Publications in VIVO

Co-author Network

Co-investigator Network

Gao, Frank (Fuchang) C Professor

Positions

Professor, Mathematics , College of Science
Member, Institute for Bioinformatics and Evolutionary Studies (IBEST) , University of Idaho

Publications

selected publications

academic article
- Metric Entropy of Classes of Sets with Positive Reach. Constructive Approximation. 47:357-371. 2018
- Metric Entropy of q-Hulls in Banach Spaces of Type-p. Proceedings of the American Mathematical Society. 145:5205-5214. 2017
- A reverse Gaussian correlation inequality by adding cones. Statistics and Probability Letters. 123:84-87. 2017
- Entropy of Convex Functions on R (d). Constructive Approximation. 46:565-592. 2017
- Upper tail probabilities of integrated Brownian motions. Science China-mathematics. 58:1091-1100. 2015
- Adaptive Minimax Regression Estimation over Sparse l(q)-Hulls. Journal of Machine Learning Research. 15:1675-1711. 2014
- A simple proof of the right-hand rule. College Mathematics Journal. 44:227-229. 2013
- Bracketing entropy of high dimensional distributions. Progress in Probability. 66:3-17. 2013
- Comparison for upper tail probabilities of random series. Journal of the Korean Statistical Society. 2013
- Global rates of convergence of the MLE for multivariate interval censoring. Electronic Journal of Statistics. 7:364-380. 2013
- Metric entropy and sparse linear approximation of l(q)-hulls for 0 < q <= 1. Journal of Approximation Theory. 166:42-55. 2013
- Persistence of iterated partial SUMS. Annales de l'Institut Henri Poincare: Probabilites et Statistiques. 49:873-884. 2013
- Small Deviations for a Family of Smooth Gaussian Processes. Journal of Theoretical Probability. 26:153-168. 2013
- On the rate of convergence of iterated exponentials. Journal of Applied Mathematics and Computing. 39:89-96. 2012
- Implementing the Nelder-Mead simplex algorithm with adaptive parameters. Computational Optimization and Applications. 51:259-277. 2012
- Exact value of the n-term approximation of a diagonal operator. Journal of Approximation Theory. 162:646-652. 2010
- How many laplace transforms of probability measures are there?. Proceedings of the American Mathematical Society. 138:4331-4344. 2010
- On the rate of convergence of the maximum likelihood estimator of a k-monotone density. Science In China Series A-mathematics. 52:1525-1538. 2009
- Entropy estimate for k-monotone functions via small ball probability of integrated Brownian motion. Electronic Communications in Probability. 13:121-130. 2008
- Metric entropy k- monotone functions via small deviation probability of integrated Brownian motions. Electronic Communications in Probability. 13:121-130. 2008
- Entropy estimate for high-dimensional monotonic functions. Journal of Multivariate Analysis. 98:1751-1764. 2007
- Logarithmic level comparison for small deviation probabilities. Journal of Theoretical Probability. 20:1-23. 2007
- Metric entropy of high dimensional distributions. Proceedings of the American Mathematical Society. 135:4009-4018. 2007
- Metric entropy of monotonic functions. Journal of Multivariate Analysis. 98:1751-1764. 2007
- Small ball probabilities for the Slepian Gaussian fields. Transactions of the American Mathematical Society. 359:1339-1350. 2007
- Logarithmic level comparison for small deviation probabilities. Journal of Theoretical Probability. 19:535-556. 2006
- Combinatorial dimension in fractional Cartesian products. Random Structures and Algorithms. 26:146-159. 2005
- Non-zero boundaries of Leibniz half-spaces. Proceedings of the American Mathematical Society. 133:1757-1762. 2005
- On the combinatorial dimensions. Random Structures and Algorithms. 26:146-159. 2005
- On the combinatorial dimensions. Random Structures and Algorithms. 26:146-159. 2005
- Entropy of absolute convex hulls in Hilbert spaces. Bulletin of the London Mathematical Society. 36:460-468. 2004
- Exact L-2 small balls of Gaussian processes. Journal of Theoretical Probability. 17:503-520. 2004
- Metric entropy of absolute convex hulls in Hilbert spaces. Bulletin of the London Mathematical Society. 36:460-468. 2004
- Comparison Theorems for Small Deviations of Random Series. Electronic Journal of Probability. 8:1-17. 2003
- Integrated Brownian motions and exact L-2-small balls. Annals of Probability. 31:1320-1337. 2003
- Intrinsic volumes and polar sets in spherical space. Mathematicae Notae. 1:159-176. 2003
- Laplace transforms via Hadamard factorization. Electronic Journal of Probability. 8:1-20. 2003
- The mean of a maximal likelihood estimator associated with Brownian bridges. Electronic Communications in Probability. 8:1-5. 2003
- Intrinsic volumes of the Brownian motion body. Discrete and Computational Geometry. 26:41-50. 2001
- Metric entropy of convex hulls. Israel Journal of Mathematics. 123:359-364. 2001
- A characterization of random Bloch functions. Journal of Mathematical Analysis and Applications. 252:959-966. 2000
- Maximal operators and Hilbert transforms along convex curves. Journal of Mathematical Research with Applications. 10:262-264. 1990

presentations

invited talk
- From Persistence to Brascamp-Lieb type inequalities, Speaker, IMS-China International Conference on Statistics and Probability 2013
- Persistence of partial sums of random walks, Speaker 2011
- An inequality of Haar Functions, Speaker, 2010 International Conference on Applied Analysis 2010
- Metric Entropy Methods in Probability, Speaker, 2010 Summer Program in Probability and Statistics 2010
- One-sided Probability of Iterated Sums of i.i.d. Random Variables, Speaker 2010
- How many Laplace transformations of probability measures are there?, Speaker 2009
- Rate of Convergence of MLE of a shape-constrained density, Speaker 2009
- Small ball probability of an infinitely differentiable Gaussian process, Speaker 2009
- Rate of convergence of the Maximum Likelihood Estimator on shape-constrained function classes, Speaker, IMS-China International Conference on Statistics and Probability 2008
- Metric Entropy Estimate of some shape-constrained function classes and its small ball connection, Speaker, Frontier Probability Days 2007 2007
- Entropy of high-dimensional monotonic functions, Speaker, CBMS/NSF Regional Research Conference in Mathematical Sciences: Probabilistic and Combinatorial Approach in Analysis 2006
- Diffusion-reaction and biofilm ecophysiology, Speaker 2005
- Riesz product and small deviation of some Gaussian random fields, Speaker, Conference on High Dimensional Probability (IV) 2005
- Small ball probability of Slepian random fields, Speaker, AMS Eastern Regional Conference 2005
- Small deviation probability estimate via analytic methods, Speaker, Joint IMS/CSSP International Conference on Statistics and Probability 2005
- Analytic methods in small deviation probability, Speaker, Conference on Gaussian Measures and Geometric Convexity 2004
- Biofilm modeling and related stochastic processes, Speaker, Fifth International India Statistics Conference 2004
- Geometric quantification via small deviation probability, Speaker, Second International Seminar in Probability 2004
- Spherical intrinsic volumes and relations with small deviation probabilities, Speaker, Mini-workshop on Small Deviation of Stochastic Processes and Related Fields 2003
- Metric entropy and the spaces of measures, Speaker, Thematic Programme on Asymptotic Geometric Analysis 2002
- Intrinsic volumes of Brownian bridges, Speaker, Summer Internship Program in Probability, the Center of Mathematical Sciences 2001
presentation
- Contributions of Wenbo Li on small ball probability and metric entropy, Speaker, IMS-China International Conference on Statistics and Probability 2013
- From Persistence to Brascamp-Lieb type inequalities, Speaker 2013
- Mathematical modeling of biofilms, Speaker 2003
- Probability problems in biofilms, Speaker 2003
- The convex hull problem and quantification of the Krein-Milman theo, Speaker, University of Idaho Mathematics Departmental Colloquium 2003
- Metric entropy on convex hulls, Speaker, University of Idaho Mathematics Departmental Colloquium 2000
- Some problems on majorizing measures, Speaker 2000
- On random Bloch functions, Speaker, University of Idaho Mathematics Departmental Colloquium 1999

Research

principal investigator on

Persistence of random processes awarded by Simons Foundation 2012 - 2017
Small deviation and geometric quantification awarded by NSF Division of Mathematical Sciences (DMS) 2004 - 2008
Solid angles and Gaussian processes 2002 - 2003

investigator on

Life at interfaces and the biocomplexity of extreme environments 2002 - 2005

Teaching

is major professor for

Metric Entropy under Generalized Convexity Thesis