202324 Courses
 Introduction to Statistical Methods: Precalculus
PSYCH 10, STATS 160, STATS 60 (Win)  Probability and gambling
MATH 77Q (Win, Spr)  Theory of Probability
STATS 116 (Aut)  Theory of Probability I
STATS 117 (Spr, Sum)  Why College? Your Education and the Good Life
COLLEGE 101 (Aut) 
Independent Studies (1)
 Independent Study
DATASCI 199 (Spr)
 Independent Study

Prior Year Courses
202223 Courses
 Applied Matrix Theory
MATH 104 (Aut, Spr, Sum)  Calculus
MATH 21 (Win)  Calculus, ACE
MATH 21ACE (Win)  Groups and Symmetry
MATH 109 (Spr)  Integral Calculus of Several Variables
MATH 52 (Aut)  Linear Algebra, Multivariable Calculus, and Modern Applications
MATH 51 (Sum)  Probability and gambling
MATH 77Q (Aut, Win)
202122 Courses
 Applied Matrix Theory
MATH 104 (Aut, Sum)  Linear Algebra, Multivariable Calculus, and Modern Applications
MATH 51 (Win, Spr, Sum)  Linear Algebra, Multivariable Calculus, and Modern Applications, ACE
MATH 51A (Spr)  Probability and gambling
MATH 77Q (Aut)
202021 Courses
 Applied Matrix Theory
MATH 104 (Sum)  Calculus
MATH 21 (Aut, Sum)  Calculus, ACE
MATH 21A (Aut)  Linear Algebra, Multivariable Calculus, and Modern Applications
MATH 51 (Win, Spr)  Linear Algebra, Multivariable Calculus, and Modern Applications, ACE
MATH 51A (Spr)
 Applied Matrix Theory
All Publications

Ultrasound Lesion Detectability as a Distance Between Probability Measures
IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL
2022; 69 (2): 732743
Abstract
Lesion detectability (LD) quantifies how easily a lesion or target can be distinguished from the background. LD is commonly used to assess the performance of new ultrasound imaging methods. The contrasttonoise ratio (CNR) is the most popular measure of LD; however, recent work has exposed its vulnerability to manipulations of dynamic range. The generalized CNR (gCNR) has been proposed as a robust histogrambased alternative that is invariant to such manipulations. Here, we identify key shortcomings of CNR and strengths of gCNR as LD metrics for modern beamformers. Using the measure theory, we pose LD as a distance between empirical probability measures (i.e., histograms) and prove that: 1) gCNR is equal to the total variation distance between probability measures and 2) gCNR is one minus the error rate of the ideal observer. We then explore several consequences of measuretheoretic LD in simulation studies. We find that histogram distances depend on bin selection that LD must be considered in the context of spatial resolution and that many histogram distances are invariant under measurepreserving isomorphisms of the sample space (e.g., dynamic range transformations). Finally, we provide a mathematical interpretation for why quantitative values such as contrast ratio (CR), CNR, and signaltonoise ratio should not be compared between images with different dynamic ranges or underlying units and demonstrate how histogram matching can be used to reenable such quantitative comparisons.
View details for DOI 10.1109/TUFFC.2021.3138058
View details for Web of Science ID 000748372800030
View details for PubMedID 34941507

Central Limit Theorem for Peaks of a Random Permutation in a Fixed Conjugacy Class of Sn
ANNALS OF COMBINATORICS
2021
View details for DOI 10.1007/s00026021005614
View details for Web of Science ID 000728240900001

On the joint distribution of descents and signs of permutations
ELECTRONIC JOURNAL OF COMBINATORICS
2021; 28 (3)
View details for DOI 10.37236/10222
View details for Web of Science ID 000685639400001

THE SYMMETRIC GROUP, ORDERED BY REFINEMENT OF CYCLES, IS STRONGLY SPERNER
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
2021; 149 (7): 27532761
View details for DOI 10.1090/proc/15183
View details for Web of Science ID 000651701800004

A central limit theorem for descents and major indices in fixed conjugacy classes of Sn
ADVANCES IN APPLIED MATHEMATICS
2021; 124
View details for DOI 10.1016/j.aam.2020.102132
View details for Web of Science ID 000604732200007

COVID19 highlights the issues facing blind and visually impaired people in accessing data on the web
W4A: Web Accessibility
2021: 115
View details for DOI 10.1145/3430263.3452432

The absolute orders on the Coxeter groups A(n) and Bn are Sperner
ELECTRONIC JOURNAL OF COMBINATORICS
2020; 27 (3)
View details for DOI 10.37236/8874
View details for Web of Science ID 000551390100001