in Honor of Ingram Olkin, Springer, New York (1989), 51-57.

``Monte Carlo Generation of Self-Avoiding Walks with Fixed Endpoints and Fixed Length,'' (with N. Madras A. Orlitsky) Journal of Statistical Physics 58, (1990) 159-183.

``Optimal Paths for a Car that Goes Both Forwards and Backwards,'' (with J. A. Reeds) Pacific Jour Math (1990), 367-393.

``Optimal Switching between a Pair of Brownian Motions,'' (with A. Mandelbaum R. J. Vanderbei) Ann. Prob. (1990), 1010-1033.

``Sets Uniquely Determined by Projections on Axes I. Continuous Case,'' (with P. C. Fishburn J. C. Lagarias J. A. Reeds) SIAM J. Appl. Math. 50, (1990), 288-306.

``The Exact Information Complexity of Indian Poker,'' (with L. H. Ozarow) IEEE Trans. Inf. Theory (1990), 232-235.

``Problem of the Nile,'' (with L. Flatto) SIAM Review 32, (1990), 302-304.

``On the Properties of a Tree-Structured Server Process,'' (with J. Komlos A. M. Odlyzko L. H. Ozarow) Ann. Appl. Prob. 1, (1991), 118-125.

``Synchronous Service on a Circle,'' (with R. W. Chen) Adv. Appl. Prob. 23, (1991), 140-151.

``Stochastic Models of Queue Storage,'' (with E. G. Coffman L. Flatto C. Knessl I. Mitrani) Probability in the Eng. and Inf. Sci. 2 (1988).

``On a Problem of Ammunition Rationing,'' (with Gordon Simons Yi-Ching Yao) Adv. Appl. Prob. 23, (1991), 624-641.

``Sets Uniquely Determined by Projections on Axes II. Discrete Case,'' (with P. C. Fishburn J. C. Lagarias J. A. Reeds) Discrete Mathematics 91, (1991), 149-159.

``Automatic Recognition of Bone for X-ray Bone Densitometry,'' (with Y. Vardi J. Lazewatsky J. Libeau J. A. Stein) SPIE-Image Processing Algorithms and Techniques II 1452, (1991), 216-224.

``Existence of Probability Measures with Given Marginals,'' (with Sam Gutmann J. H. B. Kemperman J. A. Reeds) Annals of Probability 19, (1991), 1781-1797.

``On the Integral of the Absolute Value of the Pinned Wiener Process, Acknowledgement of Priority,'' Ann. Prob. 19, (1991), 1397.

``Closed Form Characteristic Functions for Certain Random Variables Related to Brownian Motion,'' (with G. J. Foschini) Volume dedicated to M. Zakai Academic Press, Inc. (1991), 169-187.

``A Note on Conditional Exponential Moments and Osager-Machlup Functionals,'' (with Ofer Zeitouni) Ann. Prob. (1992), 652-654.

``A Conversation with Yuri Vasilevich Prokhorov,'' Stat. Sci. (1992), 123-130 ``Exponential Estimates for Convex Norms and Some Applications,'' (with Ofer Zeitouni) Progress in Probability (editor D. Nualart M. Sanz) Birkhauser (1993).

``The Sperner Capacity of Linear and Nonlinear Codes for the Cyclic Triangle,'' (with A. R. Calderbank P. Frankl R. L. Graham W.C. W. Li) J. Algebraic Combinatorics (1993), 31-48.

``The Russian Option: Reduced Regret,'' (with A. N. Shiryaev) Annals of Applied Probability 3, (1993), 631-640.

``On Optimal Stopping Rules and Maximal Inequalities for Bessel Processes,'' (with L. B. Dubins A. N. Shiryaev) Teoriya Veroyatnostey i ee Prim (in Russian) 38, (1993), 288-330.

``A Note on the Conditional Distribution of X when $|X-y|$ is given,'' (with Z. D. Bai) Statistics and Probability Letters 19, (1994), 217-219.

``A New Look at the "Russian Option",'' (with A. N. Shiryaev) Teoriya Veroyatnostey i ee Prim (in Russian) 39, (1994), 130-149.

``Inequalities and Positive-Definite Functions Arising from a Problem in Multi-dimensional Scaling,'' (with Andreas Buja B. F. Logan J. A. Reeds) Ann. Stat. 22, (1994), 406-438.

``Single-Channel User-Capacity Calculations for Self-Organizing,'' (with Leonard J. Cimini Gerard J. Foschini) Cellular Systems, IEEE Transactions on Communications 42, (1994), 3137-3143.

``Optimal tracking of Brownian motion,'' (with David Assaf Yi-Ching Yao) Stochastics and Stochastics Reports 54, (1995), 233-245.

``The complex zeros of random polynomials,'' (with Robert J. Vanderbei) Trans. Amer. Math. Soc. 347, (1995), 4365-4384.

``On the entropy of DNA: Algorithms and measurements based on memory and rapid convergence,'' (with M. Farach M. Noordewier S. Savari A. Wyner J. Ziv) Proceedings of the Sixth Annual ACM-SIAM Symposiumon Discrete Algorithms (1995).

``Hiring and firing optimally in a large corporation,'' (with Albert Shiryaev) Journal of Economic Dynamics and Control 20, (1996), 1523-1539.

``A dual Russian option for selling short,'' (with A. N. Shiryaev) Probability Theory and Mathematical Statistics, vol. ed. by Ibragimov and Zaitsev, Gordon and Breach (1996), 209-218.

``Risk vs. profit potential: A model for corporate strategy,'' (with Roy Radner) Journal of Economic Dynamics and Control 20, (1996), 1373-1393.

``The discrete Radon transform and its approximate inversion via linear programming,'' (with Peter Fishburn Peter Schwander Robert L Vanderbei) Discrete Math, 75, (1997), 39-61.

``Bandit problems with infinitely many arms,'' (with Donald A. Berry Robert W.Chen Alan Zame David C. Heath) Ann. Stat., 25, (1997), 2103-2116.

``A secretary problem with two decision makers,'' (with Robert W Chen Burton Rosenberg) J. Appl. Prob. 34, (1997), 1068-1074.

``Some linear models are necessarily parametric,'' (with Abram Kagan) Statistics and Probability Letters, 37, (1998), 77-80.

``An optimal acceptance policy for an urn scheme,'' (with Robert W Chen Alan Zame Andrew Odlyzko) Siam J Discrete Math 11, (1998), 183-195.

``Explicit sufficient invariants for an interacting particle system,'' (with Yoshiaki Itoh Colin Mallows) J Appl Prob 35, (1998), 633-641.

``A surprisingn Radon transform result and its application to motion detection,'' (with Thomas L Marzetta) IEEE Trans. on Image Proc., 8, (1999), 1039-1049.

``Parking cars with spin but no length,'' (with Yoshiaki Itoh) J Stat Phys., 97, (1999), 209-231.