NISTIR 7762 

Applied and Computational 

Mathematics Division 

Summary of Activities for Fiscal Year 2010 

NISTIR 7762 

Applied and Computational 

Mathematics Division 

Summary of Activities for Fiscal Year 2010 

Ronald F. Boisvert, Editor 

Applied and Computational Mathematics Division 

Information Technology Laboratory 

February 2, 2011 

U.S. Department of Commerce 

Gary Locke, Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Director 
 
Abstract

This report summarizes the technical work of the Applied and Computational Sciences Division of 

NIST’s Information Technology Laboratory. Part I (Overview) provides a high-level overview of the 

Division’s activities, including highlights of technical accomplishments during the previous year. Part II 

(Features) provides further details on ten projects of particular note this year. This is followed in Part III 

(Project Summaries) by brief synopses of all technical projects active during the past year. Part IV (Activity Data) provides listings of publications, technical talks, and other professional activities in which 

Division staff members have participated. The reporting period covered by this document is October 2009 

through December 2010. 

For further information, contact Ronald F. Boisvert, Mail Stop 8910, NIST, Gaithersburg, MD 20899-

8910, phone 301-975-3812, email boisvert@nist.gov, or see the Division’s web site at 

http://www.nist.gov/itl/math/index.cfm. 

Cover Visualization: The modulus of the Riemann theta function 5,0),|,(ˆθ Ω yxyixi ≤≤ , where Ω is 

the matrix defined in http://dlmf.nist.gov/21.4. Surface colors correspond to phase angle.This image, 

which originates in the NIST Digital Library of Mathematical Functions (http://dlmf.nist.gov/), was developed by Brian Antonishek, Qiming Wang, and Bonita Saunders. 

Acknowledgement: We are grateful to Robin Bickel for collecting the information and organizing the 

first draft of this report. 

Disclaimer: Certain commercial entities, equipment, or materials may be identified in this document in 

order to describe an experimental procedure or concept adequately. Such identification is not intended to 

imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it 

intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. 

Summary of Activities for Fiscal Year 2010 5

Contents

PART I: OVERVIEW......................................................................................................................... 9

Introduction............................................................................................................................... 11 

Highlights.................................................................................................................................. 13 

Technical Accomplishments .................................................................................................. 13

Technology Transfer and Professional Activities ................................................................. 15

Administrative News.............................................................................................................. 16

Recognition ........................................................................................................................... 19

PART II: FEATURES ..................................................................................................................... 23

A Special Functions Handbook for the Digital Age ................................................................. 25 

Linnik Densities, Logarithmic Diffusion Equations, and Blind Deconvolution of Hubble Space 

Telescope Imagery .................................................................................................................... 29 

Modeling Reactive Wetting ...................................................................................................... 32 

Large-scale Simulation of Suspensions .................................................................................... 34 

High Precision Calculations of Properties of Few-electron Atomic and Molecular Systems .. 36 

Nano-optics, and How to Squeeze Light Out of Quantum Dots............................................... 38 

Monte Carlo Methods for Computing Network Reliability...................................................... 40 

Up-conversion Single Photon Detectors and their Application in Measurement Science........ 42 

PART III: PROJECT SUMMARIES.................................................................................................. 45

Mathematics of Metrology........................................................................................................ 47 

Linnik Densities, Logarithmic Diffusion Equations, and Blind Deconvolution of Hubble 

Space Telescope Imagery...................................................................................................... 47

Modeling Reactive Wetting ................................................................................................... 47

Denoising of Helium Ion Microscope Nanoscale Imagery ................................................... 47

Sparse Representations in High Dimensional Geometry...................................................... 50

A Standard Candle for Extragalactic Metrology.................................................................. 50

Modeling Equilibrium, Stability and Transport during Magnetic Fusion............................ 51

A Structural Optimization Approach to Multihazard Design ............................................... 52

Analysis of Diffusion and Stress in Binary Alloys................................................................. 53

Modeling Fluid Flow in Materials Processing ..................................................................... 53

Modeling of Self-similar Grain Size Distributions................................................................ 54

Materials Data and Metrology for Application to Materials Processes............................... 54

Optimization for Inverse Problems in Mechanics................................................................. 55

Molecular Movies: Imaging Femtosecond Motion during Electrochemical Transitions..... 56

Accelerating Monte Carlo Simulation for Modeling Thermodynamic Properties................ 57
6 NIST Applied and Computational Mathematics Division 

Uncertainty in Virtual Measurements from Quantum Chemistry Models.............................57

Atmospheric Retention of Man-made CO2 Emissions ...........................................................58

Modeling the Fluid Dynamics of Tear Films on the Cornea.................................................59

Simulation of Bioregulatory Networks Involved in Cell Cycle Control ................................59

Automated Biological Cell Feature Identification.................................................................60

Estimating Volumes of Simulated Lung Cancer Nodules ......................................................61

Computing Geodesics for Shape Analysis .............................................................................62

Neural Networks ....................................................................................................................63

High Performance Computing and Visualization......................................................................64 

Large-scale Simulation of Suspensions .................................................................................64

High Precision Calculations of Properties of Few-electron Atomic and Molecular Systems

...............................................................................................................................................64

Nano-optics, and How to Squeeze Light out of Quantum Dots .............................................64

Modeling and Visualization of Cement Paste Hydration and Microstructure Development64

Modeling Clinical Tumors to Create Reference Data for Tumor Volume Measurement......65

Predicting Segmentation Accuracy for Biological Cell Images ............................................66

Visualizing Fire and the Resulting Deformation of Structures .............................................68

Measuring Errors in Polygonal Representations of Surfaces ...............................................69

Scientific Software ....................................................................................................................70 

Micromagnetic Modeling.......................................................................................................70

OOF: Finite Element Analysis of Material Microstructures.................................................71

Parallel Adaptive Refinement and Multigrid Finite Element Methods .................................72

Variable Projection for Nonlinear Least Squares Problems.................................................72

Digital Library of Mathematical Functions...............................................................................74 

A Special Functions Handbook for the Digital Age ..............................................................74

Visualization of Complex Functions Data.............................................................................74

Mathematical Knowledge Management ................................................................................75

Math Table Generation Service.............................................................................................77

Quantum Information ................................................................................................................78 

Up-conversion Single Photon Detectors and their Application in Measurement Science ....78

Quantum Computing Theory .................................................................................................78

Quantum Computing Benchmarks.........................................................................................79

Quantum State Estimation Theory and Applications.............................................................80

Quantum Communication......................................................................................................80

Foundations of Measurement Science for Information Systems...............................................82 

Monte Carlo Methods for Computing Network Reliability ...................................................82

Modeling Affiliations in Networks .........................................................................................82

Community and Cluster Detection in Network Graphs.........................................................82
Summary of Activities for Fiscal Year 2010 7

Network Modeling Toolkit..................................................................................................... 84

Network Security Risk Analysis Using Attack Graphs ......................................................... 84

Vulnerability of Selfish Routing to Attacks ........................................................................... 85

Analysis of a Distributed Protocol for a Multiple User Access Network ............................. 86

Modeling Failure Scenarios in Large Scale Computing Systems......................................... 87

Visualization and Analysis of the National Vulnerability Database..................................... 88

Visualization of Large Complex Networks............................................................................ 89

Advanced Combinatorial Testing for Systems ...................................................................... 90

Towards Self-organizing Mobile Sensor Networks............................................................... 91

PART IV: ACTIVITY DATA........................................................................................................... 93

Publications............................................................................................................................... 95 

Appeared ............................................................................................................................... 95

Refereed Journals.............................................................................................................. 95 

Journal of Research of NIST............................................................................................. 96 

Books ................................................................................................................................ 96 

Book Chapters................................................................................................................... 97 

Conference Proceedings.................................................................................................... 97 

Other Formal Publications ................................................................................................ 99 

Technical Reports ............................................................................................................. 99 

Accepted ................................................................................................................................ 99

In Review............................................................................................................................. 100

Presentations ........................................................................................................................... 101 

Invited Talks ........................................................................................................................ 101

Conference Presentations ................................................................................................... 102

Web Services........................................................................................................................... 104 

Software Released................................................................................................................... 104 

Conferences, Minisymposia, Lecture Series, Shortcourses.................................................... 105 

MCSD Seminar Series......................................................................................................... 105

Hosted Public Events .......................................................................................................... 105

External Events Organization............................................................................................. 105

Other Professional Activities .................................................................................................. 106 

Internal................................................................................................................................ 106

External............................................................................................................................... 106

External Contacts .................................................................................................................... 107 

PART V: APPENDIX..................................................................................................................... 109

Staff......................................................................................................................................... 111 

Glossary of Acronyms ............................................................................................................ 114 
8 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2010 9

Part I: Overview

 Part I 

 Overview 
10 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2010 11

Introduction

Founded in 1901, NIST is a non-regulatory federal agency within the U.S. Department of Commerce. 

NIST's mission is to promote U.S. innovation and industrial competitiveness by advancing measurement 

science, standards, and technology in ways that enhance economic security and improve our quality of 

life. The NIST Laboratory program is broad-ranging, with research efforts in physics, electrical engineering, materials science, chemistry, bioscience, engineering, fire research, and information technology. 

The Information Technology Laboratory (ITL) is one of six major laboratories at NIST. ITL seeks to 

(a) accelerate the development and deployment of information and communication systems that are reliable, usable, interoperable, and secure; (b) advance measurement science through innovations in 

mathematics, statistics, and computer science; and (c) conduct research to develop the measurements and 

standards infrastructure for emerging information technologies and applications. 

The Applied and Computational Mathematics Division (ACMD) is one of six technical Divisions in 

ITL. ACMD provides leadership within NIST in the use of applied and computational mathematics to 

solve science and engineering problems arising in measurement science and related applications. In that 

role Division staff members 

• perform research and development in applied mathematics and computer science and engineering, 

including analytical methods, numerical and symbolic algorithms, advanced computing and communications architectures and applications, and high performance scientific visualization; 

• engage in peer-to-peer collaborations in the application of mathematical and computational 

technologies to NIST problems; 

• develop and disseminate mathematical reference data, software, and related tools; and 

• work with internal and external groups to develop standards, test procedures, reference implementations, and other measurement technologies for advanced scientific computation on current and 

future architectures. 

Division staff is organized into four groups: 

Mathematical Analysis and Modeling Group (Timothy Burns, Leader) 

Performs research and maintains expertise in applied mathematics, mathematical modeling, and 

numerical analysis for application to measurement science. 

Mathematical Software Group (Daniel Lozier, Leader) 

Performs research and maintains expertise in the methodology and application of mathematical algorithms and software in support of computational science within NIST as well as in industry and 

academia. 

Computing and Communications Theory Group (Ronald Boisvert, Acting Leader) 

Performs research and maintains expertise in fundamental mathematics, physics, and measurement 

science necessary to enable the development of future computing and communications systems. 

High Performance Computing and Visualization Group (Judith Terrill, Leader) 

Performs research and maintains expertise in the methodologies and tools of high performance scientific computing and visualization for use in measurement science. 

The technical work of the Division is organized into six thematic areas; these are described in the 

sidebar. In Part III of this document we provide outlines of most ongoing technical projects of the Division. These are organized by thematic area. 

For the past three years, ITL has managed its technical work in a matrix-management structure built 

on a set of Laboratory-wide programs. During FY 2010 the ITL Programs were: 
12 NIST Applied and Computational Mathematics Division 

Complex Systems∗

Cyber and Information Security 

Enabling Scientific Discovery 

Health Care Information Technology* 

Identity Management Systems 

Information Discovery, Use and Sharing 

Pervasive Information Technology* 

Quantum Information* 

Trustworthy Information Systems 

Virtual Measurement Systems* 

 

∗

 Programs continuing into FY 2011 

Division Thematic Areas 

Mathematics of Metrology. Mathematics plays an important role 

in the science of metrology. Mathematical models are needed to 

understand how to design effective measurement systems, and to 

analyze the results they produce. Mathematical techniques are 

used to develop and analyze idealized models of physical phenomena to be measured, and mathematical algorithms are 

necessary to find optimal system parameters. Finally, mathematical and statistical techniques are needed to transform the resulting 

data into useful information. The goal of this work is to develop 

fundamental mathematical methods and analytical tools necessary 

for NIST to continue as a world-class metrology institute, and to 

apply them critical measurement science applications. 

Scientific Software. Modern science and engineering in general, 

and modern measurement science in particular, requires a wide 

variety of software tools for scientific discovery, exploration, and 

analysis. As scientific inquiry becomes deeper and more specialized, so must the supporting software tools. The goal of this work 

is to develop critical software tools that support measurement 

science at NIST, as well as computational science and engineering at large.

Foundations of Measurement Science for Information Systems. 

Modern information systems are astounding in their complexity. 

Software applications are built from thousands of interacting 

components. Computer networks interconnect millions of independently operating nodes. Large-scale networked applications 

provide the basis for services of national scope, such as financial 

transactions and electrical power distribution. In spite of our 

increasing reliance on such systems, our ability to build far outpaces our ability to secure. Protocols controlling the behavior of 

individual nodes lead to unexpected macroscopic behavior. Local 

power anomalies propagate in unexpected ways leading to largescale outages. Computer system vulnerabilities are exploited in 

viral attacks resulting in widespread loss of data and system 

availability. The long term stability of our critical infrastructure is 

simply unknown. Measurement science has long provided a basis 

for the understanding and control of physical systems. Similar 

types of deep understanding and insight are lacking for complex 

information systems. We seek to develop the mathematical foundations needed for the emergence of a true measurement science 

for complex networked information systems. 

High Performance Computing and Visualization. Computational capability is advancing rapidly. This means that modeling 

and simulation can be done with greatly increased fidelity (e.g., 

higher resolution, more complex physics). However, developing 

large-scale parallel applications remains highly challenging, requiring expertise that application scientists rarely have. In 

addition, the hardware landscape is changing rapidly so new 

algorithmic techniques must constantly be developed. We are 

developing and applying facilities and expertise of this type for 

application to NIST problems. Large scale computations and 

laboratory experiments invariably produce large volumes of scientific data, which cannot be readily comprehended without some 

form of visual analysis. We are developing the infrastructure 

necessary for advanced visualization of scientific data, including 

the use of 3D immersive environments and applying this to NIST 

problems. One of our goals is to develop the 3D immersive environment into a true interactive measurement laboratory. 

Digital Library of Mathematical Functions. The special functions of applied mathematics are fundamental tools enabling 

modeling and analysis in all areas of science and engineering. To 

make effective use of such functions, practitioners must have 

ready access to a reliable source of information on their properties. The goal of this work is the development and dissemination 

of definitive reference data on the special functions of applied 

mathematics. The centerpiece of this effort is the DLMF, a freely 

available interactive and richly linked online resource.

Quantum Information. An emerging discipline at the intersection 

of physics and computer science, quantum information science 

(QIS) is likely to revolutionize science and technology in the 

same way that lasers, electronics, and computers did in the 20th

century. By encoding information into quantum states of matter, 

one can, in theory, exploit the seemingly strange and counterintuitive behavior of quantum systems to enable phenomenal 

increases in information storage and processing capability, as well 

as communication channels with extremely high levels of security. Although many of the necessary physical manipulations of 

quantum states have been demonstrated experimentally, scaling 

these up to enable fully capable quantum computers remains a 

grand challenge. We are engaged in (a) theoretical studies to 

understand the true power of quantum computing, (b) collaborative efforts with the multi-laboratory experimental quantum 

science program at NIST to characterize and benchmark specific 

physical implementations of quantum information processing, and 

(c) the development and assessment of technologies for quantum 

communication. 
Summary of Activities for Fiscal Year 2010 13

Late in 2010 ITL changed its program management structure, maintaining only five of these programs 

(the starred ones), and transitioning the remainder to Division-level management. The project summaries 

in Part III of this report indicate ITL program affiliations during FY 2010. 

NIST itself underwent a significant organizational realignment effective October 1, 2010. The 

new structure includes two measurement labs, two technology labs, and two user facilities: 

Physical Measurement Laboratory (PML) 

Material Measurement Laboratory (MML) 

Engineering Laboratory (EL) 

Information Technology Laboratory (ITL) 

Center for Nanoscale Science and Technology (CNST) 

National Center for Neutron Research (NCNR) 

When identifying our collaborators from other NIST Laboratories in this report we use the new organizational structure. 

Highlights

In this section we identify some of the major accomplishments of the Division during the past year. We 

also provide news related to ACMD staff. 

Technical Accomplishments 

ACMD has made significant technical progress on many fronts during the past year. Here we highlight a 

few examples. Further details are provided in Part II (Features) and Part III (Project Summaries). 

 Digital Library of Mathematical Functions. The NIST Digital Library of Mathematical Functions 

(DLMF), the 21st century successor to the classic Handbook of Mathematical Functions (Abramowitz and 

Stegun, eds., NBS, 1964), was released in May 2010. The DLMF is a free interactive web service provided by NIST. Most of the mathematical content is also be available in book form as the NIST Handbook 

of Mathematical Functions which has been published by Cambridge University Press. The DLMF is the 

result of a 12 year effort managed by four NIST editors: F. W. J. Olver, D. W. Lozier, and R. F. Boisvert 

of the ACMD, and C. W. Clark of the NIST PML. In all, the project has had some 50 participants worldwide, serving as editors, authors, validators, and consultants. The web site, which includes innovative 

presentation, search, and interactive graphics, was designed and executed by ACMD staff. Reception of 

the new resources has been quite positive. The web site and book were officially launched at a workshop 

on the Numerical Solution of the Painlevé Equations on May 12 in Edinburgh, Scotland. The web site 

was “slashdotted” a few days after it was released, resulting in a single day with nearly 25,000 user visits. 

In the first four months of operation, the site has registered more than 157,000 user visits accounting for 

more than 620,000 page views. Flattering reviews have appeared in the September issue of the SIAM 

News and the October issue of Optics and Photonics News. [See page 25.] 

 Mathematics of Metrology. We continue to make critical contributions to the measurement science program at NIST via the application of our expertise in mathematical analysis and modeling. Our 

collaborative modeling efforts are highly diverse, ranging from studies of reactive wetting of metals to the 

magnetic properties of nanostructures. We also continue to develop new analysis techniques. For example, Alfred Carasso of ACMD has developed an innovative technique for removing noise from images 

while preserving fine-scale details. Existing techniques for removing noise typically wash out fine detail 

in the process. Carasso’s techniques employ extremely sophisticated mathematics, including fractional 

diffusion, low exponent Lévy stable laws, and “slow motion” solution of parabolic equations. Carasso’s 

tests demonstrate that the new method is superior to the best of existing methodologies based on the split 

Bregman iteration and on the curvelet transform. The new method has been applied to the denoising of 

state-of-the-art Helium Ion Microscope nanoscale imagery in collaboration with András Vladár of NIST 

PML. A paper describing the new method has been submitted for publication. [See page 47.] 
14 NIST Applied and Computational Mathematics Division 

 High Performance Computing and Visualization. ACMD leads NIST in the application of parallel 

computing to problems in measurement science. For example, due to ACMD involvement, NIST’s ability 

to perform high fidelity simulations of the flow of complex suspensions has achieved best-in-the-world 

status. Armed with substantial awards of computer time on Argonne National Laboratory’s Blue Gene 

supercomputer from DoE’s INCITE program, William George and his colleagues in ACMD and the 

NIST EL have significantly enhanced our understanding of the flow of fresh concrete, a dense suspension 

composed of cement, water, sand, and rocks. Novel visual analysis techniques have also been critical to 

generating insights from the voluminous simulation output. This work, performed under the aegis of the 

Virtual Cement and Concrete Testing Lab Consortium, is a critical step in transforming the design of concrete materials from an art to a science, which is expected to have significant impact on this $100B US 

industry whose products are the foundation of much of the Nation’s physical infrastructure. This work 

was recognized with the Department of Commerce’s Silver medal in 2009. [See pages 19 and 34.] 

 Scientific Software. ACMD has three major software systems under active development: 

OOMMF, a system for micromagnetic modeling, OOF, a system for modeling of materials with complex 

microstructure based on the analysis of real or simulated material imagery, and PHAML, a finite element 

partial differential equations solver implementing parallel hierarchical adaptive multigrid methods. Each 

has made significant strides this year. OOMMF, originally designed as reference software for the testing 

of solution algorithms, continues to be the solver of choice in the nano-magnetic modeling community, 

this year surpassing the milestone of 1,000 cited uses in refereed publications. [See page 70.] OOF was 

downloaded more than 1,600 times this year, and saw considerable usage via Purdue University’s 

nanoHUB portal. A 3D version of OOF, a significant undertaking, is now at the beta stage. [See page 71.] 

Finally, PHAML is being used at NIST as both the platform for a comprehensive study of hp-adaptive 

solution strategies, and for the study of the eigenstates of optical traps for neutral atoms for application in 

quantum information processing. [See page 72.] 

 Quantum Information. ACMD continues to be the principal focus at NIST for quantum information theory, providing the theoretical underpinnings for a wide variety of experimental efforts being 

undertaken in the NIST Laboratories. For example, Scott Glancy and Manny Knill of ACMD were part of 

a team of NIST researchers who this year created “quantum cats” made of photons (particles of light), 

boosting prospects for manipulating light in new ways to enhance precision measurements as well as 

computing and communications based on quantum physics. The experiments repeatedly produced light 

pulses that each possessed superpositions of two exactly opposite properties—specifically, opposite 

phases—a so-called optical Schrödinger's cat. This quantum state was the first to be realized by detecting 

three photons at once and was one of the largest and most well-defined cat states ever made from light. 

Glancy developed a survey of methods for producing optical cats that was the basis for the experiment. 

Glancy and Knill developed techniques for quantum state tomography that were used in the analysis of 

experimental results. A paper describing the accomplishment appeared in Physical Review A in September 2010; Glancy was second author of ten. The accomplishment was subsequently highlighted in Nature 

Photonics. [See page 80.] 

 Also this year, in an effort to consolidate ITL’s quantum information research program within a 

single Division, ACMD gained a group of scientists specializing in quantum optics experimentation. This 

team, lead by Xiao Tang, has been developing and evaluating quantum communication technologies and 

systems. One of their recent accomplishments, a spin-off of highly successful efforts to demonstrate highspeed quantum key distribution systems, has been the development of a highly sensitive (i.e., singlephoton-level) near-infrared spectrometer based on photon upconversion technology. This year the team 

used this device in a collaboration with physicists in the NIST CNST on a first-time demonstration of the 

conversion of near-infrared 1,300 nm wavelength single photons emitted from a true quantum source, a 

semiconductor quantum dot, to a near-visible wavelength of 710 nm. The ability to change the color of 

single photons makes them much easier to detect, thus aiding in the development of quantum systems for 

applications in quantum communication, computation and metrology. A paper describing this achievement was published in Nature Photonics in October 2010. [See page 42.] 

 Foundations of Measurement Science for Information Systems. A major new focus of ACMD, 

bolstered by a significant infusion of cybersecurity funding during the last three years, is the quest to de-
Summary of Activities for Fiscal Year 2010 15

velop the mathematical foundations of measurement science for information systems. It is hoped that this 

will begin to provide a solid science base to inform ITL’s efforts to improve computer and communication systems security and reliability within government and industry. Our early efforts in this area have 

primarily focused on developing an understanding of how the structure and dynamics of interconnected 

systems, i.e., abstract networks, relate to overall system performance. For example, a fundamental measure of the reliability of a network is its reliability polynomial. This function gives the probability that a 

network will remain connected given that each edge can fail independently with a probability p. One 

definition for the reliability polynomial R of a connected graph G with m edges and for the edge failure 

probability p is 

jmj m

j

j ppapGR −

=

∑ −= )1();(

1

where aj is the number of distinct connected subgraphs of G with exactly j edges. The problem in using 

the reliability polynomial for network analysis has been the fact that computing the polynomial itself is 

computationally intractable. (Technically, the problem is #P complete.) Thus the best we can expect to do 

in general is to approximate the polynomial. Brian Cloteaux and Isabel Beichl of ACMD have developed 

a new and highly efficient method to do this. Their approach has two advantages. First, while there are 

several algorithms that provide pointwise approximations of the polynomial, they approximate the polynomial coefficients themselves. Secondly, their method has shown much faster rate of convergence than 

previously proposed methods. A paper describing this work appeared in the March 2010 issue of the journal Congressus Numerantium. [See page 40.] 

Game theory is another important mathematical tool for modeling the dynamics of computer network attacks. This year, Vladimir Marbukh of ACMD, working with Daniel Genin and Anastase Nakassis 

of ITL’s Advanced Networking Technologies Division, used game-theoretic methods to demonstrate that 

proposed user-directed (“selfish”) Internet routing strategies are particularly vulnerable, in the sense that 

an agile attacker of very limited power can inflict significant damage on overall network performance. 

Their paper on this result was cited with a best contribution award at the 2010 International Conference of 

Information Security and Internet Engineering. [See page 85.] 

Software testing can also be greatly improved with fundamental mathematical insights. ACMD 

mathematicians are part of an ITL team making significant advances to a technology known as combinatorial testing. This is a black box testing approach in which combinations of inputs are selected in order to 

ensure that all 2-way, 3-way, 4-way, etc. combinations of input parameters appear in a test suite. This approach is notable because it ensures that the most likely sources of errors – interactions among small 

numbers of parameters – are exercised in a minimal number of tests. Raghu Kacker of ACMD and Rick 

Kuhn of the ITL Computer Security Division, working with colleagues from the University of Texas at 

Arlington have recently applied combinatorial testing to the detection of buffer overflow vulnerabilities. 

Such coding lapses are among the most common used by hackers to infect and exploit computer systems. 

The team has built a prototype tool, called Fugai, which implements this approach. Empirical results of 

applying Fugai to several open source programs show that it may be quite effective in detecting buffer 

overflows. [See page 90.] 

Technology Transfer and Professional Activities 

The volume of technical output of ACMD remains high. During the last 18 months, Division staff members were (co-)authors of 38 articles appearing in peer-reviewed journals, two books, three book chapters, 

36 papers in conference proceedings, and eight other formal publications. Fourteen additional papers have 

been accepted for publication, while 28 others are undergoing review. Division staff members gave 26 

invited technical talks and presented 35 others in conferences and workshops. 

ACMD continues to maintain an active Web site with a variety of information and services, including the Digital Library of Mathematical Functions, the Guide to Available Mathematical Software, the 

Matrix Market, and the SciMark Java benchmark. During calendar year 2010, the division web server 
16 NIST Applied and Computational Mathematics Division 

satisfied more than 9.3 million requests for pages from more than 68,000 distinct hosts. In total, there 

have been more than 272 million “hits” on ACMD Web servers since they went online as NIST’s first 

web servers in 1994. The individual software packages that we produce and distribute also continue to see 

very high usage. Table 1 lists download counts for some of our most popular ones. Another indication of 

the successful transfer of our technology is references to our software in refereed journal articles. For example, our OOMMF software for nano-magnetic modeling was cited in 96 such papers which were 

published in 2010 alone (more than 1,000 such papers have been identified since 2001). 

Members of the Division are also active in professional circles. Isabel Beichl began a second term 

as Editor-in-Chief of Computing in Science & Engineering in January 2011. Staff members hold a total of 

ten additional editorial positions in peer-reviewed journals. They are also active in conference organization, serving on nine organizing/steering/program committees. Staff members organized three 

minisymposia at technical conferences in 2010. 

Service within professional societies is also prevalent among our staff. For example, Ronald Boisvert serves as Co-Chair of the Publications Board of the Association for Computing Machinery (ACM) 

and is a member of the ACM Council, the association’s board of directors. Daniel Lozier served as Secretary of the Society for Industrial and Applied Mathematics (SIAM) Activity Group on Orthogonal 

Polynomials and Special Functions. Staff members are also active in a variety of working groups. For 

example, Ronald Boisvert serves as Chair of the International Federation for Information Processing 

(IFIP) Working Group 2.5 on Numerical Software, Donald Porter is a member of the Tcl Core Team, and 

Bruce Miller is a member of W3C’s Math Working Group. Judith Terrill represents NIST on the High 

End Computing Interagency Working Group of the Federal Networking and Information Technology Research and Development (NITRD) Program. 

For further details, see Section IV, Activity Data. 

Administrative News 

The Division undertook a significant reorganization this past year in an attempt to align our structure to 

current activities and goals. Three of our four groups underwent name changes, and all had their mission 

statements updated. Nine staff members moved between groups. Also at midyear six staff members and 

associates from ITL’s quantum communications project were moved to ACMD in an effort to consolidate 

ITL’s quantum information research in one Division. The past year also saw many additional staffing 

changes. Among these are the following. 

• Geoffrey McFadden stepped down as Leader of the Mathematical Analysis and Modeling Group after serving 10 years in that position to devote his energies to his appointment as a NIST Fellow. 

Timothy Burns, a NIST research mathematician for 25 years, was named the new Group Leader. 

• Two new National Research Council (NRC) Postdoctoral Associates joined MCSD this year. The 

first, Elizabeth Moseman, has a PhD in Mathematics from Dartmouth (2007), with a thesis on the 

Table 1. Downloads of Selected Division Software Packages During CY 2010

Package Description Downloads 

JAMA Linear algebra in Java 25,995 

TNT Linear algebra using C++ templates 6,085 

SparseLib++ Sparse linear algebra in C++ 4,645 

OOMMF Modeling of nano-magnetic phenomena 4,500 

LAPACK++ Linear algebra in C++ 4,190 

OOF Modeling materials with complex microstructure 1,663 

f90gl Fortran 90 interface to OpenGL graphics 1,424 

spblas Sparse basic linear algebra components 1,185 

REGEN Modeling of cryocoolers 569 

PHAML Parallel adaptive solution of partial differential equations 506 
Summary of Activities for Fiscal Year 2010 17

combinatorics of coordinate percolation. She comes to ACMD most recently from the US Military 

Academy (West Point) where she had a faculty appointment. At NIST she is working with Isabel 

Beichl on methods for determining robustness in infrastructure networks. The second, Howard Cohl, 

comes to ACMD from the University of Auckland, New Zealand, where he completed a thesis on 

Fourier and Gegenbauer expansions for fundamental solutions of the Laplacian and powers in R d

and H d. Cohl is working with Daniel Lozier on rotationally-invariant expansions for solving linear 

inhomogeneous partial differential equations. 

• Three of ACMD’s NRC Postdoctoral Associates completed their terms this year. Bryan Eastin, who 

worked with Manny Knill on quantum information theory, took a position with Northrop Grumman; 

he remains a guest researcher with ACMD in Boulder. Aaron Lott, who worked with Geoffrey 

McFadden on techniques for solving partial differential equations important in materials modeling, 

moved to Lawrence Livermore National Laboratory. Finally, Valerie Coffman, who worked with 

Stephen Langer on our OOF system for modeling materials with complex microstructure, was 

awarded a two-year term appointment in ACMD to complete the development of OOF3D. 

• Sandy Ressler came to ACMD this year from ITL’s Information Access Division after a 3-year detail as Manager of ITL’s Complex Systems Program. An expert in computer graphics, including 3D 

web technologies, Ressler will be working on information visualization techniques and applications 

in ACMD’s High Performance Computing and Visualization Group. 

• Andrew Reid, a long time guest researcher and contractor in ACMD, was given a regular staff appointment by the NIST Materials Measurement Laboratory. Half his support will come from 

ACMD, where he continues to be a principal developer in our 

OOF project. 

• Three ACMD staff members spent part of the year on detail to 

other organizations. Robert Bohn returned to ACMD in September 2010 after a long stint working in the National 

Coordination Office of the National Information Technology 

Research and Development (NITRD) program. Bohn is now 

working on ITL’s Cloud Computing Program, which is providing leadership and guidance to catalyze the use of cloud 

computing within industry and government. Anthony Kearsley

returned to ACMD in late 2010 after a successful three-year detail as Manager of ITL’s Enabling Scientific Discovery 

Program. Finally, Jeffrey Fong spent the year on detail in 

NIST’s Technology Innovation Program as a TIP Associate. 

• David Gilsinn of ACMD retired from NIST at the end of 2010 

after 40 years of Federal service. Gilsinn, an expert in nonlinear 

dynamics, contributed to a wide variety of projects at NIST, including studies of the dynamics of high speed machining, 

assessments of surface roughness, the modeling of construction 

sites from LIDAR data, and the identification of features in cell 

imagery. 

During FY 2010 ACMD was able to support the work of 20 student interns, including six in the Student Undergraduate Research Fellowship (SURF) program, three graduate students in Boulder’s 

Professional Research Experience Program (PREP), and three high school volunteers. We also hosted five 

graduate students from French universities, which was facilitated by a Memorandum of Understanding 

signed in late 2009 between ITL and the Institut Supérieur d’Informatique, de Modélisation et de leurs 

Applications (ISIMA) at the University of Clermont-Ferrand. See Table 2 for a complete list. 

Figure 1. David Gilsinn retired from NIST 

in 2010 after 40 years of Federal service. 
18 NIST Applied and Computational Mathematics Division 

 

Table 2. Student Interns in MCSD

Name Institution Level Program Mentor Project Title 

Styvens 

Belloge 

ISIMA 

(France) G Guest Researcher J. Terrill Visualization and analysis of the National Vulnerability Database 

Guillaume 

Bousquet 

ISIMA 

(France) G Guest Researcher F. Hunt Applied mathematics and computational science 

Luis 

Catacora 

Montgomery 

Blair HS HS SHIP J. Terrill Gestures that cause actions in the Immersive Visualization Environment 

Amanda 

Crawford 

University of 

Colorado U SURF I. Beichl Sequential importance sampling for computing entropy 

Matthew 

Du 

Thomas 

Wootton HS HS SHIP J. Terrill 

Glass breakage using bullet physics 

engine, and a logic-based approach to 

machine learning 

Mark 

Girard 

Trinity 

University U SURF S. Glancy Quantum state estimation. 

William 

Hess 

Purdue 

University U STEP J. Terrill Lighting in the Immersive Visualization Environment 

Marlene 

Hildebrand 

Polytech 

(Nice) G Guest Researcher 

J. Terrill 

A. Peskin Visualization of medical images 

Nathan 

Jacobson 

Hood College U SURF R. Kacker Numerical simulation of coverage 

intervals 

Adam 

Meier 

University of 

Colorado G PREP E. Knill Quantum computer simulation 

Michael 

Mullan 

University of 

Colorado G PREP E. Knill Quantum computing theory 

Kevin 

Rawlings 

Carnegie Mellon University U STEP J. Terrill Visualization and analysis of the National Vulnerability Database 

Clement 

Rey 

ISIMA 

(France) G Guest Researcher R. Pozo Visualization of large complex networks 

Anshu 

Rustagi 

University of 

Illinois U STEP W. George Screen Saver Science 

Poorva 

Singal 

Franklin W. 

Olin College 

of Engineering 

U SURF J. Terrill Generating realistic patterns of glass 

breakage 

Becky 

Song 

Richard Montgomery HS HS SHIP J. Terrill Visualization and analysis of de- and 

re-mineralization of teeth 

Armeen 

Taeb 

University of 

Colorado U SURF A. Peskin Image processing and volumetric measurement 

Jean-Loup 

Traore 

Université 

Blaise Pascal, 

France 

G Guest 

Researcher J. Terrill Cement hydration modeling 

Luis 

Valentin 

The College of 

William and 

Mary 

U SURF B. Cloteaux Approximating the number of leaf 

nodes in trees. 

Yanbao 

Zhang 

University of 

Colorado G PREP E. Knill Tests of local realism 

Legend G: Graduate student 

U: Undergraduate student 

HS: High school student 

SURF: NIST Summer Undergraduate Student Fellowship Program. 

 PREP: NIST Professional Research Experience Program
Summary of Activities for Fiscal Year 2010 19

Recognition 

Division staff garnered a number of professional recognitions during the past year. These are described 

below. 

Awards 

o Department of Commerce Silver Medal. William George and Judith Terrill of ACMD were cowinners of a 2009 Silver Medal from the Department of Commerce for their work on the modeling 

and simulation of complex suspensions; see Figure 2. The Silver Medal recognizes “exceptional performance characterized by noteworthy or superlative contributions which have a direct and lasting 

impact within the Department.” Dale Bentz, Jeffrey Bullard, Edward Garboczi, and Nicos Martys of 

EL were co-winners. The award citation credits the group with the creation of the virtual cement and 

concrete testing laboratory 

(VCCTL), “which uses intensive computer simulation to 

mimic a physical testing laboratory and has proven to be 

capable of revealing behavior 

beyond the limits of traditional testing instruments.” 

o NIST Allen V. Astin Measurement Science Award. 

Andrew Dienstfrey of ACMD 

was a co-winner of NIST’s 

2009 Allen V. Astin Measurement Science Award for 

work in waveform metrology; 

see Figure 3. The award recognizes “outstanding 

achievement in the advancement of measurement science 

or in the delivery of measurement services”. Paul Hale 

and Dylan Williams of PML 

and Jack Wang of ITL’s Statistical Engineering Division 

were co-winners. The team 

was cited for “providing a 

world-first method for simultaneously calibrating highspeed electrical test equipment in both time and 

frequency domains with 

point-by-point uncertainty 

analysis, and for the first time 

making waveform calibrations traceable to fundamental 

physics.” The citation goes 

on to explain “The new 

method improves accuracy in 

calibrations of oscilloscopes, 

Figure 2. DOC Silver Medal Award Recipients. William George and Judith Terrill (second 

and third from left) of ACMD with co-winners Edward Garboczi, Dale Bentz, Nicos Martys, 

and Jeffrey Bullard of the NIST Engineering Laboratory.

Figure 3. Allen V. Astin Meaurement Science Award Winners: Andrew Dienstfrey (ACMD), 

Paul Hale (Physical Measurement Laboratory), Jack Wang (Statistical Engineering Division, 

Information Technology Laboratory).
20 NIST Applied and Computational Mathematics Division 

common test instruments that measure voltage in communications and 

electronic devices, and potentially could boost performance and save 

money in other fields ranging from medical testing to structural analysis 

and remote sensing.” 

o NIST EEO/Diversity Award. Ronald Boisvert of ACMD was the recipient 

of NIST’s Equal Employment Opportunity / Diversity Award for 2010. 

He was cited for “leadership and continuous membership on the ITL 

Diversity Committee and his commitment to fostering diversity. 

o ITL Outstanding Journal Paper. Bryan Eastin and Emanuel Knill of 

ACMD received the 2010 ITL Best Journal Paper Award for their article 

“Restrictions on Transversal Encoded Quantum Gate Sets,” which appeared in Physical Review Letters, Volume 102, Article Number 110502 

(March 20, 2009). The pair was cited “for exemplary scientific research 

and exposition in the field of fault-tolerant quantum computing.” In their paper Eastin and Knill 

proved that the ability of a quantum code to detect arbitrary errors on component subsystems is incompatible with the existence of a universal, transversal, and unitary encoded gate set. This result 

completely settles this long standing fundamental question in quantum information theory, showing 

that the search for a universal transversally encoded quantum gate set is futile. 

o ITL Associate of the Year. Qiming Wang, a guest researcher in ACMD was selected at the ITL Associate of the Year for 2010. Wang was recognized for her essential contributions to the Digital Library 

of Mathematical Functions project in the area of interactive 3D computer graphics. The ITL Associate 

of the Year Award recognizes one guest researcher each year for outstanding contributions to NIST 

programs.

o NIST Alumni Portrait Gallery. Cornelius Lanczos (1893-1974) was selected for recognition by the 

NIST Alumni Association as part of the NIST Portrait Gallery of Distinguished Scientists, Engineers 

and Administrators. The Gallery honors NIST alumni for outstanding career contributions to the work 

of the Institute. Portraits and biographies of those selected are displayed in the corridor of the NIST 

cafeteria in Gaithersburg. Lanczos was a 

NIST staff member in 1943-44 participating in the NBS Math Tables Project, and 

again in 1949-52 as a member of the NBS 

Institute for Numerical Analysis. A towering figure in applied mathematics and 

theoretical physics, Lanczos’ best-known 

contribution to science, as measured by citations, was made while at NBS. The 

“Lanczos method” for calculating the eigenvalues of large matrices was published 

in the Journal of Research of NBS in 

1950. 

Best Contribution Awards 

o Best Paper Award at Info Security Conference. Vladimir Marbukh of the ACMD, 

along with Daniel Genin and Anastase 

Nakassis of the ITL Advanced Networking Technologies Division were awarded 

a Certificate of Merit for outstanding contribution to the 2010 International 

Conference of Information Security and 

Figure 5. Cornelius Lanczos’ daughter-in-law Alice (Seattle, WA) and 

grandson Andrew (Tel Aviv, Israel) attended the Alumni Portrait Gallery 

induction ceremony held in Gaithersburg, MD on October 1, 2010. Lanczos’ portrait is visible on the bottom row. 

Figure 4. Ronald Boisvert won 

NIST’s EEO/Diversity Award. 
Summary of Activities for Fiscal Year 2010 21

Internet Engineering, which was held in London on June 30 – July 2, 2010. The paper, Vulnerability 

of Selfish Routing to Attacks: Game-theoretic Models and Initial Results, presented a model of a potential strategic attack on a class of network packet routing algorithms. They demonstrated that even a 

weak attacker can inflict serious damage (as measured by degradation in system performance) in routing algorithms characterized by selfish user behavior. The paper was one of four cited as best papers 

at the conference. The conference was one of 12 co-located conferences comprising the World Congress on Engineering sponsored by the International Association of Engineers

Other Significant Recognition 

o Beichl Named Editor-in-Chief of Scientific Computing Magazine. Isabel Beichl of ACMD was selected to serve a second term as Editor-in-Chief of Computing in Science and Engineering (CiSE), a 

joint publication of the IEEE Computer Society and the American Institute of Physics. CiSE is a bimonthly publication that combines peer-reviewed articles, 

columns, tutorials, and book reviews in a magazine format. 

According to its statement of purpose, CiSE “aims to support 

and promote the emerging discipline of computational science and engineering and to foster the use of computers and 

computational techniques in scientific research and education.” Beichl’s original appointment as Editor-in-Chief, which was made by the IEEE Computer Society Board of Governors, began in January 

2009; her second term extends to December 2012. 

o Faculty Appointee G. W. Stewart’s 70th Birthday Noted. G. W. (Pete) Stewart, Professor Emeritus of 

Computer Science at the University of Maryland and long-time faculty appointee in ACMD, was 

honored by a conference, a book, and a special journal issue organized in commemoration of his 70th birthday. The conference, 

Numerical Linear Algebra: Perturbation, Performance, and Portability, which held July 19-20, 2010, in Austin, Texas, was attended 

by nearly 100 of Stewart’s friends and colleagues from around the 

world. Birkhauser, in their Contemporary Mathematicians series, has 

also recently published G. W. Stewart: Selected Works with Commentaries, in Stewart’s honor. Edited by Misha Kilmer of Tufts 

University and Dianne O’Leary of the University of Maryland (another faculty appointee in ACMD), the new book collects 44 of 

Stewart’s papers, along with over 100 pages of essays putting his 

work in historical perspective. In addition, a special issue of the 

journal Linear Algebra and Its Applications is being organized in 

Stewart’s honor. Stewart is a world-renowned expert in computational linear algebra. He has made fundamental and highly cited 

advances in the analysis of rounding error in numerical computations, perturbation of eigensystems, generalized inverses, least 

squares problems, and matrix factorizations. He has developed efficient algorithms for the singular value decomposition, updating and 

downdating matrix factorizations, and the eigenproblem that are widely used in applications. His six 

textbooks are models of exposition that have educated multiple generations of researchers. Stewart’s 

contributions have led to numerous honors, including election to the National Academy of Engineering. Stewart was 70 years old on October 1, 2010. 

Figure 6. Pete Stewart. (Photo by Eric 

de Sturler of Virginia Tech. Used with 

permission.) 
22 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2010 23

Part II: Features 

 Part II 

 Features 
24 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2010 25

A Special Functions Handbook for the Digital Age 

In May 2010 NIST released the Digital Library of 

Mathematical Functions (DLMF), a free online repository of information on the special functions of applied 

mathematics. The culmination of a 12-year effort involving some 50 researchers from around the globe, 

the DLMF details the mathematical properties of some 

33 classes of functions. The richly linked resource also 

includes interactive 3D graphics, a comprehensive 

index of available software, and a math-aware search 

engine. The DLMF is a successor to the enormously 

successful Handbook of Mathematical Functions (M. 

Abramowitz and I. Stegun, eds.), which was published 

by NBS in 1964. A print companion, the NIST Handbook of Mathematical Functions has also been 

published by Cambridge University Press. 

Ronald F. Boisvert 

With an estimated 40,000 citations1, the classic 

NBS Handbook of Mathematical Functions [1] is 

among the most cited works in the mathematical literature. Edited by Milton Abramowitz and Irene Stegun 

and released in 1964, the Handbook was the result of a 

10 year project to compile essential information on the 

special functions of applied mathematics (e.g., Bessel 

functions, hypergeometric functions, and orthogonal 

polynomials) for use in applications [2]. In spite of its 

enormous success, the NBS 

Handbook is also old: (a) more 

than half of its 1,046 pages are 

tables of function values whose 

use has largely been superseded 

by modern numerical software, 

(b) there have been enormous 

advances in the field of special 

function in the last 45 years, and 

(c) modern communications networks provide unique new 

opportunities for effectively conveying information. 

Recognizing these problems 

and opportunities, in 1997 we 

undertook a project to update and 

modernize the Abramowitz and 

Stegun Handbook. Our main goals 

were to identify those mathematical functions and their properties 

that are most important in applica-

 

1 This estimate was produced with the help of the Thomson Reuters 

Web of Science. It is an estimate because the Handbook was cited in 

hundreds of different ways, making a complete harvest of citations 

quite laborious. 

tion, to present this information in a concise form accessible to practitioners, and to disseminate it to the 

widest possible audience. The culmination of that project was the release in May 2010 of the online and 

freely available NIST Digital Library of Mathematical 

Functions (DLMF) and its print companion, the NIST 

Handbook of Mathematical Functions [3]. 

Mathematical Content. The mathematical content of 

the DLMF2

 is organized into 36 chapters; see Table 3. 

The first three are methodological in nature, providing 

essential definitions and background needed for the 

analysis and computation of special functions. The 

remaining 33 chapters each address a particular class of 

functions. These each have a similar organization. The 

first section provides a brief description of the notation 

that is used and its relation to alternate notations. 

Next comes an enumeration of the function’s 

mathematical properties, such as the defining differential equation, special values, periods, poles, zeros, 

elementary identities, series representations, integral 

representations, transformations, relations to other 

functions, asymptotic expansions, derivatives, integrals, sums, and products. All of these are presented in 

the telegraphic style characteristic of the Abramowitz 

and Stegun Handbook. One noteworthy new feature of 

the DLMF is that references are provided that connects 

every formula to a proof. Not only is this a means of 

verification, but it allows researchers to learn proof 

techniques that may help them 

derive variations on the formulae. 

In each function chapter a section entitled Graphics provides a 

set of 2D and 3D views of the 

functions designed to convey visually their essential features. 

Complex-valued functions are 

displayed by showing a 3D surface 

representing the modulus of the 

function; the surface is color coded 

to convey information about the 

phase (a 4D effect). Each function 

chapter also has a brief section 

pointing out mathematical and 

physical applications. 

Finally, each chapter ends 

with a section on computation. 

Here the DLMF provides a set of 

hints on fruitful numerical approaches with references. 

 

2 We use DLMF to refer to both the online handbook and its print 

companion. 

Figure 7. The print companion to the NIST 

Digital Library of Mathematical Functions.
26 NIST Applied and Computational Mathematics Division 

Online-only Content. The online version of the DLMF provides additional 

technical content in comparison with its 

print counterpart. For example, in some 

cases additional instances in a series of 

formulae, such as weights and nodes of 

higher-order Gauss quadrature formulae, 

are available online. The online DLMF 

also has a much larger collection of visualizations, and all 3D visualizations there 

are interactive [4]. The DLMF provides 

its interactive 3D content in two separate 

formats: Virtual Reality Modeling Language (VRML) [5] and Extensible 3D 

(X3D) [6], a newer standard. 

Another substantial collection of 

online-only content is information about 

software for the special functions. In 

each chapter, a Software section lists 

research articles describing software development efforts associated with 

functions covered in the chapter. In addition, a table of links is provided to help 

users identify available software for each 

function. Open source software, software 

associated with published books, and 

commercial software are all included. 

The online DLMF also provides a 

rich set of tools which enhance its use as 

an interactive reference work. For example, each equation has a link providing 

the following additional information 

(metadata): 

• The name of each symbol in the 

equation linked to its definition. 

• Reverse links to places in the DLMF 

where the equation is cited. 

• Alternate encodings of the equation: 

TeX, MathML, png (image). 

The online references have a similarly rich set of links 

associated with them: 

• Links to reviews in the AMS’s MathSciNet and 

Zentralblatt’s MATH database. 

• Links to full text of articles online. 

• Links to software associated with the reference. 

• Reverse links to places in the DLMF where the 

reference is cited. 

Math Search. While the DLMF does have an extensive index, the main way in which one finds reference 

information online is through search engines. Existing 

search technology is largely based upon analysis of 

words in documents. As a mathematical reference written in a “telegraphic” style, there is not a wealth of 

words in the DLMF for a search engine to index. As a 

result, it was necessary to develop our own mathoriented search engine. The DLMF search engine is 

based on Lucene3

, an open-source text-based search 

engine maintained by the Apache project. To enable 

math search this tool was augmented with additional 

data and processing layers [7, 8]. 

The query interface is a single text box. Query 

terms can be English text or mathematical expressions. 

The latter can be expressed in a LaTeX-like form, or 

using notation used in common computer algebra systems. Examples are given in Table 4. To match 

mathematical expressions, the underlying search engine should understand elementary arithmetic rules like 

commutative and associative laws. It should also realize that a search for sin(x) should probably also return 

expressions with sin(y), etc. Providing a search engine 

with such mathematical smarts remains a challenge. 

Instead, we approximate this using query relaxation. If 

 

3 http://lucene.apache.org/

Table 3. Chapters of the DLMF.

1 Algebraic and Analytic Methods 

2 Asymptotic Approximations 

3 Numerical Methods 

4 Elementary Functions 

5 Gamma Function 

6 Exponential, Logarithmic, Sine, and Cosine Integrals 

7 Error Functions, Dawson’s and Fresnel Integrals 

8 Incomplete Gamma and Related Functions 

9 Airy and Related Functions 

10 Bessel Functions 

11 Struve and Related Functions 

12 Parabolic Cylinder Functions 

13 Confluent Hypergeometric Functions 

14 Legendre and Related Functions 

15 Hypergeometric Function 

16 Generalized Hypergeometric Functions and Meijer G-Function 

17 q-Hypergeometric and Related Functions 

18 Orthogonal Polynomials 

19 Elliptic Integrals 

20 Theta Functions 

21 Multidimensional Theta Functions 

22 Jacobian Elliptic Functions 

23 Weierstrass Elliptic and Modular Functions 

24 Bernoulli and Euler Polynomials 

25 Zeta and Related Functions 

26 Combinatorial Analysis 

27 Functions of Number Theory 

28 Mathieu Functions and Hill’s Equation 

29 Lamé Functions 

30 Spheroidal Wave Functions 

31 Heun Functions 

32 Painlevé Transcendents 

33 Coulomb Functions 

34 3j, 6j, 9j Symbols 

35 Functions of Matrix Argument 

36 Integrals with Coalescing Saddles 
Summary of Activities for Fiscal Year 2010 27

a user’s search does not result in any matches, the system will allow matches with successively larger 

numbers of intervening symbols or matches with symbols in any order. 

The page of search results delivered by the DLMF 

is a list of matched objects, which can include displayed equations, figures, tables, section titles or text, 

and references. Matched portions of equations and text 

are highlighted to help the user understand why the 

item was matched. Clicking on any item follows a link 

to see the object in context. 

Math on the Web. Displaying mathematical content 

on the web presents its own set of challenges. For the 

DLMF we have decided to embrace MathML4

, the 

open community standard for representing mathematics 

developed by the World Wide Web Consortium 

(W3C). MathML provides a number of advantages. It 

allows equations to be scaled automatically when one 

scales the text size in the browser. It enables accessibility features to be deployed. It also has the potential to 

support semantics-preserving exchange of mathemati-

 

4 http://www.w3.org/Math/

cal content5

. One example is 

cut-and-paste of equations between web pages, text editors, 

and computation systems, or 

other types of interoperability 

between computer algebra systems. 

MathML presents some 

practical problems, however. 

First, it is not yet supported by 

all browsers. It is supported 

natively in Firefox, but in 

Internet Explorer only with a 

specialized (free) 3rd party 

plug-in. Because of this, the 

DLMF is delivered in two 

forms: with MathML and with 

equations as images. The 

DLMF server identifies the 

requesting browser and sends 

the most appropriate form. 

The second issue is that 

MathML is a language for 

computers, not humans, and 

hence authoring in MathML is 

a challenge. Authors are more 

comfortable writing in LaTeX, 

and hence this was used as the 

input language for the DLMF. 

From this we wished to generate each of XHTML + 

MathML, HTML + images, 

and a traditional printed handbook. Generating MathML from LaTeX source is far 

from trivial, especially if one wants to represent 

mathematical semantics in the MathML. A LaTeX to 

MathML translator was developed at NIST to confront 

this problem. LaTeXML6

 is a Perl program that completely mimics the processing of TeX, but generates 

XML rather than DVI. A postprocessor converts the 

XML into other formats such as HTML or XHTML, 

with options to convert the math into MathML or images. The system relies on additional declarations and a 

variety of heuristics to perform the generation. While it 

was developed specifically for the DLMF project, 

LaTeXML is a general-purpose tool and has been applied to much broader collections of scientific 

publications [9]. 

Putting It All Together. No one institution has the 

resources and technical expertise to carry out a project 

like this one alone. NIST is fortunate to have had the 

 

5 MathML comes in two flavors: Presentation Markup and Content 

Markup. The former is focused only on proper display, while the 

latter includes some semantic-preserving markup. Most current implementations only support Presentation Markup. 

6 http://dlmf.nist.gov/LaTeXML/

Table 4. Examples of DLMF queries.

Query Interpretation 

Gamma(?) = int Г(x) = Û, for any x. ? is a single-character wildcard. 

int_$^$ BesselJ Any definite integral containing a J Bessel function. $ is 

a multi-character wildcard, which will match “infinity” 

and “pi/2” for example 

sum_infinity^infinity 

BesselJ 

Any sum with limits -∞ to ∞ containing the J Bessel 

function 

zeta contour integral Text search for contour integrals of the zeta function 

Figure 8. | ψ(x + i y) | , the modulus of the complex psi function. 
28 NIST Applied and Computational Mathematics Division 

cooperation of a large number of experts worldwide in 

the assembly of the technical information contained in 

the DLMF. The DLMF chapters were assembled by 29 

external authors working under contract to NIST. NIST 

was responsible for editing the material so as to 

achieve the necessary depth and breadth of coverage 

and to ensure a uniform style of presentation. In addition, a set of 25 independent validators were enlisted to 

check the accuracy of the technical content. Development of the DLMF web site and its interactive content 

was performed by NIST staff. 

A project as complex (both technically and organizationally) as this one takes time. The initial plans for 

the project were laid out at a workshop held at NIST in 

1997. So, the DLMF has been some 12 years in the 

making. It is to their credit that NIST management had 

the patience to see these efforts through such a long 

and exacting process. 

The Future. NIST is committed to the continued maintenance and development of the DLMF. We already 

have had suggestions for extensions. New chapters are 

under consideration. We are also considering bringing 

back tables, but, rather than static tables, tables generated on demand with certified correct values. We do 

hope that the DLMF provides a firm foundation for 

extending the legacy of Abramowitz and Stegun far 

into the 21st century. 

References 

[1] M. Abramowitz and I. Stegun, 

eds., Handbook of Mathematical Functions, with Formulas, 

Graphs and Tables, Applied 

Mathematics Series 55, National Bureau of Standards, 

Washington, DC, 1964. 

[2] R. F. Boisvert and D. W. Lozier, Handbook of 

Mathematical Functions, in A 

Century of Excellence in 

Measurements, Standards, and 

Technology – A Chronicle of 

Selected NBS/NIST Publications, 1901-2000 (D. Lide, 

ed.), NIST Special Publication 

958, 2000, pp. 135-139. 

[3] F. W .J. Olver, D. W. Lozier, 

R. F. Boisvert, and C. W. 

Clark, eds., NIST Handbook of 

Mathematical Functions, 

Cambridge University Press, 

2010. 

[4] Q. Wang and B. Saunders, 

Web-based 3D Visualization 

in a Digital Library of 

Mathematical Functions, in 

Proceedings of the 10th International Conference on 3D 

Web Technology, Bangor, Wales, UK, 2005, 151-157. 

[5] A. Ames, D. R. Nadeau, and J. L. Moreland, VRML 2.0 

Sourcebook, Wiley, 1996. 

[6] D. Brutzman and L. Daly, X3D: Extensible 3D Graphics 

for Web Authors, Morgan Kaufmann, 2007. 

[7] A. Youssef, Information Search And Retrieval of 

Mathematical Contents: Issues And Methods, in Proceedings of the ISCA 14th International Conference on 

Intelligent and Adaptive Systems and Software Engineering, Toronto, July 20-22, 2005, pp. 100-105. 

[8] A. Youssef, Methods of Relevance Ranking and Hitcontent Generation in Math Search, in Proceedings of 

the 6th International Conference on Mathematical 

Knowledge Management, Hagenberg, Austria, June 27-

30, 2007, pp. 393-406. 

[9] H. Stamerjohanns, M. Kohlhase, D. Ginev, C. David, 

and B. Miller, Transforming Large Collections of Scientific Publications to XML, Mathematics in Computer 

Science 3 (2010), pp. 299-307. 

Participants 

Frank Olver, Daniel Lozier, Charles Clark (NIST 

PML), Ronald Boisvert, Bruce Miller, Bonita Saunders, Abdou Youssef, Marjorie McClain, Qiming 

Wang, Brian Antonishek (NIST ITL). In addition, the 

DLMF benefited from the active participation of some 

50 external editors, authors, validators, and consultants. 

A complete list can be found on the DLMF website. 

http://dlmf.nist.gov/

Figure 9. DLMF editors and developers at NIST included the following (l. to r.): Abdou Youssef, 

Brian Antonishek, Daniel Lozier, Marjorie McClain, Bruce Miller, Bonita Saunders, Charles 

Clark, Frank Olver, and Ronald Boisvert. 
Summary of Activities for Fiscal Year 2010 29

Linnik Densities, Logarithmic Diffusion Equations, and Blind 

Deconvolution of Hubble Space Telescope Imagery

An important mathematical construct involving 

Brownian motion in randomized time, and used extensively on Wall Street as a tool for pricing options, has 

been successfully applied at NIST to sharpen galaxy 

images obtained with the Hubble Space Telescope’s 

ultra sophisticated Advanced Camera for Surveys, 

(ACS). This work is discussed in detail in a recently 

published paper in the SIAM Journal on Imaging Sciences [1]. In May 2009, the ACS camera and other 

vital instruments aboard the Hubble were refurbished 

and upgraded, in a heroic mission by Space Shuttle 

Atlantis astronauts. In private discussions at NIST in 

September 2010, Debra Elmegreen, President of the 

American Astronomical Society, praised NIST’s Hubble image sharpening technology. 

Alfred Carasso 

Optical Transfer Functions and Blind Deconvolution. Images produced by scientific instrumentation are 

commonly blurred in such a way that important fine 

scale information is poorly reproduced. Many factors 

may contribute to this blur, including optical aberrations, scattering properties of the intervening medium, 

possible atmospheric effects, motion of the object, and 

the cumulative effect of various interfacing electronic 

acquisition devices, each with its own imperfect response. Mathematically, it is helpful to lump all of 

these various effects into a single optical transfer function (OTF) that describes how each Fourier harmonic 

in the unknown desired sharp image, is attenuated by 

the imaging process. The result of all these individually 

attenuated Fourier components is the recorded blurred 

image. In principle, knowledge of the OTF can be used 

to deblur the image. However, special precautions are 

necessary, as deblurring is an ill-conditioned problem 

which is prone to severe noise amplification.

Unfortunately, accurate knowledge of the OTF is 

seldom available. Over the last several years, Carasso 

has developed and refined a blind deconvolution approach that seeks to identify a plausible OTF from the 

asymptotic behavior in the Fourier transform of the 

blurred image. Brownian motion is pervasive in many 

branches of science, and the familiar bell-shaped Gaussian probability distribution is the DNA of Brownian 

motion. Naturally, Gaussian OTFs are ubiquitous in 

image science. A blind identification method might be 

based on appropriate curve-fitting of a Gaussian candidate OTF to the Fourier transform behavior in the 

given blurred image. Surprisingly, Gaussian OTFs turn 

out to be poor candidates for Hubble images, indicating 

Figure 10. Blurred M51 image data log gˆ ξ )0,( can be well-fitted 

with a Lévy stable OTF, as well as with a generalized Linnik OTF. 

Both OTFs have similar behavior away from the origin, but differ 

fundamentally near the origin. This difference plays a crucial role. 
30 NIST Applied and Computational Mathematics Division 

that the blurring is not the result of an underlying 

Brownian motion process. 

Linnik OTFs and Brownian Motion in Randomized 

Time. As is now being increasingly recognized, many 

types of random processes that play significant roles in 

applied science, involve a fundamental modification of 

Brownian motion. This is the seminal notion of a subordinated process put forth by Princeton mathematician 

Salomon Bochner in 1949. This concept refers to the 

stochastic process obtained when Brownian motion is 

observed at an appropriate randomized operational 

time T(t), rather than in standard clock time t. An 

analogous idea would be to record the values of the 

Dow Jones Industrial Average at intervals of 10 million 

shares traded (the trading clock), rather than at ten 

minute intervals. Commonly occurring Lévy stable 

motions are examples of subordinated Brownian motion, and Lévy stable OTFs were successfully applied 

by Carasso and his NIST collaborators in deblurring 

nanoscale scanning electron microscope imagery. 

Generalized Linnik processes are obtained by 

evaluating Lévy stable motions at the stochastic time 

Г(t), where, for each t > 0, Г(t) obeys a gamma probability distribution on u ≥ 0. This amounts to two 

consecutive, independent, subordinations of Brownian 

motion. The Variance Gamma process, a standard tool 

used on Wall Street for options trading, is a special 

case of such generalized Linnik processes. An important new NIST idea was to consider generalized Linnik 

characteristic functions as candidate OTFs in blind 

deconvolution of Hubble imagery. While Linnik processes are unknown in image science, Carasso was 

drawn to consider such OTFs because of their mathematical properties. As shown in Figure 10 for the 

Whirlpool galaxy, both Linnik and Lévy stable OTFs 

have the same desirable high frequency behavior, one 

that accords well with a large class of astronomical 

images. However, while Lévy stable OTFs exhibit nondifferentiable cusps near the origin, Linnik OTFs are 

smoothly differentiable at the origin. It is this difference in behavior that enables Linnik OTFs to produce 

superior reconstruction of fine scale information. 

Deblurring Hubble Imagery. Carasso’s slow motion 

blind deconvolution procedure is based on solving an 

ill-posed logarithmic diffusion equation backwards in 

time. The defining parameters of the Linnik candidate 

OTF enter this diffusion problem. These are estimated 

directly from the blurred image by least squares curve 

fitting of the absolute value of the blurred image Fourier transform, as shown in Figure 10. 

The Advanced Camera for Surveys (ACS) is Hubble’s most powerful camera. However, in many cases, 

Linnik blind deconvolution can extend the range of that 

instrument by making faint background objects more 

visible, while the structure of foreground objects becomes more clearly defined. The first example, in 

Figure 11, is a February 2006 ACS image of the Pinwheel Galaxy NGC1309. Here, the Linnik deblurred 

image exhibits a multitude of previously faint stars, the 

scythe-shaped structure at eleven o’clock is now 

brighter and more clearly defined, and the previously 

barely visible outer spiral arms have been recovered. 

Within the galaxy’s main body, the bluish star clusters 

along the spiral arms, and the dust lanes, are now much 

better resolved. 

The second example, in Figure 12, is an April 

2008 ACS image of NGC 6050, involving a collision 

between two spiral galaxies. As in Figure 11, the Linnik deblurred image is brighter and displays better 

resolution of the structural details in the two galaxies. 

Also, background galaxies have become more visible. 

 

Figure 11. Pinwheel Galaxy NGC1309 (left). Linnik deblurred image (right) exhibits multitude of previously faint stars, scytheshaped structure at eleven o’clock is more clearly defined, and outer spiral arms have been recovered. 
Summary of Activities for Fiscal Year 2010 31

The last example, the barred spiral galaxy 

NGC6217 in Figure 13, is significant. This was the first 

celestial object imaged by Hubble using the upgraded 

ACS camera after the May 2009 refurbishing. Again, 

the Linnik deblurred image shows substantial sharpening of the dust lanes and other structural details. The 

outer spiral arms and background galaxies have also 

become more visible. 

References 

[1] A. Carasso, Bochner Subordination, Logarithmic Diffusion Equations, and Blind Deconvolution of Hubble 

Space Telescope Imagery and Other Scientific Data, 

SIAM Journal on Imaging Sciences 3 (2010), pp. 954-

980. 

 

Figure 12. Colliding galaxies NGC6050 (left). Linnik deblurred image (right) is brighter and displays better resolution of the 

structural details in the two galaxies. Also, background galaxies have become more visible. 

 

Figure 13. Barred spiral galaxy NGC6217. First celestial object imaged by Hubble using May 2009 upgraded ACS camera. Linnik 

deblurred image shows substantial sharpening of dust lanes and other structural details. Outer spiral arms and background galaxies have become more visible.
32 NIST Applied and Computational Mathematics Division 

Modeling Reactive Wetting 

The term “wetting” usually refers to the tendency of a 

liquid to spread on a substrate; for example, a drop of 

oil will spread on the surface of water until it reaches 

atomic-level thicknesses (“complete wetting”). A water 

drop placed on a stainless steel surface will form a 

spherical cap with characteristic “contact angles” at 

the water-steel-air tri-junction that are determined by 

the surface energies of the three interfaces (“partial 

wetting”). On the other hand, a drop of mercury placed 

on glass surface beads up in an attempt to minimize its 

area of contact (“non-wetting”). The tendency of a 

fluid to wet a substrate is an important consideration 

for many technological applications, including coating 

flows, soldering, and electronic interconnects. We have 

developed mathematical and computational models of 

the process in order to improve our understanding of 

the complex dynamics involved in this process. 

Geoffrey B. McFadden 

Reactive wetting occurs when a liquid and substrate 

can interact chemically; for example, the substrate may 

dissolve in the liquid, or the liquid may diffuse into the 

substrate. In this case the understanding of the wetting 

process involves not only capillary considerations but 

also the thermodynamics of the components and their 

tendency to combine in order to minimize the free energy of the system. This results in a more complicated 

process, since the substrate plays an active, rather than 

a passive, role in establishing the system geometry, 

including the determination of the free surfaces and 

contact angles that appear in the system. An example 

of the resulting geometry during reactive wetting is 

shown in Figure 14. 

An interesting aspect of 

wetting concerns the dynamics associated with the 

motion of the contact lines 

at the junction of the liquid, 

solid, and vapor phases. For 

the simpler problem of 

spreading on an inert planar 

substrate, it is well-known 

that the imposition of standard no-slip boundary 

conditions at the moving 

contact line leads to a nonphysical singularity in the 

flow field at the contact line 

[1]. This is often alleviated 

by introducing a notion of 

“slip” as the fluid flows 

along the substrate [2]. Another approach [3], the one we adopt, involves the introduction of a diffuse interface description of the 

inter-phase boundaries, which also tends to relieve the 

hydrodynamic singularity. In the case of reactive wetting, another mechanism for dissipation is the diffusion 

of solute near the contact line, which introduces possible non-equilibrium effects (“solute trapping”) in the 

dynamical description of the motion. 

The mechanisms of reactive wetting thus involve 

the interplay of fluid flow, heat and mass transport, 

capillary phenomena, and phase transformations. A 

mathematical model of reactive wetting in an isothermal, three-component, four-phase system is currently 

under development. To treat free surfaces and contact 

lines in the problem, a diffuse-interface (“phase-field”) 

model is used [4], which involve the introduction of 

additional unknowns (“order parameters”) that track 

the local phase at each point and incorporate the effects 

of capillarity and interfacial adsorption of solute [5]. 

In practice the model requires the numerical determination of surface energies that depend on 

phenomenological coefficients in the model. This can 

be done using a steady-state one-dimensional computation. An example of the phase field and solute profiles 

is shown in Figure 15, which illustrates that a form of 

wetting can also occur in the interfacial region as well 

as in the bulk; in this case, the solid-liquid interface is 

being wet by an intruding intermetallic phase localized 

to the interfacial region. This intermediary surface 

phase alters the interfacial surface energy considerably, 

which complicates the relation between the model’s 

phenomenological coefficients and the surface energy. 

Once the surface energies of the model are known, 

time-dependent, axisymmetric numerical simulations 

are performed to assess the dynamical behavior of the 

model (see Figure 

16). The figure illustrates the nucleation 

and growth of intermetallic at the solidliquid interface, and 

the spread of the 

intermetallic phase 

towards the region of 

the solid-liquidvapor trijunction. 

The original trijunction then is replaced 

by two other trijunctions: liquid-vaporintermetallic and 

solid-vaporintermetallic. At an 

intermediate stage 

Figure 14. Liquid tin (top) has coated a copper substrate (bottom), leading 

to the formation of a tin-copper compound (“intermetallic”) near the solidliquid interface; The image is taken after the liquid has been quenched to 

lower temperatures and become solid. The image focuses on the liquid-solid 

interface; a larger scale image would include the region surrounding the 

contact line, which would involve the vapor, liquid, solid, and intermetallic 

phases. The system components are binary alloy and the inert gas. 
Summary of Activities for Fiscal Year 2010 33

there is a transient quadrijunction where all four phases 

coexistence instantaneously. Thus, issues of existence 

and stability of quadrijuctions are also raised by the 

calculation, which are currently under consideration. 

We are also studying the control of intermetallic formulation by various parameters in the model. This can 

be approached by computing the size and shape of an 

axisymmetric lenticular “seed” of intermetallic placed 

at the solid-liquid interface to determine the seed’s 

“critical radius” from a balance between surface and 

bulk energies. Seeds smaller than this size shrink as 

surface energy considerations dominate bulk energies 

and, conversely, larger seeds will grow as the dominance is reversed. Preliminary comparisons between 

the model’s computation results and the analytical theory for the critical radius show good agreement. 

These calculations are performed using an adaptive finite element code developed by W. Villanueva 

and colleagues. A manuscript describing the model 

appeared in recent conference proceedings [6], and 

another on the latest aspects of the research is currently 

in preparation. 

References 

[1] C. Huh and L. E. Scriven, Hydrodynamic model of 

steady movement of a solid/liquid/fluid contact line. 

Journal of Colloid Interface Science 35 (1971), pp. 85–

101. 

[2] E. B. Dussan, On the spreading of liquids on solid surfaces: Static and dynamic contact Lines, Annual Review 

of Fluid Mechanics 11 (1979), pp. 371–400. 

[3] T. Qian, X. P. Wang, and P. Sheng, A variational approach to moving contact line hydrodynamics, Journal 

of Fluid Mechanics 564 (2006), pp. 333-360. 

[4] D. M. Anderson, G. B. McFadden, and A. A. Wheeler, 

Diffuse-interface methods in fluid mechanics, Annual 

Review of Fluid Mechanics 30 (1998), pp. 139-165. 

[5] G. B. McFadden and A. A. Wheeler, On the Gibbs adsorption equation for diffuse interface models, 

Proceedings of the Royal Society (London) A 458

(2002), pp. 1129--1149. 

[6] W. Villanueva, W.J. Boettinger, G.B. McFadden, and 

J.A. Warren, A Multicomponent and Multiphase Model 

of Reactive Wetting, Proceedings of the 7th International Conference on Multiphase Flow, 2010, pp. 1-8. 

Participants 

Geoffrey B. McFadden. William J. Boettinger and 

James A. Warren (NIST MML), W. Villanueva (Royal 

Institute of Technology, Stockholm, Sweden) 

Figure 15. Numerical simulation of the spreading of a molten 

metal drop (red) on a solid substrate (green) with the formation of 

intermetallic phase (blue) between the drop and the substrate. 

Figure 16. One-dimensional profiles of the phase field (top) and 

solute field (bottom) for a diffuse interface model of a solidliquid interface. The liquid phase field parameter is in blue, and 

the solid is in black. The red curve shows the intrusion of intermetallic phase which “wets” the solid-lquid interface and 

altering its surface energy (the green curve represents the vapor 

phase).The solute profiles for the three components of the ternary system assume values in the intermediate region which can 

be understood using thermodynamic concepts from “nucleation 

theory” which can be applied to the intruding phase. 
34 NIST Applied and Computational Mathematics Division 

Large-scale Simulation of Suspensions 

Understanding the mechanisms of dispersion or agglomeration of particulate matter in fluids, such as 

suspensions, is of technological importance in many 

industries such as pharmaceuticals, coatings, and concrete. These fluids are disordered systems consisting of 

a variety of components with disparate properties that 

can interact in complex ways. Modeling and predicting 

the flow of such systems represents a great scientific 

and computational challenge, requiring large scale 

simulations. In collaboration with scientists in NIST's 

Engineering Laboratory, we are developing an application, called QDPD (Quaternion based Dissipative 

Particle Dynamics), which is capable of performing 

large scale simulations of suspensions. QDPD is 

highly parallel and has been shown to efficiently scale 

up to at least 16,000 processors when running on a 

Blue Gene supercomputer at Argonne National Laboratory. Our goal is to advance our understanding of 

the flow properties of a specific material, fresh concrete, which is a dense suspension composed of 

cement, water, sand, and rocks. 

William L. George 

Nicos Martys 

Concrete is the most widely used building material, representing a $100B US industry crucial for our 

nation's physical infrastructure. There is now a strong 

interest in making concrete a more sustainable material 

by finding new ways to recycle it, and by changing its 

ingredients in order to reduce the amount of greenhouse gas from its production (the manufacture of 

concrete’s key ingredient, cement, accounts for 8-10% 

of global CO2). As new concrete mixtures are developed to meet these needs, it is important to control 

rheological properties, i.e., flow properties, to satisfy 

performance specifications. Failure to control the flow 

of concrete on a job site can lead to significant cost 

overruns and delay by having to correct errors. 

Yield stress and viscosity, both functions of shear 

rate, are important quantities for characterizing fluids. 

Yield stress is the force applied per unit area to initiate 

the flow. Viscosity is the applied force per unit area 

needed to maintain a shear rate. Shear rate is the velocity gradient perpendicular to the flow direction. 

Many factors control viscosity and yield stress. 

For example, in building materials like concrete, viscosity and yield stress depend on the ratio of water to 

cement, the volume of sand or rocks used, as well as 

their shape and size distribution. There can be great 

variation among samples depending on their history 

and where they were obtained. For example, rocks 

from quarries are usually angular because they are 

crushed when processed, whereas rocks obtained from 

river beds are typically rounded due to erosion. Also, 

the more similar the size of the rocks in a concrete suspension, the harder it is to get it to flow. In this case, 

the concrete may actually jam when poured through a 

narrow opening causing construction delays. Clearly, 

to optimize the flow properties of concrete and other 

suspensions, one needs to understand the relationship 

between flow and properties of the fluid’s constituents. 

High fidelity modeling of the flow of concrete is a 

great scientific challenge. In particular, accounting for 

the size and shape variation of the solid components 

(cement, sand, and rocks) poses many computational 

difficulties. A representative system may entail keeping 

track of up to 100,000 particles of varying shape and 

size. Further, many of the forces between particles depend on the local surface curvature of the aggregate at 

points close to neighbors, which requires keeping track 

of the location, orientation and shortest distance between neighboring particles. Clearly, modeling such 

systems necessitates large-scale simulations. We have 

adopted and developed some novel approaches that can 

successfully take into account many of the features of a 

suspension. Our code, QDPD [1], has been validated 

by both theory and experiments on idealized systems 

and has been extended to account for random shaped 

objects with different inter-particle interactions. 

QDPD uses modified versions of the recently developed DPD (Dissipative Particle Dynamics) 

technique [2] for the simulation of Newtonian fluids, 

and the Smoothed Particle Hydrodynamics technique 

(SPH) [3], for the simulation of non-Newtonian fluids, 

to simulate dense suspensions such as cement paste, 

mortar, and concrete. In addition to the forces computed using DPD and SPH, other forces are computed 

to better account for the interaction between inclusions 

(large particles). These include lubrication forces that 

help keep the inclusions separated, and van der Waals 

forces that introduce an attractive interparticle force. 

Brownian forces are also present in QDPD to maintain 

system temperature. 

We started with the original serial version of 

QDPD and enhanced it to utilize large parallel machines with 500+ processors, sometimes using 2,000 or 

more processors, to simulate systems with more than 

32,000 inclusions and 1M mesoscopic fluid particles. 

QDPD remains under constant development improve 

its parallel performance and to add new capabilities. 

During 2010 we had access to the 164,000 processor IBM Blue Gene/P supercomputer Intrepid, having 

been awarded 2M CPU-hours of compute time as part 

of DOE’s INCITE program. This has enabled us to 

perform several very large simulations. For example, 
Summary of Activities for Fiscal Year 2010 35

we performed a simulation of a relatively sparse suspension (15% volume fraction) sheared at a very low 

rate, which alone required approximately 360,000 

processor hours, for comparison to a physical experiment for validation. We also used some of our 2010 

allocation to develop code improvements to QDPD that 

now enable us to run simulations efficiently on up to 

16,000 processors. This new capability will be needed 

in the next few years as we extend our research into 

larger systems and the simulation of vane rheometers. 

Our latest proposal to DOE resulted in an award of 

25M processor hours for 2011, with the possibility of 

equivalent support for 2012 and 2013. This will allow 

us to continue this research into areas not previously 

possible due to intensive computational requirements. 

Through numerical modeling and visualization, 

our work has provided insights into the physical 

mechanisms associated with the onset of concrete flow. 

Aspects of yield stress and viscosity can now be linked 

to spatio-geometric properties of suspensions including 

the number of neighboring rocks and their relative orientation. Further, by examining very long time scale 

behavior, we can link the motion of suspended rocks to 

visco-elastic material properties. 

Our recent simulations have shown that the 

mechanisms that control the onset of flow can be 

linked to macroscopic properties such as yield stress 

and viscosity. We developed a novel way of describing 

the interparticle stress fields and their spatial correlations. Through this, it was discovered that under 

shearing, although the suspended particles remain in a 

liquid order, the interparticle stress is strongly anisotropic [4]. In addition, a transition under flow was 

observed: during a transient regime at low deformation, 

the stress propagates along the compression direction 

of the shear, whereas at larger deformations the stress 

is organized into layers parallel to the flow direction. 

Further, we found that yield stress is shear rate dependent [5]. The higher the shear rate the greater the yield 

stress. However, in the limit of zero shear rate, yield 

was found to go to zero due to of temperature effects. 

We have recently modeled cementitious materials 

composed of cement and fly ash [6]; see Figure 17. We 

studied the effect on flow of substituting 10% of cement with fly ash. To do this we modeled a system of 

angular shaped particles (cement) combined with 

smaller spheres (ultra fine fly ash) and found that there 

is a decrease in yield stress and viscosity in comparison 

to the same system without fly ash. 

Finally, while our main interest is on predicting 

the rheological properties of cement based materials, 

the improved understanding of flow properties of complex suspensions derived from this research should 

have a broad impact. Understanding mechanisms for 

the dispersion or agglomeration of such systems remains a challenge in many industries ranging from 

pharmaceuticals to coatings. 

References 

[1] N. S. Martys, Study of a dissipative particle dynamics 

based approach for modeling suspensions, Journal of 

Rheology 49(2) (March/April 2005), pp. 401-424. 

[2] P. J. Hoogerbrugge and J. M. V. A. Koelman, Simulating microscopic hydrodynamic phenomena with 

dissipative particle dynamics, Europhysics Letters 19

(1992), pp. 155-160. 

[3] J. J. Monaghan, Smoothed particle hydrodynamics. Reports on Progress Physics 68 (2005), pp. 1703-1759. 

[4] N. S. Martys, D. Lootens, W. George and P. Hebraud, 

Contact and stress anisotrophies in start-up flow of colloidal suspensions, Physical Review E 80 (2009), article 

031401. 

[5] N. S. Martys, M. Khalil, W. George, D. Lootens, and P. 

Hebraud, Stress propagation in a concentrated colloidal 

suspension under shear, submitted. 

[6] N. S. Martys, Multiscale modeling of the flow of cement 

based materials, Rilem State of the Art Report on Numerical Simulations of Fresh Concrete Flow, 2010. 

Participants 

William George, Steve Satterfield, Marc Olano, Judith 

Terrill; Nicos Martys and Ed Garboczi (EL); Pascal 

Hebraud (CNRS/ESPCI, France). 

http://www.nist.gov/itl/math/hpcvg/dpdhpc.cfm

http://www.nist.gov/itl/math/hpcvg/concretevis.cfm

Figure 17. Snapshot of a flowing cement paste. The cement paste 

is composed of 33 percent cement particles (angular particles) and 

67 percent fly ash (round). This simulation is part of a study to 

determine the effect of replacing cement particles with fly ash, a by 

product of burning coal in energy plants. This allows us to identify 

the optimal size distribution of particles to improve flow. 
36 NIST Applied and Computational Mathematics Division 

High Precision Calculations of Properties of Few-electron 

Atomic and Molecular Systems 

NIST has long been involved in supplying criticallyevaluated data on atomic and molecular properties 

such as the atomic properties of the elements contained 

in the Periodic Table and the vibrational and electronic 

energy level data for neutral and ionic molecules contained in the NIST Chemistry WebBook. Fundamental 

to this endeavor is the ability to predict, theoretically, a 

property more accurately than even the most accurate 

experiments. It is our goal to be able to do this for fewelectron atomic and molecular systems. The quantum 

chemical wave function methods in current use for most 

electronic structure computations have accuracy limits 

arising from their fundamental inability to properly 

describe electron-electron cusp behavior. Our work is 

devoted to the development of a rigorous, “explicitlycorrelated” method that solves the electron cusp problem and delivers energy levels for small atomic and 

molecular systems of high precision in parallel computing environments. 

James S. Sims 

The revolutions in physics in the early decades of the 

past century provided essentially exact, predictive theories for all chemical properties and processes. However, 

the mathematical intractability of the Schrödinger equation prevented the computation of accurate numerical 

solutions for atomic and molecular systems until recently. In the past two decades, there have been 

breathtaking improvements in computer hardware and 

innovations in mathematical formulations and algorithms, leading to “virtual experiments” becoming a 

more and more cost-effective and reliable way to investigate chemical and physical phenomena. 

Virtually all ab initio methods of quantum chemistry in some way involve the orbital approximation, in 

which the many-electron wave function (Ψ) is represented as superpositions of antisymmetrized products of 

one-electron functions. Such configuration interaction 

(CI) methods have been quite successful in approaching 

experimental accuracy for relative energies of modestly-sized atoms and molecules. However, orders of 

magnitude improvements are needed to expand the 

spectroscopic databases into inaccessible realms, establish its building blocks beyond dispute, and supersede 

expensive experimental approaches. 

The essential flaw in theoretical methods built on 

the orbital approximation is their inability to correctly 

describe the mathematical cusp behavior of many-body 

wave functions in regions of close electron proximity, 

the so-called electron cusp region of the exact electronic wave function [1-3]. This flaw leads to 

incomplete accounting of instantaneous, short-range 

correlation among electrons. We are undertaking theoretical development of our hybrid Hylleraas-CI wave 

function method to solve the electron cusp problem and 

bring subchemical accuracy to atomic systems with 

more than two electrons. 

A depiction of the electron-electron cusp in an essentially exact Hy-CI wave function of the helium (He) 

atom ground state is shown in Figure 18. In the region 

of the electron coalescence point, the exact wave function is linear in the interelectronic distance (r12). 

However, conventional quantum chemical CI wave 

functions effectively incorporate only even powers of

r12, do not have sufficient flexibility to fully relax into 

the conical region of the cusp, and thus poorly account 

for the short-range electron correlation. In Figure 18, 

these deficiencies are clearly exhibited by CI wave 

functions using special analytical and numerical techniques for extremely high angular momentum (l) 

cutoffs. With an orbital (one-electron) basis saturated 

through l = 5, CI is too large by 14% at the coalescence 

point, and the corresponding error in the electronic energy is 807 microhartree (μh). Even after extending the 

basis set to an unprecedented l = 30, the result of some 

70 years of trying [4] is that the best CI treatment for 

He is accurate to only 5 decimal places, demonstrating 

that converging absolute energies even to the μh level is 

impossible in computations with orbital treatments. 

In contrast, the early work of Hylleraas [5] showed 

the superiority of explicitly-correlated methods, which 

directly incorporate the r12 variable into the wave funcFigure 18. Failure of conventional CI wave functions to describe 

the electron cusp in the helium atom. The cusp region of the full 

Cartesian coordinate space can be envisioned by reflecting the 

plots about the vertical axis. 
Summary of Activities for Fiscal Year 2010 37

tion. Our hybrid Hylleraas-CI result, shown in Figure 

18, achieved better than 20 digits of accuracy in the 

absolute energy [4], at least 14 orders of magnitude 

better than the best conventional CI treatments. The 

challenge for computational scientists is to extend the 

phenomenal accomplishments on atomic helium to 

three, four, and more electron states and to molecular 

systems. 

Hylleraas's original method (Hy) has been extended to three electrons [6, 7] resulting in some of the 

most accurate calculations on lithium (Li) and Li-like 

systems to date, way beyond spectroscopic accuracy. 

Like helium, virtual experiments can be done that are 

more accurate than current experimental capabilities, 

but not without huge computational costs (the lithium 

calculations require an estimated 6,000 times more 

computational power than helium). However, already at 

the four electron level there are significant unresolved 

integration problems with the original Hy approach. To 

get around these problems we have developed a hybrid 

Hy-CI method that merges the ease of calculation of the 

CI method with the more rapid achievement of accurate 

results and offers the hope of breaking the four electron 

integral barrier (with only a single rij in any term, the 

most difficult integrals are the 4-electron integrals present in beryllium), enabling extension to systems with 

more than four electrons. 

Our hybrid Hy-CI method has been employed this 

past year to explore its utility for both three electron 

lithium systems and the four electron beryllium atom. 

In the case of lithium, we have computed four excited 

states of the lithium atom to two orders of magnitude 

greater than has been done before [8]. 

At the four electron level, it is still an open theoretical question whether unlinked terms like r12m r34n

with m and n odd are really necessary in either Hy or 

Hy-CI or is it sufficient to use Hy-CI or the formally 

equivalent Hy with only a single odd power of unlinked 

rij factors. In calculations submitted for publication [9], 

we have demonstrated the ability of Hy-CI calculations 

to achieve 0.1 μh accuracy for beryllium. 

All results reported in the lithium and beryllium 

calculations were obtained using quadruple precision 

(30+ digits) floating point subroutines written in Fortran 90, and required removing the bottleneck to highly 

accurate Hy-CI calculations, the three electron triangle 

integrals [10], and treating the remaining three-electron 

kinetic energy and nuclear attraction integrals [11], as 

well as treating all four-electron integrals [12]. 

In going from He (two electrons) to Li (three electrons) to Be (four electrons), the situation vis a vis high 

precision calculations degrades to the point that already 

at four electrons (Be) there are no calculations of the 

ground or excited states with an error of less than a 

nanohartree. Our Be calculations, submitted for publication, are preliminary results and we are currently 

reworking our four electron integral codes with the goal 

of achieving nanohartree accuracy for Be. This (unfinished) beryllium calculation will determine whether 

really accurate calculations on atoms with more than 

four electrons will become a reality. 

References 

[1] T. Kato, On the eigenfunctions of many-particle systems 

in quantum mechanics, Communications in Pure and 

Applied Mathematics 10 (1957), pp. 151-177. 

[2] R. T. Pack and W. B. Brown, Cusp conditions for molecular wavefunctions, Journal of Chemical Physics 45 

(1966), pp. 556-559. 

[3] W. Kutzelnigg and J. D. Morgan III, Rates of convergence of the partial-wave expansions of atomic 

correlation energies, Journal of Chemical Physics 96

(1992), pp. 4484-4508. 

[4] J. S. Sims and S.A. Hagstrom, High precision Hy-CI 

variational calculations for the ground state of neutral helium and helium like ions, International Journal of 

Quantum Chemistry 90 (2002), pp. 1600-1609. 

[5] E. A. Hylleraas, Z. Phys. 54 (1929), pp. 347-366. 

[6] Z.-C. Yan, W. Nörtershäuser, and G. W. F. Drake, High 

Precision Atomic Theory for Li and Be+: QED Shifts 

and Isotope Shifts, Physical Review Letters 100 (2008), 

article 243002. 

[7] M. Puchalski, D. Kedziera and K. Pachucki, Ground 

state of Li and Be+ using explicitly correlated functions, 

Physical Review A 80 (2009), article 020101. 

[8] J. S. Sims and S. A. Hagstrom, Hy-CI Study of the 2 

doublet S ground state of neutral Lithium and the first 

five excited doublet S states, Physical Review A 80

(2009), article 052507. 

[9] J. S. Sims and S. A. Hagstrom, Hylleraas-configuration 

interaction study of the singlet S ground state of beryllium, Physical Review, to appear. 

[10] J. S. Sims and S. A. Hagstrom, Math and computational 

science issues in high-precision Hy-CI calculations I.

Three-electron integrals, Journal of Physics B: Atomic, 

Molecular, and Optical Physics 37 (2004), pp. 1519-

1540. 

[11] J. S. Sims and S. A. Hagstrom, Math and computational 

science issues in high-precision Hy-CI calculations II. 

Kinetic Energy and electron-nucleus interaction integrals, Journal of Physics B: Atomic, Molecular, and 

Optical Physics 40 (2007), pp. 1575-1587. 

[12] J. S. Sims and S. A. Hagstrom, Math and computational 

science issues in Hy-CI calculations III. 4-electron integrals, in preparation. 

Participants 

James S. Sims. Stanley A. Hagstrom (Indiana University). 

http://www.nist.gov/itl/math/hpcvg/atomic.cfm
38 NIST Applied and Computational Mathematics Division 

Nano-optics, and How to Squeeze Light Out of Quantum Dots 

Research and development of nanotechnology, with 

applications ranging from smart materials to quantum 

computation to biolabs on a chip, has the highest 

national priority. Semiconductor nanoparticles, also 

known as nanocrystals and quantum dots, are one of 

the most intensely studied nanotechnology paradigms. 

Nanoparticles are typically 1 nm to 10 nm in size and 

contain a thousand to a million atoms. Precise control 

of particle size, shape and composition allows one to 

tailor charge distributions and control quantum effects 

to tailor properties completely different from either the 

bulk material or small clusters. 

As a result of enhanced quantum confinement 

effects, nanoparticles act as artificial, man-made atoms 

with discrete electronic spectra that can be exploited as 

light sources for novel enhanced lasers, discrete 

components in nanoelectronics, qubits for quantum 

information processing, and enhanced ultrastable 

fluorescent labels for biosensors to detect, for example, 

cancers, malaria or other pathogens, and to do cell 

biology. We are working with the NIST Physical 

Measurement Laboratory to develop computationally 

efficient large scale simulations of such nanostructures. 

This past year these simulations were used to show that 

nanomechanical strain can be used to dynamically reengineer the optics of quantum dots and, conversely, 

that quantum dots can be used as a local probe or 

control for nanomechanical strain. 

We are also working to develop interactive immersive visualization techniques and tools to enable 

measurement and analysis of highly complex computational results of this type. Such techniques not only 

encapsulate the physics but also allow one to easily see 

features that might be missed by just perusing the voluminous amounts of data coming from supercomputer 

size computations. 

James S. Sims 

Quantum dots (QD) have attracted great interest for 

applications in photonics, sensors, quantum information, and precision measurement. Passive control of 

QDs is obtained by tailoring dot size, shape, and composition via growth. Dynamical control of exciton 

energies, polarization, and phase is highly desirable for 

QD nanophotonics. An imposed nanomechanical strain 

provides a route to dynamically reengineer QD structural symmetry to control excitations, polarize 

transitions, tune exchange splitting, induce entanglement, or modify coupling between QDs. These are 

capabilities needed to use QDs in nanophotonics, quantum information processing, and in optically active 

devices, such as optomechanical cavities and semiconductor nanotubes. Employing an imposed 

nanomechanical strain to dynamically reengineer QD 

devices leads to hybrid nanomechanical-QD devices. 

Such hybrid systems are becoming increasingly important areas of study, the goal being to connect multiple 

functionalities from the components into new capabilities of the hybrids. 

We are engaged in a joint effort with the NIST 

Physical Measurement Laboratory to develop computationally efficient large scale simulations, along with 

visualization and analysis tools to enable the study of 

such hybrid nanomechanical-QD devices. Highly parallel computational platforms are critical for obtaining 

the computational speeds required for systematic study. 

Our approach utilizes an atomistic tight-binding 

theory of quantum dots in nanomechanically strained 

structures, such as a nanomechanical cantilever or 

bridge. Excitons in mechanically strained dots (mechanoexcitons) are studied in detail in order to focus on 

the optical response of QDs. Conversely, we also show 

how the response of the quantum dots could be used as 

a local probe of the applied strain. Using an atomistic 

model is critical for an accurate description of nanomechanical-QD hybrids with atomic scale variations in 

composition and shape, and significant local and imposed strain. Our tight-binding theory for electron and 

hole states employs an sp3

s

* orbital model, nearestneighbor coupling, spin-orbit effects, strain from lattice 

mismatch, and imposed mechanical strain. Relaxation 

of local and imposed strain is included via atomistic 

valence force field theory. Exciton states are determined with a configuration-interaction treatment. 

To understand how applied stress can be used to 

actively control dot optical properties, dots buried at 

different points in a nanobridge oscillator or cantilever 

are considered. For the simulations, the bridge is 80 nm 

wide in the lateral directions and 25 nm thick, with 10 

million atoms. A bend in a nanomechanical structure 

acts like a DC electric field, inducing Stark-like level 

shifts. The strain can mimic either a vertical or a lateral 

electric field, depending on how the strain is applied. 

The results are sensitive to bend geometry and dot location. Calculations for different bends, boundary 

conditions, and dot positions must be done to build a 

complete picture of nanomechanical strain effects. 

As the computational model has been extended to 

handle more complex and larger systems by including 

not only the nanostructures but also the substrate and 

environment around them, parallel processing has become even more of a necessity. Both shared memory 

OpenMP parallelization and distributed memory MPI 

are employed. Calculations were carried out on NIST's 

394-processor Linux cluster. 
Summary of Activities for Fiscal Year 2010 39

In a paper published this year [1], we show that 

nanomechanical strain can be used to reengineer the 

optics of quantum dots and, conversely, that quantum 

dots can be used as a local probe or control for 

nanomechanical strain. Specifically, we show that: 

• Electron and hole energies and distributions shift 

together, or in opposite directions, depending on 

how strain is applied, giving control to tune optical 

response. We explain why applied mechanical 

strain provides such control. 

• Strain can be used to transfer carriers between dots. 

This control provides a tool to move qubits between 

adjacent dots for quantum information processing. 

• Changes in band gap, fine-structure splitting, charge 

shifts and polarization correlate to applied strain, 

giving signatures to use QDs as a local strain gauge. 

• Internal strain from lattice mismatch, nanomechanical strain, and internal readjustment to undo the 

applied strain must all be included. 

• The applied strain can be used to manipulate the 

mechanoexciton fine structure and tune the phase of 

spin mixing and rotate polarization, providing control to modify the inner workings of excitons. 

Polarization rotation in a variety of contexts has 

been predicted or measured. These results provide 

the first clear explanation of how and why this occurs by bringing out the connection between the 

phase and spin mixing, the polarization, and the orientation of the exciton. Because applied strain can 

be used to tune the phase of the mixing, this gives a 

tool to control directly the phase of qubits. 

Usually, this polarization change is thought of 

as a single-particle dipole matrix element effect. As 

our results show, that is not the dominant effect. 

Phase control via the engineering of the phase of 

the asymmetric exchange coupling is the dominant 

effect. The results provide a new interpretation of 

these effects. This is perhaps the most important 

contribution of our work: that strain can not only be 

used to control exciton energies and splittings, but 

also exciton phase, which is a critical new feature. 

This year we also released NanoVis, a visualization and analysis tool, which we are using to measure 

orbital data. See Figure 19. In the coming year, we will 

use this tool to study the spatial distribution of spin. 

References 

[1] G. W. Bryant, M. Zieliński, N. Malkova, J. Sims, W. 

Jaskólski, and J. Aizpurua, Effect of Mechanical Strain 

on the Optical Properties of Quantum Dots: Controlling 

Exciton Shape, Orientation, and Phase with a Mechanical Strain, Physical Review Letters 105 (2010), article 

067404 (4 pages). 

Participants 

James S. Sims, John Kelso and Marc Olano (ACMD). 

Garnett Bryant and Natalia Malkova (PML). M. 

Zieliński and W. Jaskólski (Instytut Fizyki UMK, Torun, Poland). Javier Aizpurua (Centro Mixto de Física 

de Materiales CSIC-UPV/EHU Spain). 

http://www.nist.gov/itl/math/hpcvg/nanohpc.cfm

http://www.nist.gov/itl/math/hpcvg/nanovis.cfm

Figure 19. Using NanoVis, the Nano-Structure Visualization, Measurement, and Analysis tool, to measure the properties of 

orbitals bounded by a user selected geometric object.
40 Summary of Activities for FY 2010 

Monte Carlo Methods for Computing Network Reliability 

Graphs are embedded in structures that we use daily 

such as communications networks and the power grid. 

Ability to measure network properties is essential to 

maintaining the reliability, safety and, in some cases, 

the security of these systems. Many aspects of complex 

systems can be presented as questions about graphs. 

Examples include determining the reliability of a network and computing the number of linear extensions of 

a directed acyclic graph. Some of the most important 

aspects of these graphs are computationally intractable. Obtaining exact solutions is often NP hard. But 

sometimes the solutions to these hard problems can be 

approximated using Monte Carlo methods. Methods to 

compute network reliability as well as insights into how 

and when they can be used have been developed by the 

group here at NIST. 

Isabel Beichl 

A graph is a set of vertices and edges (or links) between 

the vertices. Graphs can be used to model computer 

networks and other infrastructure networks such as the 

power grid. A quick way to estimate the reliability of 

large-scale networks would have great impact. One 

measure of reliability is the probability that a graph is 

connected given the probability that each edge is connected [1]. 

If p is the probability that an edge is connected, 

then the reliability of a graph with n vertices and m

edges, R(p), is defined as 

...

...

−+ +

+−+=

−

−

kmk

k

m m

ppC

ppCppR

)1(

)( )1( 1

1

where Ck is the number of connected spanning subgraphs with m-k edges. Determining the Ck and thus 

R(p) is a counting problem. While there is earlier work 

on finding point estimates for reliability [3], previously 

suggested methods for the computation of reliability 

coefficients are impractical [4]. 

We have developed two methods for determining 

approximate values of the Ck. The first is based on sequential importance sampling (SIS). This method 

operates by removing edges from the graph until a 

spanning tree is reached [2]. The edges are chosen from 

the set of edges whose deletion does not disconnect the 

graph, called “good” edges. Before an edge is deleted 

at step k, we note the number of possible choices and 

use this to give an estimate, g(k). This selection of 

edges produces a tree as in Figure 20, whose size, that 

is, number of nodes at level k, gives 

kkgggmeanC )!/)()2()1(( k = "

This SIS method is very fast, but the variance can be 

bad. Importance sampling, a variance reducing technique, can sometimes help. Instead of sampling 

uniformly, we sample with a different probability, 

called the importance of the sample. We get an unbiased sample by dividing the estimate by its importance. 

But a good importance function is hard to find and, 

generally, more computation is needed per sample. For 

reliability, we have an excellent importance function, 

namely, the number of spanning trees removed by deleting an edge e. When normalized, this quantity can be 

used as the importance of e. This quantity is not too 

difficult to compute because it is a certain determinant 

Figure 20. Approximating the number of connected subgraphs of 

a given graph is equivalent to counting the leaves of a certain tree. 

Here the given graph is the root of the tree and selection and deletion of a ``good'' edge leads to selecting a branch of the tree. This 

figure illustrates all possible selections.

Figure 21. The approximate coefficients of the reliability polynomial for a 1,000 node, 3,000 edge graph whose degrees were 

selected from a power-law distribution. Approximation was done 

with the SIS method. 
Summary of Activities for Fiscal Year 2010 41

which can be computed from previous steps by a low 

rank update. Figure 21 shows the reliability of a 1,000 

node power-law graph with more than 3,000 edges 

computed with our SIS method. 

Another way to compute the reliability coefficients 

is the Monte Carlo Markov Chain method (MCMC). 

MCMC is a class of algorithms for sampling from a 

limiting distribution by a series of “steps” from one 

configuration to the next. In this case, we step from 

one connected spanning subgraph to another by swaps, 

deletions, and additions between edges. After a large 

number of steps determined by the mixing time of the 

chain, the first sample is taken. The mixing time (or 

mixing rate) is the number of steps needed to give a 

sample that is independent of the previous sample. 

MCMC is slow even in the rapidly mixing case, but the 

theory of MCMC, and especially the theory of variance, 

is much better developed than that of SIS. No such parameter exists for predicting the variance of SIS. In 

MCMC, the first and second eigenvalues of the transition matrix will give the mixing rate, but writing down 

the transition matrix is impractical and equivalent to, or 

harder than, the original question. This turns the focus 

to computing bounds on the eigenvalue. 

One method of computing bounds for the eigenvalue is to simplify the Markov chain into aggregated 

Markov chains where many states are collapsed into 

one. For reliability, we aggregate by the m-n+1 levels, 

that is, number of edges that we have removed. The 

transition matrix for the aggregated chain is much 

smaller than the transition matrix for the entire Markov 

chain and thus easier to work with. The aggregated 

process is also the process that gives the quantities of 

interest, in this case the coefficients Ck, the number of 

spanning connected subgraphs of size m-k. 

In an effort to make the MCMC method usable, we 

have used our SIS method to estimate the mixing rate of 

the Markov chain for a particular graph in question. 

We do this by using SIS to approximate the aggregated 

transition matrix and then compute the eigenvalue directly. The spectral gap is the difference between the 

first and second eigenvalues. The mixing rate is determined by the spectral gap. 

We also use the SIS method to estimate optimal 

fugacities for the MCMC method. Use of fugacity is a 

MCMC technique that allows us to sample in areas that 

would not be sampled ordinarily, but does so in a way 

that does not create bias. The value of the fugacity determines the rate at which proposed Monte Carlo moves 

are accepted. It is called “fugacity” by analogy with the 

term used in chemistry related to the rate of reaction. 

The optimal fugacity is not known, so in practice many 

fugacities are selected, usually more than are needed. 

We have used the SIS method to generate optimal fugacities for the reliability MCMC. 

References 

[1] C. J. Colbourn, The Combinatorics of Network 

Reliability, Oxford University Press, New York, 1987. 

[2] I. Beichl, B. D. Cloteaux, F. Sullivan, An approximation 

algorithm for the coefficients of the reliability 

polynomial, Conrgessus Numerantium 197 (2009) pp. 

143-151. 

[3] R. Karger, A randomized fully polynomial time 

approximation scheme for the all-terminal reliability 

problem. SIAM Journal on Computing 29 (1999), pp. 

492-514. 

[4] C. J. Colbourn, B. M. Debroni and W. J. Myrvold 

Estimating the coefficients of the reliability polynomial, 

Congressus Numerantium 62 (1988) pp. 217-223. 

Participants 

Isabel Beichl, Brian Cloteaux, Elizabeth Moseman, 

Francis Sullivan. 

Figure 22. The spectral gap versus the number of spanning trees 

for 1,000 random graphs. The spectral gap gives the mixing rate 

for a given MCMC algorithm. Computation of the spectral gap 

used our SIS method.
42 NIST Applied and Computational Mathematics Division 

Up-conversion Single Photon Detectors and their Application in 

Measurement Science 

The development of quantum computer networks 

requires the efficient and reliable transmission of 

quantum information over long distances. Photons 

traveling over optical fiber are a typical transmission 

media. Photons experience the least lost (and hence 

longest distance) at typical telecom wavelengths of 

1310 or 1550 nm. Unfortunately, cost-effective photon 

detectors, such as silicon avalanche photon detectors 

(Si-APDs), are very inefficient at these wavelengths. To 

alleviate this mismatch, we have developed wavelength 

conversion technology to upconvert 1310 nm photons 

to visible or near-visible wavelengths for efficient detection. We have since made performance 

improvements and developed significant new applications. For example, we developed an upconversion 

spectrometer that can measure spectra of single photons in the near infrared, the sensitivity of which is 

three orders of magnitude higher than that of existing 

commercial optical spectra analyzers. Using these detectors we demonstrated, for the first time, that the 

converted single photons preserve their original quantum properties. This technology is being transferred to 

US industry through the NIST SBIR Program. 

Xiao Tang 

Light in the telecom wavelengths in the near infrared 

(NIR) range, most commonly in the 1310 nm and 1550 

nm bands, can be transmitted in optical fiber for long 

distances since the optical attenuation and/or dispersion 

in fiber are lowest at the wavelengths. When light intensity is reduced to the single photon level, detection 

of photons at the telecom wavelengths becomes very 

challenging. InGaAs-based detectors are effective at 

these wavelengths, but their performance needs improvement. Superconducting-based detectors work well 

but they need to be cooled to liquid helium temperature. On the other hand, commercially available 

silicon-based single photon detectors (Si-APDs) perform extremely well for visible and near visible 

photons, but do not work at the telecom wavelengths. 

For some time researchers have sought methods for 

converting telecom photons to visible or near visible 

wavelengths with high conversion efficiency for detection by Si-APDs with low dark count rates. 

In 2007 we developed upconversion detectors for 

our quantum key distribution (QKD) system operating 

at 1310 nm for longer distance secure communication. 

The upconversion detectors reached a high overall 

conversion efficiency of 32%, and dark count rates as 

low as 2,000 c/s, 25 times lower than that reported by 

other groups. Due to the excellent performance of these 

detectors, our 10-km fiber-based 1310 nm QKD system 

generated sifted keys at a rate of 1 Mb/s, enough to 

demonstrate one-time pad encryption and decryption of 

streaming video signals in real time [1]. 

The wavelength conversion is based on sum frequency generation in a nonlinear optical crystal, such 

as a periodically poled lithium niobate (PPLN) 

waveguide. A signal photon at the telecom wavelength 

can be converted to a visible wavelength by a strong 

pump beam under the so called quasi-phase matching 

(QPM) condition, which requires energy and momentum conservation for the pump, signal and idler 

photons. These conditions make the device a tool with 

unique properties of interest in many applications. 

One important extension has been to develop the 

upconversion detector into an upconversion spectrometer. Due to the requirement of energy conservation, if 

we tune the pump photon wavelength, the signal photon wavelength must be tuned accordingly, generating 

an output photon at a fixed wavelength. Here, the tuning of the pump photon wavelength is equivalent to the 

tuning of a grating or a prism in a traditional spectrometer for input wavelength selection. Based on this 

principle, an upconversion single photon detector can 

be modified into an upconversion spectrometer with 

high detection sensitivity and low noise. In August 

2009, we demonstrated such a spectrometer for signals 

at single photon levels in the near infrared region [2]. 

The overall single photon detection efficiency of the 

up-conversion spectrometer is about 32%. The spectrometer also demonstrates ultra high sensitivity, 

measuring spectra for signals at a power level as low as 

-126 dBm, three orders of magnitude better than that of 

commercial optical spectra analyzers. This development opens up new research opportunities in 

Figure 23. The ITL upconversion single photon detector. 
Summary of Activities for Fiscal Year 2010 43

measurement science, providing a powerful tool for 

practical applications in many areas. 

The upconversion spectrometer is sensitive to the 

polarization of input signal photons due to the QMP 

requirement in the conversion process. This could be a 

useful feature if one wants to measure spectra of signal 

photons at a certain polarization orientation. But it 

could also be a drawback if the polarization of the input photons is in arbitrary directions. To overcome this 

problem, we further developed a polarization independent upconversion spectrometer [3]. This 

improvement retains all advantages in the original, but 

desensitizes polarization for input signal photons. 

More recently we further improved the performance of our upconversion detectors, reducing the dark 

count rate and increasing the data transmission rate. In 

particular, by using a holographic grating to filter out 

residual noise around the signal, the dark count rate of 

the upconversion detector was further reduced by another order of magnitude, from 2,000 c/s to 100 c/s [4]. 

In a conventional quantum communication system the 

data transmission rate is limited by the jitter of the SiAPDs. We proposed and experimentally demonstrated 

a multi-wavelength pumping technique that increased 

the system data rate beyond the jitter limitation [5]. 

The difficulty of detecting single photons in 

NIR/IR had been a barrier to much scientific research. 

Our wavelength conversion technique overcomes this, 

enabling new research in quantum measurement and 

quantum information. Recently we conducted a joint 

experiment in collaboration with colleagues in the 

NIST Center for Nanoscale Science and Technology. 

Our upconversion detectors were used to detect single 

photons from a semiconductor quantum dot. Exciton 

lifetimes were measured using both a commercial InGaAs IR single photon detector and our upconversion 

detector. The dynamic range of the data measured by 

the upconversion detector was 25 times better than that 

of the InGaAs-based detector. Because of this the exciton lifetime can be determined with a much higher 

accuracy. It has been well known that photons emitted 

from a quantum dot possess their special quantum 

characteristic, known as antibunching. Because of the 

high sensitivity and low dark count rate, our upconversion detector was able to measure the second order 

intensity correlation function for the photons from the 

quantum dot. This measurement demonstrated for the 

first time that the converted photons preserve the quantum antibunching characteristic. This important 

conclusion was reported in Nature Photonics [6]. 

Through the NIST Small Business Innovative Research (SBIR) Program, the technology of our 

upconversion detectors is being adapted for commercialization by two US companies, AdvR Inc. and 

Lepton Technologies Inc. Phase 1 of this work has 

been completed and Phase 2 is at an advanced stage. 

We plan further study to enable full utilization of 

the unique features of wavelength conversion devices. 

The first task is to expand the detection wavelength 

from 1.3 μm to 1.5 and 0.98 μm. Upconversion devices 

at 1.5 μm is being developed in collaboration with researchers at Stanford University. A device at 0.98 μm 

will be produced by AdvR Inc. The second and most 

important task will be to develop quantum interfaces 

based on wavelength conversion devices. In order to 

connect two independent quantum systems to form a 

quantum network, photons from two independent systems must be made to interfere with each other. 

However, this requires that the two photons have exactly same wavelength and polarization, and arrive at 

an exactly same time. A quantum interface can be used 

to adjust the wavelength of the two photons, and a 

quantum memory can be used to adjust their arrival 

time so that better interference can take place. These 

are necessary steps towards our final goal, the development of a quantum repeater. 

References 

[1] H. Xu, L. Ma, A. Mink, B. Hershman, and X. Tang, 

1310-nm quantum key distribution system with upconversion pump wavelength at 1550 nm, Optics Express 15 (2007), article 7247. 

[2] L. Ma, O. Slattery, and X. Tang, Experimental study of 

high sensitivity infrared spectrometer with waveguidebased up-conversion detector, Optics Express 17 (2009), 

article 14395. 

[3] L. Ma, O. Slattery and X. Tang, Single Photon Level 

Spectrum Measurement at Fiber Communication Band 

Using Frequency Up-conversion Technology, Laser 

Physics 20 (7) (May 27, 2010), pp. 1612-1617. 

[4] X. Tang, L. Ma and O. Slattery, Ultra Low Dark-countrate Up conversion Single Photon Detector, 2010 IEEE 

Photonics Society Annual Meeting, Denver, CO, November 7-11, 2010, IEEE catalog: CFP10LEO-CDR. 

[5] L. Ma, J. C. Bienfang, O. Slattery and X. Tang, Upconversion single-photon detector using multiwavelength sampling techniques, submitted. 

[6] M. T. Rakher, L. Ma, O. Slattery, X. Tang and K. Srinivasan, Quantum transduction of telecommunicationsband single photons from a quantum dot by frequency 

upconversion, Nature Photonics 4 (2010), pp. 786-791. 

Participants 

Lijun Ma, Oliver Slattery Barry Hershman, Alan Mink, 

Hai Xu and Xiao Tang. Joshua C. Bienfang (PML). 

Matthew T. Rakher and Kartik Srinivasan (CNST). Li 

Yan (University of Maryland Baltimore County). Jason 

S. Pelc and Martin M. Fejer (Stanford University). 
44 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2010 45

Part III: Project Summaries 

 Part III 

 Project Summaries
46 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2010 47

Mathematics of Metrology

Mathematics plays an important role in the science of metrology. Mathematical models are needed to understand how to design effective measurement systems, and to analyze the results they produce. Mathematical 

techniques are used to develop and analyze idealized models of physical phenomena to be measured, and 

mathematical algorithms are necessary to find optimal system parameters. Finally, mathematical and statistical techniques are needed to transform the resulting data into useful information. Our goal is to develop 

fundamental mathematical methods and analytical tools necessary for NIST to continue as a world-class metrology institute, and to apply them critical measurement science applications. 

Linnik Densities, Logarithmic 

Diffusion Equations, and Blind 

Deconvolution of Hubble Space 

Telescope Imagery 

Alfred Carasso 

See feature article, page 29. 

ITL Program: Enabling Scientific Discovery 

Modeling Reactive Wetting 

Geoffrey B. McFadden 

William J. Boettinger 

James A. Warren (NIST MML) 

W. Villanueva (Royal Inst. of Technology, Sweden) 

See feature article, page 31. 

ITL Program: Enabling Scientific Discovery 

Denoising of Helium Ion Microscope 

Nanoscale Imagery 

Alfred Carasso 

András Vládar (NIST PML) 

ACMD mathematical technology involving fractional 

diffusion equations, used successfully in NIST image 

deblurring work, has now found an unexpected, but 

highly significant, new application: denoising state-ofthe-art nanoscale imagery. Surprisingly, this method 

can outperform computationally more sophisticated 

denoising techniques based on curvelet transform 

thresholding, or on minimizing image total variation. 

Helium ion microscopes (HIM) are an exciting 

new tool in nanoscale imaging, producing images that 

are particularly rich in morphological surface detail. 

Such imagery is very much needed in current research 

and development, as well as production. The important 

nano-structures are usually very small, and only the 

sharpest focused beams can resolve them. Such beams 

involve a few hundred to a few thousand atoms, and do 

not generate a lot of signal. This necessarily produces 

very noisy images. Any technique that can reduce this 

noise is very much needed, and would result in otherwise unavailable acquisition speed and/or information. 

However, preserving the fidelity of the essential sample-related fine details is of paramount interest. 

A denoising technique that has been applied successfully in medical computed tomography is based on 

appropriately thresholding the image curvelet transform. A MATLAB implementation of that approach 

has been developed by its authors. Another well-known 

method is based on minimizing the image total variation (TV) norm Û| “f(x,y) | dxdy. The split Bregman 

iterative procedure is an efficient method for solving 

the TV minimization problem, and a MATLAB implementation of the TV Bregman procedure has 

likewise been developed. 

The fractional diffusion method uses the given 

noisy image f(x,y) as initial data in the well-posed 

problem wt = -(-Δ)

β w, t > 0, with fixed β, 0 < β á 1. 

The denoised image is the solution at some positive 

time, determined interactively by the user. Fast Fourier 

Transform algorithms are used to generate the forward 

evolution. When b o 0.2, smoothing is very gentle as t

increases, and small-scale features in the initial data 

f(x,y) tend to persist for small positive t, while the noise 

is considerably reduced. This is not the case with 

Gaussian or heat equation smoothing (b = 1), which 

leads to aggressive smoothing out of edges and smallscale information, in addition to eliminating noise. 

Both the curvelet and TV methods are especially 

useful when the ideal sharp image is piecewise smooth, 

and consists of isolated smooth objects with welldefined edges. Such images belong to the class BV(R2

) 

of functions of bounded variation. However, HIM images are not in BV(R2

). Rather, they are examples of 

images where texture and detailed surface morphology 

are of prime interest, and for which TV or curvelet denoising may not be appropriate. This expectation is 
48 NIST Applied and Computational Mathematics Division 

borne out in practice. When TV or curvelet denoising 

is applied to the two noisy HIM images below, fidelity 

to the original surface morphology cannot be maintained. The image L1

 norm is not conserved, while 

7 “f 71 is reduced by factors of five to nine, and the 

image Lipschitz exponent is sometimes tripled. In contrast, with fractional diffusion or Lévy stable 

smoothing, a considerable portion of the noise is removed, while conserving most of the original surface 

texture, including jagged edges. In addition, the image 

L1

 norm is maintained, 7 “f 71 is moderately reduced, 

while the image Lipschitz exponent is not even doubled. 

Figure 24. Poor recovery of surface morphology in TV and Curvelet denoising, as compared with Lévy stable processing, in Au-decorated gold on carbon sample. Field of view is 300 nm. Relative performance in the three denoising 

methods is quantified in Table below. 

Table. Behavior of 7 f 71, 7 f 72, 7 “f 71 and Lipschitz a in above denoising 

experiment. Note severe 7 “f 71 reduction in curvelet and TV denoising.

Image f(x,y) 7 f 71 7 f 72 7 “f 71 Lip a

Noisy original (600 nm) 88 99 25000 0.236 

Lévy stable (b = 0.2, t

† = 0.1) 88 94 8500 0.462 

Split Bregman TV (w = 0.025) 74 89 3400 0.778 

Curvelet thresholding (sn = 30) 81 91 2700 0.845 
Summary of Activities for Fiscal Year 2010 49

Figure 25. Examination of parts of the salt crystals in above radiolaria sample under magnification, reveals significant erosion of surface 

morphology in TV and curvelet images, as compared with Lévy stable image. Field of view is 45 μm. Relative performance in the three denoising methods is quantified in the Table below. 

Table. Behavior of 7 f 71, 7 f 72, 7 “f 71 and Lipschitz a in above denoising 

experiment. Note severe 7 “f 71 reduction in curvelet and TV denoising.

Image f(x,y) 7 f 71 7 f 72 7 “f 71 Lip a

Noisy original (90 μm) 54 65 14000 0.288 

Lévy stable (b = 0.2, t

† = 0.1) 54 61 4900 0.492 

Split Bregman TV (w = 0.025) 37 57 3000 0.666 

Curvelet thresholding (sn = 30) 46 56 2600 0.674 
50 NIST Applied and Computational Mathematics Division 

Sparse Representations in High 

Dimensional Geometry 

Bradley Alpert 

Yu Chen (New York University) 

Laboratory and clinical diagnostic systems often produce images that lack quantitative information or 

comparability across imaging systems, which can lead 

to difficulties in diagnosis and long-term management 

of disease that requires patient monitoring. Elaborate 

measurements are taken, digitally processed, then reported in essentially qualitative form. For MRI, 

functional MRI, and other processes, formation of the 

images relies on filtering and Fourier transformation. 

 Although the computational recovery of functions 

from their Fourier representations is considered routine, aside from possible efficiency concerns arising 

from non-grid data, standard approaches assume that 

the functions are smooth and can be recovered with the 

discrete Fourier transform (computed via the FFT). 

When this assumption fails, as is evident from Fourier 

data that are not small at the highest frequencies measured, some sort of attenuation, or belling, scheme is 

typically used. This procedure tends to blur sharp features and, being more art than science, can lead to 

different functions (images) in different systems. Although this problem, and the Gibbs phenomenon, has 

received considerable attention, recently developed 

methods tend to work well only in an asymptotic sense; 

they do not exploit available data efficiently. 

 Despite inherent limits on resolution that can be 

obtained from truncated Fourier data, a change of assumptions from smooth to piecewise smooth can lead 

to significantly improvement. Procedures implementing this idea are not completely established even for 

functions (signals) in one dimension; they are yet more 

challenging in two and three dimensions, where discontinuities may be expected to occur along mostly 

smooth curves or surfaces. This constraint, which magnifies the advantage of the piecewise smoothness 

assumption, must be appropriately reflected in the 

methods used. Alpert and Yu Chen are conducting numerical experiments to understand this environment 

and to develop reliable procedures for these problems. 

 In recent months, understanding is developing of 

how to generate, test, and refine hypotheses regarding 

locations of discontinuities. This approach uses a spatial (i.e., physical domain) divide-and-conquer strategy 

enabled by use of prolate spheroidal wave functions in 

a statistical estimation procedure. These tools are used 

to cope with the non-convexity of the problem. As 

estimates are increasingly aggregated spatially, lesssupported hypotheses are eliminated and moresupported ones are refined. Once the discontinuity locations are known, recovery of the discontinuous 

function is a generally well-conditioned procedure consisting of solving a linear system of equations. 

 A related, yet more general, challenge is parsimonious, or sparse, representation and recovery of functions 

under assumptions appropriate to an application. Although there is considerable current interest in the 

mathematical community in these problems (L1

-norm 

minimization, compressive sensing, sparse representation in high-dimensional geometry), and much recent 

progress (initiated in pivotal work by Candes, Romberg, and Tao) most of the methods being explored are 

limited to linear spaces. While linearity is a natural 

starting point, strong evidence suggests that image recovery cannot be done this way yet nevertheless is 

within reach. It is the goal of this project to develop 

procedures for robust recovery of piecewise smooth, or 

otherwise constrained, functions from Fourier data. 

ITL Program: Enabling Scientific Discovery 

A Standard Candle for Extragalactic 

Metrology 

Bert W. Rust 

Dianne P. O’Leary 

Katharine M. Mullen (NIST MML) 

Type Ia supernovae are often more luminous at maximum brightness than are their parent galaxies, and their 

light curves are so regular and uniform that they make 

good “standard candles” for estimating extragalactic 

distances. An empirically established correlation between peak absolute magnitudes and the rates of 

decline of the light curves provides a means of estimating the peak absolute magnitude of a distant supernova 

from its observed decline rate. The estimate thus obtained can then be combined with a measurement of its 

peak apparent magnitude to give an estimate of its distance. We have developed mathematical model for the 

luminosity which, using seven adjustable parameters, 

gives superior fits to measured light curves and should 

prove useful in calibrating the correlation described 

above. Such fits are given in Figure 26 and Figure 27 

where the model explains 99.91% of the variance in the 

record. 

It is widely believed that, beginning a few days after maximum luminosity, the light curve is powered by 

the radioactive decay chain Ni → Co → Fe, even 

though observed luminosity decline rates do not match 

the terrestrial decay rates of Ni and Co. In 1976 Rust, 

Leventhal and McCall [Nature 262, pp. 118-120] presented evidence that those decay rates are accelerated 

because the decays occur in the extremely high density 

interior of a carbon-oxygen white dwarf. 
Summary of Activities for Fiscal Year 2010 51

Our current model [1] is a sum of three terms corresponding to luminosity generated by (1) the fusion 

reactions that deposit the Ni, (2) the radioactive decay 

of the Ni to Co, and (3) the radioactive decay of the Co 

to Fe. We use a three-parameter Weibull probability 

distribution function to model the pulse of Ni deposition and three coupled linear ordinary differential 

equations to model the radioactive decays. The three 

luminosity components for SN1990N are plotted in 

Figure 28. The strong similarity of the pulse locations 

and shapes for the Ni deposition and the Ni decay 

pulses make the seven-parameter fitting problem impossibly ill conditioned, but assuming that the total 

energies emitted by the two decays (the areas under the 

two decay pulse curves) have the same ratio as the 

known energies emitted by the decay of a single atom 

of each isotope makes it possible to reduce the number 

of free parameters to six, thus making the estimation 

problem tractable. 

Fits of our model imply an acceleration of radioactive decay rates as compared to the terrestrial values, in 

accordance with the results of Rust, Leventhal and 

McCall. This acceleration and the prolonged presence 

of the fusion pulse indicate that the star remains intact 

after the initial explosion for durations of a month or 

more, challenging previous light curve interpretations. 

[1] B. W. Rust, D. P. O’Leary, and K. M. Mullen, “Modelling Type Ia Supernova Light Curves,” in Exponential 

Data Fitting and its Applications, (Victor Pereyra and 

Godela Scherer, eds.), Bentham Electronic Books, 2010, 

pp. 145-164. 

Modeling Equilibrium, Stability and 

Transport during Magnetic Fusion 

Geoffrey B. McFadden 

Paul R. Garabedian (New York University) 

A hot plasma of hydrogen isotopes can be confined in a 

strong magnetic field with toroidal geometry so the 

ions fuse to form helium and release energetic neutrons. Models of such magnetic fusion devices 

developed in computational science have been implemented previously by P. Garabedian and his students 

and colleagues at New York University as codes that 

comprise an effective numerical simulation of the most 

essential features of modern tokamak and stellarator 

experiments. This has led to the discovery of advanced 

concepts that make fusion reactors a future prospect for 

a commercial source of energy. In recent work [1] we 

have applied computer codes to issues of equilibrium, 

stability and transport that provide an example of the 

theory. The codes have been used to evaluate possible 

stellarator designs as candidates for follow-up 

(“DEMO”) experiments that may eventually be performed after the completion of the planned 

international experiments (“ITER”) that are based on 

tokamak configurations. Tokamaks have axisymmetric 

Figure 26. The B-magnitude light curve for the supernova

SN1990N. The time variable is measured in Julian Day units. The

discrete data points are the observed B-magnitudes and the smooth

curve is the model fit. 

Figure 27. The light curve of SN1990N in relative luminosity units.

The time scale has been shifted to have t = 0 at maximum luminosity.

Figure 28. The three components of luminosity for SN1990N. The 

time scale here is the same as in Figure 27. 
52 NIST Applied and Computational Mathematics Division 

symmetry, which is an advantage for purposes of particle confinement, but they rely on strong toroidal 

currents in the plasma to generate the magnetic fields 

that can lead to stability issues. The magnetic fields for 

stellarators are generated by external coils which can 

alleviate many of the stability problems of tokamaks, 

but generally lack the high symmetry of tokamaks associated with enhanced confinement. The stellarator 

designs reported recently [1] offer the advantages of a 

type of quasi-axisymmetry (see Figure 29) that combines the best features of each, with the possibility of 

both good stability and transport properties. 

Professor Garabedian passed away in May, 2010. 

G. McFadden contributed an obituary to SIAM News

[2], and served as co-organizer of a memorial conference held in his honor at the NYU Courant Institute in 

December 2010. 

[1] P. R. Garabedian and G. B. McFadden, The DEMO 

quasiaxisymmetric stellarator, Energies 3 (2010) pp. 

277-284. 

[2] SIAM News 43, No. 7 (September 2010), pp. 2-3. 

A Structural Optimization Approach 

to Multihazard Design 

Florian Potra 

Emil Simiu (NIST EL) 

Multihazard design is a branch of structural engineering aimed at developing design practices that achieve 

superior performance by accounting holistically for all 

the hazards to which a structure is exposed. For some 

types of hazard no more than one hazard may be expected to occur at any one time. This is true, for 

example, of strong winds and earthquakes. In current 

practice structures that may be subjected to wind loads 

and seismic loads are typically not designed by using a 

multihazard approach. Rather, they are designed separately for each of the two loads; for each structural 

member the controlling design then corresponds to the 

more demanding of the two loads. 

It is desirable to achieve design synergies, that is, 

when performing the design for one of the two hazards 

it is desirable to take advantage of features inherent in 

the design for the other hazard, and conversely. This 

can in principle be accomplished in some cases through 

ad-hoc, practical engineering judgment. However ingenious and useful ad-hoc design solutions may be, 

there is a need for fundamental, science-based approaches to multihazard design. 

The purpose of this study is to propose such approaches which bring to bear on the multihazard 

structural design problem the powerful mathematical 

apparatus of modern optimization theory. Instead of 

designing a structure so that it performs satisfactorily, 

or optimally, given that it is subjected to seismic loads, 

and then repeating the design process independently for 

wind loads, we propose that the structure be designed 

so that it performs optimally given that it is subjected 

to either seismic or wind loads [1]. 

We have developed such an optimization-based 

approach to multihazard design. Here the design variables are member sizes, the constraints pertain to 

structural strength and serviceability (e.g., keeping the 

load-induced stresses and deflections below specified 

thresholds), and the objective function is the structure 

cost or weight. In a multihazard context, the design 

variables are subjected to the constraints imposed by 

all the hazards to which the structure is exposed. 

In [2] we describe this methodology and illustrate 

it by identifying the optimal design for supporting steel 

columns with hollow elliptical cross sections with constant thickness subject to wind and seismic forces. The 

numerical experiments show that interior point methods are significantly more efficient in solving the 

resulting nonlinear programming problem than classical numerical optimization methods. Although the 

structure considered in the numerical experiments is 

relatively simple, we argue that our methodology has 

the potential for being used, more generally, under a 

wide variety of hazards, types of structure, and structural engineering constraints. 

[1] F. Potra and E. Simiu, Optimization and Multihazard 

Structural Design, Journal of Engineering Mechanics

135 (2009), pp. 1472-1475. 

[2] F. Potra and E. Simiu, Multi-hazard Design: A Structural Approach, Journal of Optimization Theory and 

Applications 144 (2010), pp. 120-136. 

Figure 29. Magnetic fusion of hydrogen forms helium and emits 

energetic neutrons from a torus of plasma shaped to optimize confinement. Modular coils generate a field keeping the ions from hitting

walls. 
Summary of Activities for Fiscal Year 2010 53

Analysis of Diffusion and Stress in 

Binary Alloys 

Geoffrey B McFadden 

William J. Boettinger (NIST MML) 

The Kirkendall effect refers to the motion of lattice 

planes in a crystalline binary alloy that is caused by a 

difference in the rates of diffusion of the two species. 

The difference in diffusion rates leads to a stress-free 

stain in the sample, and the process is an example of 

the coupling between diffusion and elasticity during 

phase transformations. Current interest in stress generation in thin films due to diffusion processes has 

stimulated new interest in this classical problem. The 

effect can lead to measurable shape changes perpendicular to the direction of diffusion. It is often detected 

by a shift of inert markers parallel to the diffusion direction; that is, deformation with pure axial 

displacement. 

In recent work [1] we analyzed the time-dependent 

bending of a bimetallic strip due to interdiffusion in a 

binary alloy. In this case the deformation is due to diffusion across the short dimension of the strip, making 

deformation and diffusion co-linear. The results, which 

use a Fourier method, couple beam theory and diffusion, and are in agreement with experiments. 

Current work includes the development of models 

for grain boundary motion coupled to the Kirkendall 

effect, including the effect of stress on vacancy concentration at the interface. Idealized one-dimensional 

models with a sharp interface are being studied, and 

compared with alternate phase-field (diffuse interface) 

models that allow computation of more complicated 

geometries such as whisker growth. Here, long, thin 

single crystals are extruded from individual grains that 

are under high stress in thin films. These whiskers can 

bridge the gaps that separate individual components in 

electronic devices, causing electrical failure in some 

cases. Understanding the mechanisms behind whicker 

growth is important for the prediction of the lifetimes 

and performance of small-scale electronic components. 

[1] W. J. Boettinger and G. B. McFadden, Bending of a 

bimetallic beam due to the Kirkendall effect, Journal of 

Phase Equilibria and Diffusion 31 (2010) 6-14. 

ITL Program: Enabling Scientific Discovery 

Modeling Fluid Flow in Materials 

Processing 

Geoffrey B. McFadden 

P. Aaron Lott 

Sam R. Coriell (NIST MML) 

Daniel Anderson (George Mason University) 

Bruce Murray (SUNY Binghamton) 

The study of the stability of a fluid-fluid interface is 

important in a number of scientific and technological 

applications. In this project we consider two fluid layers separated by a horizontal planar interface subject to 

a vertical temperature gradient. The effects of various 

driving forces on the stability of the system can be 

taken into account, including buoyancy (known as 

Rayleigh-Benard convection), the effects of bulk density differences (known as Rayleigh-Taylor 

instabilities), and the effects of surface tension gradients along the interface (known as Marangoni 

instabilities). If the two layers represent different 

phases of the same material the stability results for a 

two-phase bi-layer system are quantitatively and even 

qualitatively different than for those of an immiscible 

system. To estimate the relative importance of these 

types of instabilities for a two-phase system, we have 

considered a bi-layer geometry in which a horizontal 

fluid-fluid interface separates two semi-infinite layers 

of a binary (two-component) fluid [1,2]. We have performed linear stability calculations for horizontal fluid 

bi-layers that can undergo a phase transformation, taking into account both buoyancy effects and 

thermocapillary effects. We find that the phase transformation gives rise to an instability that is independent 

of buoyancy and thermocapillary effects, and can occur 

for either heating from above or from below. The instability can give rise to traveling waves, and can occur 

in the limit of large wavelength perturbations. These 

large-wavelength instabilities can be studied analytically by employing a lubrication approximation to 

obtain a simplified set of governing equations. We 

have been able obtain both numerical and analytical 

solutions which help explain the physical mechanism 

of the instability. 

In a related study, the effect of buoyant convection 

on the stability of a mushy zone in a ternary alloy has 

been considered. The mushy zone is an idealized model 

of a two-phase region where liquid and solid comingle. With a three component system we show that 

instabilities can occur that are driven by the difference 

in the rates of diffusion of heat and solute (“double 

diffusive convection”), even when the density in the 

system is stably stratified, with heavy fluid underlying 

light fluid. This work was published in an issue of the 

Journal of Fluid Mechanics (Cambridge University 

Press) that was dedicated to Professor S. H. Davis of 

Northwestern University on his 70th birthday; the guest 
54 NIST Applied and Computational Mathematics Division 

editors of the volume were G. B. McFadden and P. H. 

Steen from Cornell University. 

[1] G. B. McFadden, S. R. Coriell, and P. A. Lott, Onset of 

convection in two layers of a binary liquid, Journal of 

Fluid Mechanics 647 (2010) 105-124. 

[2] G. B. McFadden, S. R. Coriell, and P. A. Lott, Onset of 

Morphological Instability in Two Binary Liquid Layers, 

submitted. 

[3] D. M. Anderson, G. B. McFadden, S. R. Coriell, and B. 

T. Murray, Convective instabilities during the solidification of an ideal ternary alloy in a mushy layer, Journal 

of Fluid Mechanics 647 (2010) 309-333. 

ITL Program: Enabling Scientific Discovery 

Modeling of Self-similar Grain Size 

Distributions 

Geoffrey B. McFadden 

C.S. Pande (Naval Research Laboratory) 

Polycrystalline solids typically consist of a large number of grains that differ in the orientation of their 

crystallographic axes. These grains have a distribution 

of sizes, and are separated by curved grain boundaries 

that in turn meet at grain boundary junctions. Driven 

by combinations of elasticity, diffusion, or capillary 

forces the grain boundaries migrate in time, and the 

distribution of grain sizes consequently evolves dynamically. 

A statistical description of the process is given by 

a grain size distribution function, which is assumed to 

depend on a mean grain radius and time. Grain growth 

under usual circumstances is known to approach a 

quasi-stationary distribution of grain sizes after a 

transient period. The quasi-stationary state in a wide 

variety of materials exhibits a scaling 

property, such that the grain size 

distribution has an invariant form when 

expressed in terms of the grain size scaled 

by its mean value. An accurate description 

of the spatial and temporal evolution of a 

polycrystal from an initial stage, through 

the transient period, and finally to the 

quasi-stationary state is still only poorly 

understood. 

In this work, a size-based continuum 

stochastic formulation is presented based 

on topological considerations. This analysis leads to a Fokker-Planck equation for 

the size distribution which admits a similarity solution that describes the long time 

behavior of the grain growth [1]. The resulting grain size distributions are shown 

to be in agreement with those obtained 

from computer simulations, indicating the validity of 

the stochastic approach. 

[1] C. S. Pande and G. B. McFadden, Self-similar grain size 

distribution in three dimensions: A stochastic treatment, 

Acta Materialia 58 (2010) 1037-1044. 

ITL Program: Enabling Scientific Discovery 

Materials Data and Metrology for 

Application to Materials Processes 

Timothy Burns 

Steven Mates (NIST MML) 

Richard Rhorer (NIST EL) 

Eric Whitenton (NIST EL) 

Debasis Basak (Orbital Sciences Corporation) 

Prediction of the best machining parameters for a particular process and work material continues to be a 

challenge in manufacturing. The fundamental problem 

that needs to be modeled is chip formation. Here, the 

workpiece interacts with a cutting tool under extreme 

pressure and temperature, and large plastic deformation 

takes place at a very high strain rate, both in the thin 

primary shear zone, and in the secondary shear zone 

along the tool/work interface, as the newly cut material 

slides up the rake face of the tool (see Figure 30). In 

some materials, the temperature during high-speed 

cutting can rise to a significant percentage of the melting temperature. Even though great strides have been 

made in modeling and simulation capabilities in the 

last few decades, due in large part to the development 

of user friendly finite-element software packages, there 

continues to be a need for higher precision and reliability in the modeling and simulation of machining 

processes. One of the major challenges to improved 

α

Chip Primary 

Shear Zone

φ

Workpiece V

VN

Tool

d h

Secondary 

Shear Zone

L

α

Chip Primary 

Shear Zone

φ

Workpiece V

VN

Tool

d h

Secondary 

Shear Zone

L

Figure 30. Schematic illustration of orthogonal cutting.
Summary of Activities for Fiscal Year 2010 55

modeling and simulation is the determination of an 

appropriate material description, i.e., constitutive response model, for the flow stress in the workpiece. 

Over the past several years, our research program 

in the NIST Pulse-Heated Kolsky Bar Laboratory has 

been directed towards obtaining improved constitutive 

response data under conditions of rapid heating for 

application to machining studies, as well as for other 

applications. This year, new experimental data on AISI 

1075 carbon steel have been published [1], [2]. The 

material AISI 1075 is known as a spring steel, and it is 

not frequently formed in high-speed machining operations. This specific steel was chosen for our study 

because it begins to undergo a phase transformation to 

a weaker crystalline form, i.e., austenite, at approximately the lowest temperature among the carbon steels; 

see Figure 31. The material has been shown to exhibit a 

stiffer response to compressive loading when it has 

been preheated using pulse-heating than it does when it 

has been preheated more slowly to a testing temperature that is below the eutectoid temperature (723 oC). 

Furthermore, when the material is pulse-heated to a 

temperature that exceeds the eutectoid temperature 

prior to compressive loading on the Kolsky Bar, it has 

been shown to exhibit a significant (~50 %) loss of 

strength. As a result, fixed-parameter constitutive models, such as the well-known Johnson-Cook model, 

cannot be used to describe this flow stress behavior. 

Because the lower-carbon steel AISI 1045 is used 

in the manufacture of automobile parts, and is often 

shaped by high-speed machining processes, we are 

designing new pulse-heated Kolsky bar experiments to 

investigate whether this material has constitutive response behavior similar to that of AISI 1075. Some 

preliminary results indicate that this is indeed so [3] 

[1] T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. Whitenton, 

and D. Basak, Dynamic Properties for Modeling and 

Simulation of Machining: Effect of Pearlite to Austenite 

Phase Transition on Flow Stress in AISI 1075 Steel Machining Science and Technology, to appear. 

[2] T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. Whitenton, 

D. Basak, and R. H. McFadden, Modeling of the Temperature Field in the Chip and in the Tool in High-Speed 

Machining of a Carbon Steel: Effect of Pearlite to Austenite Phase Transition in AISI 1075, International 

Journal of Material Forming 3 (2010), Supplement 1, 

pp. 491-494. 

[3] T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. Whitenton, 

and D. Basak On Modeling the Peak Temperature on the 

Tool-Chip Interface During High-Speed Machining of 

AISI 1045 Steel, in Proceedings of the Eighth International Conference on High-Speed Machining, Metz, 

France, December 8-10, 2010. 

ITL Program: Enabling Scientific Discovery 

Optimization for Inverse Problems 

in Mechanics 

Peter M. Ketcham 

Steven P. Mates (NIST MML) 

We are collaborating on the development of optimization tools suitable for deducing parameters for 

viscoplastic constitutive models of metals by inverse 

methods. The project involves full-field displacement 

history data and force history data combined with finite 

element models of dynamic materials tests performed 

in a Kolsky bar. Optimization is used to minimize cost 

functions representing differences between the simulations and the data with constitutive constants and 

friction as the primary unknown variables. Particular 

attention is paid to the uniqueness and stability of the 

optimized parameter set in order to assess the usefulness of the discovered parameters in modeling a variety 

of viscoplastic problems. 

This year we investigated optimization approaches, identified relevant mathematical resources, 

and established foundations for the associated software 

tools. Future work will include the development of 

prototype optimization tools with Mathematica and the 

evaluation of finite element analysis packages with 

respect to models of dynamic materials tests. 

910 oC 1147 oC 

0.02 0.75 2.1 

Temperature, oC 

Eutectoid 

 (0.77 % C) 

Liquid + 

 Austenite 

723 oC 

Ferrite + 

 Austenite 

Austenite + 

 Cementite 

Austenite 

Ferrite + Cementite 

Figure 31. Schematic drawing of equilibrium iron-carbon phase 

diagram for carbon percentages and temperatures of interest in 

this study. Dotted vertical line at 0.75 % carbon is close to the 

eutectoid composition at 0.77 % carbon. 
56 NIST Applied and Computational Mathematics Division 

Molecular Movies: Imaging 

Femtosecond Motion during 

Electrochemical Transitions 

Bradley Alpert 

Joel Ullom et al. (NIST PML) 

Christopher Cromer et al. (NIST PML) 

Ralph Jimenez et al. (NIST PML/JILA) 

Henry Kapteyn et al. (University of Colorado/JILA) 

Vital to the development of next-generation nanomaterials, including photovoltaics and industrial catalysts, is 

an understanding gained through measurement of electron generation, transport, and transfer in engineered 

nanostructures. This project, recently chosen for an 

Innovations in Measurement Science (IMS) award, 

proposes a revolutionary, table-top x-ray imaging system to capture the motion of electrons, atoms, and 

molecules on femtosecond time scales and with picometer spatial resolution. 

 The combination of table-top x-ray lasers, a dramatic recent breakthrough developed at JILA, with 

transition-edge sensor (TES) microcalorimeter spectroscopy, intensively developed and refined in NIST’s 

Quantum Electrical Metrology Division, promises to 

enable these new measurement capabilities. The integration of these components, accompanied by 

significant increase in detector array sizes, to achieve 

large increases in temporal and spatial resolution while 

maintaining extraordinary TES energy resolution, requires new data modeling and processing techniques. 

These techniques will overcome current limitations by 

• Resolving temporal overlap in photon detection 

while achieving energy resolution of temporally 

isolated arrivals, 

• Improving efficiency in elimination of lowfrequency background noise, and 

• Extending multiplexing and reducing cross talk in 

extracting the signals from below 1 degree kelvin 

to room temperatures. 

 Wiener filtering, long used among astronomers for 

estimating amplitudes of pulses of known shape contaminated with noise of known spectral (frequency) 

content, is suitable for measuring isolated pulses. 

Novel processing approaches are being developed and 

characterized that rely on this knowledge but are suitable for overlapping pulses. 

 Another processing issue concerns sensor nonlinearities at higher frequencies. As the new systems are 

built and characterized, other sources of uncertainty 

will undoubtedly arise and need to be understood, and 

this broad collaboration has been assembled for this 

purpose. 

Figure 32. The steep transition of superconducting film (a Mo/Cu 

proximity bilayer), provides temperature sensitivity that enables its 

use for photon spectroscopy. Note the narrow temperature range 

of approximate linearity. 

Figure 33. For overlapping responses due to multiple photons 

poorly separated in time, accurate amplitude determination requires good elimination of low-frequency background noise. 
Summary of Activities for Fiscal Year 2010 57

Accelerating Monte Carlo Simulation for Modeling Thermodynamic 

Properties 

Bradley Alpert 

Andrei Kazakov (NIST MML) 

Kenneth Kroenlein (NIST MML) 

To provide critically-evaluated data essential to industrial processes, the NIST Thermodynamics Research 

Center (TRC) develops and applies to published laboratory measurements several modeling technologies to 

evaluate, extend, and establish uncertainties for reported quantities. 

Metropolis Monte Carlo simulation, despite having 

been developed more than a half century ago, widely 

known, and extensively studied, has not been an important tool in this arsenal due to its extraordinarily high 

computational cost for all but the simplest compounds. 

Nevertheless, steadily improving computational power, 

continuing advances in Monte Carlo methods, and increasing demands for properties data beyond what can 

be feasibly obtained in labs, continue to shift the balance in favor of these computations. 

In addition, a major refrigerant properties characterization effort previously undertaken at NIST for the 

transition away from hydrochlorofluorocarbon refrigerants (such as Freon), successful in characterizing 

substitutes, now is no longer sufficient to enable compliance with new European environmental laws. The 

TRC intends to perform Monte Carlo simulations to 

obtain, for some currently poorly-characterized refrigerants, property data including critical parameters, 

saturated densities, saturated pressures, liquid densities, 

and vaporization enthalpies. These computations are 

barely feasible currently and therefore TRC has considerable interest in accelerating the code, MCCCS 

Towhee, used for the simulations. 

Alpert’s initial involvement in the effort arose 

from the potential to accelerate the many-body Coulomb interaction energy computations through use of 

the fast multipole method (FMM). To do so requires 

development of an incremental FMM in which energy 

changes due to position changes of a small number of 

atoms are computed efficiently. This algorithm work is 

underway. In addition, the Towhee random number 

generator has been replaced, for improved efficiency, 

and other code changes under consideration will improve the ease of incorporating additional algorithm 

changes, such as Hamiltonian Monte Carlo. 

Uncertainty in Virtual 

Measurements from Quantum 

Chemistry Models 

Raghu Kacker 

Ruediger Kessel 

Karl K. Irikura (NIST MML) 

Russell D. Johnson III (NIST MML) 

By a virtual measurement we mean a prediction along 

with its associated uncertainty for the value of a measurand determined from a computational model as an 

alternative to a physical measurement. An important 

application is quantum chemistry, where carefully determined uncertainties have not been reported. As the 

technology improves, the need and importance of reliable uncertainties in virtual measurements is being 

recognized. We are developing and applying methods 

for quantifying the uncertainty associated with a virtual 

measurement in quantum chemistry. The benefits accrue to R&D of chemical processes, materials 

development, and drug discovery 

Predictions from computational quantum chemistry models seldom agree with the corresponding highquality physical measurements. The differences are 

not random but systematic. Therefore, a common practice is to apply an empirical scaling factor to 

computational predictions to bring them closer to the 

true quantity values. The empirical scaling factor carries uncertainty. We have developed a methodology to 

quantify the uncertainty associated with a scaling factor. This approach is based on the Guide to the 

Expression of Uncertainty in Measurement, which is an 

international standard. The uncertainties for scaling 

factors lead to the corresponding uncertainties for virtual predictions. We reported in 2005 uncertainties in 

the scaling factors for ab initio vibrational frequencies 

Figure 34. The fast multipole method divides space into cubes 

hierarchically, with communications based on 6 x 6 x 6 aggregations (left to right, bottom then top). In the incremental update 

algorithm for Coulomb energy, additional efficiency gains are 

achieved by revised aggregations, involving 2 x 2 x 2 blocks (dark 

gray), 2 x 2 x 1 blocks (blue), 2 x 1 x 1 blocks (gray), and 1 x 1 x 1 

blocks (yellow). The white cubes are nearest neighbors to the 

source cube (black). 
58 NIST Applied and Computational Mathematics Division 

from 40 models (combinations of theory and basis sets) 

intended for predicting fundamental frequencies from 

computed harmonic frequencies [1]. The uncertainties 

were larger than generally acknowledged. This paper 

has received 121 citations. 

Subsequently in 2006-2007, we determined a new 

reference data set of 60 diatomic and 15 polyatomic 

experimental vibrational zero-point energies (ZPEs) 

that includes estimated uncertainties. In 2008 we refined the methodology for calculating uncertainties and 

reported uncertainties for 32 models intended for predicting vibrational ZPEs form computed harmonic 

frequencies. Our paper on this appeared in 2009 [2]. 

This year we considered anharmonic scaling factors and their associated uncertainties for six theorybasis set pairs [3]. Recent comments on our papers 

indicate that scientific community has started paying 

attention to uncertainties in computational models. 

In FY 2011 we will investigate the benefit of computing anharmonic frequencies which are much more 

expensive but do not avoid need of scaling. 

[1] K. K. Irikura, R. D. Johnson III, R. N. Kacker, Uncertainties in Scaling Factors for ab Initio Vibrational 

Frequencies, Journal of Physical Chemistry A 109

(2005), pp. 8430-8437. 

[2] K. K. Irikura, R. D. Johnson III, R. N. Kacker, and R. 

Kessel, Uncertainties in Scaling Factors for ab Initio Vibrational Zero-Point Energies, Journal of Chemical 

Physics 130 (2009), article 114102 (11 pages). 

[3] R. D. Johnson III, K. K. Irikura, R. Kacker, and R. Kessel, Scaling Factors and Uncertainties for ab-initio 

Anharmonic Vibrational Frequencies, Journal of 

Chemical Theory and Computation 6 (9) (2010), pp. 

2822-2828. 

ITL Program: Virtual Measurement Systems 

Atmospheric Retention of Man-made 

CO2 Emissions 

Bert W. Rust 

Most scientists agree that the observed warming of the 

Earth is chiefly caused by increases in atmospheric 

CO2 concentration c(t), which are driven by man-made 

CO2 emissions F(t). Figure 35 shows that these emissions have increased quasi-exponentially since 1850. 

If γ(t) is the fraction of the emissions in year t which 

remains in the atmosphere, then c(t) can be related to 

F(t) by the first kind integral equation 

)( .1)(0,)()( 8501 1850 += ≤≤ ∫ ctc tdF tγτττγ

Discretizing by quadrature gives an 83 x 151 linear 

system which, even with the constraints on γ(t), yields 

highly unstable estimates of γ(t). 

Figure 35. The lower plot gives yearly total CO2 emissions F(t), 

measured in megatons of carbon per year [Mt/yr C]. The upper 

plot gives the atmospheric CO2 concentration c(t), measured in 

parts per million by volume [ppmv]. The c(t) measurements after 

1959 are highly accurate averages of weekly air samples over the 

South Pole, but earlier measurements were obtained from Antarctic ice cores, which are less accurate, with many missing years. 

Figure 37. Estimates of the fraction of CO2 emissions remaining in 

the atmosphere. 

Figure 36. Harmonic approximation fits to c(t). After 1960 the 

highly precise South Pole measurements dominate, causing all of the 

fits to merge very closely. 
Summary of Activities for Fiscal Year 2010 59

 Assuming a harmonic expansion for γ(t) on the interval 1850 ≤ t ≤ 2000, i.e., 

∑=

⎥

⎦

⎤ ⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛ ⎟ +

⎠

⎞ ⎜

⎝

⎛ += h n

k

k k

kt B kt AAt 1

0 150

2 sin

150

2 )( cos

π π

γ

allows the parameters A0, Ak, Bk to be estimated by 

least squares, so long as 2nh < 83. The fits for nh = 0, 

1, 2, 3 are shown in Figure 36. Each successive fit in 

the sequence estimated 2 more free parameters than did 

the preceding one, so the standard F-test provides a 

criterion for terminating the sequence. A new harmonic should be included only if the two additional 

parameters produce a statistically significant reduction 

in the SSR. In the present case, the nh = 4 fit failed to 

produce such a reduction. The γ(t) estimates corresponding to the fits are plotted in Figure 37 which also 

gives the nh = 4 estimate for comparison. It is clearly 

more wiggly than the preceding estimates, and if nh is 

pushed to even higher values, the corresponding estimates become wildly oscillating and violate the 0 ≤ γ(t) 

≤ 1 constraint, so nh = 3 is clearly the optimal choice. 

[1] B. W. Rust, Atmospheric Retention of Man-made CO2

Emissions, Mathematics and Computers in Simulation, 

to appear. 

Modeling the Fluid Dynamics of 

Tear Films on the Cornea 

Geoffrey B. McFadden 

Richard J. Braun (University of Delaware) 

Toby A. Driscoll (University of Delaware) 

L. P. Cook (University of Delaware) 

R. Usha (Indian Institute of Technology) 

P. E. King-Smith (Ohio State University) 

Dry eye disorders refer to eye problems associated with 

insufficient amounts of fluids coating the surface of the 

cornea. They can be caused by reduced production of 

aqueous tears, and/or increased evaporation due to a 

deficient lipid layer in the fluid. In both of these conditions, tear film breakup is more rapid than normal. 

Breakup can be observed either as dark spots in fluorescein-stained tear films, or, noninvasively, by 

distortions in the reflected image of a grid. 

In order to better understand the dynamics of the 

spreading of tear films on the human eye we have studied two hydrodynamic models based on lubrication 

theory [1]. The eye is modeled by an ellipsoid of revolution, using a prolate spheroidal coordinate system. 

One model is a self-consistent leading-order hyperbolic 

PDE for relatively large substrate curvatures; the other 

retains another order resulting in a fourth order parabolic partial differential equation (PDE) for the film 

dynamics. We consider both Newtonian viscous flow 

models and non-Newtonian models that take into account shear-thinning of the tear fluid. We explore a 

wide parameter range of shear thinning and find a significant effect on finite-time singularities present in the 

model, representing discontinuous solutions allowed by 

the underlying hyperbolic PDE. Approximate results 

illustrating the nature of the flows are obtained both 

numerically and analytically. 

We are able to use this approach to evaluate the influence of the cornea's shape in providing a driving 

force for fluid motion through the Laplace-Young 

boundary condition that relates pressure and interface 

curvature, an effect neglected in previous studies. 

[1] R. J. Braun, R. Usha, G. B. McFadden, T. A. Driscoll, 

L. P. Cook, and P. E. King-Smith, Thin Film Dynamics 

on a Prolate Ellipsoid with Application to the Cornea, in 

review.

Simulation of Bioregulatory 

Networks Involved in Cell Cycle 

Control 

Geoffrey B. McFadden 

Mirit Aladjem (National Institutes of Health) 

S. Kim (National Institutes of Health) 

Kurt Kohn (National Institutes of Health) 

A. Luna (National Institutes of Health) 

G. McFadden is a co-advisor to Sohyoung Kim, a postdoctoral fellow, and Augustin Luna, a graduate student 

from Boston University, who are both doing research at 

the Laboratory of Molecular Pharmacology in the National Cancer Institute at NIH; their co-advisors are 

NIH researchers M. Aladjem and K. Kohn. The team is 

developing models of bioregulatory networks that are 

involved in cell cycle control. The models consist of 

systems of nonlinear ordinary differential equations or 

delay differential equations that typically exhibit 

switching behavior, limit cycles, and other types of 

bifurcations. 

Proper cell growth depends on a network of interacting molecules that monitors cellular metabolism and 

environmental signals. This network ensures that cells 

halt their growth in response to unfavorable conditions 

such as the absence of sufficient nutrients or the presence of potentially damaging agents. When cells 

escape these controls, the results are developmental 

abnormalities, genomic instability, and cancer. 

Much current work focuses on a protein known as 

p53, a tumor suppressor that causes cell cycle arrest or 

programmed cell death in response to stress signals 

such as DNA damage. Regulating the appropriate levels of p53 is essential for cell survival. Two associated 

proteins, Mdm2 and Mdmx, are known regulators of 
60 NIST Applied and Computational Mathematics Division 

p53. Mdm2 can facilitate degradation of p53, whereas 

the mechanism of the regulatory interaction of Mdmx 

with p53 is not clear. It is also not obvious how those 

three molecules will operate together under various 

conditions. 

To address those questions a mathematical model 

has been developed [1] to investigate the interactions 

of these three partner molecules by numerical simulations. An interesting feature of this system is the 

experimental observation of time-periodic behavior of 

the measured amounts of p53 and Mdm2 in the system 

under certain conditions. These results show the stabilizing effect that Mdmx has on the system at long 

times: for large enough amounts of Mdmx in the system the entire branch of steady state solutions is found 

to be linearly stable. 

This modeling work is intended to guide experimental investigations of the role of Mdmx in the cell 

cycle that are being performed by Dr. Kim. Augustin 

Luna has recently joined the team to conduct his Ph.D. 

research, which includes the development of models of 

the role played by a protein, SirT1, in regulating cellular response to DNA damage. Resveratol, naturally 

found in red wine and linked with extended lifespans in 

rodents, stimulates the gene that produces SirT1. G. 

McFadden is serving on his Ph.D. committee at Boston 

University. 

[1] S. Kim, M.I. Aladjem, G.B. McFadden, and K.W. Kohn, 

Predicted functions of MdmX in fine-tuning the response of p53 to DNA damage, PLoS Computational 

Biology 6 (2010), article e1000665 (18 pages). 

Automated Biological Cell Feature 

Identification 

David E. Gilsinn 

Kiran Bhadriraju (NIST MML) 

John T. Elliott (NIST MML) 

Biological cells are composed of many subsystems and 

organelles. The subsystem called the cytoskeleton is 

composed of long rod-shaped filaments. They give the 

cell form and help attach the cell to the substrate and 

neighbors. One of the filaments is called actin. 

In studying cells, biologists use microscopes that 

can be focused at different levels and can be automated 

to take multiple images. Stain treatments are used to 

bring out cell characteristics. In this study a computational method is implemented that automatically 

isolates the actin structures in cell imagery. 

Figure 38(a) shows a cell with the actin fiber cytoskeleton structure. This is one isolated cell in a group 

of thousands of cells. Cell biologists are interested in 

automatically identifying and sometimes measuring the 

groupings of fibers. The computer program developed 

for this project uses imaging techniques coupled with a 

data structure, called a graph, to identify and isolate 

groupings of actin fibers. 

The program begins by using an image processing 

method called watershed image segmentation. This 

method decomposes the image into regions with similar properties by outlining the boundaries of areas with 

valleys. However, due to image noise and the large 

Figure 38. (a) Top: Cell image showing the actin fiber structure. 

(b) Middle: Oversegmented image of the cell in top image. (c)

Final feature isolation for the cell in the top image.
Summary of Activities for Fiscal Year 2010 61

number of minima, this technique has a tendency to 

break the image into too many small segments. This is 

referred to as oversegmentation. An oversegmentation 

of the cell in Figure 38(a) is shown in Figure 38(b). It 

is clear from the figure that this segmentation does not 

create regions that isolate groups of fibers, for example. The objective of the program was to group the 

segments into more meaningful regions or features. 

The approach was to develop a measure of similarity or closeness of regions. In the current program the 

average image intensity of the regions was used as the 

defining characteristic of a region. A distance function 

to differentiate between regions was then created based 

on the average intensity differences. A tolerance was 

established that isolated nearest neighbor regions and 

an adjacency graph (or adjacency matrix) was created 

that established links between regions and their nearest 

neighbors. Regions that are neighbors are not necessarily nearest neighbors. It would depend on whether the 

distance function between them fell below the tolerance. Each region would have an associated list of 

nearest neighbors. All of these nearest neighbors themselves have linked nearest neighbors, thus forming a 

chain of connected regions. This allowed the use of an 

efficient search algorithm to link all regions with nearest neighbors within the tolerance into connected 

components. These connected components were taken 

as the desired features. Figure 38(c) shows the result of 

applying the algorithm to the image in Figure 38(a).

Although this image has areas with more segments 

than necessary, the program successfully identifies the 

major groupings of actin fibers. Further work is underway to develop an iterative approach to feature 

identification. Initial experiments on an iterative approach using the same average intensity measure did 

not produce fewer feature groupings. Different measures of region nearness have to be developed for the 

second and subsequent iterations. The initial algorithm 

and program are documented in [1]. 

[1] D. E. Gilsinn, K. Bhadriraju, J. T. Elliott, Biological 

Cell Feature Identification by a Modified WatershedMerging Algorithm, NISTIR 7750, November 2010, (47 

pages). 

ITL Program: Information Discovery, Use and Sharing 

Estimating Volumes of Simulated 

Lung Cancer Nodules 

David Gilsinn 

Bruce R. Borchardt (NIST PML) 

Amelia Tebbe (St. Mary’s College) 

Lung cancer is a disease of uncontrolled cell growth in 

tissues of the lung. It is the most common cause of 

cancer related deaths in men and second most in 

women and is responsible for an estimated 560,000 

deaths in the US in 2007. Lung cancer lesions may be 

seen in computed tomography (CT) images. Modern 

computer tomography is a medical imaging method 

that uses tomography but also employs digital image 

processing techniques to generate three dimensional 

images built from a sequence of two-dimensional Xray images made around a single axis. 

The Food and Drug Administration (FDA) is developing reference cancer lesions, called phantoms, to 

test CTs and their software. Two samples were loaned 

to NIST to estimate volumes. The material of which 

the phantoms are composed simulates lung cancer material. The FDA can insert these into a simulated body 

torso for testing CT scanning and image recognition. 

The two phantoms are shown in Figure 39. Although 

they seem spherical they are slightly non-spherical. 

The phantom on the right in Figure 39 is referred to as 

Green and the one on the left is referred to as Pink. 

The approach chosen for this study is based on a 

fundamental theorem in calculus, called the Divergence 

Theorem, in which a volume integral is shown to be 

equal to a particular surface integral. In order to develop a surface model of the phantoms, surface data 

was measured by a coordinate measuring machine 

(CMM) at NIST; see Figure 40. This machine produced a set of precisely measured (x, y, z) points on the 

surface of each phantom. As a reference, surface data 

was obtained on a well calibrated metal sphere in order 

to test the surface modeling process. In each case, two 

sets of data points were measured, which we referred to 

as coarse (121 points) and dense (181 points). 

The measured data were transformed to spherical 

coordinates and modeled using a set of basis functions, 

called B-splines. The initial best fit, in the sense of 

Figure 39. Simulated Lung Cancer Nodules.
62 NIST Applied and Computational Mathematics Division 

least squares, of linear combinations of bivariate forms 

of the B-splines exhibited undesirable oscillations. To 

mitigate these effects, the least squares objective function was modified to include smoothing terms. This 

process, called regularization, produced very satisfactory extrapolation values at triangle vertices on the 

phantom surfaces. The surface triangulation was then 

used to compute the necessary surface integrals and 

finally the volumes using the Divergence Theorem. 

To test the B-spline modeling process two approaches were taken with surface data from the 

calibrated metallic sphere. A spherical model was fit by 

least squares parameter fitting and the B-spline model 

was fit using the regularized objective function. The 

predicted volumes differed by approximately 0.01%. 

This confirmed that the B-spline modeling process, 

using regularization, was a valid process and volume 

estimates of the phantoms would be acceptable 

As a check on the potential non-spherical shape of 

the phantoms, a spherical model was fit to each. These 

produced volume estimates for the coarse and dense 

data from the Green phantom of 4331.3 mm3

 and 

4296.5 mm3

 respectively. The expanded uncertainties 

for the center point and radius were estimated as order 

10-1 and 10-2 respectively. For the Pink phantom the 

volumes were estimated as 3892.1 mm3

 for the coarse 

data and 3912.5 mm3

 for the dense data. The expanded 

uncertainties for the center point and radius were of the 

order 1 and 10-1 respectively. This suggested a spherical shape for the Green phantom and a slight nonspherical shape for the Pink. 

When volumes were estimated using the B-spline 

model, the values for the Green phantom were computed as 4331.8 mm3

 and 4296.8 mm3 for the coarse 

and dense data respectively, Notice the closeness to the 

spherical model results. The expanded uncertainties for 

the volumes were estimated as approximately 12 mm3

for the coarse data and 8 mm3

 for the dense data. For 

the Pink phantom the volume results were 3854.7 mm3

and 3906.5 mm3

 with expanded uncertainties of approximately 28 mm3

 and 18 mm3. These differed 

slightly from the spherical model fit, again indicating a 

potential non-spherical form for the Pink phantom. A 

preliminary [1] and final report [2] have been published. 

[1] D. E. Gilsinn, B. R. Borchardt, and A. Tebbe, Estimating Volumes of Simulated Lung Cancer Nodules, 

NISTIR 7571, July 2009. 

[2] D. E. Gilsinn, B. R. Borchardt, and A. Tebbe, Estimating Volumes of Near-Spherical Artifacts, Journal of 

Research of the National Institute Standard Technology

115 (2010), pp. 149-177. 

ITL Program: Information Discovery, Use and Sharing 

Computing Geodesics for Shape 

Analysis 

Javier Bernal 

Charles Hagwood (NIST ITL) 

John Elliott (NIST MML) 

Michael Halter (NIST MML) 

The recognition and classification of objects in observed images is an important goal in image analysis. 

For this purpose the analysis of shapes of objects in 

images has become an important tool. Accordingly 

biomedical image analysis is a major application of 

shape analysis. In particular biomedical images that 

show cells responding to stimuli are good candidates 

for shape analysis. This is because change in shape is a 

known response of a cell to stimuli. 

Shape space can be formalized with the Riemannian metric. In a space with this metric, a line between 

two points is generalized to a geodesic path between 

two shapes. The shapes of two cells can then be compared by computing the Riemannian length of the 

geodesic path between the two cells. 

 In this work numerical routines for computing geodesics for shape analysis will be implemented. 

Implementation will be used for understanding changes 

in shape of biological cells as a response to stimuli. 

ITL Program: Information Discovery, Use and Sharing 

Figure 40. Coordinate Measuring Machine
Summary of Activities for Fiscal Year 2010 63

Neural Networks 

Javier Bernal 

As part of the Computational Biology project, a backpropagation algorithm is being implemented for 

training neural networks. It is hoped that the neural 

network approach will be useful for the identification 

of subcellular features in cell images relevant to cell 

biologists. Approaches exist for recognizing objects or 

pattern classes associated with an image based on the 

use of sample patterns (training patterns) to estimate 

statistical parameters of each pattern class. However 

the statistical properties of the pattern classes might not 

be known or might be difficult to estimate. Therefore a 

method such as the neural network approach that produces the required decision functions based solely on 

training without assumptions about probability density 

functions associated with the pattern classes may be 

more successful at handling the problem. 

A neural network is a computational model that 

consists of computing elements called “neurons” organized as a network reminiscent of the way in which 

neurons are believed to be interconnected in the brain. 

It is an adaptive system that changes its structure based 

on information that flows through the network during a 

training phase. It is mostly used for modeling relationships between input and output data and for 

partitioning data into classes. 

During the training with the backpropagation algorithm the average squared error between the networks 

output and a target value is minimized for each point or 

pattern (in d-dimensional space) in the training set using gradient descent. Via training, coefficients of 

decision functions are obtained and associated with 

neurons in the network. Once the training is done other 

data points or patterns are put through the network and 

assigned to a class according to the output obtained. 

For our purposes the resulting implementation will be 

used for identifying pattern classes in d-dimensional 

space as each pixel in an image is associated with a ddimensional pattern, the coordinates of the pattern corresponding to d distinct attributes associated with the 

pixel. 

ITL Program: Information Discovery, Use and Sharing 
64 NIST Applied and Computational Mathematics Division 

High Performance Computing and Visualization

Computational capability is advancing rapidly. This means that modeling and simulation can be done with 

greatly increased fidelity (e.g. higher resolution, more complex physics). However, developing large-scale 

parallel applications remains highly challenging, requiring expertise that application scientists rarely have. 

In addition, the hardware landscape is changing rapidly so new algorithmic techniques must constantly be 

developed. We are developing and applying facilities and expertise of this type for application to NIST problems. Large scale computations and laboratory experiments invariably produce large volumes of scientific 

data, which cannot be readily comprehended without some form of visual analysis. We are developing the infrastructure necessary for advanced visualization of scientific data, including the use of 3D immersive 

environments and applying this to NIST problems. One of our goals is to develop the 3D immersive environment into a true interactive measurement laboratory. 

Large-scale Simulation of 

Suspensions 

William George 

Steve Satterfield 

Marc Olano 

Judith Terrill 

Nicos Martys (NIST EL) 

Edward Garboczi (NIST EL) 

Pascal Hebraud (CNRS/ESPCI, France) 

See feature article, page 31. 

ITL Program: Enabling Scientific Discovery 

High Precision Calculations of 

Properties of Few-electron Atomic 

and Molecular Systems 

James S. Sims 

Stanley A. Hagstrom (Indiana University) 

See feature article, page 36. 

ITL Program: Virtual Measurement Systems 

Nano-optics, and How to Squeeze 

Light out of Quantum Dots 

James S. Sims 

John Kelso 

Marc Olano 

Garnett Bryant (NIST PML) 

Natalia Malkova (NIST PML) 

See feature article, page 38. 

ITL Program: Enabling Scientific Discovery 

Modeling and Visualization of 

Cement Paste Hydration and 

Microstructure Development 

William George 

Steven Satterfield 

Judith Terrill 

Jeffrey Bullard (NIST EL) 

Edith Enjolras (NIST EL) 

Clarissa Ferraris (NIST EL) 

Edward Garboczi (NIST EL) 

Nicos S. Martys (NIST EL) 

Paul E. Stutzman (NIST EL) 

http://www.nist.gov/itl/math/hpcvg/hydrationhpc.cfm 

http://www.nist.gov/itl/math/hpcvg/hydrationvis.cfm

When cement powder is mixed with water, the process 

that transforms the paste from a fluid suspension into a 

solid (hydration) involves complex chemical and microstructure changes. Understanding and predicting the 

change rates is a longstanding but extremely challenging technological goal. Fundamental computational 

modeling of the hydration of cement is difficult because it involves a large number of coupled nonlinear 

rate equations that must be solved in an irregular threedimensional spatial domain. 

To address these challenges, we are applying a 

new computational model called HydratiCA, which has 

several advantages over previous attempts to model 

cement paste hydration. HydratiCA is based on the 

principles of mass action and detailed balances and 

uses stochastic cellular automaton algorithms to simultaneously model 3-D reaction and transport 

phenomena. This allows us to track the detailed kinetics and equilibria that occur in a diverse range of 

cementitious systems. At the length scales required to 

finely resolve the reaction mechanisms and microstructure changes in cement paste, HydratiCA must take 

small time steps (approximately 105

 per second) to 

remain numerically stable. In other words, tens of millions of time steps are required to simulate the behavior 
Summary of Activities for Fiscal Year 2010 65

of cement paste for just one hour. Therefore, parallelization of the model is important so that we can 

simulate systems that are large enough to be realistic, 

avoiding finite size effects, and still be able to complete the simulations in a reasonable amount of time. 

Visualization of the output of this model is important both for validation and to understand the 

distribution of phases in 3D; see. Figure 41 The output 

is a 3D volume of data with percentage values for each 

of multiple material phases at each lattice site. Over the 

course of the simulation time, a series of data volumes 

is produced at the time values of interest. This year we 

completed a simulation of a large-scale alite system on 

Columbia, the NASA/NAS SGI Altix machine. This 

simulation required approximately 100,000 CPUhours, running on 448 CPUs for over 240 hours. 

We will be using HydratiCA to help resolve two 

prominent hypotheses for reduced alite dissolution 

rates during the induction period. 

[1] J. W. Bullard, E. Enjolras, W. L. George, S. G. 

Satterfield, and J. E. Terrill, Validating a Scalable Parallel Computer Model of Cement Hydration and 

Microstructure Development, Modeling and Simulation, 

Materials Science and Engineering 18(2) (March 2010), 

article 025007 (16 pages). 

[2] E. Garboczi, J. Bullard, N. Martys, and J. Terrill, The 

Virtual Cement and Concrete Testing Laboratory: Performance Prediction, Sustainability, and the CSHub, in 

Proceedings of the NRMCA Concrete Sustainability 

Conference, Tempe, AZ, April 13-15, 2010. 

[3] J. W. Bullard, E. J. Garboczi, W. L. George, N. S. Martys, S. G. Satterfield, and J. E. Terrill, in Advancing the 

Materials Science of Concrete with Supercomputers, to 

appear. 

[4] J.W. Bullard, C.F. Ferraris, E.J. Garboczi, N.S. Martys, 

P.E. Stutzman, and J.E. Terrill, Virtual Cement and 

Concrete, Innovations in Portland Cement Manufacturing, in press. 

ITL Program: Enabling Scientific Discovery 

Modeling Clinical Tumors to Create 

Reference Data for Tumor Volume 

Measurement 

Adele Peskin 

Alden Dima (NIST ITL) 

http://www.nist.gov/itl/math/hpcvg/bioimgvis.cfm

The change in pulmonary nodules over time is an extremely important indicator of tumor malignancy and 

rate of growth. Physicians base both diagnoses and 

treatment on perceived changes in size, so accurate and 

precise measurement of such changes can have significant implications for the patient. Many techniques exist 

for calculating tumor volumes and/or the change in 

tumor size between two sets of data on the same tumor. 

To compare volumetric techniques, we need reference 

data with a variety of known tumor volumes with different levels of background noise, and no ground truth 

data is available is a realistic environment. Current 

phantom data do not replicate the complications of 

calculating volume change where tumors are embedded 

in the lung wall and attached to blood vessels. In this 

work, we create reference data sets to test volumetric 

change measurement in realistic lung environments. 

We are able to recreate clinical tumor shapes using 

combinations of spheres, ellipsoids, cones, and cylinders, which can be assembled at arbitrary sizes and 

angles with respect to one another. During assembly, 

partial voxel volumes are calculated by subdividing 

each voxel and testing for the appearance of each geometric object in the subsections. Using this technique, 

we are able to get an accurate estimate of the final volume for the combined set of objects. We first 

approximate the pixel intensity distribution of a clinical 

tumor in the same data set, using a normal distribution 

and the mean and standard deviation of the clinical 

tumor’s pixel distribution. Any grid point completely 

inside of the synthetic tumor is then assigned a random 

value from this normal distribution. Pixel intensities for 

the partially filled voxels are computed based on parameters that we derive from the clinical tumor data, 

which define the upper and lower boundaries for pixel 

intensities at the tumor surface. We find the lower 

boundary for surface pixel intensity from the magnitude of the gradient of the pixel intensities at the tumor 

surface. K2, the lower boundary for surface pixel intensity, is the intensity with the maximum average 

Figure 41. A snapshot from an interactive visualization of a hydration run at a very early stage of the hydration process. Only the 

calcium sulfate and calcium aluminate phases are shown. Using a 

virtual interactive tool, the sulfate ion concentration in solution is 

measured at a spot in the pore space. 
66 NIST Applied and Computational Mathematics Division 

gradient magnitude at the tumor edge. The upper limit 

for edge pixels, K1, is determined from a ratio based 

on our previous work [1]. Figure 42 shows the 8 geometric objects that were inserted into the clinical data. 

Figure 43 shows a few example slices, where both the 

clinical tumors and modeled synthetic tumors can be 

seen. Future work includes a further study of lung tumor shapes and growth patterns. 

[1] A, Peskin , K. Kafadar, A. Dima , J. Bernal, and D. 

Gilsinn, Synthetic Lung Tumor Data Sets for Comparison 

of Volumetric Algorithms, in The 2009 International 

Conference on Image Processing, Computer Vision, and 

Pattern Recognition, Las Vegas, NV, July 13-16, 2009. 

[2] A. Peskin and A. Dima, Modeling Clinical Tumors to 

Create Reference Data for Tumor Volume Measurement, 

in The 6th International Symposium on Visual Computing 

2010, Las Vegas, NV, November 22-December 1, 2010. 

ITL Program: Information Discovery, Use and Sharing

Predicting Segmentation Accuracy 

for Biological Cell Images 

Adele P. Peskin 

Alden Dima (NIST ITL) 

Joe Chalfoun (NIST ITL) 

John Elliott (NIST MML)

http://www.nist.gov/itl/math/hpcvg/bioimgvis.cfm

Cell microscopy is used extensively to monitor cellular 

behavior under experimental settings. One of the most 

common image analysis procedures for cellular images 

is segmentation of an image object from the remainder 

of the image, which provides information on cell characteristics and comparisons of experimental conditions. 

In this project we provide a method to estimate segmentation error based on the clarity of the image and 

the geometry of the image objects. We developed a 

new concept called the extended edge neighborhood to 

quantify the accuracy that can be expected from data 

used in cellular analysis [1]. 

Many software packages are available for segmentation of cellular objects in biological images. Our 

NIST collaborators were in need of methods to help 

evaluate which methods to use and how to use them 

most effectively. It became clear that quantitative 

methods were needed to evaluate how to use the image 

data they were creating. To study this problem, a range 

of cellular image data was created that varied in cell 

geometry and imaging conditions. A10 rat smooth vascular muscle cells and 3T3 mouse fibroblasts were 

stained with Texas Red cell body stain and compared 

under five sets of imaging conditions: combinations of 

low, medium, and high illumination, and an optimal 

and non-optimal filter, to span a wide range of image 

qualities [2]. Figure 44 provides a visual rendition of 

the five conditions. 

In an initial study of a large number of segmentation methods tested over all of our imaging conditions, 

it became apparent that information about the image 

clarity and cell characteristics could be used to determine how segmentation methods performed. We were 

able to quantify these factors into a single concept that 

can be used to predict how segmentation methods will 

work and the accuracy that be expected when using 

them. The apparent cell edges vary widely in clarity 

and sharpness across the five different images of the 

same cells. Cell edge quality can be measured in terms 

of the number of pixel lengths (distance between pixels) needed to represent the thickness of the edge 

regions, which we have previously quantified as the 

cell edge quality index (QI) [3]. In a paper in which we 

compare manual segmentation masks on a set of 16 of 

the images used here, we find that our manual segmentation sets differ from one another, and that the extent 

of misalignment from one set to another depends upon 

Figure 42. The eight geometric objects that were inserted into 

clinical data at the initial time of the test. 

Figure 43. Clinical tumors in blue boxes; synthetic tumors in red; 

One slice from each of 2 of the data sets produced for this study.
Summary of Activities for Fiscal Year 2010 67

the cell geometry [4]. We combine these concepts into 

a single quantity that can be calculated quickly for each 

cell. The metric represents the size of the extended 

edge neighborhood of pixels and is a fraction derived 

from the ratio of pixels at risk to the total cell area. The 

pixels at risk are determined by multiplying the cell 

perimeter by a factor determined from the QI representing the physical thickness (Th) of the cell edge. 

 40,000 cell images from the two cell lines and five 

imaging conditions were tested. In order to scale up our 

study to this size, we created reference data for segmentation comparisons automatically, using a new 

technique also created this year in our group [6]. We 

then segment each of the cell images using four different segmentation techniques. We compare the 

reference pixel set T, with a segmentation mask, pixel 

set E, with a pair of indices designed to distinguish 

between under- and over-segmentation. A single overall score for an individual segmentation can measured 

as a function of these bivariate indices. 

Segmentation analysis was performed on all 

40,000 images using four techniques, chosen from a 

previous study as the most consistent techniques that 

do not require large quantities of computational time: 

5-means, 4-means, and 3-means clustering, and a 

Canny edge segmentation [4]. Figure 45 shows the 

combined results from all the cell images as a function 

of extended edge neighborhood. 5-means clustering 

gives the best results for all but very low extended edge 

neighborhoods, where Canny edge segmentation does a 

better job for images with very high edge quality. 

To see the direct relationship between extended 

edge neighborhood and segmentation accuracy, we 

looked only at those results for which we had the most 

data: for each cell line, we chose the region of the extended edge neighborhood curve where 90% of our 

results appeared. These regions include 0.05-0.2 for the 

A10 cells, and 0.2-0.5 for the NIH 3T3 cells. Cell 

counts plotted along with 5-means clustering results for 

these two regions are shown in Figure 46. In Figure 47, 

we graph the A10 cells in the extended edge region 

Figure 44. Individual pixel intensities are color-coded over the range in each image, to show differences in edge sharpness. The ground truth 

mask is shown for comparison. 

Figure 45. Average segmentation distance as a function of extended edge neighborhood for 3-means clustering (red), 4-means 

clustering (green), 5-means clustering (blue), and Canny edge 

(purple). 

Figure 46. Averaged segmentation distance (red) for the A10 cells 

(top) and 3T3 cells (bottom) along with a plot of cell numbers as a 

function of extended edge neighborhood (blue). 
68 NIST Applied and Computational Mathematics Division 

from 0.02 to 0.2, and the NIH3T3 results in the extended edge region 0.2 to 0.5, where 90% of the cells 

from each cell line occur. Both of these data sets are 

fitted with a linear model, which is also plotted in 

Figure 47: predicted distance = 0.051 + EEN × 0.477, 

with a correlation coefficient of 0.9815. 

From this large scale test, we define a method to 

pre-process images and determine their vulnerability to 

segmentation error. The accuracy possible from any 

segmentation technique is directly proportional to the 

extended edge neighborhood of each cell in an image. 

Future work will include tests on a wider variety of 

methods, as well as using the extended edge neighborhood concept to choose appropriate segmentation 

methods during large scale screening tests. 

[1] A. Peskin, A. Dima, J. Chalfoun, and J. Elliot, Predicting Segmentation Accuracy for Biological Cell Images, 

in The 6th International Symposium on Visual Computing 2010, Las Vegas, NV, Nov. 22 - Dec. 1, 2010. 

[2] A. L. Plant, J. T. Elliott, A. Tona, D. McDaniel, and K. 

J. Langenbach, Tools for Quantitative and Validated 

Measurements of Cells, High Content Screening: A 

Powerful Approach to Systems Cell Biology and Drug 

Discovery. Humana Press, (L. Taylor, K. Giuliano, and 

J. Haskins, eds.), Totowa (2006). 

[3] A. Peskin, K. Kafadar, and A. Dima, A Quality PreProcessor for Biological Cell Images in Computational 

Bioimaging 2009, 5th International Symposium on Visual Computing, Las Vegas, NV, Nov. 30 – Dec. 2, 2009. 

[4] J. Chalfoun, A. Dima, A. Peskin , J. Elliot and J. Filliben, A Human Inspired Local Ratio-Based Algorithm 

for Edge Detection in Fluorescent Cell Images, in The 

6th International Symposium on Visual Computing 

2010, Las Vegas, NV, Nov. 22 – Dec. 1, 2010. 

[5] A. Dima, J. Elliott, J. Filliben, M. Halter, A. Peskin, J. 

Bernal, B. Stottrup, M. Kociolek, M. Brady, H. Tang, A. 

Plant, Comparison of Segmentation Algorithms for 

Fluorescence Microscopy Images of Cells, submitted. 

ITL Program: Information Discovery, Use and Sharing 

Visualizing Fire and the Resulting 

Deformation of Structures 

Pradeep Gaddam 

Marc Olano 

Judith Terrill 

Dilip Banerjee (NIST EL) 

John Gross (NIST EL) 

http://www.nist.gov/itl/math/hpcvg/firedeformvis.cfm

We are collaborating with researchers in the NIST Engineering Laboratory (EL) to study the effects of fire 

on building structures to improve structural engineering and building safety. We are using a sequential 

process in which the EL Fire Dynamics Simulator 

(FDS) is used to simulate the start and propagation of 

fire in a room, after which a second code (heat transfer 

analysis) calculates how gas temperatures computed by 

FDS diffuses into the structural members. A third program takes the output of the second code and computes 

how the structure deforms over time due to combined 

effects of thermal and mechanical loads. We use a test 

case with a single beam in a room. We link the fire, 

thermal, and structural data with a separate real-time 

visualization capability that can be run on the desktop 

and in the NIST 3D immersive environment. This enables interactive analysis of the resulting data. 

This year we integrated the data output from the 

three simulations into the analysis tools and performed 

validation on the results. We developed tools to interactively examine and visualize the scalars, vectors, and 

tensors output from the simulations. We created utilities to make fracture patterns in windows (see Figure 

48), and calculate the dynamics of the glass shards 

blowing out using the Bullet Physics Engine. 

Figure 47. Results from the A10 cells (red) and NIH3T3 cells 

(blue) fit to a straight line. 

Figure 48. Random fracture pattern in a glass window. 
Summary of Activities for Fiscal Year 2010 69

In the coming year, we will be expanding the interface and adding additional visualization and analysis 

techniques. 

[1] D. Banerjee, J. Gross, P. Reddy Gaddam, M. Olano, W. 

Hess, J. Terrill, T. Griffin, J. Hagedorn, J. Kelso, and S. 

Satterfield, “An Integrated Interactive Visualization and 

Analysis Environment to Study the Impact of Fire on 

Building Structures,” in Proceedings of SIGGRAPH’10, 

ACM SIGGRAPH 2010 Posters, Los Angeles, CA, July 

25-29, 2010, article 149 (1 page). 

Measuring Errors in Polygonal 

Representations of Surfaces 

John Hagedorn 

Marc Olano 

Judith Terrill 

http://www.nist.gov/itl/math/hpcvg/psurferr.cfm

Surfaces are important in diverse scientific disciplines 

and the depiction of surfaces and interactions with 

them are important tasks in scientific visualization. In 

this context, we typically work with surface models 

that are approximations of the true surfaces that they 

represent. When surface representations are used to 

make decisions or to make quantitative assessments of 

properties of the underlying surfaces, it is critical to 

understand the errors inherent in the representations. 

The most common way of approximating surfaces is 

with sets of polygons. We have developed metrics for 

assessing how well these polygonal representations 

portray the underlying surfaces. 

We look at three types of errors in polygonized 

surfaces: distance, surface area, and volume. For distance errors, we start by looking at a point on the 

polygonal representation and seeing how far away from 

the true surface that point lies. We can then assess the 

error over the entire surface by integrating over the 

surface. Surface area and volume errors are much simpler to assess. For surface area, we sum the areas of the 

polygons in the polygonal representation and compare 

with the true surface area of the underlying surface. 

Similarly, for closed polygonal representations, we can 

easily calculate the enclosed volume, which can be 

compared with the analytically determined volume. 

We have implemented these error metrics in software and tested them on a variety of quadric surfaces. 

We polygonized each surface in several ways, either 

directly from the analytic definition of the surface or by 

creating a gridded data set and generating a polygonal 

isosurface. The isosurface polygonizations are intended 

(in some ways) to emulate an experimental situation, 

and in that vein we added various levels of noise to the 

gridded data sets. These methods can be applied to any 

surface type and any polygonization. 

For each surface and each scheme, we tested polygonizations at progressively finer scales. The finer 

polygonizations have more polygons and are expected 

to more closely approximate the surfaces. The results 

of our tests enable us to quantify the errors of these 

polygonal representations relative to the underlying 

true surfaces. Furthermore, we see clear relationships 

between the measured errors and the number of triangles in a given approximation. These relationships can 

be modeled with simple formulas. Figure 49 shows a 

scatterplot of our normalized mean distance error metric versus the number of triangles for each of four 

polygonization schemes for elliptic paraboloids. This 

plot also shows the curves fit to the data. 

Unlike the other statistics, the surface area error 

metric does not appear to tend to zero as the number of 

triangles increase in the presence of noise. By analyzing the marching cubes isosurface polygonization 

algorithm we were able to explain this limit behavior. 

The limits predicted by our analysis correspond closely 

to those calculated by fitting the error data. 

Qualitatively our results are entirely expected; for 

example, coarser polygonizations have greater error. 

But these methods enable us to quantify this qualitative 

understanding. This quantitative understanding of error 

is critical as we apply other quantitative methods to 

these polygonal approximations of surfaces. 

[1] J. Hagedorn, M. Olano, and J. Terrill, Measuring Errors 

in Polygonal Representations of Surfaces, in preparation. 

ITL Program: Virtual Measurement Systems

Figure 49. Scatterplot of normalized mean distance error versus 

number of triangles for all polygonizations of the elliptic paraboloids. Data for each of the four polygonization schemes has been 

fitted and the resulting lines plotted. 
70 NIST Applied and Computational Mathematics Division 

Scientific Software

Modern science and engineering in general, and modern measurement science in particular require a wide 

variety of software tools for scientific discovery, exploration, and analysis. As scientific inquiry becomes 

deeper and more specialized, so must the supporting software tools. The goal of this work is to develop critical software tools that support measurement science at NIST, as well as computational science and 

engineering at large.

Micromagnetic Modeling 

Michael Donahue 

Donald Porter 

Robert McMichael (NIST CNST) 

June Lau (NIST MSEL) 

http://math.nist.gov/oommf/

Advances in magnetic devices such as recording heads, 

field sensors, magnetic nonvolatile memory (MRAM), 

and magnetic logic devices are dependent on an understanding of magnetization processes in magnetic 

materials at the nanometer level. Micromagnetics, a 

mathematical model used to simulate magnetic behavior, is needed to interpret measurements at this scale. 

MCSD is working with industrial and academic partners, as well as with colleagues in the NIST CNST, 

MML, and PML, to improve the state-of-the-art in micromagnetic modeling. 

Michael Donahue and Donald Porter in ACMD 

have developed a widely used public domain computer 

code for doing computational micromagnetics, the Object-Oriented Micromagnetic Modeling Framework 

(OOMMF). OOMMF serves as an open, welldocumented environment in which algorithms can be 

evaluated on benchmark problems. OOMMF has a 

modular structure that allows independent developers 

to contribute extensions that add to the basic functionality of OOMMF. OOMMF also provides a fully 

functional micromagnetic modeling system, handling 

both two and three-dimensional problems, with sophisticated extensible input and output mechanisms. 

In FY 2010 alone, the software was downloaded 

more than 4,500 times, and use of OOMMF was acknowledged in more than 120 peer-reviewed journal 

articles. This year OOMMF also passed the milestone 

of more than 1,000 citations. OOMMF has become an 

invaluable tool in the magnetics research community. 

Key recent developments in OOMMF include 

- Focused development on measurement, analysis, 

and improvement of the performance of the new 

modules providing multi-threaded computation on 

multi-processor, multi-core computers, while 

maintaining the cross-platform nature of the code. 

- Development of new techniques to compute the 

elements of the demagnetization tensor. Prior 

methods produced a loss of accuracy of six decimal digits per decade in the far field. New 

algebraic and asymptotic methods preserve at least 

ten decimal digits of accuracy at all distances. 

 Ongoing work includes extending parallelization to 

tens of processor cores on non-uniform memory access 

(NUMA) architectures, and evaluating various methods 

for modeling finite temperature effects, such as the 

Landau-Lifshitz-Bloch equation which adjusts the local 

effective saturation magnetization as a function of temperature and magnetic configuration. 

OOMMF is part of a larger activity, the Micromagnetic Modeling Activity Group (μMAG), formed 

to address fundamental issues in micromagnetic modeling through two activities: the development of public 

domain reference software, and the definition and dissemination of standard problems for testing modeling 

software. MCSD staff members are involved in development of the standard problem suite as well. There are 

currently four standard problems in the suite, testing 

both static and dynamic magnetization properties. A 

new standard problem proposed jointly by several authors [1] aims at validation of simulations of spin 

momentum transfer in the “current parallel to plane” 

geometry. While testing the proposed problem, we 

discovered errors in the treatment of boundaries in the 

OOMMF module for computing spin momentum transfer. This discovery also highlighted the need to have a 

set of boundary condition assumptions specified in the 

problem itself. Work continues to develop additional 

standard problems to address the spin momentum 

transfer phenomenon in other geometries. 

In addition to the continuing development of 

OOMMF, the project also does collaborative research 

using OOMMF. The project plays an instrumental role 

in the 2007 NIST Innovation in Measurement Science 

project (with CNST, MML and PML), “Magnetic 

nanostructures for post-CMOS electronics.” We also 

provide modeling and simulation consultation for work 

in PML on spin momentum transfer. In collaboration 

with the University of Konstanz we have used 

OOMMF to study magnetic structures in nanowires. 

The ACMD micromagnetic project produced three 
Summary of Activities for Fiscal Year 2010 71

Figure 50. A element finite element mesh created by OOF3D from 

a micrograph of trabecular bone. The micrograph consisted of 

8,000,000 voxels, and the mesh contains 50,000 elements. 

journal papers [2-4] and two conference presentations 

this past year. 

[1] M. Najafi, et al., Proposal for a Standard Problem for 

Micromagnetic Simulations Including Spin-transfer 

Torque, Journal of Applied Physics 105 (2009), pp. 

113914-113921. 

[2] M. J. Donahue, Parallelizing a Micromagnetic Program 

for Use on Multi-processor Shared Memory Computers, 

IEEE Transactions on Magnetics 45 (2009), pp. 3923-

3925. 

[3] K. M. Lebecki and M. J. Donahue, Comment on ‘Frustrated Magnetization in Co Nanowires: Competition 

between Crystal Anisotropy and Demagnetization Energy,’ Physical Review B 82 (2010), article 096401 (4 

pages). 

[4] H. Min, R. D. McMichael, M. J. Donahue, J. Miltat, M. 

D. Stiles, Effects of Disorder and Internal Dynamics on 

Vortex Wall Propagation, Physical Review Letters 104

(2010), article 217201 (4 pages). 

ITL Program: Enabling Scientific Discovery

ITL Program: Virtual Measurement Systems

OOF: Finite Element Analysis of 

Material Microstructures 

Stephen A. Langer 

Andrew C. E. Reid 

Valerie R. Coffman 

Gunay Dogan 

Lingda Tang 

http://www.ctcms.nist.gov/oof/

The OOF Project, a collaboration between ACMD and 

MML, is developing software tools for analyzing real 

material microstructure. The microstructure of a material is the (usually) complex ensemble of 

polycrystalline grains, second phases, cracks, pores, 

and other features occurring on length scales large 

compared to atomic sizes. The goal of OOF is to use 

data from a micrograph of a real or simulated material 

to compute the macroscopic behavior of the material 

via finite element analysis. OOF is intended to be a 

general tool, applicable to a wide variety of microstructures in a wide variety of physical situations. 

OOF is currently being used in research at industrial, academic, and government laboratories and as a 

teaching tool in universities. Including all available 

versions, OOF2 was downloaded 1,683 times this year, 

a 40% increase from last year. The on-line version, 

available at Purdue’s nanohub site for computational 

materials science, was run by 143 users. 

During FY10 the OOF team concentrated on improving the nonlinear and time dependent solvers in the 

2D program, OOF2, and on developing the 3D version, 

OOF3D. Issues addressed in the 2D code included: 

simultaneous solutions of static and time dependent 

equations; nonlinear versions of time stepping algorithms; time dependent boundary conditions; new user 

interfaces for time dependent problems; better status 

reporting; finite-element based image segmentation 

algorithms; new programming interfaces for material 

physics, with examples for users writing OOF extensions; nonlinear large strain elasticity; surface and 

interface physics; plasticity models; and new code governing multi-threaded execution and progress bars. All 

of these improvements will carry over into the 3D 

code. In addition, this year large portions of the 3D 

code were rewritten to improve speed and memory use, 

enabling OOF3D to create meshes on a scale suitable 

for research on realistic problems. Figure 50 shows a 

meshed sample of a 3D bone micrograph. 

OOF contains extensive test suites for both its internal workings and its graphical user interface. 

Maintaining compatibility with tests while adding features and fixing bugs helps to guarantee a quality 

product and avoid development delays. 

Plans for FY 2011 include releasing OOF2 version 

2.1 and a beta version of OOF3D, including work on 

parallelization, 3D image segmentation, plasticity, and 

merging the 2D and 3D code bases. 

[1] V. R. Coffman, A. C. E Reid, S. A. Langer, and G. 

Dogan, OOF3D: An Image-based Finite-element Solver 

for Materials Science, in review. 

ITL Program: Enabling Scientific Discovery
72 NIST Applied and Computational Mathematics Division 

Parallel Adaptive Refinement and 

Multigrid Finite Element Methods 

William F. Mitchell 

Marjorie A. McClain 

Eite Tiesinga (NIST PML) 

Thomas Hanna (NIST PML) 

http://math.nist.gov/phaml

Finite element methods using adaptive refinement and 

multigrid techniques have been shown to be very efficient for solving partial differential equations. 

Adaptive refinement reduces the number of grid points 

by concentrating the grid in the areas where the action 

is, and multigrid methods solve the resulting linear 

systems in an optimal number of operations. Recent 

research has been with hp-adaptive methods where 

adaptivity is in both the grid size and the polynomial 

order of approximation, resulting in exponential rates 

of convergence. W. Mitchell has been developing a 

code, PHAML, to apply these methods on parallel 

computers. The expertise and software developed in 

this project have been useful for many NIST laboratory 

programs, including material design, semiconductor 

device simulation, and the quantum physics of matter. 

This year the effort was focused on three areas. 

The first is a numerical experiment to study the effectiveness of several competing strategies for hp-adaptive 

refinement. This involves implementing these methods 

in PHAML, defining a set of test problems, and performing the computations. The second is the 

application of PHAML to solve the time-dependent 

Schrődinger Equation for eigenvalues and eigenstates 

relevant to optical traps for neutral atoms, in collaboration with the Quantum Processes Group of NIST’s 

Atomic Physics Division. Understanding the interactions of adjacent atoms corresponding to qubits of a 

quantum gate involves computing multiple eigenvalues 

in the middle of the spectrum, with eigenstates that 

have sharp gradients, which is a very challenging computation. The third is the extension of PHAML to a 

different parallel paradigm, that of multicore computers, using OpenMP. This implementation can also 

be used in a hybrid MPI/OpenMP parallel paradigm on 

clusters of multicore computers. 

The major accomplishments for FY 2010 are: 

- Completion of the implementation of hp-adaptive 

strategies in PHAML. 

- Performed computations and summary reports for 

19 of the 23 test problems of the numerical experiment. 

- Began implementation of a time-dependent model 

of two dipolar molecules held in a cylindrically 

symmetric trap. 

- Modified PHAML to solve Schrödinger’s equation 

with complex potentials. 

- Began adding OpenMP directives to PHAML. 

 Future work will continue to enhance PHAML with 

additional capabilities and robustness, complete the 

experiment to compare the effectiveness of hp-adaptive 

strategies, used lessons learned from the experiment to 

design a more effective hp-adaptive strategy, complete 

the addition of OpenMP directives in PHAML, apply 

PHAML to a time-dependent model of two dipolar 

molecules held in a cylindrically symmetric trap, and 

perform further physics experiments using the code. 

[1] W. F. Mitchell, The hp-Multigrid Method Applied to 

hp-Adaptive Refinement of Triangular Grids, Numerical 

Linear Algebra with Applications 17 (2010), pp. 211-

228. 

[2] W. F. Mitchell and M. A. McClain, A Survey of hpAdaptive Strategies for Elliptic Partial Differential 

Equations, Annals of the European Academy of Sciences, to appear. 

[3] W. F. Mitchell, A Collection of 2D Elliptic Problems for 

Testing Adaptive Algorithms, NISTIR 7668 (2010). 

[4] W. F. Mitchell, Some Computational Results with hpAdaptive Refinement, SIAM Conference on Parallel 

Processing for Scientific Computing, February 2010. 

[5] W. F. Mitchell, A Summary of hp-Adaptive Finite Element Strategies, Workshop on Adaptive Finite Elements 

and Domain Decomposition Methods, June, 2010 (invited talk). 

[6] W. F. Mitchell, A Summary of hp-Adaptive Finite Element Strategies, 2nd European Seminar on Coupled 

Problems, June 2010 (plenary lecture). 

ITL Program: Enabling Scientific Discovery

Variable Projection for Nonlinear 

Least Squares Problems 

Dianne P. O’Leary 

Bert W. Rust 

Fitting a model to measured data is essential for discovering patterns and causality. Yet data fitting 

problems are often numerically challenging. In fitting 

exponential models, for example, small changes in the 

data can make large changes in parameter estimates. 

And data fitting problems are most often nonconvex, so 

a set of parameter estimates can be locally optimal 

without being globally optimal, and software can be 

fooled into accepting a suboptimal estimate. 

We focus on fitting nonlinear models in a 

(weighted) least-squares sense. Most such models 

have some parameters that appear linearly. For example, in fitting a sum of two exponentials, the model for 

the data observations y(t1), ..., y(tm) might be 
Summary of Activities for Fiscal Year 2010 73

)( ).,,( 1 2

1 2ececty t t t η α c α α ≡+≈

The parameters c = [c1, c2] appear linearly, so for every 

choice of nonlinear parameters α = [α1, α2], optimal 

estimates for c can be found by solving a linear leastsquares problem. Consider the (full) nonlinear leastsquares problem 

,),(min 2

2 ,

αη c α cy −

where yi is the observed value y(ti), and ηi is the model 

prediction at ti. Then the solution to the full problem is 

the same as the solution to the reduced problem 

,))(,(min 2

2 αη c α α

y −

where η(α,c(α)) denotes the model predictions when, 

given α, we determine the parameters c optimally. 

In 1973 Gene Golub and Victor Pereyra presented 

a variable projection algorithm based on the reduced 

problem, and this was subsequently used by John Bolstad in a Fortran program VARPRO. VARPRO also 

used some ideas of Linda Kaufman to speed up the 

computation of derivatives. The beauty of variable projection is that it reduces the number of parameters, thus 

improving efficiency, and possibly reducing the number of local minimizers. Convergence to the globally 

optimal solution is therefore more likely. But implementation of the idea is complicated because the 

derivative matrix for the reduced problem must be derived from that for the full problem. 

The present work provides a 21st century sample 

implementation of the variable projection method that 

allows a more general problem formulation (i.e., with 

constraints on the parameters), more clearly identifies 

its key ingredients so that improvements can be made, 

and makes future implementations in other languages 

easy. This implementation, in Matlab, contains more 

than 400 lines of comments for fewer than 160 lines of 

code. We have used a high-quality (constrained) 

nonlinear least-squares algorithm to solve the reduced 

problem and a high-quality linear least-squares algorithm to determine the linear parameters. We have 

derived the derivative matrix for the reduced problem 

from sparse information for the full problem and 

shown that foregoing the Kaufman idea leads to better 

performance. Finally, our program computes statistical 

diagnostics for the estimate in order to help the user 

validate the computed parameters. 

We validated our implementation on many test 

problems, comparing the results with those obtained 

from the Fortran version and from other standard software, and demonstrating enhanced robustness. One 

resulting fit to supernova light curve data is shown in 

Figure 51. 

[1] B. W. Rust, D. P. O’Leary, and K. M. Mullen, “Modelling Type Ia Supernova Light Curves,” in Exponential 

Data Fitting and its Applications, Victor Pereyra and 

Godela Scherer, eds., Bentham Electronic Books, 2010, 

pp. 145-164. 

Figure 51. The data fit for a supernova light curve.
74 NIST Applied and Computational Mathematics Division 

Digital Library of Mathematical Functions

The special functions of applied mathematics are fundamental tools enabling modeling and analysis in all 

areas of science and engineering. To make effective use of such functions, practitioners must have ready access to a reliable source of information on their properties. The goal of this work is the development and 

dissemination of definitive reference data on the special functions of applied mathematics. The centerpiece of 

this effort is the DLMF, a freely available interactive and richly linked online resource.

A Special Functions Handbook for 

the Digital Age 

Frank Olver 

Daniel Lozier 

Charles Clark (NIST PML) 

Ronald Boisvert 

Bruce Miller 

Bonita Saunders 

Abdou Youssef 

Marjorie McClain 

Qiming Wang 

Brian Antonishek (NIST ITL) 

http://dlmf.nist.gov/

See feature article page 25. 

Visualization of Complex Functions 

Data 

Bonita Saunders 

Brian Antonishek (NIST ITL) 

Qiming Wang 

Sandy Ressler 

Daniel Lozier 

Frank Olver 

A mathematical or physical scientist can gain useful 

information about the behavior of a complex function 

from the visualization of its data, but providing that 

visualization to a wide audience on the web presents 

many challenges. One must ensure the accuracy of both 

the data and plot, choose software to create the web 

visualization, find appropriate software for users to 

view the visualizations on various platforms, and monitor the performance of the software when operating 

systems or internet browsers are updated. Over the past 

few years we have tackled all of these problems and 

successfully created over 200 3D visualizations for the 

NIST Digital Library of Mathematical Functions 

(DLMF). Since the release of the DLMF this past 

May, we have concentrated on the update and maintenance of the visualizations. 

Currently the visualizations are rendered using two 

common technologies for 3D graphics on the web: Virtual Reality Modeling Language (VRML) and X3D. 

Users may view the visualizations by downloading a 

free plugin. Numerous choices are available for Windows and Mac platforms, but fewer for Linux. We are 

making the changes needed to view our graphics files 

in the most widely used Linux operating systems. We 

are also attacking the portability problem from another 

direction by determining file modifications needed to 

view our files in a WebGL environment. HTML5 will 

contain WebGL attributes that allow users to view our 

visualizations inside a web page without the need of a 

special plugin. We have already successfully displayed 

simplified versions of our files in experimental 

HTML5 browsers. 

We continue to make improvements to the features 

of the visualizations. Testing of new cutting plane 

software is in progress. The modifications will produce smoother cutting plane movement and more 

accurate cutting plane intersection curves for most 

visualizations. Improvements are also being made to 

the underlying grids on which the functions are computed to improve the surface color maps and further 

improve cutting plane accuracy. 

Figure 52. Scaled Riemann theta function )|0,( θ

ˆ iyx Ω+ where Ω

is a specially defined matrix. 
Summary of Activities for Fiscal Year 2010 75

Regular maintenance and testing of the visualizations is important not only because of problems that 

can arise from operating system and internet browser 

updates, but also because of VRML/X3D plugin updates. Hopefully this will become a fairly minor effort 

once we complete the changes needed for WebGL and 

stable HTML5 compatible browsers are released. 

[1] B. Saunders and Q. Wang, “Tensor Product B-Spline 

Mesh Generation for Accurate Surface Visualization in 

the NIST Digital Library of Mathematical Functions”, in 

Mathematical Methods for Curves and Surfaces, (M. 

Dæhlen, et al., eds.), Lecture Notes in Computer Science 

5862 (2010), pp. 385-393.. 

[2] B. Saunders, Q. Wang, Tensor Product Grid Generation 

for Complex Surface Visualizations in a Digital Library 

of Mathematical Functions, in Proceedings of the 11th

International Society for Grid Generation (ISGG) Conference, Montreal Canada, May 25-28, 2009, p. SV.3. 

[3] Q. Wang , B. Saunders, and S. Ressler, Dissemination of 

3D Visualizations of Complex Function Data for the 

NIST Digital Library of Mathematical Functions, CODATA Data Science Journal 6 (2007) pp. S146- S154. 

[4] B. Saunders, Q. Wang, From B-Spline Mesh Generation 

to Effective Visualizations for the NIST Digital Library 

of Mathematical Functions, in Curve and Surface Design: Avignon 2006, Sixth International Conference on 

Curves and Surfaces, Avignon, France, Nashboro Press, 

2007, pp. 235-243. 

Mathematical Knowledge 

Management 

Bruce Miller 

Abdou Youssef (George Washington University) 

Michael Kohlhase (Jacobs University, Germany) 

Heinrich Stamerjohanns (Jacobs University, Germany) 

Although the World Wide Web was originally created 

to distribute scientific documents, its rapid adoption for 

entertainment and commerce almost left the scientific 

community behind. While the web and electronic 

books are blossoming, assuring that scientific literature 

benefits from advanced communications technologies 

requires attention. 

Knowledge management deals with the practices 

used to create, represent, distribute and find “knowledge”; mathematical knowledge management deals 

with the special aspects of mathematical knowledge. 

The special symbols and notations of mathematics create unique difficulties for authoring and delivery. In 

addition, the disconnect between the familiar notations 

(“presentation”) and the underlying meaning (“semantics”) inhibit reuse and accessibility. Each effect 

creates difficulties for both indexing and querying, 

making it hard to locate mathematical material. 

In 1998 the Math Working Group7

 of the World 

Wide Web Consortium released Version 1 of the 

Mathematical Markup Language (MathML) specification. MathML provides a means for describing 

mathematics as a basis for machine to machine communication. In particular, it provides a foundation for 

the inclusion of mathematical expressions in Web 

pages. The adoption of MathML has been slow but 

steady. This last year has been a good one, however, 

with increased interest amongst browser developers, 

and more material appearing on the web — not least, of 

which is our own Digital Library of Mathematical 

Functions8

 (DLMF) which was released in May. 

The working group released Version 3 of the 

MathML specification this last fall. Increased usage of 

MathML by publishers for educational materials demanded better coverage of elementary mathematical 

constructs such as long division and multiplication. 

Likewise, increased interest around the world called for 

support for use of mathematics in right-to-left languages such as Hebrew and Arabic, as well as for 

mathematics itself written right-to-left, as is done in 

some parts of the Arabic speaking world. Within the 

more theoretical communities, such as automated theorem proving, it was important to consolidate efforts 

towards representing the deeper semantics of mathematical material. Complete alignment of Content 

MathML, that subset specific to semantics, with the 

OpenMath standard9

 achieved this goal, as well as providing MathML with fully extensible semantics. These 

enhancements, along with many additional clarifications and corrections, were incorporated into the 

updated specification. 

Developing the DLMF, forced us to face both authoring and publishing difficulties. The only feasible 

way to collect the material from the world’s special 

functions experts was to accept it in LaTeX format. 

And yet, this material must be not only printed, but 

converted to XML and MathML for use on the web — 

a non-trivial task, given the complex and powerful nature of TeX. We thus developed LaTeXML as a tool to 

enable such conversions. 

With such a system, a strategy for enriching the 

semantics of documents, as well as standardizing nota-

 

7 http://www.w3.org/Math/

8 http://dlmf.nist.gov/

9 http://www.openmath.org/

Figure 53. Phase density plot of Hankel function )()1(

5 + iyxH .
76 NIST Applied and Computational Mathematics Division 

tions, was to develop and use semantic-oriented 

markup. In particular, to use markup that reflects the 

meaning of each function or operator, rather than just 

its appearance. Among other benefits, this technique 

generates a richer index from which mathematical 

searches can be carried out. A technique for conversion of mathematical structure and symbols into a 

flattened textual form allowed us to leverage a powerful text search engine to support mathematical search 

[1]. Figure 54 shows several such search features. 

While LaTeXML was initially focused on the 

needs of the DLMF project, it was clear that such a tool 

had broader application. A research group at Jacobs 

University in Bremen, Germany, sought a large body 

of scientific literature in electronic format with which 

to carry out a variety of document processing experiments. They established a project to convert as much 

of the arXiv10 as possible to MathML, and LaTeXML 

was used for this purpose. The arXiv is a large preprint 

collection hosted at Cornell University, where the 

documents are publicly available and almost all are 

written using LaTeX. A large number of LaTeX document styles and format files were prepared and a 

cluster of workstations was used to carry out document 

conversion [2]. Currently, over 500,000 documents 

 

10 http://arxiv.org/

have been processed with the conversion of 67% being 

of good quality. 

Current and future work on LaTeXML aims to 

continue to increase its coverage of mathematics, but 

also to leverage the XML to various other uses, such as 

ePub, used in electronic books, or Daisy, an accessible 

document format. Improving the mathematics grammar 

along with inferring and enhancing the semantic content of documents is also a continuing goal. 

[1] B. Miller and A. Youssef, Technical Aspects of the 

Digital Library of Mathematical Functions, Annals of 

Mathematics and Artificial Intelligence 38 (2003), pp. 

121 -136. 

[2] H. Stamerjohanns, M. Kohlhase, D. Ginev, C. David, 

and B. Miller, Transforming Large Collections of Scientific Publications to XML, Mathematics in Computer 

Science 3 (2010), pp. 299-307. 

ITL Program: Information Discovery, Use and Sharing

Figure 54. A search result for a query with both semantic (“Hankel”) and presentational (“Ai”) terms. The result shows how query relaxation adjusts the query to match the material, as needed. Term highlighting is aided by indexing semantics in parallel to the presentation 
Summary of Activities for Fiscal Year 2010 77

Math Table Generation Service 

Daniel Lozier 

Bruce Miller 

Marjorie McClain 

Bonita Saunders 

Chris Schanzle 

Annie Cuyt (University of Antwerp) 

Stefan Becuwe (University of Antwerp) 

Old-fashioned published tables have long been used to 

supply numerical values of elementary and selected 

special functions. In recent years these have been employed in numerical exploration, software validation, 

program debugging, algorithm construction, and graphics production. For example, it is known that the 

special function procedures in Mathematica were validated by comparison with the 1964 NBS Handbook of 

Mathematical Functions. More recently, in August 

2010, a communication was received from Microsoft, 

which is developing a numerical library and needs assistance with validation of math functions in the 

library. 

The purpose of our project, which we call the Live 

Tables Project (LTP), is to develop a website at NIST 

that provides 21st century tools to escape the severe 

limitations the old published tables: low precision, 

sparsity of arguments and parameters, lack of coverage 

of complex variables, and inability to accommodate 

definitional variations. It will allow users to specify 

(within reasonable limits) these attributes, and it will 

return values with an accuracy certification. 

The LTP was initiated after the public release in 

May 2010 of the Digital Library of Mathematical 

Functions (DLMF). The first step was to identify 

sources of reliable software, that is, software that establishes an error bound, preferably a priori, together with 

each function value. A group at the University of Antwerp has developed just such a software package, using 

continued fractions as the main tool. This package covers a substantial subset of the functions in the DLMF. 

Prof. Dr. Cuyt and Dr. Becuwe visited NIST in October for intensive discussions, which resulted in an 

agreement to collaborate and an action plan for FY 

2011. The plan calls for a prototype design for the user 

interface, web software, and computational engine to 

be completed by midyear, and for a prototype web service to be operational at the end of the year. 

ITL Program: Virtual Measurement Systems
78 NIST Applied and Computational Mathematics Division 

Quantum Information

An emerging discipline at the intersection of physics and computer science, quantum information science 

(QIS) is likely to revolutionize science and technology in the same way that lasers, electronics, and computers did in the 20th century. By encoding information into quantum states of matter, one can, in theory, 

exploit the seemingly strange and counter-intuitive behavior of quantum systems to enable phenomenal increases in information storage and processing capability, as well as communication channels with extremely 

high levels of security. Although many of the necessary physical manipulations of quantum states have been 

demonstrated experimentally, scaling these up to enable fully capable quantum computers remains a grand 

challenge. We are engaged in (a) theoretical studies to understand the true power of quantum computing, (b) 

collaborative efforts with the multi-laboratory experimental quantum science program at NIST to characterize and benchmark specific physical implementations of quantum information processing, and (c) the 

development and assessment of technologies for quantum communication. 

Up-conversion Single Photon 

Detectors and their Application in 

Measurement Science 

Xiao Tang 

Lijun Ma 

Oliver Slattery 

Barry Hershman 

Alan Mink 

Hai Xu 

Joshua Bienfang (NIST PML) 

Matthew Rakher (NIST CNST) 

Kartik Srinivasan (NIST CNST) 

Li Yan (University of Maryland Baltimore County) 

Jason Pelc (Stanford University) 

Martin Fejer (Stanford University) 

See feature article, page 42. 

ITL Program: Quantum Information

Quantum Computing Theory 

Scott Glancy 

Emanuel Knill 

Adam Meier 

Mike Mullan 

Yanbao Zhang 

B. Eastin (Northrop Grumman) 

R. Somma (Perimeter Inst. and Los Alamos Nat. Lab.) 

S. Boixo (California Institute of Technology) 

G. Ortiz (Indiana University) 

H. M. Vasconcelos (U. Federal do Ceará, Brazil) 

L. Sanz (U. Federal de Uberlândia, Brazil) 

Our work on quantum computing theory aims to make 

quantum computers more robust given realistic resources, improve the efficiency of algorithms that take 

advantage of quantum physics, and obtain rigorous 

tests of the basic principles of quantum mechanics. 

In previous years, we contributed several very efficient techniques for realizing quantum computations 

insensitive to unavoidable noise in the underlying 

quantum devices. One of these involved general strategies for obtaining high-quality encoded states by 

purification. We are now revisiting an instance of these 

purification strategies and applying it to the problem of 

preparing so-called magic states, which are states enabling universal quantum computing for information 

encoded in quantum error-correcting codes. 

One proposal for optical quantum computation requires encoding the information of a two dimensional 

quantum bit into the continuous state space of an optical field. The proposal is attractive, because the 

encoded qubits can be manipulated fault-tolerantly and 

logic operations can be performed with only linear devices, squeezing, homodyne detection, and special 

input states. Unfortunately, we lack a practical method 

to prepare the encoded qubit states. In 2010 we developed a method to prepare these states by a scheme that 

uses optical Schrodinger cat states (such as those described in the “Quantum State Estimation Theory and 

Applications” project), homodyne measurements, and 

feed-forward. A description of this scheme was published in Optics Letters. 

Some of the potentially most important applications of quantum computers are to search, optimization 

and physics simulation problems. Many quantum 

strategies for solving these problems are based on preparing special states. For example, many physics and 

optimization problems can be solved by making measurements of ground states for different physical 

systems. A powerful strategy for preparing the desired 

states is to start with a simple-to-prepare eigenstate of 

an operator and then “walk” it toward the desired state 

by following eigenstates of a path of operators. We 

have developed efficient strategies for walking along 

such paths [4]. One strategy can be applied even if 

little control is available, such as in proposed “analog” 
Summary of Activities for Fiscal Year 2010 79

quantum simulators. A more efficient strategy was designed for the case where universal quantum 

computing is possible. Both strategies are better and 

more reliable than conventional adiabatic strategies. 

Quantum strategies can also be used to improve 

measurement accuracy beyond the so-called classical 

limit. In particular, it may be possible to improve the 

accuracy of the quantum logic clocks under development in the ion storage group by taking advantage of 

quantum correlations among two or more ions. We are 

investigating the application of semidefinite programming techniques originally developed for optimizing 

quantum query algorithms. These techniques can determine the optimal strategy for measuring the 

frequency of a clock transition in ion qubits. Unlike 

previous work, we are taking into consideration the fact 

that the frequency is already known within a narrow 

range, and that phase noise in the classical oscillator 

driving the clock contributes to frequency noise. The 

goal is to determine how much improvement is possible with the use of two correlated versus two 

independent ions in the quantum logic clocks. 

A goal of the quantum optics community is to realize a "loop-hole free" test for the absence of a locallyrealistic explanation of quantum mechanical measurements. The biggest hurdle at present is the absence of 

sufficiently low-loss optical elements. Additional problems are that experiments so far rarely account for 

drifts and dependencies. Furthermore, the results of a 

test are usually reported in the form of “number of 

standard deviations of violation” of a Bell inequality. 

We have found that this leads to over-optimistic estimates of the confidence of rejecting local realism. We 

have developed a prediction based ratio test that works 

even in the presence of experimental drifts and dependencies while being asymptotically optimal for 

ideal experiments. The test reports a provable significance level for rejecting local realism and can be used 

for on-line monitoring of experimental progress. We 

are planning on releasing code implementing the test. 

[1] E. Knill, News and Views Q&A: Quantum Computing, 

Nature 463 (Jan. 2010), pp. 441-443. 

[2] H. M. Vasconcelos, L. Sanz, and S. Glancy, All-optical 

Generation of States for Encoding a Qubit in an Oscillator, Optics Letters 35 2010, pp. 3261-3263. 

[3] Y. Zhang, E. Knill, and S. Glancy, Statistical Strength of 

Experiments to Reject Local Realism with Photon Pairs 

and Inefficient Detectors, Physical Review A 81 (March 

2010), 032117. 

[4] S. Boixo, E. Knill, and R. Somma, Fast Quantum Algorithms for Traversing Paths of Eigenstates, submitted. 

ITL Program: Quantum Information

Quantum Computing Benchmarks 

Emanuel Knill 

Adam Meier 

Dietrich Leibfried (NIST PML) 

David Wineland (NIST PML) 

Today, researchers claim to be able to quantum computing with two or more qubits with ions, atoms, 

superconducting circuits, impurities in diamond, nuclear spins and photons. But how can we compare 

experimental results from such a diverse collection of 

physical systems? Which ones have demonstrated the 

most accurate computations? Can we quantify the 

“amount” of computation performed? The quantum 

computing benchmark project aims to answer these 

questions and to establish standardized sets of experiments to quantify the answers in a device independent 

way. We collaborate with experimental groups to implement the proposed experiments. 

Our most successful benchmark so far is a randomized benchmarking strategy for determining the 

effective error probability per gate (EPG) for physical 

qubits. Previously, we have standardized the strategy 

for one qubit and implemented it with ion qubits, demonstrating a good EPG of about 0.005. The benchmark 

has now been implemented by others with nuclear spin, 

superconducting and atomic qubits. We are in the 

process of demonstrating better EPGs with other ion 

qubits being developed in the ion storage group. We 

are collaborating with the quantum dot group at Stanford to implement the benchmark with their very fast 

one-qubit gates. Although the basic benchmarking 

strategy is the same, we have greatly improved the 

toolkit used for generating and analyzing the benchmark. It is easily adaptable to a wide variety of qubits. 

Although the randomized benchmark is a very effective way to determine EPGs, as originally 

conceived, it was not a good diagnostic tool. We are 

improving the analysis of data from such benchmarks 

to back out more information about the individual gate 

errors. Eventually such information might be useful 

for optimizing strategies for error correction. 

Another important ongoing research track is to establish straightforward and equally device independent 

benchmarking strategies for multiple qubits. The difficulty is that for more than one qubit the number of 

possible ways in which gates can be randomized increases greatly, making standardization and 

comparison less obvious. We are pursuing several 

strategies for comparing experiments using different 

randomization strategies based on a small number of 

quantitative measures. 

ITL Program: Quantum Information
80 NIST Applied and Computational Mathematics Division 

Quantum State Estimation Theory 

and Applications 

Scott Glancy 

Emanuel Knill 

Mark Girard 

Bryce Calkins (NIST PML) 

Thomas Gerrits (NIST PML) 

Gene Hilton (NIST PML) 

Kent Irwin (NIST PML) 

Konrad Lehnert (NIST PML) 

Adriana Lita (NIST PML) 

Alan Migdall (NIST PML) 

Richard Mirin (NIST PML) 

Sae Woo Nam (NIST PML) 

Leila Vale (NIST PML) 

Manuel A. Castellanos-Beltran (Yale University) 

Tracy Clement (University of Colorado) 

Hsiang S. Ku (University of Colorado) 

Francois Mallet (University of Colorado) 

Aaron Miller (Albion College) 

Many emerging technologies will exploit quantum mechanical effects to enhance metrology, computation, 

and communication. Developing these technologies 

requires improved methods to measure the state of 

quantum systems. Quantum state estimation is a statistical problem of estimating an underlying quantum 

state using a collection of measurements made on independently prepared copies of the state. Accurate 

quantum state estimation allows experimentalists to 

answer the questions “What quantum state does my 

device prepare?” and “How confident am I that it has 

prepared that state?” In the last year we have made a 

few small improvements to the algorithms used to answer these questions. We implemented a new strategy 

for choosing the step size of the iterative algorithm 

used to infer the quantum state. We also explored a 

new method to associate confidence intervals to the 

results of quantum state estimation based on the ability 

of the estimate to predict the results of an independent 

set of measurements. 

We have been applying quantum state estimation 

in two experiments. The first of these is an experiment 

to prepare Schrödinger cat states of light, which is part 

of the NIST Innovations in Measurement Science project “Quantum Optical Metrology with N-Photons”. 

This experiment uses high efficiency transition edge 

sensors to subtract three photons from a pulse of 

squeezed vacuum light. The photon subtraction prepares the Schrodinger cat state, which is measured by 

homodyne detection. Our quantum state estimation 

software is used to reconstruct the state from the measurements. Our state estimation algorithm corrects for 

the photon loss and electronic noise of the homodyne 

detector to infer the originally created state. The state 

created in the laboratory has a fidelity of 4 59 14

+

− % with 

an ideal Schrodinger cat state and had a mean of 06.0

24.0 75.2 +− photons. This work was published in Physical Review A and received some attention in the 

popular press. 

The second experiment where we have been applying quantum state estimation is the DARPA funded 

collaboration with JILA titled “Analog Quantum Integrated Circuits”. The goal of this project is to create 

entangled states in superconducting microwave circuits 

and to use that entanglement for quantum teleportation. 

In 2010 we successfully prepared a squeezed state of 

quantum microwaves and verified the squeezing with 

full quantum state tomography, which has never been 

done before in a microwave system. Our analysis 

shows that the squeezed state's noise is reduced to 

%48 45

19

+

− of the noise present in the vacuum. In the next 

phase of this project we will use two squeezed states to 

create entanglement between two microwave modes. 

[1] T. Gerrits, S. Glancy, T. Clement, B. Calkins, A. Lita, 

A. Miller, A. Migdall, S.W. Nam, and R. Mirin, Generation of Optical Coherent-state Superpositions by 

Number-resolved Photon Subtraction from the Squeezed 

Vacuum, Physical Review A 82 (2010), 031802(R). 

[2] Research Highlights: Quantum Information Coherentstate Superposition, Nature Photonics 4 (2010), pp. 

804–805. 

[3] F. Mallet, M. A. Castellanos-Beltran, H. S. Ku, S. 

Glancy, E. Knill, K. D. Irwin, G. C. Hilton, L. R. Vale, 

and K. W. Lehnert, Quantum State Tomography of an 

Itinerant Squeezed Microwave Field, 

arXiv:1012.0007v1 [quant-ph], in review. 

ITL Program: Quantum Information

Quantum Communication 

Alan Mink 

Barry Hershman 

Joshua Bienfang (NIST PML) 

We negotiated an agreement for NIST to partner with 

Telcordia that allows NIST to participate in the development of QKD standards that are currently being 

managed through the European Telecommunications 

Standards Institute (ETSI). Normally NIST is not able 

to participate in groups such as ETSI, because they are 

governed under European law. But by partnering with 

an existing ETSI member, Telcordia (a U.S. based 

company), NIST is able to participate without obligation to European law. Although ETSI normally focuses 

on European standards, the expertise in this area is too 

small to support multiple standards groups. So the 

ETSI QKD group is now a worldwide effort with rep-
Summary of Activities for Fiscal Year 2010 81

resentatives from North America and Asia as well and 

interest from Africa (South Africa). 

NIST has attended the three ETSI/QKD meetings 

in Europe during 2010 and reviewed all draft documents. NIST was instrumental in drafting the QKD 

“Application Interface” document, which specifies the 

interface between security applications and a QKD 

system and is based on the NIST QKD approach. This 

document has been recently approved as an ETSI standard. This standard neatly dovetails with a pending 

IETF RFC for the IPsec security protocol using QKD 

keys. NIST has become a principal contributor to this 

ETSI QKD group. 

For the high-speed data handling part of our quantum communications project, we have developed and 

tested an entangled photon pair measurement system 

and an associated signal interface to our entangled photon generation system. This repurposing of our highspeed instrumentation will allow continuous measurement of our correlated and entangled photon generation 

experiments. We have also redesigned our newer highspeed instrumentation for 2.5 GHz operations on our 

current hardware, twice the previous speed. That design is now running in our lab. This design 

incorporates the complete QKD protocol in hardware, 

entirely freeing CPU cycles for supporting applications 

rather than running the error correction and privacy 

amplification portions of the QKD protocol – a set of 

very CPU cycle demanding algorithms. We will be 

using this higher speed hardware in a pending experiment with the NIST Physical Measurement Lab for a 

free-space QKD system. We continue to investigate 

some alternative photon measurement techniques, that 

will achieve 100 ps time-bin resolution and possibly as 

low as 25 ps. 

[1] Mink, L. Ma, B. Hershman and X. Tang, An Application of Quantum Networks for Secure Video 

Surveillance, in Video Surveillance I-TECH Education 

and Publishing, Vienna, Austria, to appear. 

ITL Program: Quantum Information
82 NIST Applied and Computational Mathematics Division 

Foundations of Measurement Science for Information Systems

Modern information systems are astounding in their complexity. Software applications are built from thousands of interacting components. Computer networks interconnect millions of independently operating nodes. 

Large-scale networked applications provide the basis for services of national scope, such as financial transactions and electrical power distribution. In spite of our increasing reliance on such systems, our ability to 

build far outpaces our ability to secure. Protocols controlling the behavior of individual nodes lead to unexpected macroscopic behavior. Local power anomalies propagate in unexpected ways leading to large-scale 

outages. Computer system vulnerabilities are exploited in viral attacks resulting in widespread loss of data 

and system availability. The long term stability of our critical infrastructure is simply unknown. Measurement science has long provided a basis for the understanding and control of physical systems. Similar types 

of deep understanding and insight are lacking for complex information systems. We seek to develop the 

mathematical foundations needed for the emergence of a true measurement science for complex networked 

information systems. 

Monte Carlo Methods for 

Computing Network Reliability 

Isabel Beichl 

Brian Cloteaux 

Francis Sullivan (IDA Center for Computing Sciences) 

See feature article, page 40. 

ITL Program: Complex Systems

Modeling Affiliations in Networks 

Brian D. Cloteaux 

Many networks can be naturally represented as relationships between entities and the groups (or 

affiliations) to which the entities belong. An affiliation 

network is a bipartite graph which links the set of entities in a network to the set of groups. An example of a 

network and its associated affiliation network is shown 

in Figure 55. 

We are currently researching new methods to extract and analyze affiliations in arbitrary networks. 

One purpose of this research is to be able to better classify network structure and to understand how a 

network’s affiliations affects its characteristics, such as 

reliability and security. Understanding affiliations also 

has applications to national security. 

Currently, we have developed new methods to 

mine the affiliations associated with a network, and, in 

particular, when there are missing links in the network. 

Links can be missing because of measurement error or 

purposeful obfuscation; but in either case, incomplete 

information can dramatically alter the structure of the 

affiliations. In a recent result, we have implemented a 

new method for finding affiliations associated with a 

network even when there are some missing links. In 

our method, we collect the possible affiliations using a 

relaxed definition for the network. Then we process 

those collected affiliations to minimize the size of the 

set while still being consistent with the information in 

the original network. We have tested our method on a 

number of synthetic networks, and are now extending 

our research to analyze real networks. 

ITL Program: Complex Systems

Community and Cluster Detection in 

Network Graphs 

Roldan Pozo 

Clement Rey 

Detecting meaningful community structure in large 

graphs is one of the fundamental challenges in network 

science. This line of research can be critical in revealing the underlying structure of complex graphs. A 

Figure 55. A example network (top) and an associated affiliation 

network (bottom). 
Summary of Activities for Fiscal Year 2010 83

community is loosely defined as a subset of nodes 

which are highly connected to each other, but less connected to nodes in the remaining graph. Identifying 

such node groups is important in understanding graph 

evolution, synchronization, and the dynamics of networks. In various application contexts community 

detection can classify customers with similar purchasing habits, model the spreading of infectious diseases, 

help identify crime cells, and determine graph layouts 

for visualization. 

Extracting such structure reliably from large-scale 

networks, however, is a difficult problem. First, one 

must devise a metric for what constitutes a graph 

community; secondly, an algorithm for finding such 

communities must be prescribed (some such problems 

are NP-complete); lastly, there must be some method 

of verifying that the computed groups are indeed meaningful. Various metrics have been proposed and several 

corresponding algorithms have been introduced in the 

literature. 

 The underlying question remains: how well do these 

approaches work in practice? So far, there has been 

little work in verifying and validating the results on a 

wide array of application domains. We aim to do this. 

As part of this study, we are currently investigating 

eigenvalue-based methods and fast greedy algorithm 

approaches which run in O(n log2 n) for sparse graphs, 

and studying their behavior on specific data sets for 

which we have detailed community information available. The results show that current state-of-the-art 

algorithms work well in some situations, such as when 

vertices clearly belong to one (and only one) community. But the real world is not so ideal. More 

complicated approaches allow for overlapping communities, but fundamental problems remain. For example, 

one issue with modularity-based approaches is the difficulty of correctly identifying small clusters. (This is 

referred to as the “resolution limit” in the literature, 

and is an artifact of using a random graph with similar 

degree distribution as the null model.) 

As an alternative approach, we have been investigating a different notion of “community” which does 

not fit previous methodologies but nonetheless provides interesting insights. Rather than being based on 

conventional graph cuts, this approach builds “cells” or 

“clusters” from the ground up by isolating low-degree 

nodes into a separate subgraph and analyzing the connectedness of the resulting network. That is, given a 

degree threshold, we create a subgraph consisting of 

only nodes with that degree value or less. This subgraph is largely fragmented into disconnected 

components, which can be useful in finding small, isolated fringe groups amidst the noise of large-degree 

hubs. 

Figure 57, for example, shows the fragments of a 

web network (math.nist.gov) obtained by restricting it 

to a subgraph of nodes with degree 30 or less. It reveals 

various components: e.g. DNA-like ladders, as well as 

star and cluster patterns representing tightly coupled 

web pages. These form the nucleus of graph communities, and by varying the degree parameter we can direct 

the size and granularity of communities revealed. This 

information can be used to augment a conventional 

algorithm to better identify small communities. 

We are expanding this line of investigation by asking the question of what happens as one varies the 

degree parameter in this experiment. At a low degree 

threshold (near 1) we get a small fragmented graph of 

either isolated nodes, or individual pairs of nodes. 

(These usually represent terminal nodes.) As we increase this value, we include more nodes in the 

subgraph, increasing the number of communities, but 

some of these communities increase in size and merge 

with others, thus effecting a contraction. As the threshold is increased to the maximum degree, we are left 

with a single community: the whole graph. Thus, as 

Figure 57. Isolation profiles of the math.nist.gov webgraph. 

Figure 56. Isolated communities of nodes with degree 30 or less 

of the webgraph of http:// math.nist.gov/. 
84 NIST Applied and Computational Mathematics Division 

one turns the degree-threshold parameter, the number 

of components (communities) starts out small, grows, 

and finally shrinks down to one. A graph of this phenomenon is shown in Figure 56, which we refer to as a 

graph isolation profile. This profile provides a characteristic fingerprint of the graph structure that is 

different from conventional community metrics. We 

are currently investigating these ideas to develop hybrid metrics which better describe the nature of 

community structure in graphs. 

ITL Program: Complex Systems

Network Modeling Toolkit 

Brian Cloteaux 

Over the past two years, in our research into the measurement and characterization of networks, we have 

produced a number of new algorithms. In an effort to 

release this research to the public in a usable form, we 

are integrating the various versions of our algorithms 

into a software package for network modeling. We 

have entitled this the Network Modeling Toolkit. 

In the current version, we have implemented several network generating algorithms that create models 

with constraints such as s-metric or clustering coefficient value. In addition, we are able to build network 

models which contain a pre-defined subgraph. We also 

have code to measure certain characteristics of a given 

network such as number of spanning trees and s-metric 

and we are able to manipulate degree sequences such 

as finding the closest graphical sequence to a given 

non-graphical sequence. We continue to work in adding support for analysis of affiliation networks and to 

prepare the code base for a release. Accompanying this 

release will be a paper describing the system and a 

website for maintaining the code base. 

ITL Program: Complex Systems

Network Security Risk Analysis 

Using Attack Graphs 11

Anoop Singhal (NIST ITL) 

Lingyu Wang (Concordia University) 

Sushil Jajodia (George Mason University) 

Steven Noel (George Mason University) 

Duminda Wijesekera (George Mason University) 

At present, computer networks constitute the core 

component of information technology infrastructures in 

areas such as power grids, financial data systems and 

emergency communication systems. Protection of these 

networks from malicious intrusions is critical to the 

economy and security of our nation. To improve the 

security of these networked systems, it is necessary to 

measure the amount of security provided by different 

network configurations. The objective of our research 

is to develop a standard model for measuring the security of computer networks. A standard model will 

enable us to answer questions such as “are we more 

secure today than yesterday” or “how does the security 

of one network configuration compare with another 

one.” Also, having a standard model to measure network security will bring together users, vendors and 

researchers to evaluate methodologies and products for 

network security. 

Good metrics should be measured consistently, be 

inexpensive to collect, be expressed numerically, have 

units of measure, and have specific context. We meet 

this challenge by capturing vulnerability interdependencies among nodes in a network and measuring 

security in the same way as real attackers do in penetrating the network. Our methodology for security risk 

analysis is based on the model of attack graphs [3]. We 

analyze all attack paths through a network, providing a 

probabilistic metric of the overall system risk. Through 

this metric, we analyze tradeoffs between security costs 

and security benefits. Our metric is consistent, unambiguous, and provides context for understanding the 

security risk of computer networks. 

In FY 2010, we developed a new model of security 

analysis for “zero day” attacks. We proposed a novel 

security metric called k zero day safety, based on the 

number of unknown zero day vulnerabilities [2]. The 

metric counts how many (unknown) vulnerabilities 

would be required to compromise a particular network 

asset. We also did performance analyses to understand 

how our method will scale up for enterprise networks 

consisting of multiple hosts. 

In FY 2010, we also developed an ontology for enterprise level security in terms of the entities and 

relationships among them [1]. This data model can be 

used to measure the appropriate things needed to un-

 

11 This research performed in the ITL Computer Security Division 

was supported by ACMD funding. 

Figure 58. A display from the Network Modeling Toolkit.
Summary of Activities for Fiscal Year 2010 85

derstand the effectiveness of current security mechanisms and the benefits that they provide. 

Numerous papers were published in conferences 

and workshops based on this work. In FY 2011, we 

plan to integrate the proposed techniques into existing 

attack graph based security tools and validate our results. We also plan to make progress on 

implementation of ontologies for enterprise level security using the Web Ontology Language (OWL). 

[1] A. Singhal and D. Wijesekera, Ontologies for Modeling 

Enterprise Level Security Metrics, in Proceedings of the 

Sixth Annual Cyber Security and Information Intelligence Research Workshop (CSIRW’10), Oak Ridge 

National Laboratory, April 21-23, 2010. 

[2] L. Wang, A. Singhal, S. Jajodia, S. Noel, k-Zero Day 

Safety: Measuring the Security of Networks against Unknown Attacks, in Computer Security – ESORICS 2010, 

(D. Gritzalis, B. Preneel, and M. Theoharidou, eds.), 

Lecture Notes in Computer Science 6345 (2010), 

Springer, pp. 573-587. 

[3] S. Noel, L. Wang, A. Singhal, S. Jajodia, Measuring 

Security Risk of Networks Using Attack Graphs, International Journal of Next Generation Computing 1

(2010). 

Vulnerability of Selfish Routing to 

Attacks 

Vladimir Marbukh 

Daniel Genin (NIST ITL) 

Anastase Nakassis NIST ITL) 

An emergent trend in networking is an attempt to resolve inefficiencies of network-defined routing by 

shifting responsibility for routing from the network to 

end users. Examples include so-called source routing 

or overlay routing. Despite the emerging understanding 

that user-defined routing is much better in addressing 

specific user concerns, the downside may be the inherent selfish nature of user-centric routing, in which each 

user attempts to optimize its own performance objective without concern for overall network performance. 

This selfishness may, in fact, lead to loss in overall 

network performance. 

While the performance limits of network-defined 

routing can be assessed by using optimization techniques, the performance of selfish routing is typically 

identified with a Nash equilibrium in a corresponding 

non-cooperative game-theoretic model. Due to the 

typical multiplicity of Nash equilibria, loss in overall 

network performance resulting from user selfishness is 

defined by the so-called price of anarchy: the worstcase ratio of the aggregate cost of selfish and socially 

optimal routing. This definition assumes that the network-defined socially optimal routing minimizes aggregate routing cost, and thus the price of anarchy 

always exceeds or equals one. 

This project attempts to gain understanding of the 

effect of an adversarial presence, i.e., attacker(s), on 

the performance of selfish routing. To this end we extend the conventional framework for performance 

evaluation of selfish routing by including a possibility 

of attacker(s) capable of manipulating the route costs in 

attempt to maximize the aggregate transportation cost 

for all or some users. For example, an attacker might 

damage the physical infrastructure in a transportation 

network, insert malicious traffic in a denial of service 

attack on a communication network, or jam links in a 

wireless network. We propose an extended gametheoretic model, where strategic attacker(s) are modeled as separate agent(s) with the corresponding 

utilities and limits on ability to manipulate route costs 

reflecting attacker power. 

Previous work on the effect of malicious agents on 

selfish routing by legitimate users assumed that neither 

attackers nor legitimate users have an “agility advantage”, i.e., they operate on the same time scale. The 

corresponding loss in performance, called “price of 

malice” was calculated based on the worst-case scenario Nash equilibrium of the corresponding game. 

The key difference between these previously studied 

models and our model [1] is that we assume “agile” 

adversaries capable of observing and exploiting strategies employed by the legitimate agents. To investigate 

the effect of this agility we consider a Stackelberg 

game with legitimate user(s) being the leader(s) and 

attacker(s) being the follower(s). 

Quite surprisingly, our initial results [1] indicate 

that an agile attacker of very limited power can inflict 

significant damage on overall network performance. 

The reason for this disproportional effect is that an 

adversarial presence creates incentive for selfish users 

to avoid being attacked by making other users more 

appealing targets for attacker(s). This incentive may 

create positive feedback eliminating the socially optimal equilibrium and driving selfish users to a very 

inefficient equilibrium. Also, the presence of attacker(s) can make Braess’s paradox12 more 

pronounced. 

These initial results demonstrate the importance of 

further research on the effect of adversarial actions on 

selfish routing, including the possibility of mitigating 

this effect while preserving the distributed nature of 

resource allocation. One of the issues currently under 

investigation is developing a tractable model of at-

 

12 Braess’s paradox states that adding additional capacity to a network can sometimes actually decrease performance if network 

routing is based on the selfish choices of users. 
86 NIST Applied and Computational Mathematics Division 

tacker(s) with controlled agility relative to legitimate 

users. This model would provide an opportunity to 

investigate the effect of the attacker(s) ability to acquire and exploit system information on system 

performance. Our initial results suggest that such a 

model should be interdisciplinary, combining elements 

of both game and information theories. 

[1] D. Genin, V. Marbukh, and A. Nakassis, Vulnerability 

of Selfish Routing to Attacks: A Game-theoretic Model 

and Initial Results, in Proceedings of 2010 International 

Conference of Information Security and Internet Engineering, World Congress on Engineering 2010 (WCE 

2010), June 30, 2010. 

Analysis of a Distributed Protocol 

for a Multiple User Access Network 

Fern Y. Hunt 

Vladimir Marbukh 

Congestion control is critical to the smooth functioning 

of modern communication networks in particular and 

the Internet in general. The goal of a congestion protocol is to allow many users to share network resources 

without overloading the system. In addition it is desirable to use as much of the available network capacity 

as possible while ensuring fairness in the allocation of 

bandwidth. It was first shown by Frank Kelly and later 

by many others that these objectives can be achieved 

by protocols that are based on solving a global optimization problem for maximizing system utility, where 

some notion of fairness is expressed by a choice of 

utility function. The implication is that the operation of 

a protocol can be characterized and studied mathematically by analyzing the dynamics of a distributed 

algorithm for solving the optimization problem. As the 

need for system robustness has grown amidst cybersecurity concerns, this paradigm has been extended to the 

problem of designing and characterizing protocols that 

control routing as well as congestion. 

Recently Hunt and Marbukh analyzed a protocol 

for allocating traffic that assigns routes randomly to 

users with prescribed path diversity. The entropy of the 

distribution of routes defined by an allocation is introduced in the corresponding utility maximization 

problem as a constraint so that users cannot use a single cheapest route as in the OSPF (open shortest path 

first) allocation. Introducing this feature reduces the 

risk of instability that arises in the uncontrolled use of 

this protocol. In previous work on example networks 

with a single source and destination [2, 3], we showed 

that maximum utility could be achieved with an allocation of traffic that minimizes the mean route cost. In 

that work we analyzed the dynamics of the prices of 

constituent links that make up the routes. 

This year we extended our work to a network topology with multiple and possibly large numbers of 

sources with a single destination. Such a topology 

could model multiple users (each associated with a 

source) accessing a single trunk line. Each source has 

two possible routes, a direct link to the destination and 

a second route that employs links connecting to its 

nearest neighbor. To aid the tractability of the problem, 

route allocations for each source are assumed to be 

fixed in time but, as in our previous work, we associate 

a distribution entropy with this allocation. 

Some justification for fixing the allocations can be 

made based on our work on a two link topology. For an 

arbitrary number of users we find sufficient conditions 

for the existence and uniqueness of an optimal solution 

and global convergence of the algorithm. The optimal 

utility of a source depends in general on the choice of 

entropies of all the sources and the capacities of the 

links joining them. Of interest is the behavior of the 

optimal utility as a function of the source entropies. For 

example when all the source entropies are the same 

some rather surprising results are observed numerically. Depending on the value of the entropy, the 

source utilities are heterogeneous or homogeneous. In 

the heterogeneous case, the utilities break up into clusters depending on their position in a circular network. 

At a critical value of the entropy, the utilities collapse 

into a single utility curve, as if the network collapsed 

into a single source and destination. This phenomenon 

seems to be independent of the number of sources [1]. 

Gaining better understanding of this transition is our 

current focus 

Future work will center on developing ways of 

measuring the overall performance of a network under 

various route allocation regimes by calculating the total 

optimal system utility as a function of the allocation 

entropy. 

[1] F.Y. Hunt and V. Marbukh, A Mathematical Model of 

Congestion Control with Multiple Sources, Dynamics 

Days Conference 2010, Bristol, UK, September 2010. 

[2] F.Y. Hunt and V. Marbukh, A Model of Joint Congestion Control and Routing Through Random Assignment 

of Paths, NISTIR 7590, February 2010. 

[3] F.Y. Hunt and V. Marbukh, Measuring the Utility/Path 

Diversity Trade-Off in Multipath Protocols, in Proceedings of the 4th International Conference on Performance 

Evaluation Methodologies and Tools, Pisa, Italy, 2009. 

ITL Program: Complex Systems
Summary of Activities for Fiscal Year 2010 87

Modeling Failure Scenarios in Large 

Scale Computing Systems 

Fern Y. Hunt 

Christopher Dabrowski (NIST ITL) 

Katherine Morrison (University of Nebraska–Lincoln) 

In recent years, the advent of large-scale distributed 

systems such as computing grids and cloud systems has 

made mass computing services available to large populations of users. These systems are dynamic, 

heterogeneous and, due to the interactions of many 

components, subject to the emergence of unpredictable 

system-wide behaviors that can have deleterious consequences. Their rapid growth and increasing economic 

importance underline the need for tools and methodologies that enable understanding and prediction of 

complex system behavior in order to insure the availability and reliability of these services. Key questions 

are the effect of changes in workload, system design, 

and other operational parameters on overall system 

performance. For example, studies of alternative economic strategies and system failure scenarios have 

shown that small variations in system parameters can 

lead to large differences in performance (see references 

in [1]). 

By large scale simulation we mean discrete event 

simulations that follow in detail the various stages encountered by an individual task being processed by a 

system over time. While large-scale simulations used 

in such studies are more practical than operational testbeds, computational expense rises dramatically with 

model size, a critical roadblock to investigation of dynamical behavior in large scale systems. 

To address this situation, we introduced in earlier 

work [3] a succinct Markov chain representation of the 

dynamics of a large scale grid system over time. The 

chain simulates the progress of a large number of computing tasks from the time they are submitted by users 

to the time they either complete or fail. The evolution 

of the Markov chain itself occurs in discrete time 

through a set of transition probability matrices (TPMs). 

Each TPM simulates the grid system over a distinct 

time period, and thus the Markov chain is piece-wise 

homogeneous. Changes in system parameters can be 

modeled by perturbing the TPMs of the Markov chain. 

The corresponding sample paths are altered and represent altered system execution paths that arise as a result 

of perturbed parameters [3]. 

Through systematic perturbation of the TPM matrices followed by simulation of the resulting perturbed 

Markov chain we were able to identify scenarios that 

led to degradations of system performance and systemwide failure. Our results compared very favorably with 

large scale simulation results while being obtained with 

a substantial reduction in computational cost (hours vs. 

weeks of simulation) [3]. Nevertheless, as the number 

of states of the Markov chain grows, the computational 

cost of this method significantly increases. Thus it is 

very difficult to quickly identify the set of perturbed 

TPMs that lead to system deterioration or failure when 

the number of states is large. Prediction and control of 

these systems will depend on the ability discover such 

scenarios quickly. This is the motivation of the work 

that is described in the report [1]. 

This paper summarizes our work on graph theory 

and Markov chain methods for discovering perturbations in operational parameters that lead to decreases in 

system performance and system failure. They are based 

on efficiently identifying cut sets in the graph of the 

Markov Chain on the one hand, and use of the spectral 

representation theorem and properties of the absorbing 

Markov Chain on the other. See [1] for more detailed 

discussion and derivation of our method. 

Our contribution based on the spectral properties 

of the Markov Chain is in two parts. The first is a 

method for quickly generating the time course of a key 

variable of the system, the proportion of tasks completed for arbitrary system parameters. The second is a 

method for measuring the effect of perturbations on the 

spectral properties of the matrices associated with the 

Markov chain. Elevated levels of the quantities computed in the second method correlate well with 

deterioration in the number of tasks completed. We 

were able to identify all of the failure scenarios found 

by large scale simulations; however the correlation is 

not perfect. In a few cases, elevated values occurred 

without any sign of a decrease in system performance. 

Nevertheless, we believe that this methodology offers a promising first step toward the development of 

scalable and efficient methods. The use of Markov 

Chains to approximate the dynamics of systems is well 

known. However most applications involve the use of 

time homogeneous systems that reach steady state. 

Grid and cloud computing systems are both time inhomogeneous and absorbing. Thus much of the literature 

on perturbations of Markov chains does not apply. 

Papers describing the work on the spectral approach are [2] and the graph theory approach [4]. 

[1] C. Dabrowski, F. Hunt, and K. Morrison, Improving 

Efficiency of Markov Chain Analysis of Complex Distributed Systems, NISTIR 7744, November 2010. 

[2] F. Hunt, C. Dabrowski, K. Morrison, Identifying Failure 

Scenarios in Large Scale Systems Using Absorbing 

Markov Chains, in preparation. 

[3] C. Dabrowski and F. Hunt, Markov Chain Analysis for 

Large-Scale Grid Systems, NISTIR 7566, April 2009. 

[4] C. Dabrowski and F. Hunt, Using Markov Chain and 

Graph Theory Concepts to Analyze Behavior in Complex Distributed Systems, ASME 2011 Pressure Vessels 

and Piping Conf., Symposium on Risk Informed Online 

Monitoring of Aging Complex Systems, Oct. 2010. 

ITL Program: Complex Systems
88 NIST Applied and Computational Mathematics Division 

Visualization and Analysis of the 

National Vulnerability Database 

Judith Terrill 

Kevin Rawlings 

John G. Hagedorn 

Styvens Belloge 

Terrance Griffin 

David Waltermire (NIST ITL) 

Harold Booth (NIST ITL) 

Murugiah Souppaya (NIST ITL) 

Charles Wergin (NIST ITL) 

Christopher McCormick (NIST ITL) 

http://www.nist.gov/itl/math/hpcvg/nvdvis.cfm

The National Vulnerability Database13 (NVD) is a continuously updated U.S. government repository of 

computer security vulnerability management data represented using the Security Content Automation 

Protocol14 (SCAP). This year we have developed a 

tool, NVDvis that allows interactive analysis of the 

National Vulnerability Database. 

Using our tool, the user can choose the NVD’s 

Common Vulnerabilities and Exposures (CVE) 2.0 or 

CVE 1.2 databases. The tool does an initial analysis 

that is displayed in the Data Analysis pane of the tool; 

see Figure 59. It displays which CVE database was 

selected and how many entries there were. It provides 

the average vulnerability score as well as the distribution of the scores. It shows the number of elements, as 

well as the percentage for each value of the six attributes that make up the score, the part, Common 

Weakness Enumeration ID (CWE-ID), and distribution 

of date-time. The data is visualized with a Parallel Coordinate plot; see Figure 60. The tool enables the user 

to do the following. 

1. Filter the data in a variety of ways. NVDvis can 

filter on the vulnerability score as well as the six 

attributes that contribute to the score: Access 

vector, access complexity, authentication, 

confidentiality impact, integrity impact, and 

availability impact. It also provides access to 

Part (application, hardware, operating system), 

CWE-ID, date-time, and vendor. After each 

filtering operation, the Data Analysis pane is 

updated as well as the visualization. 

2. Generate Parallel Coordinate plots. These are a 

way to visualize multidimensional data. Our 

visualization can be viewed both on the desktop 

as well as in our immersive environment. 

3. Output data in a variety of formats: 

 

13 http://nvd.nist.gov/ 14 http://scap.nist.gov/

• csv format (comma separated values). Easily 

read by the R Statistical Package. R provides 

access to many analysis techniques as well as 

other visualization packages. This format is 

also read by many other packages. 

• arff format. Read by the Weka open source 

data mining software. This format is also read 

by other machine learning software packages. 

• Binary format. Enables a user to pick up 

where he or she left off. 

• Descriptions to enable text mining. 

This year we performed an examination of the distribution of SQL Injection Vulnerability Scores 

Relative to the 7.5 Standardized Score. We studied the 

distribution of XSS Vulnerability Scores Relative to 

the 4.3 Standardized Score. 

We gave NVDvis demos and ran requested scenarios using the tool at the 6th Annual IT Security 

Automation Conference, September 27-29, 2010 in 

Baltimore. 

Figure 59. The NVDvis interface.

Figure 60. NVDvis parallel coordinate plot. 
Summary of Activities for Fiscal Year 2010 89

Visualization of Large Complex 

Networks 

Clement Rey 

Roldan Pozo 

Terence Griffin 

One of the fundamental challenges in complex systems 

is understanding the nature and structure of large-scale 

networks. These are often in the form of information 

networks (like the World Wide Web), biological networks (like protein-protein interactions, food webs), 

social networks (like online social sites, personal interactions, criminal rings, terrorist cells), and engineering 

networks. Such networks can be abstracted to graphs 

typically exhibiting thousands to millions of nodes and 

about 10 times as many edges. Given the rapid growth 

of electronic data, networks with billions of nodes will 

soon be readily available for analysis, providing opportunity for insight into large-scale system behavior. 

To the aid the understanding of such systems, we 

have developed visualization techniques that utilize the 

latest immersive and 3D environments, together with 

state-of-the-art graph layout algorithms, so that researchers can walk around and examine these 

structures interactively. 

This year, we developed a portable stand-alone 

version of this viewer, LightViewer, which can run on 

various platforms, requiring only an Open Scene Graph 

(OSG) library. This allows visualizations to be conducted on remote workstations, as well as local 3D 

immersive environments. One can rotate, zoom, pan, 

and fly through the graph interactively. By clicking on 

a node, one can see its annotations (for example, the 

page’s URL for web graphs). The OSG library is available for Linux, Windows, and Mac OS X platforms. 

For example, Figure 61 illustrates the visualization 

of a web graph were nodes are individual web pages of 

math.nist.gov. In this instance, we have highlighted 

the community structure by using a fatpoint shader 

Figure 61. Three-dimensional visualization of the community structure of a reduced Web graph corresponding to math.nist.gov. Each node 

is a separate Web page and the colors indicate different community groups. The graph is navigated in real time (pan, zoom, rotate) and the 

URL is displayed for a selected node, allowing researchers to study its structure interactively. 
90 NIST Applied and Computational Mathematics Division 

(with an interactive size control) to render the nodes of 

the graph. The largest groups (7 in this case) are colored individually. The set of small groups (179 in this 

case) is colored a transparent grey. An individual node 

can be selected using a cross-hair glyph and its URL 

displayed in a box tethered to the node with lines. In 

addition, the web page that the node represents can be 

displayed, so researchers can investigate its content. 

ITL Program: Complex Systems

Advanced Combinatorial Testing for 

Systems 

Raghu Kacker 

D. Richard Kuhn (NIST ITL) 

Vincent Hu (NIST ITL) 

Jeff Yu Lei (University of Texas at Arlington) 

James Lawrence (George Mason University) 

Renee Bryce (Utah State University) 

Sreedevi Sampath (Univ. of MD Baltimore County) 

Tao Xie (North Carolina State University) 

http://csrc.nist.gov/groups/SNS/acts/index.html

A combinatorial interaction fault is a software defect 

that may cause a complex system to fail when particular values of certain inputs combine with particular 

values of other inputs. Such faults remain dormant 

until the unfortunate combination of values is encountered in practice. Many critical system failures in 

recent times have been traced to interaction faults in 

the underlying software. Eradicating such faults is 

critical to ensure trustworthy software in business, industrial, medical, scientific, and transport systems. 

To test for interaction faults one must check all 

possible combinations of input parameters. This is impossibly difficult for any real-world system. There are 

just too many combinations to check. Combinatorial 

testing is an approach to detecting interaction faults 

based on the observation that most such faults involve 

only a relatively few parameters. Thus, one effective 

strategy is to devise a testing plan in which all interactions between small numbers of parameters are tested 

in a minimum number of trial runs. For example, a 

system with 10 parameters, each with two possible 

values, would require 1024 trial runs to test every possible combination of inputs. However, a judicious 

selection of just 13 input sets is sufficient to cover all 

possible 3-way combinations. Unfortunately, in general, automatically generating testing plans with a 

minimum number of runs is itself very computationally 

challenging. 

Most combinatorial testing has until recently been 

limited to pair-wise (2-way) testing in which all interactions involving two parameters are detected. 

Software testing tools have not been available for 

higher strength testing. The goal of this project is to 

advance combinatorial testing technology from pairwise to higher order (strength) testing and to demonstrate successful applications of high strength 

combinatorial testing. 

 In Octover 2010 we released version 2 of the ACTS 

(Advanced Combinatorial Testing System) tool to generate high strength test suites based on covering arrays. 

The major features of ACTS tool are: 

- t-way test set generation: given a set of parameters 

and values, ACTS can generate a test set that 

achieves t-way coverage for t = 1 to 6. (For t = 1, 

base choice coverage is implemented, which is 

more meaningful than naïve 1-way testing.) 

- Constraint support: ACTS allows the user to specify constraints among different parameters, and 

then generates a t-way test set that satisfies these 

constraints. 

- Mixed-strength support: ACTS allows the user to 

create groups of parameters with different 

strengths, and then generates a test set that satisfies 

the different coverage strengths. 

- Test set augmentation: given a test set that does 

not satisfy t-way coverage, ACTS can generate 

additional tests to make this test set complete. 

- Coverage check: ACTS can check the coverage of 

a test set, with or without constraints. It also allows the user to graph coverage increments against 

each test. 

- Expected output specification: ACTS allows expected output to be specified for each test. 

- Accessible user interfaces: ACTS provides both 

command-line and graphic user interfaces. Generating test suits which allow for complex 

constraints among parameter values in software 

testing is very challenging problem. 

The current version includes an innovative method of 

generating constrained test sets. We revised constraint 

parser to provide better error reporting about constraint 

specification. The current version computes coverage 

correctly when there are constraints. The GUI version 

of ACTS allows multiple systems to be opened at the 

same time. We have distributed (as of December 8, 

2010), 540 copies of ACTS tool to individuals. We put 

no restrictions of those individuals to re-distribute to 

others. The users include US government agencies, 

global corporations including Microsoft, Lockheed 

Martin, Cisco, SAP, AT&T, Intel, and SAIC. The 

number of users is believed to some multiple of 500. 

Based on the feedback received we continue to improve the ACTS tool. 

Since the project’s inception, we have published 

nine papers in refereed publications and four magazine 
Summary of Activities for Fiscal Year 2010 91

articles. This year we published a refereed article in the 

Proceedings of Modeling and Simulation World 2009 

[3]. We also wrote an article for LogiGear Magazine

[6]. This issue also includes an interview of Rick Kuhn 

by LogiGear, a company based in San Mateo, California dedicated to improving software test efficiency. 

Our NIST Special Publication 800-142, “Practical 

Combinatorial Testing,” [5] has been downloaded by 

about 5,000 people since its release in October 2010. 

In FY 2010 NIST and the Lockheed Martin Corporation signed a cooperative research and development 

agreement (CRADA) on combinatorial testing (CT). 

Under this CRADA, Lockheed Martin will apply CT to 

one or more application areas and NIST will provide 

R&D assistance. The results will be described in a 

white paper for public release. We are also collaborating with the Food and Drug Administration, and the 

Johns Hopkins Applied Physics Lab, the US Air Force, 

and the US Army. We are investigating applications in 

computer security [7], health care, GUI based applications, web-applications, and for optimization and 

testing of simulations of complex systems. 

[1] R. C. Bryce, Y. Lei, D. R. Kuhn, and R. Kacker, Combinatorial Testing, Chapter 14, in Handbook of Research 

on Software Engineering and Productivity Technologies: Implications of Globalization, M. Ramachandran 

and R. Atem de Carvalho, eds., IGI Global, 2010. 

[2] B. Johnasson, R. Kacker, R. Kessel, C. McLean, and R. 

Sriram, Utilizing Combinatorial Testing to Detect Interactions and Optimize a Discrete Event Simulation 

Model for Sustainable Manufacturing, in Proceedings of 

the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in 

Engineering Conference, IDETC/CIE 2009, San Diego, 

CA, Aug. 30 - Sept. 2, 2009, CD-ROM Paper I: 

DETC2009-86522. 

[3] D. R. Kuhn, R. N. Kacker and Y. Lei, Random vs. 

Combinatorial Methods for Discrete Event Simulation 

of a Grid Computer Network, in Proceedings of ModSim 

World 2009, Virginia Beach, VA, Oct. 14-17, 2009. 

[4] W. Wang, Y. Lei, S. Sampath, R. Kacker, D. R. Kuhn 

and J. Lawrence, A Combinatorial Approach to Building 

Navigation Graphs for Dynamic Web Applications, in 

Proceedings of 25th IEEE International Conference on 

Software Maintenance, ICSM, Edmonton, Alberta, Canada, Sept. 20-26, 2009, pp. 211-220. 

[5] D. R. Kuhn, R. Kacker and Y. Lei, Practical Combinatorial Testing, NIST Special Publication 800-142, October 

2010. 

[6] D. R. Kuhn, R. Kacker and Y. Lei, What is Combinatorial Testing and Why Should Testers Care, LogiGear 

Magazine, November 2010. 

[7] R. Kacker, Y. Lei, D. R. Kuhn, and W. Wang, A Combinatorial Approach to Detecting Buffer Overflow 

Vulnerabilities, in review. 

ITL Program: Trustworthy Information Systems

Towards Self-organizing Mobile 

Sensor Networks 

Vladimir Marbukh 

Kamran Sayrafian (NIST, ITL) 

Amir G. Aghdam (Concordia University) 

Hamid Mahboubi (Concordia University) 

Ahmadreza Momeni (Concordia University) 

Mobile sensor networks (MSNs) are envisioned to enable a novel set of applications in detecting, monitoring 

and tracking people, targets or events in pervasive 

computing environments. Locations of sensors in a 

MSN affect both their ability to acquire information on 

the intended targets and events, as well as their ability 

to communicate this information to the intended recipients. Information acquisition needs, which require 

proximity to targets, could potentially compete with 

communication needs, which require proximity to intended recipients of the sensor information. 

Communication ability can be improved if sensors are 

capable of forming and optimizing a multi-hop Mobile 

Ad-hoc NETwork (MANET) with some sensors relaying the other sensor information possibly in addition to 

transmitting their own information. 

In [1] we consider a network of collaborative 

sensors tracking a single target. The objective is to 

compute (in real time) the effective sensing and 

communication radii of sensors as well as their location 

at each time instant, such that a set of prescribed 

specifications are achieved. These specifications 

include end-to-end connectivity preservation from the 

target to a fixed destination, while durability of sensors 

is maximized and the overall energy consumption is 

minimized. The problem is formulated as a constrained 

optimization problem, and a procedure is presented to 

solve it. Simulation results demonstrate the 

effectiveness of the proposed techniques. However, 

the formulation in [1] is based on a number of 

simplifying assumptions, including flat terrain, energyfree sensor relocation, etc. 

Due to the difficulty of incorporating these and 

other inherent traits of MSNs, such as lack of centralized control, a variety of performance criteria, 

operational uncertainties, etc., into a conventional optimization framework, we suggest in [2] a unified 

pricing/evolutionary framework for MSN selforganization. Framework [2] involves sensor cooperation in data acquisition and communication, as well as 

sensor relocation in a general non-flat terrain, and accounts for the energy expenditure for sensor relocation. 

Decentralized MSN optimization is achieved through 

socially optimal pricing, which internalizes the effect 

of each sensor action on overall MSN performance. 

Results of a MSN tracking a single target are presented 
92 NIST Applied and Computational Mathematics Division 

in [2] that suggest the viability of the proposed framework for prolonging MSN life-span. 

The first step in developing a co-evolutionary 

framework for MSN self-organization is identifying 

“socially optimal” individual sensor fitness/utility landscapes in the inherently distributed environment of a 

MSN. Social optimality implies that each sensor 

maximization of its individual fitness results in overall 

performance optimization of the network. This is a 

challenging problem since MSN performance critically 

depends on sensors cooperation, while “selfish” sensors behavior typically results in drastic deterioration 

of overall performance. For example, selfish sensor 

positioning can quickly deplete some sensor battery 

power, resulting in the network’s inability to carry out 

its mission. 

Framework [2] builds on extending pricing-based 

network utility maximization (NUM) framework for 

MSN distributed optimization that includes sensor location. The appeal of this unified MSN NUM 

framework is that while system utility maximization 

over sensor information flow rates in a “fast” time 

scale yields the optimal cross-layer design of the MSN 

MANET, system utility maximization over sensor locations in a “slow” time scale controls sensors motion. 

Major issues discussed in [2] are information asymmetry, cost of sensor relocation, and simulated annealing 

for MSN optimization. 

[1] H. Mahboubi, A. Momeni, A. G. Aghdama, K. 

Sayrafian-Pour, and V. Marbukh, Minimum cost routing 

with controlled node mobility for target tracking in 

mobile sensor networks, in Proceedings of the 2010 

American Control Conference (ACC2010), USA, 2010. 

[2] V. Marbukh, K. Sayrafian-Pour, H. Mahboubi, A. 

Momeni, and Amir G. Aghdam, Towards evolutionarypricing framework for mobile sensor network selforganization, in Proceedings of the 2010 IEEE World 

Congress on Computational Intelligence, Barcelona, 

Spain, 2010 

ITL Program: Pervasive Information Technology 
Summary of Activities for Fiscal Year 2010 93

Part IV: Activity Data 

 Part IV 

 Activity Data 
94 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2010 95

Publications

Appeared 

Refereed Journals 

1. D. M. Anderson, G. B. McFadden, S. R. Coriell, 

and B. T. Murray, “The Solidification of an Ideal 

Ternary Alloy in a Mushy Layer,” Journal of 

Fluid Mechanics 647 (2010), pp. 309-333. 

2. I. Beichl, B. Cloteaux, and F. Sullivan, “An Approximation Algorithm for the Coefficients of the 

Reliability Polynomial,” Congressus Numerantium

197 (2010), pp. 143-151. 

3. J. D. Benson, C. C. Chicone, and J. K. Critser, 

“Optimal Control of Cryoprotective Agent Addition and Removal Protocols,” Cryobiology 59 (3) 

(December 2009), p. 382. 

4. W. J. Boettinger and G. B. McFadden, “Bending 

of a Bimetallic Beam Due to the Kirkendall Effect,” Journal of Phase Equilibria and Diffusion

31 (2010), pp. 6-14. 

5. G. W. Bryant, M. Zieliński, N. Malkova, J. S. 

Sims, W. Jaskólski, and J. Aizpurua, “Effect of 

Mechanical Strain on the Optical Properties of 

Quantum Dots: Controlling Exciton Shape, Orientation, and Phase with a Mechanical Strain,” 

Physical Review Letters 105 (6) (2010), article 

067404 (4 pages). 

6. J. W. Bullard, E. Enjolras, W. L. George, S. G. 

Satterfield, and J. E. Terrill, “A Parallel Reactiontransport Model Applied to Cement Hydration and 

Microstructure Development,” Modeling and 

Simulation in Materials Science and Engineering

18 (2) (March 2010), article 025007 (16 pages). 

7. T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. 

Whitenton, D. Basak, and R. H. McFadden, 

“Modeling of the Temperature Field in the Chip 

and in the Tool in High-speed Machining of a 

Carbon Steel: Effect of Pearlite to Austenite Phase 

Transition in AISI 1075,” International Journal of 

Material Forming 3 (Supplement 1) (June 17, 

2010), pp. 491-494. 

8. A. Carasso, “Bochner Subordination, Logarithmic 

Diffusion Equations, and Blind Deconvolution of 

Hubble Space Telescope Imagery and Other Scientific Data,” SIAM Journal on Imaging Sciences 3

(2010), pp. 954-980. 

9. B. Cloteaux and N. Serova, “Matching Observed 

Alpha Helix Lengths to Predicted Secondary 

Structure,” International Journal of Computational Bioscience 1 (2010), pp. 103-110. 

10. R. V. Datla, R. Kessel, A. W. Smith, R. N. Kacker, 

and D. B. Pollock, “Uncertainty Analysis of Remote Sensing Optical Sensor Data: Guiding 

Principles to Achieve Metrological Consistency,” 

International Journal of Remote Sensing 31 (4) 

(2010), pp. 867-880. 

11. M. J. Donahue, “Parallelizing a Micromagnetic 

Program for Use on Multi-processor Shared Memory Computers,” IEEE Transactions on Magnetics

45 (2009), pp. 3923-3925. 

12. P. R. Garabedian and G. B. McFadden, “The 

DEMO Quasisymmetric Stellarator,” Energies 3

(2010), pp. 277-284 

13. T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, 

A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, 

R. P. Mirin, E. Knill, “Generation of Optical Coherent-State Superpositions by Number-Resolved 

Photon Subtraction from the Squeezed Vacuum,” 

Physical Review A 82 (2010), article 031802 (4 

pages). 

14. A. I. Glazar, S. F. Mullen, J. Liu, J. D. Benson, J. 

K. Critser, E. L. Squires, and J. K. Graham, “Osmotic Tolerance Limits and Membrane 

Permeability Characteristics of Stallion Spermatozoa Treated with Cholesterol,” Cryobiology 59 (2) 

(October 2009), pp. 201-206. 

15. C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. 

O’Hara, A. E. Azad, and A. J. Taylor, “A Discussion on the Interpretation and Characterization of 

Metafilms/Metasurfaces: The Two-dimensional 

Equivalent of Metamaterials,” Metamaterials 3

(2009), pp. 100-112. 

16. R. D. Johnson III, K. K. Irikura, R. Kacker, and R. 

Kessel, “Scaling Factors and Uncertainties for abinitio Anharmonic Vibrational Frequencies,” 

Journal of Chemical Theory and Computation 6

(9) (2010), pp. 2822-2828 

17. R. N. Kacker and J. F. Lawrence, “Rectangular 

Distribution Whose End-points Are Not Exactly 

Known: Curvilinear Trapezoidal Distribution,” 

Metrologia 47 (3) (March 11, 2010), pp. 120-126. 

18. S. Kim, M. I. Aladjem, G. B. McFadden, and K. 

W. Kohn, “Predicted Functions of MdmX in Fine 

Tuning the Response of p53 to DNA Damage,”

PLoS Computational Biology 6 (2010), pp. 1-18. 

19. E. Knill, “News and Views Q&A: Quantum Computing,” Nature 463 (January 21, 2010), pp. 441-

443. 

20. K. M. Lebecki and M. J. Donahue, “Comment on 

‘Frustrated Magnetization in Co Nanowires: Competition between Crystal Anisotropy and 
96 NIST Applied and Computational Mathematics Division 

Demagnetization Energy,’” Physical Review B 82

(2010), article 096401 (4 pages). 

21. A. Lewandowski, D. F. Williams, P. D. Hale, J. C. 

M. Wang, and A. Dienstfrey, “Covariance-Based 

Vector-Network-Analyzer Uncertainty Analysis 

for Time-and Frequency-Domain Measurements,” 

IEEE Transactions on Microwave Theory and 

Techniques 58 (7) (2010), pp. 1877-1887. 

22. L. Ma, O. Slattery, and X. Tang, “Detection and 

Spectral Measurement of Single Photons in Communication Bands Using Up-conversion 

Technology,” Laser Physics 20 (5) (April 2, 2010), 

pp. 1244-1250. 

23. L. Ma, O. Slattery and X. Tang, “Single Photon 

Level Spectrum Measurement at Fiber Communication Band Using Frequency Up-conversion 

Technology,” Laser Physics 20 (7) (May 27, 

2010), pp. 1612-1617. 

24. N. S. Martys, D. Lootens, W. L. George, P. 

Hebraud, “Spatio-temporal Organization of Colloids in Start-up Flows,” Physical Review E 80 (3) 

(2009), article 031401 (7 pages). 

25. N. S. Martys, W. L. George, B.-W. Chun, and D. 

Lootens, “A Smoothed Particle Hydrodynamics 

Based Fluid Model with a Spatially Dependent 

Viscosity: Application to Flow of a Suspension 

with a Non-Newtonian Fluid Matrix,” Rheologica 

Acta 49 (10) (2010). 

26. G. B. McFadden, S. R. Coriell, and P. A. Lott, 

“Onset of Convection in Two Layers of a Binary 

Liquid,” Journal of Fluid Mechanics 647 (2010), 

pp. 105-124. 

27. H. Min, R. D. McMichael, M. J. Donahue, J. Miltat, M. D. Stiles, “Effects of Disorder and Internal 

Dynamics on Vortex Wall Propagation,” Physical 

Review Letters 104 (2010), article 217201 (4 

pages). 

28. W. F. Mitchell, “The hp-Multigrid Method Applied to hp-Adaptive Refinement of Triangular 

Grids,” Numerical Linear Algebra with Applications 17 (March 16, 2010), pp. 211-228. 

29. J. Obrzut, A. Anopchenko, J. F. Douglas, and B. 

W. Rust, “Relaxation and Antiplasticization 

Measurements in Trehalose Glycerol Mixtures – A 

Model for Protein Preservation,” Journal of NonCrystalline Solids 356 (2010), pp. 777-781. 

30. C. S. Pande and G. B. McFadden, “Self-similar 

Grain Size Distribution in Three Dimensions: A 

Stochastic Treatment,” Acta Materialia 58 (2010), 

pp. 1037-1044. 

31. F. Potra and E. Simiu, “Multi-hazard Design: A 

Structural Approach,” Journal of Optimization 

Theory and Applications 144 (2010), pp. 120-136. 

32. M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. 

Srinivasan, “Quantum Transduction of 

Telecommunications-band Single Photons from a 

Quantum Dot by Frequency Upconversion,” 

Nature Photonics 4 (2010), pp. 786-791.

33. K. Sayrafian-Pour, W.-B. Yang, J. Hagedorn, J. 

Terrill, K. Y. Yazdandoost, and K. Hamaguchi 

“Channel Models for Medical Implant Communication,” International Journal of Wireless 

Information Networks 17 (2010), pp. 105-112.

34. J. S. Sims and S. A. Hagstrom, “Hy-CI Study of 

the 22

S Ground State of Neutral Lithium and the 

First Five Excited 2

S States,” Physical Review A

80 (2009), article 052507 (8 pages). 

35. H. Stamerjohanns, M. Kohlhase, D. Ginev, C. 

David, B. Miller, Transforming Large Collections 

of Scientific Publications to XML, Mathematics in 

Computer Science 3 (2010), pp. 299-307.

36. H. Vasconcelos, L. Sanz, and S. Glancy, “Alloptical Generation of States for ‘Encoding a Qubit 

in an Oscillator’,” Optics Letters 35 (2010), pp. 

3261-3263. 

37. L. Yan, L. Ma, and X. Tang, “Bragg-grating enhanced Narrowband Spontaneous Parametric 

Down-conversion,” Optics Express 18 (6) (2010), 

p. 5957- 5963. 

38. Y. Zhang, E. Knill, and S. Glancy, “Statistical 

Strength of Experiments to Reject Local Realism 

with Photon Pairs and Inefficient Detectors,” 

Physical Review A 81 (March 2010), article 

032117 (7 pages). 

Journal of Research of NIST 

1. D. E. Gilsinn, B. R. Borchardt, and A. Tebbe, “Estimating Volumes of Near-Spherical Molded 

Artifacts,” Journal of Research of the NIST 115

(3) (May-June 2010), pp. 149-177. 

Books 

1. M. E. Kilmer and D. P. O’Leary, eds., G. W. Stewart: Selected Works with Commentaries, 

Birkhauser Press, Boston (2010). 

2. F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and 

C. W Clark, eds., NIST Handbook of Mathematical 

Functions, Cambridge University Press, New 

York, 2010. 
Summary of Activities for Fiscal Year 2010 97

Book Chapters 

1. R. C. Bryce, Y. Lei, D. R. Kuhn, and R. Kacker, 

“Combinatorial Testing,” Chapter 14, in Handbook of Research on Software Engineering and 

Productivity Technologies: Implications of Globalization, M. Ramachandran and R. Atem de 

Carvalho, eds., IGI Global, 2010. 

2. L. Ma, O. Slattery, and X. Tang, “NIR Single Photon Detectors with Up-conversion Technology and 

Its Applications in Quantum Communication Systems” Chapter 15 in Advances in Lasers and 

Electro Optics, INTECH, April 2010, pp. 315-336. 

3. B. W. Rust, D. P. O’Leary, and K. M. Mullen, 

“Modelling Type Ia Supernova Light Curves,” in 

Exponential Data Fitting and its Applications, 

Victor Pereyra and Godela Scherer, eds., Bentham 

Electronic Books, 2010, pp. 145-164. 

Conference Proceedings 

1. D. Banerjee, J. Gross, P. Reddy Gaddam, M. 

Olano, W. Hess, J. Terrill, T. Griffin, J. Hagedorn, 

J. Kelso, and S. Satterfield, “An Integrated Interactive Visualization and Analysis Environment to 

Study the Impact of Fire on Building Structures,” 

in Proceedings of SIGGRAPH’10, ACM SIGGRAPH 2010 Posters, Los Angeles, CA, July 25-

29, 2010, article 149 (1 page). 

2. I. Beichl and B. Cloteaux, “A Structural Approach 

to the Temporal Modeling of Networks,” in Proceedings of the Winter Simulation Conference 

(WSC09), Austin, TX, December 13-16, 2009, pp. 

788-796. 

3. T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. 

Whitenton, D. Basak, and R. H. McFadden, 

“Modeling of the Temperature Field in the Chip 

and in the Tool in High-speed Machining of a 

Carbon Steel: Effect of Pearlite to Austenite Phase 

Transition in AISI 1075,” in Proceedings of ESAFORM 2010, Brescia, Italy, April 7-9, 2010. 

4. T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. 

Whitenton, and D. Basak, “On Modeling the Peak 

Temperature on the Tool-Chip Interface during 

High-Speed machining of AISI 1045 Steel,” in 

Proceedings of the Eigth International Conference 

on High Speed Machining, Metz, France, December 8-10, 2010. 

5. J. Chalfoun, A. Dima, A. Peskin, J. Elliot and J. 

Filliben, “A Human Inspired Local Ratio-Based 

Algorithm for Edge Detection in Fluorescent Cell 

Images,” in Advances in Visual Computing, (G. 

Bebis, et al., eds.), Lecture Notes in Computer 

Science 6453 (2010), pp. 23-34. 

6. B. Cloteaux and N. Serova, “Matching Observed 

Alpha Helix Lengths to Predicted Secondary 

Structure,” in Proceedings of the 2009 IEEE International Conference on Bioinformatics and 

Biomedicine Workshops, Bethesda, MD, November 1-4, 2009, pp. 113-119. 

7. B. Cloteaux, “Modeling Affiliations in Networks,” 

in Proceedings of the Winter Simulation Conference (WSC10), Baltimore, MD, December 5-8, 

2010, pp. 2958-2967. 

8. J. M. Conroy, J. D. Schlesinger, P. A. Rankel, and 

D. P. O'Leary, “CLASSY 2010: Summarization 

and Metrics,” in Proceedings of the Text Analysis 

Conference (TAC) 2010 Workshop, NIST, November 15-16, 2010. 

9. G. Dogan, “A Flexible and Efficient Numerical 

Framework for Image Segmentation by Energy 

Minimization,” in Proceedings of the Workshop on 

Applications of Digital Geometry and Mathematical Morphology, Istanbul, Turkey, August 22-23, 

2010. 

10. J. T. Fong and P. V. Marcal, “Artificial Intelligence Tools for Failure Event Data Management 

and Probabilistic Risk Analysis for Failure Prevention,” in Proceedings of the Materials Science & 

Technology 2009 Conference, Pittsburgh, PA, Oct. 

25-29, 2009, Charles R. Morin Memorial Symposium on Failure Analysis and Prevention, R. 

Parrington and D. McGarry, eds., American Ceramic Society, Association for Iron & Steel 

Technology, ASM International, and Minerals, 

Metals & Materials Society (2009). 

11. E. Garboczi, J. Bullard, N. Martys, and J. Terrill, 

“The Virtual Cement and Concrete Testing Laboratory: Performance Prediction, Sustainability, and 

the CSHub,” in Proceedings of the National Ready 

Mixed Concrete Association Concrete Sustainability Conference, Tempe, AZ, April 13-15, 2010. 

12. D. Genin, V. Marbukh, and T. Nakassis, “Vulnerability of Selfish Routing to Attacks: A Gametheoretic Model and Initial Results,” in Proceedings of 2010 International Conference of 

Information Security and Internet Engineering, 

World Congress on Engineering 2010 (WCE 

2010), June 30, 2010. 

13. P. D. Hale and A. Dienstfrey, “Waveform Metrology and a Quantitative Study of Regularized 

Deconvolution,” in Proceedings of the Instrumentation and Measurement Technology Conference 

(I2MTC), Austin, TX, May 3-6, 2010, pp. 386-

391. 

14. F. Hunt and V. Marbukh, “Measuring the Utility/Path Diversity Tradeoff In Multipath 
98 NIST Applied and Computational Mathematics Division 

Protocols,” in Proceedings of the 4th International 

Conference on Performance Evaluation Methodologies and Tools, Pisa, Italy, Oct. 20-22, 2009. 

15. B. Johnasson, R. Kacker, R. Kessel, C. McLean, 

and R. Sriram, “Utilizing Combinatorial Testing to 

Detect Interactions and Optimize a Discrete Event 

Simulation Model for Sustainable Manufacturing,” 

in Proceedings of the ASME 2009 International 

Design Engineering Technical Conferences & 

Computers and Information in Engineering Conference, IDETC/CIE 2009, San Diego, CA, Aug. 

30-Sept. 2, 2009, CD-ROM Paper I: DETC2009-

86522. 

16. R. N. Kacker, R. Kessel, K.-D. Sommer, and X. 

Bian, “Comparison of Statistical Consistency and 

Metrological Consistency,” in Proceedings of the 

XIX IMEKO World Congress on Fundamental and 

Applied Metrology, Lisbon, Portugal, Sept. 6-11, 

2009. 

17. R. Kacker, R. Kessel, and K.D. Sommer, “Metrological Compatibility and Statistical Consistency,” 

in Proceedings of the Tenth International Symposium on Measurement and Quality Control, Osaka, 

Japan, September 5-9, 2010, article 157. 

18. R. Kessel and R. N Kacker, “Correlation in Uncertainty of Measurement - A Discussion of State of 

the Art Techniques,” in Proceedings of the XIX 

IMEKO World Congress on Fundamental and Applied Metrology, Lisbon, Portugal, Sept. 6-11, 

2009. 

19. R. Kessel, R. Kacker and K.D. Sommer, “A More 

General Type A Evaluation,” in Proceedings of the 

Tenth International Symposium on Measurement 

and Quality Control, Osaka, Japan, September 5-9, 

2010, article 35. 

20. D. R. Kuhn, R. N. Kacker and Y. Lei, “Random 

vs. Combinatorial Methods for Discrete Event 

Simulation of a Grid Computer Network,” in Proceedings of ModSim World 2009, Virginia Beach, 

VA, Oct. 14-17, 2009. 

21. L. Ma, O. Slattery and X. Tang, “Ultra Sensitive 

NIR Spectrometer Based on Frequency Upconversion Detector,” Proceedings of the SPIE 7680

(April 7, 2010), article 76800 (10 pages). 

22. L. Ma, O. Slattery, and X. Tang, “Study on Noise 

Reduction in Up-conversion Single Photon Detectors,” Proceedings of the SPIE 7815 (2010), article 

781508 (8 pages). 

23. L. Ma, O. Slattery, and X. Tang, “Optimization of 

the Optical Gating Width in Up-conversion Single 

Photon Detectors,” in Proceedings of the SPIE

7815 (2010), article 781508 (8 pages). 

24. V. Marbukh, H. Mahboubi, A. Momeni, A.G. 

Aghdama, and K. Sayrafian-Pour, “Optimal Target 

Tracking Strategy with Controlled Node Mobility 

in Mobile Sensor Networks,” in Proceedings of 

2010 American Control Conference (ACC2010), 

June 30, 2010. 

25. V. Marbukh, H. Mahboubi, A. Momeni, A. G. 

Aghdama, and K. Sayrafian-Pour, ”Towards Evolutionary-pricing Framework for Mobile Sensor 

Network Self-organization,” in Proceedings of the 

IEEE World Congress on Computational Intelligence (WCCI2010), Barcelona, Spain, July 18-23, 

2010. 

26. A. Peskin, K. Kafadar, and A. Dima, “A Quality 

Pre-Processor for Biological Cell Images,” in Advances in Visual Computing, Part I, (G. Bebis, et 

al., eds.), Lecture Notes in Computer Science 5875

(2009), pp. 1051-1062. 

27. A. Peskin, A. Dima, J. Chalfoun and J. Elliot, 

“Predicting Segmentation Accuracy for Biological 

Cell Images,” in Advances in Visual Computing, 

Part I, (G. Bebis, et al., eds.), Lecture Notes in 

Computer Science 6453 (2010), pp. 549-560. 

28. A. Peskin and A. Dima, “Modeling Clinical Tumors to Create Reference Data for Tumor Volume 

Measurement,” in Advances in Visual Computing, 

Part II, (G. Bebis, et al., eds.), Lecture Notes in 

Computer Science 6454 (2010), pp. 736-746. 

29. M. T. Rakher, L. Ma, O. Slattery, X. Tang, K. 

Srinivasan, “Quantum Transduction of Telecommunications-band Single Photons from a Quantum 

Dot by Frequency Upconversion”, in Proceedings 

of Frontiers in Optics 2010, Rochester, New York, 

October 24-28, 2010. 

30. B. Saunders and Q. Wang, “Tensor Product BSpline Mesh Generation for Accurate Surface 

Visualization in the NIST Digital Library of 

Mathematical Functions”, in Mathematical Methods for Curves and Surfaces, (M. Dæhlen, et al., 

eds.), Lecture Notes in Computer Science 5862

(2010), pp. 385-393. 

31. X. Tang, L. Ma and O. Slattery, “Ultra Low Darkcount-rate Up conversion Single Photon Detector,” 

in Proceedings of the 2010 IEEE Photonics Society Annual Meeting, Denver, CO, November 7-11, 

2010, IEEE catalog: CFP10LEO-CDR. 

32. W. Villanueva, W. J. Boettinger, G. B. McFadden, 

and J.A. Warren, “A Multicomponent and Multiphase Model of Reactive Wetting,” Proceedings of 

the 7th International Conference on Multiphase 

Flows (ICMF 2010), Tampa, FL, May 30-June 4, 

2010. 
Summary of Activities for Fiscal Year 2010 99

33. W. Wang, Y. Lei, S. Sampath, R. Kacker, R. Kuhn 

and J. Lawrence, “A Combinatorial Approach to 

Building Navigation Graphs for Dynamic Web 

Applications,” in Proceedings of 25th IEEE International Conference on Software Maintenance, 

ICSM, Edmonton, Alberta, Canada, Sept. 20-26, 

2009, pp. 211-220. 

34. J. C. Wu, A. F. Martin, R. Kacker and C. R. Hagwood, “Significance Test in Operational ROC 

Analysis” in Proceedings of SPIE Defense, Security, and Sensing Conference, Orlando FL, April 5-

9, 2010, article 76670I (15 pages). 

35. W.-B. Yang, K. Sayrafian-Pour, J. Hagedorn, J. 

Terrill, and K. Y. Yazdandoost, “Simulation Study 

of Body Surface RF Propagation for UWB Wearable Medical Sensors,” in Proceedings of the 2nd 

International Symposium on Applied Sciences in 

Biomedical and Communication Technologies, 

Bratislava, Slovak Republic, November 24-27, 

2009. 

36. L. Yan, L. Ma, and X. Tang, “Narrow-band Photon Pairs Generated from Spontaneous Parametric 

Down Conversion in a Bragg-grating Enhanced 

Waveguide,” in Proceedings of the SPIE 7815

(2010), article 781511 (7 pages). 

Other Formal Publications 

1. I. Beichl, “Where the Rubber Meets the Road,” 

Computing in Science & Engineering 11 (5) 

(Sept.-Oct. 2009), p. 3. 

2. I. Beichl, “Ephemera,” Computing in Science & 

Engineering 12 (1) (January 2010), p. 3. 

3. I. Beichl, “You Say You Want a Revolution,” 

Computing in Science & Engineering 12 (2) 

(March 2010), p. 5. 

4. I. Beichl, “Good Policy Makes Good Science,” 

Computing in Science & Engineering 12 (3) (May 

2010), p. 5. 

5. I. Beichl, “Revitalizing Work in CiSE,” Computing in Science & Engineering 12 (5) (September 

2010), p. 4. 

6. W. L. George, “Modeling the Rheological Properties of Concrete,” in High End Computing at 

NASA - Highlights of Science and Engineering 

Achievements on NASA’s Supercomputers (2007-

2008), pp. 112-113. 

7. R. Kessel and T. Hewison, “Common Reference 

Channels for Metrological Comparability,” Global 

Space-based Inter-Calibration Systems Quarterly

4 (4) (2010), pp. 1-2. 

8. D. R. Kuhn, R. Kacker and Y. Lei, What is Combinatorial Testing and Why Should Testers Care, 

LogiGear Magazine, November 2010. 

Technical Reports 

1. J. Bernal, “Linking Canny Edge Pixels with 

Pseudo-watershed Lines,” NISTIR 7673, March 

2010. 

2. R. F. Boisvert (ed.), “Mathematical and Computational Sciences Division, Summary of Activities 

for Fiscal Year 2009”, NISTIR 7671, February 25, 

2010 (110 pages). 

3. A. Carasso and A. Vládár, “Fractional Diffusion, 

Low Exponent Levy Stable Laws, and Slow Motion Denoising of Helium Ion Microscope 

Nanoscale Imager,” NISTIR 7727, September 

2010 (20 pages). 

4. C. Dabrowski, F. Hunt and K. Morrison “Improving Efficiency of Markov Chain Analysis of 

Complex Distributed Systems,” NISTIR 7744, 

November 2010.

5. D. E. Gilsinn, K. Bhadriraju, J. T. Elliott, “Biological Cell Feature Identification by a Modified 

Watershed-Merging Algorithm”, NISTIR 7750, 

November 2010 (47 pages). 

6. F. Hunt and V. Marbukh, “A Model of Joint Congestion Control and Routing Through Random 

Assignment of Paths,” NISTIR 7590, February 

2010. 

7. R. Kuhn, R. Kacker and Y. Lei, “Practical Combinatorial Testing,” NIST Special Publication 800-

142, October 2010. 

8. W. F. Mitchell, “A Collection of 2D Elliptic Problems for Testing Adaptive Algorithms,” NISTIR 

7668, March 5, 2010. 

9. S. Ramamurti and D. Gilsinn, “Bicubic B-spline 

Surface Approximation of Invariant Tori”, NISTIR 

7731, October 20, 2010. 

10. J. C. Wu, A. F. Martin, C. S. Greenberg, and R. N. 

Kacker, „Measurement Uncertainties in Speaker 

Recognition Evaluation,” NISTIR 7722, September 15, 2010 (16 pages). 

Accepted 

1. J. D. Benson, C. C. Chicone, and J. K. Critser, “A 

General Model for the Dynamics of Cell Volume, 

Global Stability, and Optimal Control,” Journal of 

Mathematical Biology. 
100 NIST Applied and Computational Mathematics Division 

2. J. D. Benson, A. Bagchi, X. Han, J. K. Critser, and 

E.J. Woods, “Melting Point Equations for the Ternary System Water-sodium Chloride-ethylene 

Glycol Revisited,” Cryobiology. 

3. J. W. Bullard, C. F. Ferraris, E. J. Garboczi, N. S. 

Martys, P. E. Stutzman, J. E. Terrill, “Virtual Cement and Concrete,” Innovations in Portland 

Cement Manufacturing. 

4. J. W. Bullard, E. J. Garboczi, W. L. George, N. S. 

Martys, S. G. Satterfield, J. E. Terrill, “Advancing 

the Materials Science of Concrete with Supercomputers,” Concrete International. 

5. T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. 

Whitenton, D. Basak, “Dynamic Properties for 

Modeling and Simulation of Machining: Effect of 

Pearlite to Austenite Phase Transition on Flow 

Stress” AISI 1075 Steel, Machining Science and 

Technology. 

6. B. Cloteaux, “Approximating the Number of Bases 

for Almost All Matroids,” Congressus Numerantium. 

7. V. R. Coffman, J. P. Sethna, J. Bozek, A. Ingraffea, N. P. Bailey and E. I. Barker, “Challenges in 

Continuum Modeling of Intergranular Fracture,” 

Strain.

8. A. A. Dima, J. T. Elliott, J. J. Filliben, M. Halter, 

A. Peskin, J. Bernal, B. L. Stottrup, M. Kociolek, 

M. C. Brady, H. C. Tang, and A. L. Plant, “Comparison of Segmentation Algorithms for 

Fluorescence Microscopy Images of Cells,” Cytometry Part A. 

9. V. Marbukh, H. Mahboubi, A. Momeni, A.G. 

Aghdama, and K. Sayrafian-Pour ”SelfDeployment Algorithms for Coverage Problem in 

a Network of Mobile Sensors with Un-identical 

Sensing Range” IEEE Globecom 2010. 

10. A. Mink, L. Ma, B. Hershman and X. Tang “An 

Application of Quantum Networks for Secure 

Video Surveillance,” in Video Surveillance, ITECH Education and Publishing, Vienna, Austria. 

11. W. F. Mitchell and M. A. McClain, “A Survey of 

hp-Adaptive Strategies for Elliptic Partial Differential Equations,” Annals of the European 

Academy of Sciences. 

12. B. W. Rust, “Atmospheric Retention of Man-made 

CO2 Emissions,” Mathematics and Computers in 

Simulation. 

13. J. S. Sims, G. W. Bryant, W. L. George, T. G. 

Griffin, J. G. Hagedorn, J. T. Kelso, T. M. Olano, 

A. P. Peskin, S. G. Satterfield, and J. D. Terrill, 

“Computation and Visualization of Nanostructures and Nano-optics,” Computing and Visualization in Science. 

14. J. S. Sims and S. A. Hagstrom, “Hylleraasconfiguration-interaction Study of the Singlet S 

Ground State of Neutral Beryllium,” Physical Review. 

In Review 

1. G. S. Abo, Y. K. Hong, B. C. Choi, S. Bai, J. Jalli, 

J. H. Park, J. J. Lee, M. J. Donahue, M. H. Park, 

and S. H. Gee, “Micromagnetic Computer Simulated Scaling Effect of S-shaped Permalloy nanoelement on Operating Fields for AND or OR 

Logic.” 

2. I. Beichl, “Working in Computational Science.” 

3. I. Beichl, “Dystopia.” 

4. J. D. Benson, C. C. Chicone, and J. K. Critser, “An 

Optimal Method for the Addition and Removal of 

Cryoprotective Agents.” 

5. J. D. Benson, “Stability Analysis of Several Nondilute Multiple Solute Transport Equations.” 

6. J. D. Benson, C. T. Benson, and J. K. Critser, 

“Mathematical Model Formulation and Validation 

of Water and Cryoprotective Agent Transport in 

Whole Hamster Pancreatic Islets.” 

7. R. Braun, R. Usha, G. McFadden, T. Driscoll, L. 

P. Cook and P. King-Smith, “Thin Film Dynamics 

on a Prolate Ellipsoid with Application to the Cornea.”

8. A. Carasso and A. Vladár, “Fractional Diffusion, 

Low Exponent Levy Stable Laws, and ‘Slow Motion’ Denoising of Helium Ion Microscope 

Nanoscale Imagery.” 

9. V. R. Coffman, A. C. E Reid, S. A. Langer, and G. 

Dogan, “OOF3D: An Image-based Finite-element 

Solver for Materials Science.” 

10. C. Dabrowski and F. Hunt, “Using Markov Chain 

and Graph Theory Concepts to Analyze Behavior 

in Complex Distributed Systems.” 

11. G. Dogan and R. Nochetto, “First Variation of the 

General Curvature-dependent Surface Energy.” 

12. D. Duthinh and F. Potra, “Probabilistic and Optimization Considerations in Multi-hazard 

Engineering.” 

13. D. Gilsinn, K. Bhadriraju, J. Elliott, “Biological 

Cell Feature Identification by a Modified Watershed-Merging Algorithm.” 
Summary of Activities for Fiscal Year 2010 101

14. X. Han, Y. Liu, J. D. Benson, and J. K. Critser, 

“A Calorimetric Method to Measure Watercryoprotectant Mutual Diffusivity in Biological 

Tissues at Both Super- and Sub-zero Temperatures.” 

15. D. Harris, F. Sullivan, and I. Beichl, “Fast Sequential Importance Sampling to Estimate the Graph 

Reliability Polynomial.” 

16. R. Kacker and J. Lawrence, “Derivation of Isosceles Trapezoidal Distributions.” 

17. R. Kacker, Y. Lei, D. R. Kuhn, and W. Wang, “A 

Combinatorial Approach to Detecting Buffer 

Overflow Vulnerabilities.” 

18. R. Kessel, R. Kacker, and J. Lawrence, “Effective 

Degrees of Freedom for Correlated Input Quantities.” 

19. R. Kessel and T. Hewison, “Treatment of Spectral 

Response in Inter-calibration.” 

20. J. Lawrence, R. Kacker, Y. Lei, D. R. Kuhn, and 

M. Forbes, “A Survey of Binary Covering Arrays.” 

21. J. D. D. Melo and J. T. Fong, “A New Approach to 

Creating Composite Materials Elastic Property Database with Uncertainty Estimation Using a 

Combination of Mechanical and Thermal Expansion Tests.” 

22. D. P. O’Leary and B. W. Rust, “Variable Projection for Nonlinear Least Squares Problems.” 

23. L. Ma, J. C. Bienfang, O. Slattery and X. Tang, 

“Multi-wavelength Pumping Technique for Upconversion Single-photon Detectors.” 

24. L. Ma, J. C. Bienfang, O. Slattery and X. Tang, 

“Up-conversion Single-photon Detector using 

Multi-wavelength Sampling Techniques.” 

25. J. S. Pelc, C. R. Phillips, C. Langrock, Q. Zhang, 

L. Ma, O. Slattery, X. Tang, and M. M. Fejer, 

“Single-Photon Detection at 1550 nm via Upconversion Using a Tunable Long-Wavelength Pump 

Source.” 

26. M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. 

Srinivasan, “Upconversion of Triggered Single 

Photon Emission from a Telecommunicationsband Semiconductor Quantum Dot.” 

27. P. E. Shah, J. D. D. Melo, C. A. Cimini, and J. T. 

Fong, “Composite Material Property Database Using Smooth Specimens to Generate Design 

Allowables with Uncertainty Estimation.” 

28. W. Wang, Y. Lei, D. Liu, D. Kung, C. Callner, D. 

Zhang, R. Kacker and R. Kuhn, “A Combinatorial 

Approach to Detecting Buffer Overflow Vulnerabilities.” 

Presentations

Invited Talks 

1. J. D. Benson, “Basic Principles of Sperm Cryopreservation,” European Society for Human 

Reproduction and Embryology (ESHRE), Granada, Spain, March 25-26, 2010. 

2. A. Carasso, “Randomizing the Time in the Heat 

Equation and Blind Deconvolution of Galaxy Images,” AMS-SIAM Minisymposium “Frontiers in 

Geomathematics,” American Mathematical Society Annual Meeting, San Francisco, CA, January 

13, 2010. 

3. A. Carasso, “Bochner Subordination, Logarithmic 

Diffusion Equations, and Blind Deconvolution of 

Hubble Space Telescope Imagery and Other Scientific Data,” Applied Analysis Seminar, Department 

of Mathematics, Yale University, New Haven, CT, 

January 27, 2010. 

4. A. Carasso, “Bochner Subordination, Logarithmic 

Diffusion Equations, and Blind Deconvolution of 

Hubble Space Telescope Imagery and Other Scientific Data,” Department of Mathematics 

Colloquium, George Mason University, Fairfax, 

VA, March 26, 2010. 

5. A. Carasso, “Randomizing the Time Variable in 

Brownian Motion and Blind Deconvolution of 

Hubble Telescope Imagery,” SIAM Conference on 

Imaging Science, Chicago, IL, April 13-15, 2010. 

6. V. Coffman, “Object-Oriented Finite Elements 

(OOF) for Modeling Materials Behavior,” 21st 

NIST Computer Modeling Workshop, Gaithersburg, MD, August 12, 2010. 

7. A. Dienstfrey, “Numerical Solution of RiemannHilbert Problems Related to Random Matrix Theory and the Painlevé Equations,” International 

Center for Mathematical Sciences Workshop on 

the Numerical Solution of the Painlevé Equations, 

Edinburgh, UK, May 10-15. 

8. A. Dienstfrey, “Uncertainty Quantification for 

Scientific Computation,” National Academy of 

Sciences Committee on Mathematical Science 

Foundations of Verification, Validation, and Uncertainty Quantification, Albuquerque, NM, June 

11, 2010. 

9. F. Hunt, “A Model of Routing in a Computer 

Network,” Oxtoby Centennial Conference, Bryn 

Mawr College, October 30, 2010. 
102 NIST Applied and Computational Mathematics Division 

10. J. Fong, “Aging Plant Risk-Informed In-Service 

Inspection (RI-ISI) Methods and Artificial Intelligence Tools for Probabilistic Risk Assessment,” 

Department of Aeronautics and Astronautics 

Seminar, Stanford University, Stanford, CA, Oct. 

7, 2009. 

11. J. Fong, “Artificial Intelligence Tools for Failure 

Event Data Management and Probabilistic Risk 

Analysis for Failure Prevention,” Materials Science & Technology 2009 Conference, Pittsburgh, 

PA, Oct. 25-29, 2009, Charles R. Morin Memorial 

Symposium on Failure Analysis and Prevention, 

sponsored by the American Ceramic Society, Association for Iron & Steel Technology, ASM 

International, and Minerals, Metals & Materials 

Society, Oct. 27, 2009.

12. J. Fong, “Application of Artificial Intelligence 

(AI) Tools to Failure Event Data Management and 

Probability Risk Analysis for Failure Prevention,” 

Department of Mechanical & Aerospace Engineering Seminar, George Washington University, 

Washington, DC, Nov. 23, 2009. 

13. J. Fong, “Application of Artificial Intelligence 

(AI) Tools to On-line Monitoring of Aging Structures, and Research Opportunities at National 

Institute of Standards & Technology,” Department 

of Mechanical Engineering Seminar, Stanford 

University, Stanford, CA, Dec. 8, 2009. 

14. F. Hunt, “How to Write A Grant Proposal,” Infinite Possibilities Conference, Institute for Pure and 

Applied Mathematics, UCLA, Las Angeles, CA, 

March 18-20, 2010. 

15. F. Hunt, “A Mathematician Looks at Hollywood, 

DNA and Paint,” Career Workshop on Minorities 

and Applied Mathematics, Institute for Mathematics and Its Applications, University of Minnesota, 

Minneapolis, MN, March 25-27, 2010. 

16. E. Knill, “Building Quantum Computers,” Indiana 

University, Bloomington, IN, Nov. 21, 2009 

16. P. A. Lott, “Fast Solvers for Models of Fluid Flow 

with Spectral Elements,” Applied and Computational Math Seminar, George Mason University, 

Washington, DC, Dec. 4 2009. 

17. P. A. Lott, “Fast Solvers for Models of Fluid Flow 

with Spectral Elements,” Differential Equations 

Seminar, University of Maryland Baltimore 

County, Dec. 7 2009. 

18. P. A. Lott, “Fast Solvers for Models of Fluid Flow 

with Spectral Elements,” Department of Mathematics Colloquium Howard University, 

Washington, DC, Feb. 2010. 

19. P. A. Lott, “Fast Solvers for Models of Fluid Flow 

with Spectral Elements,” Center for Applied Scientific Computing, Lawrence Livermore National 

Lab, Livermore, CA, Feb. 2010. 

20. P. A. Lott, “Fast Solvers for Models of Fluid Flow 

with Spectral Elements,” Computer Science and 

Mathematics Division Seminar, Oak Ridge National Lab, Oak Ridge, TN, May 6, 2010. 

21. D. Lozier, “Public Release of the NIST DLMF and 

Handbook,” Workshop on Numerical Solution of 

the Painlevé Equations, International Centre for 

Mathematical Sciences, Edinburgh, Scotland, May 

10-14, 2010. 

22. G. B. McFadden, “QAS Design of the DEMO Reactor,” 17th International Stellarator/Heliotron 

Workshop, Princeton Plasma Physics Laboratory, 

Princeton, NJ, October 12-16, 2009. 

23. G. McFadden, “Phase-field Modeling of Reactive 

Wetting,” SIAM Conference on Mathematical Aspects of Materials Science, Philadelphia, PA, May 

22 - May 26, 2010. 

24. B. Saunders, “Applying Numerical Grid Generation to the Visualization of Complex Function 

Data,” Institute for Mathematics and its Applications/Minnesota Center for Industrial Mathematics 

(IMA/MCIM) Industrial Problems Seminar, University of Minnesota, Minneapolis, MN, April 9, 

2010. 

25. B. Saunders, “Creating Interactive 3D Graphs for a 

Digital Library: So How Is This Math?” Kappa 

Mu Epsilon Honorary Mathematics Society, Stevenson University, Stevenson, MD, September 21, 

2010. 

26. W.-B. Yang, K. Sayrafian-Pour, J. Hagedorn, J. 

Terrill, and K. Y. Yazdandoost, “Simulation Study 

of Body Surface RF Propagation for UWB Wearable Medical Sensors,” in Proceedings of the 2nd 

International Symposium on Applied Sciences in 

Biomedical and Communication Technologies, 

November 24-27, 2009, Bratislava, Slovak Republic. 

Conference Presentations 

1. D. Banerjee, J. Gross, P. R. Gaddam, M. Olano, 

W. Hess, J. Terrill, T. Griffin, J. Hagedorn, J. 

Kelso, and S. Satterfield, “An Integrated Interactive Visualization and Analysis Environment to 

study the Impact of Fire on Building Structures,” 

SIGGRAPH 2010, Los Angeles, CA, July 25-29, 

2010. 
Summary of Activities for Fiscal Year 2010 103

2. J. D. Benson, “Exact and Numerical Boundary 

Control of the Diffusion Equation in Cryobiology,” Annual International Meeting of the Society 

for Cryobiology, Bristol, UK, July 2010. 

3. B. Cloteaux, “Matching Observed Alpha Helix 

Lengths to Predicted Secondary Structure,” Computational Structural Bioinformatics Workshop 

2009, Bethesda, MD, November 1, 2009. 

4. B. Cloteaux, “A Structural Approach to the Temporal Modeling of Networks,” Winter Simulation 

Conference 2009, Austin, TX, December 14, 2009. 

5. B. Cloteaux, “Approximating the Number of Bases 

for Almost All Matroids,” 41st Southeastern International Conference on Combinatorics, Graph 

Theory, and Computing 2010, Florida Atlantic 

University, Boca Raton, FL, March 11, 2010. 

6. V. R. Coffman, “OOF3D: An Image-based Finite 

Element Solver for Materials Science,” SEM Annual Conference and Exposition on Experimental 

and Applied Mechanics, Indianapolis, IN, June 10, 

2010. 

7. G. Dogan, “Image-Based Analysis of Microstructures with OOF,” SIAM Conference on 

Mathematical Aspects of Materials Science, Philadelphia, PA, May 25, 2010. 

8. G. Dogan, “A Flexible and Efficient Numerical 

Framework for Image Segmentation by Energy 

Minimization,” Workshop on Applications of Discrete Geometry and Mathematical Morphology, 

Istanbul, Turkey, August 22, 2010. 

9. M. Donahue, “Accurate Computation of the Demagnetization Tensor for Finite Difference 

Micromagnetics,” Joint Intermag/MMM 2010 

Conference, Washington, DC, January 20, 2010. 

10. E. Garboczi, J. Bullard, N. Martys, and J. Terrill, 

“The Virtual Cement and Concrete Testing Laboratory: Performance Prediction, Sustainability, and 

the CSHub,” National Ready Mix Cement Association Concrete Sustainability Conference, 

Tempe, AZ, April 13-15. 

11. W. George, N. Martys, S. Satterfield, J. Hagedorn, 

M. Olano, J. Terrill, and E. Garboczi, “Simulation 

of Non-Newtonian Suspensions: Shear Thinning 

Case,” animation, International Conference for 

High Performance Computing, Networking, Storage, and Analysis (SC09), Portland, OR, 

November 2009. 

12. F. Hunt, “Measuring the Utility/Path Diversity 

Tradeoff In Multipath Protocols,” 4th International 

Conference on Performance Evaluation Methodologies and Tools, Pisa, Italy, October 20-22, 

2009. 

13. F. Hunt, “A Mathematical Model of Congestion 

Control in a Network with Multiple Sources,” Dynamics Days Conference, University of Bristol, 

Bristol, UK, September 9, 2010. 

14. E. Knill, “Building Quantum Computers,” SURF 

Seminar, Boulder, CO, June 24, 2010. 

15. P.A. Lott, “Fast Solvers for Models of Fluid Flow 

with Spectral Elements,” SIAM Conference on 

Applied Linear Algebra, Monterey, CA, October 

26-29, 2009. 

16. A. Lott, “Fast Solvers for Models of Fluid Flow 

with Spectral Elements,” AMS/MAA Joint 

Mathematics Meetings, San Francisco, CA, January 14, 2010. 

17. A. Lott, “Fast Solvers for Models of Thermosolutal Convection,” APS/AAPT Joint Physics 

Meeting, Washington, DC, February 15, 2010. 

18. A. Lott, “Fast Solvers for Models of Fluid Flow 

with Spectral Elements,” 11th Copper Mountain 

Conference on Iterative Methods, Copper Mountain, CO, April 5, 2010. 

19. L. Ma, O. Slattery, and X. Tang, “NIR Spectrometer Based on Frequency Up-conversion 

Technology,” American Physical Society March 

Meeting 2010, Portland, OR, March 15–19, 2010. 

20. V. Marbukh, D. Genin, and T. Nakassis paper 

“Vulnerability of Selfish Routing to Attacks: A 

Game-theoretic Model and Initial Results” 2010 

International Conference of Information Security 

and Internet Engineering, World Congress on Engineering 2010 (WCE 2010), London, UK, June 

30 – July 2, 2010. 

21. V. Marbukh, H. Mahboubi, A. Momeni, A. G. 

Aghdama, and K. Sayrafian-Pour, “Towards Evolutionary-pricing Framework for Mobile Sensor 

Network Self-organization,” IEEE World Congress on Computational Intelligence (WCCI2010), 

Barcelona, Spain, July 18-23, 2010. 

22. N. S. Martys, W. George, S. Satterfield, D. 

Lootens, P. Hebraud, and J. Hagedorn, “A 

Smoothed-particle-hydrodynamics-based Fluid 

Model with a Local Shear-rate Dependent Viscosity: Application to flow of a Suspension with a 

Non-Newtonian Fluid Matrix,” Society for Rheology 81st Annual Meeting, Madison, WI, October 

18-22, 2009. 

23. N. S. Martys, D. Lootens, W. L. George, and P. 

Hebraud, “Contact and Stress Anisotropies in the 

Start-up Flow of Colloidal Suspensions,” 2009 Society of Rheology Meeting, Madison, WI, October 

18-22, 2009. 
104 NIST Applied and Computational Mathematics Division 

24. A. Meier, “Using and Extending Randomized 

Benchmarks for Trapped-Ion Quantum Computing,” 41st Annual Meeting of the Division of 

Atomic, Molecular, and Optical Physics (DAMOP), Houston, TX, May 26, 2010. 

25. W. F. Mitchell, Some Computational Results with 

hp-Adaptive Refinement, SIAM Conference on 

Parallel Processing for Scientific Computing, February 2010. 

26. W. Mitchell, “A Summary of hp-Adaptive Finite 

Element Strategies,” Workshop on Adaptive Finite 

Elements and Domain Decomposition Methods, 

Milano, Italy, June 17-19, 2010. 

27. W. Mitchell, “A Summary of hp-Adaptive Finite 

Element Strategies,” 2nd European Seminar on 

Coupled Problems, Pilsen, The Czech Republic, 

June 28-July 2, 2010. 

28. M. Mullan, “A Numerical Quantum and Classical 

Adversary,” 10th Canadian Summer School on 

Quantum Information and the associated Workshop on Quantum Algorithms, Computational 

Models, and Foundations of Quantum Mechanics, 

Vancouver, Canada, July 17-30, 2010. 

29. A. Peskin, K. Kafadar, and A. Dima, “A Quality 

Pre-Processor for Biological Cell Images,” poster 

presentation, Computational Bioimaging 2009, 5th 

International Symposium on Visual Computing, 

Las Vegas, NV, November 30 – December 2, 

2009. 

30. A. Peskin, A. Dima, J. Chalfoun and J.J. Filliben, 

“Accuracy in Cell Image Segmentation Algorithms” The International Symposium on Business 

and Industrial Statistics (IBIS), Portoroz, Slovenia, 

July 5-9, 2010. 

31. A. Peskin, A. Dima, J. Chalfoun and J. Elliot, 

“Predicting Segmentation Accuracy for Biological 

Cell Images,” Bioimage Informatics 2010, Pittsburg, PA, September 17-19, 2010. 

32. B. W. Rust, “Using Confidence Ellipsoids to 

Choose the Regularization Parameter for Ill-Posed 

Problems,” SIAM Conference on Applied Linear 

Algebra, Monterey, CA, October 26-29, 2009. 

33. B. Saunders, “B-Spline Mesh Generation for the 

Visualization of Complex Function Data” Seventh 

International Conference of Curves and Surfaces, 

Avignon, France, June 24-30, 2010. 

34. W.-B. Yang, K. Sayrafian-Pour, J. Hagedorn, J. 

Terrill, and K.Y. Yazdandoost, “Simulation Study 

of Body Surface RF Propagation for UWB Wearable Medical Sensors,” 2nd International 

Symposium on Applied Sciences in Biomedical 

and Communication Technologies, Bratislava, 

Slovak Republic, November 24-27, 2009. 

35. Y. Zhang, “The Statistical Strength of Experiments 

to Reject Local Realism with Photon Pairs and Inefficient Detectors,” 41st Annual Meeting of the 

Division of Atomic, Molecular, and Optical Physics (DAMOP), Houston, TX, May 28, 2010. 

Web Services

1. Digital Library of Mathematical Functions15: a 

repository of information on the special functions 

of applied mathematics. 

2. Guide to Available Mathematical Functions16: a 

virtual repository of mathematical software components. 

3. Matrix Market17: a repository of matrices for testing of algorithms and software for numerical linear 

algebra. 

4. SciMark18: a benchmark for scientific computing 

in Java. 

Software Released19

1. f90gl20: Fortran 90 interface for the OpenGL 

graphics library. Version 1.2.15 (December 2, 

2009). – W. Mitchell

2. Network Graph Toolkit21: a suite of applications 

for graph files for analysis, visualization, conversion between graph formats. Version 3.2 

(December 2, 2010). – R. Pozo

3. NGraph22: a simplified C++ graph library for 

analysis of complex networks. Version 3.5 (December 2, 2010). – R. Pozo

4. OOF223. Object Oriented Finite Elements, modeling of materials with complex microstructures. 

Version 2.0.5a11 (May 17, 2010). - S. Langer

5. PHAML24: Parallel Hierarchical Adaptive Multi 

Level, general purpose software for 2D elliptic 

 

15 http://dlmf.nist.gov/ 16 http://gams.nist.gov/ 17 http://math.nist.gov/matrixmarket/ 18 http://math.nist.gov/scimark/ 19 In cases where multiple versions have been released during the 

year we only list the last. 

20 http://math.nist.gov/f90gl 21 http://math.nist.gov/~RPozo/ngraph/ngraph_toolkit_index.html 22 http://math.nist.gov/pozo/ngraph 23 http://www.ctcms.nist.gov/oof/ 24 http://math.nist.gov/phaml/
Summary of Activities for Fiscal Year 2010 105

partial differential equations. Version 1.8.0 (April 

2010). – W. Mitchell

6. Tcl/Tk25: Tool Command Language and Toolkit. 

Version 8.5.9, (September 8, 2010). – D. Porter

7. PCrawler26: suite of Python modules to build network graphs by crawling the World Wide Web. 

Version 2.1 (December 3, 2010). – R. Pozo

Conferences, Minisymposia, 

Lecture Series, Shortcourses

MCSD Seminar Series 

1. S. Jordan (California Institute of Technology), 

“Approximating Topological Invariants on a 

Quantum Computer,” February 3, 2010. 

2. H. Elman (University of Maryland), “Numerical 

Methods for Partial Differential Equations with 

Random Data,” June 24, 1010. 

3. E. Cox (Purdue University), “Constrained Regularization for Lagrangian Actinometry,” Sept. 21, 

2010. 

4. J. Benson (NIST), Modeling and Optimization in 

Cryobiology, Oct. 19, 2010. 

5. I. Saniee (Bell Laboratories), The Large Scale 

Curvature of Networks and Its Implications for 

Network Management and Security, Nov. 9, 2010. 

6. M. Cromer, Jr. (University of Delaware), Modeling and Simulation of a Complex Fluid: Wormlike 

Micellar Solutions, Nov. 30, 2010. 

Hosted Public Events 

1. R. Boisvert, Member, Organizing Committee, 

From Quantum Information and Complexity to 

Post Quantum Information Security, University of 

Maryland, October 27-29, 2010. 

2. R. Boisvert, Chair, Organizing Committee, IFIP 

Working Conference on Uncertainty Quantification in Scientific Computing, Boulder, CO, Aug. 

1-4, 2011. 

3. A. Dienstfrey, Chair, Program Committee, IFIP 

Working Conference on Uncertainty Quantification in Scientific Computing, Boulder, CO, Aug. 

1-4, 2011. 

 

25 http://tcl.sourceforge.net/ 26 http://math.nist.gov/~RPozo/ngraph/webcrawler.html

4. D. Lozier, Member, Organizing Committee, International Conference on Special Functions in the 

21st Century: Theory and Applications, Washington, DC, April 6-8, 2011. 

External Events Organization 

1. M. Donahue, Member, Organizing Committee, 6th 

SIAM meeting on Mathematical Aspects of Materials Science, Philadelphia, PA, May 23-26, 2010. 

2. M. Donahue, Minisymposium Organizer, Micromagnetic Modeling and Computation, 6th SIAM 

meeting on Mathematical Aspects of Materials 

Science, Philadelphia, PA, May 23-26, 2010. 

3. J. Fong, Minisymposium Organizer, Pressure Vessels and Piping Failure Databases, Probability of 

Failure Prediction, Consequence of Failure Estimation, and Risk Analysis for Aging Plants, 

ASME PVP Conference, Bellevue, WA, July 19-

23, 2010. 

4. E. Knill, Member, Organizing Committee, From 

Quantum Information and Complexity to Post 

Quantum Information Security, University of 

Maryland, October 27-29, 2010. 

5. D. P. O’Leary, Member, Organizing Committee, 

SIAM Annual Meeting, Pittsburgh, PA, July 12-

16, 2010. 

6. D. P. O’Leary, Member, Organizing Committee, 

Numerical Linear Algebra: Perturbation, Performance, and Portability, Conference in honor of G. 

W. Stewart, Austin, TX, July 19-20, 2010. 

7. D. P. O’Leary, Member, Organizing Committee, 

SIAM Conference on Applied Linear Algebra 

(LA12), Valencia, Spain, June 18-22, 2012. 

8. B. Miller, Member, Program Committee, 9th 

Mathematical Knowledge Management Conference, Paris, France, July 2010. 

9. B. Miller, Program Committee, 10th Mathematical 

Knowledge Management Conference, Bertinoro, 

Italy, July 18-22, 2011. 

10. W. F. Mitchell, Member, Scientific Committee, 

International Conference of Numerical Analysis 

and Applied Mathematics, Rhodes, Greece, September 19-25, 2010. 

11. Y. Parker and J. Terrill, Organizers, NIST Exhibit 

and Demonstration Booth, SC10, the 2010 International Conference for High Performance 

Computing, Networking, Storage and Analysis, 

New Orleans, November 13-19, 2010. 

12. B. Rust and K. Mullen (MML), Minisymposium 

Organizers, Recent Advances in Separable 
106 NIST Applied and Computational Mathematics Division 

Nonlinear Least Squares, International Congress 

on Industrial and Applied Mathematics, Vancouver, July 18-22, 2011. 

Other Professional Activities 

Internal 

1. I. Beichl, Member, NIST Research Advisory 

Committee. 

2. I. Beichl, Co-organizer, ITL Summer Undergraduate Research Fellowship (SURF) program. 

3. R. Boisvert, Member, NIST Scientific Computing 

Steering Group. 

4. R. Boisvert, Member, ITL Diversity Committee. 

5. D. Gilsinn, Division Safety Representative (term 

ended October 2010). 

6. Barry Hershman, Division Safety Representative 

(term began October 2010). 

7. W. Mitchell, Chair, ITL Awards Committee. 

8. A. O’Gallagher, Organizer, ITL Diversity Book 

Club. 

9. A. O’Gallagher, Member, Boulder Labs Diversity 

Council, 

10. A. O’Gallagher, Member, ITL Diversity Committee. 

11. A. Peskin, Member, Boulder Research Advisory 

Council. 

12. O. Slattery, Member, NIST Laser Safety Committee. 

13. O. Slattery, Member, NIST Safety Operational 

Committee. 

External 

Editorial 

1. I. Beichl, Editor-in-Chief, Computing in Science & 

Engineering. 

2. J. Benson, Associate Editor, CryoLetters. 

3. R. Boisvert, Associate Editor, ACM Transactions 

on Mathematical Software. 

4. R. Boisvert, Editor, Numerical Analysis, Mathematical Software, and Computational Engineering, 

Finance, and Science areas of the Computing Research Repository (CoRR) preprint service hosted 

by www.arXiv.org. 

5. D. Lozier, Associate Editor, Journal of Numerical 

Analysis, Industrial and Applied Mathematics. 

6. G. McFadden, Associate Editor, Journal of Crystal 

Growth. 

7. G. McFadden, Associate Editor, Interfaces and 

Free Boundaries. 

8. G. McFadden, Guest Co-editor, Special issue of 

the Journal of Fluid Mechanics in honor of the 

70th birthday of the main editor, Professor Stephen 

H. Davis, of the Engineering and Applied Sciences 

Department at Northwestern University. 

9. W. Mitchell, Associate Editor, Journal of Numerical Analysis, Industrial and Applied Mathematics. 

10. D. P. O’Leary, Editor-in-Chief, SIAM Journal on 

Matrix Analysis and Applications. 

11. D. P. O’Leary, Member, Editorial Board, Education Section, SIAM Review. 

12. D. P. O’Leary, Member, Editorial Board, SIAM 

Books. 

13. D. P. O’Leary, Member, Editorial Board, SIAM 

book series on “Fundamentals of Algorithms.” 

14. D. P. O’Leary, Member, Editorial Board, Computing in Science & Engineering. 

15. D. Porter, Guest Editor, IEEE Transactions on 

Magnetics, November 2009 (Selected papers from 

the 2009 Hysteresis and Micromagnetic Modeling 

Symposium). 

16. R. Pozo, Associate Editor, ACM Transactions on 

Mathematical Software. 

Boards and Committees 

1. I. Beichl, Member, IEEE Electronic Products and 

Services Subcommittee. 

2. R. Boisvert, Chair, International Federation for 

Information Processing’s (IFIP) Working Group 

2.5 on Numerical Software. 

3. R. Boisvert, Co-chair, Publication Board, Association for Computing Machinery (ACM). 

4. R. Boisvert, Ex-Officio Member, Association for 

Computing Machinery (ACM) Council. 

5. R. Boisvert, Member, Program Review Committee, Center for Computing Sciences, Institute for 

Defense Analysis. 

6. R. Boisvert, Member, External Review Committee, Computer Science Department, George 

Washington University. 
Summary of Activities for Fiscal Year 2010 107

7. D. Lozier, Secretary, Activity Group on Orthogonal Polynomials and Special Functions, Society for 

Industrial and Applied Mathematics (SIAM). 

8. D. Lozier, Founding Member, Painlevé Project27. 

9. G. McFadden, Member, Nomination Committee, 

SIAM Activity Group on Mathematical Aspects of 

Materials Science. 

10. B. Miller, Member, Math Working Group, World 

Wide Web Consortium (W3C). 

11. D. P. O’Leary, Member, Oversight Committee, 

Gene Golub SIAM Summer School. 

12. D. P. O’Leary, Member, Advisory Committee, 

SIAM Linear Algebra Activity Group International Summer School on Numerical Linear 

Algebra. 

13. D. P. O’Leary, Chair, Committee on Committees, 

Association for Women in Mathematics. 

14. D. Porter, Member, Tcl Core Team. 

15. B. Saunders, Member, Mathematics Advisory 

Panel, Department of Mathematics and Statistics, 

American University, Washington, DC. 

16. B. Saunders, Member, Advisory Group, NSF 

CoSMIC Scholars Program, Towson University. 

17. J. Terrill, Member, Federal High End Computing 

Implementation Task Force. 

18. J. Terrill, Member, High End Computing Research 

and Development, and Infrastructure Interagency 

Working Groups, Networking and Information 

Technology R&D (NITRD) National Coordination 

Office. 

Reviewing 

Division staff members referee manuscripts for a wide 

variety of journals and conferences including ACM 

Transactions on Mathematical Software, Annals of the 

European Academy of Sciences, Computing in Science 

& Engineering, CryoLetters, IEEE/ACM Transactions 

on Networking, IEEE Transactions on Magnetics, International Journal of Computer Mathematics, Inverse 

Problems, Journal of Applied Physics, Journal of 

Computing and Information Science in Engineering, 

Journal of Fluid Mechanics, Journal of Numerical 

Analysis, Industrial and Applied Mathematics, Journal 

of Physics B: Atomic, Optical and Molecular Physics, 

Journal of Supercomputing, Linear Algebra and its 

Applications, Mathematical Reviews, Nature, New 

Journal of Physics, Nonlinear Dynamics, Physical Review A, Physical Review B, Physical Review Letters, 

 

27 http://math.nist.gov/~lozier/PainleveProject/

Reviews of Modern Physics, SIAM Journal on Scientific Computing.

MCSD staff reviewed proposals for the following 

agencies/competitions during FY 2010: Canada Research Chairs, DOE, NSF, NIST ARRA Measurement 

Science and Engineering Grants Program. 

External Contacts

MCSD staff members make contact with a wide variety 

of organizations in the course of their work. Examples 

of these follow. 

Industrial Labs 

Achronix Semiconductor 

ADVR Inc. 

Alcatel-Lucent Bell Laboratories 

Deepwoods Software 

Lepton Technologies Inc. 

Lockheed Martin 

Marintek (Norway) 

Microsoft 

Morson Projects Ltd. (UK) 

Motorola 

Northrup Grumman 

NVIDIA 

Orbital Sciences Corporation 

Palantir Technologies 

RSA 

Toptica Photonics 

Wipro Technologies 

Government/Non-profit Organizations 

Army Research Laboratory 

Association for Computing Machinery 

Food and Drug Administration 

IDA Center for Computing Sciences 

Institut Geographique National (France) 

Institute for Defense Analysis 

Lawrence Livermore National Laboratory 

Los Alamos National Laboratory 

Moscow Engineering Physics Institute (Russia) 

NASA 

National Institutes of Health 

National Security Agency 

Naval Research Laboratory 

Perimeter Institute for Theoretical Physics (Canada) 

Sandia National Laboratories 

Santa Fe Institute 

Society for Industrial and Applied Mathematics 

SP Technical Research Institute of Sweden 

US Air Force 

US Army 
108 NIST Applied and Computational Mathematics Division 

Universities 

Abo Akademi University (Finland) 

Aalto University (Finland) 

Albion College 

Boston University 

California Institute of Technology 

California State University 

Concordia University (Canada) 

Clemson University 

Colorado State University 

École Supérieure de Physique et de Chimie Industrielles (France) 

George Mason University 

George Washington University 

Indian Institute of Technology (India) 

Indiana University 

Johns Hopkins University Applied Physics Lab 

Nicolaus Copernicus University (Poland) 

Kettering University 

King Abdullah Univ. of Sci. and Tech. (Saudi Arabia) 

Nancy University (France) 

Nottingham University 

Ohio State University 

Princeton University 

Purdue University 

Royal Institute of Technology (Sweden) 

Saint Mary’s College 

Stanford University 

SUNY Binghamton 

Technische Univ. Bergakademie Freiberg (Germany) 

Tulane University 

Universidade Federal do Rio Grande do Sul (Brasil) 

Universidade Federal do Ceará (Brazil) 

Universidade Federal de Uberlândia (Brazil) 

University of Antwerp (Belgium) 

University of California at Berkeley 

University of the Basque Country (Spain) 

University of California at Irvine 

University of Central Florida – Orlando 

University of Colorado 

University of Delaware 

University of Edinburgh (Scotland) 

University of Hawaii 

University of Maryland 

University of Maryland Baltimore County 

University of Montana 

University of Nebraska – Lincoln 

University of Nevada – Reno 

University of Texas at Arlington 

University of Palermo (Italy) 

University of Utah 

University of Vienna (Austria) 

University of Virginia 

University of Washington 

University of Wisconsin 

Vassar College 

Virginia Tech 

Yale University 
Summary of Activities for Fiscal Year 2010 109

Part V: Appendix 

 Part V 

 Appendix 
110 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2010 111

Staff

ACMD consists of full time permanent staff located at NIST laboratories in Gaithersburg, MD and Boulder, CO. This is supplemented with a variety of faculty appointments, guest researchers, postdoctoral 

appointments, and student appointments. The following list reflects all appointments held during any portion of the reporting period. (*) Denotes staff at the NIST Boulder Laboratory. 

Division Staff 

Ronald Boisvert, Chief, Ph.D. (Computer Science), Purdue University, 1979 

Robin Bickel, Secretary 

Robert Bohn, Ph.D. (Physical Chemistry), University of Virginia, 1991 

Alfred Carasso, Ph.D. (Mathematics), University of Wisconsin, 1968 

Roldan Pozo, Ph.D. (Computer Science), University of Colorado at Boulder, 1991 

Christopher Schanzle, B.S. (Computer Science), University of Maryland Baltimore County, 1989 

Mathematical Analysis and Modeling Group 

Timothy Burns, Leader, Ph.D. (Mathematics), University of New Mexico, 1977 

*Bradley Alpert, Ph.D. (Computer Science), Yale University, 1990 

 Javier Bernal, Ph.D. (Mathematics), Catholic University, 1980 

*Andrew Dienstfrey, Ph.D. (Mathematics), New York University, 1998 

Jeffrey Fong, Ph. D. (Applied Mechanics and Mathematics), Stanford University, 1966 

David Gilsinn, Ph.D. (Mathematics), Georgetown University, 1969 

Fern Hunt, Ph.D. (Mathematics), New York University, 1978 

Raghu Kacker, Ph.D. (Statistics), Iowa State University, 1979 

Anthony Kearsley, Ph.D. (Computational and Applied Mathematics), Rice University, 1996 

Peter Ketcham. M.S. (Mathematics), University of Minnesota, 1997 

Geoffrey McFadden, NIST Fellow, Ph.D. (Mathematics), New York University, 1979 

*Agnes O’Gallagher, M.S. (Applied Mathematics), University of Colorado at Boulder, 1991 

Bert Rust, Ph.D. (Astronomy), University of Illinois at Urbana-Champaign, 1974 

 NRC Postdoctoral Associates 

James Benson, Ph.D. (Mathematics), University of Missouri – Columbia, 2009 

P. Aaron Lott, Ph.D. (Mathematics), University of Maryland, 2008 

 Faculty Appointee (Name, Degree / Home Institution)

Daniel Anderson, Ph.D. / George Mason University 

Saul Gass, Ph.D. / University of Maryland College Park 

Dianne O’Leary, Ph.D. / University of Maryland College Park 

Florian Potra, Ph.D. / University of Maryland Baltimore County 

Guest Researchers (Name, Degree / Home Institution)

Mirit Aladjem, Ph.D. / National Institutes of Health 

Richard Braun, Ph.D. / University of Delaware 

Guillaume Bousquet / ISIMA, Campus de Clermont-Ferrand, France

David Cotrell, Ph.D. / Lawrence Livermore National Laboratory 

*John Gary, Ph.D. / NIST (retired) 

Katharine Gurski, Ph.D. / George Washington University 

Rüdiger Kessel, Ph.D. / Metrodata GmbH, Germany 

Sohyoung Kim, Ph.D. / National Institutes of Health 

Yu (Jeff) Lei, Ph.D. / University of Texas at Arlington 
112 NIST Applied and Computational Mathematics Division 

Bruce Murray, Ph.D. / SUNY Binghampton 

Sita Ramamurti, Ph.D. / Trinity Washington University 

Christoph Witzgall, Ph.D., NIST Scientist Emeritus

Students (Name / Home Institution)

Nathan Jacobson / Hood College 

Mathematical Software Group 

Daniel Lozier, Leader, Ph.D. (Applied Mathematics), University of Maryland, 1979 

Michael Donahue, Ph.D. (Mathematics), Ohio State University, 1991 

Stephen Langer, Ph.D. (Physics), Cornell University, 1989 

Marjorie McClain, M.S. (Mathematics), University of Maryland College Park, 1984 

Bruce Miller, Ph.D. (Physics), University of Texas at Austin, 1983 

William Mitchell, Ph.D. (Computer Science), University of Illinois at Urbana-Champaign, 1988 

Donald Porter, Ph.D. (Electrical Engineering), Washington University, 1996 

Bonita Saunders, Ph.D. (Mathematics), Old Dominion University, 1985 

NRC Postdoctoral Associates 

Valerie Coffman, Ph.D. (Physics), Cornell University, 2006 

Howard Cohl, Ph.D. (Mathematics), University of Auckland, 2010 

Contractors 

Andrew C.E. Reid, Ph.D. (Physics), Queen’s University, Kingston, Ontario, 1994 

Gunay Dogan, Ph.D. (Applied Math and Scientific Computing), University of Maryland, 2006 

Faculty Appointees (Name, Degree / Home Institution)

Frank Olver, D.Sc. / University of Maryland College Park 

G.W. Stewart, Ph.D. / University of Maryland College Park 

Abdou Youssef, Ph.D. / George Washington University 

Guest Researchers (Name, Degree / Home Institution)

Leonard Maximon, Ph.D. / George Washington University 

Qiming Wang / NIST (retired) 

Computing and Communications Theory Group 

Ronald Boisvert, Acting Leader 

 Isabel Beichl, Ph.D. (Mathematics), Cornell University, 1981 

Brian Cloteaux, Ph.D. (Computer Science), New Mexico State University, 2007 

*Scott Glancy, Ph.D. (Physics), University of Notre Dame, 2003 

Barry Hershman, A.A. (Electronics Engineering), Capitol College, 1979 

 *Emanuel Knill, NIST Fellow, Ph.D., (Math), University of Colorado at Boulder, 1991 

 Vladimir Marbukh, Ph.D. (Mathematics) Leningrad Polytechnic University, 1986 

Alan Mink, Ph.D. (Electrical Engineering), University of Maryland, 1980. 

Oliver Slattery, M.S. (Electrical Engineering), Johns Hopkins University, 2008 

Xiao Tang, Ph.D (Physics), Chinese Academy of Sciences, 1985 

NRC Postdoctoral Associates 

 *Bryan Eastin, PhD. (Physics), University of New Mexico, 2007 

Elizabeth Moseman, Ph.D. (Mathematics), Dartmouth College, 2007 

Contractors 

 Lijun Ma, Ph.D. (Optical Engineering), Tsinghua University, 2001 
Summary of Activities for Fiscal Year 2010 113

Faculty Appointees (Name, Degree / Home Institution)

James Lawrence, Ph.D. / George Mason University 

Guest Researchers (Name, Degree / Home Institution)

Stephen Bullock, Ph.D. / IDA Center for Computing Sciences 

Robert Carpenter / NIST (retired) 

Francis Sullivan, Ph.D. / IDA Center for Computing Sciences 

Students (Name, Degree / Home Institution)

Amada Crawford / University of Colorado 

Mark Girard / Trinity University 

*Michael Mullan / University of Colorado at Boulder 

*Adam Meier / University of Colorado at Boulder 

*Yanbao Zhang / University of Colorado at Boulder 

High Performance Computing and Visualization Group 

Judith Terrill, Leader, Ph.D. (Information Technology), George Mason University, 1998 

Yolanda Parker, Office Manager 

William George, Ph.D. (Computer/Computational Science), Clemson University, 1995 

Terence Griffin, B.S. (Mathematics), St. Mary’s College of Maryland, 1987 

John Hagedorn, M.S. (Mathematics), Rutgers University, 1980 

John Kelso, M.S. (Computer Science), George Washington University, 1984 

*Adele Peskin, Ph.D. (Chemical Engineering), University of Colorado at Boulder, 1985 

Sandy Ressler, M.F.A. (Visual Arts), Rutgers University, 1980 

Steven Satterfield, M.S. (Computer Science), North Carolina State University, 1975 

James Sims, Ph.D. (Chemical Physics), Indiana University, 1969 

Faculty Appointees 

Marc Olano / University of Maryland Baltimore County 

Guest Researchers (Name, Degree / Home Institution)

Dennis Backhaus / Fachhochschule Wiesbaden (Germany) 

Styvens Belloge / ISIMA, Campus de Clermont-Ferrand, France 

Pradeep Gaddam / Core Projects and Technologies PVT LTD, India 

Stanley Hagstrom, Ph.D. / Indiana University 

Marlene Hildebrand / Polytech Nice-Sophia, France 

Clement Rey / ISIMA, Campus de Clermont-Ferrand, France 

Jean-Loup Traore / Université Blaise Pascal Clermont Ferrand II, France 

Students (Name / Home Institution)

Luis Catacora / Montgomery Blair High School 

Matthew Du / Thomas Wootton High School 

William Hess / Purdue University 

Kevin Rawlings / Carnegie Mellon University 

Anshu Rustagi / University of Illinois 

Poorva Singal / Franklin W. Olin College of Engineering 

Becky Song / Richard Montgomery High School 
114 NIST Applied and Computational Mathematics Division 

Glossary of Acronyms

AAPT American Association of Physics Teachers 

ACM Association for Computing Machinery 

ACMD NIST/ITL Applied and Computational Mathematics Division 

ACTS Advanced Combinatorial Test Suites (software) 

ACS Advanced Camera for Surveys 

AISI American Iron and Steele Institute 

AMS American Mathematical Society 

APD avalanche photo diode (photon detector) 

APS American Physical Society 

ASME American Society of Mechanical Engineers 

BLAS Basic Linear Algebra Subprograms 

CI configuration interaction 

CiSE Computing in Science & Engineering 

CMM coordinate measuring machine 

CMOS complementary metal-oxide semiconductor 

CNST NIST Center for Nanoscale Science and Technology 

CODATA Committee on Data for Science and Technology 

CPU central processing unit 

CRADA Cooperative Research and Development Agreement 

CT computed tomography 

CVE Common Vulnerabilities and Exposures 

CY calendar year 

DARPA DOD Defense Advanced Research Projects Agency 

DIVERSE Device Independent Virtual Environments ― Reconfigurable, Scalable, Extensible (software) 

DLMF Digital Library of Mathematical Functions 

DNA deoxyribonucleic acid 

DOD U.S. Department of Defense 

DOE U.S. Department of Energy 

DPD dissipative particle dynamics 

EL NIST Engineering Laboratory 

EM electromagnetic 

EM expectation maximization 

EPG error probability per gate 

ETSI European Telecommunications Standards Institute 

FDA Food and Drug Administration 

FDS Fire Dynamics Simulator 

FFT fast Fourier transform 

FMM fast multipole method 

FY fiscal year 

F90gl Fortran 90 interface to OpenGL graphics standard 

GAMS Guide to Available Mathematical Software 

GUI graphical user interface 

HEC high-end computing 

HIM helium ion microscope 

HTML hypertext markup language 

Hy-CI Hylleraas-Configuration Interaction technique 

IDA Institute for Defense Analysis 

IEEE Institute of Electronics and Electrical Engineers 

IETF Internet Engineering Task Force 

IFIP International Federation for Information Processing 

IMS Innovations in Measurement Science 

INCITE Innovative and Novel Computational Impact on Theory and Experiment (DOE Program) 

IR infrared 

ISIMA Institut Supérieur d'Informatique, de Modélisation et de leurs Applications (France) 
Summary of Activities for Fiscal Year 2010 115

IT information technology 

ITL NIST Information Technology Laboratory 

IWG Interagency Working Group 

JAMA Java Matrix package (software) 

LANL Los Alamos National Laboratory 

LAPACK++ software for numerical linear algebra in C++ 

LaTeXML LaTeX to MathML translator 

LTP Live Tables Project 

MAA Mathematical Association of America 

MANET mobile ad-hoc network 

MathML Mathematical Modeling Language (W3C standard) 

MCMC Markov Chain Monte Carlo 

MKM mathematical knowledge management 

MML NIST Material Measurement Laboratory 

MMM magnetism and magnetic materials 

MPI Message Passing Interface 

MRAM magneto-resistive random access memory 

MRI magnetic resonance imaging 

MSN mobile sensor network 

μmag Micromagnetics Activity Group 

NASA National Aeronautics and Space Administration 

NBS National Bureau of Standards 

NCNR NIST National Center for Neutron Research 

NIH National Institutes of Health 

NIR near infrared 

NIST National Institute of Standards and Technology 

NISTIR NIST Internal Report 

NITRD Networking and Information Technology Research and Development 

NRC National Research Council 

NSF National Science Foundation 

NUM network utility maximization 

NUMA non-uniform memory access 

NVD National Vulnerability Database 

NYU New York University 

OOF Object-Oriented Finite Elements (software) 

OOMMF Object-Oriented Micromagnetic Modeling Framework (software) 

OSG Open Scene Graph 

OSPF open shortest path first 

OTF optical transfer function 

OWL Web Ontology Language 

PDE partial differential equation 

PHAML Parallel Hierarchical Adaptive Multi Level (software) 

PML NIST Physical Measurement Laboratory 

PPLN periodically poled lithium niobate 

PREP Professional Research Experience Program 

QD quantum dot 

QDPD quarternion-based dissipative particle dynamics 

QI quality index 

QIS quantum information science 

QKD quantum key distribution 

QPM quasi phase matching 

R&D research and development 

PDE partial differential equation 

REGEN software for modeling of cryocoolers 

SAVG MCSD Scientific Applications and Visualization Group 

SBIR Small Business Innovative Research 

SCAP Security Content Automation Protocol 
116 NIST Applied and Computational Mathematics Division 

SciDAC Scientific Discovery through Advanced Computing (DOE Program) 

SHIP NIST Summer High School Internship Program 

SIAM Society for Industrial and Applied Mathematics 

SIGGRAPH ACM Special Interest Group on Graphics 

SIS sequential importance sampling 

SparseLib++ software for spare linear algebra in C++ 

Spblas sparse basic linear algebra subprograms 

SPIE International Society for Optical Engineering 

STEP NIST Student Temporary Employment Program 

SUNY State University of New York 

SURF Student Undergraduate Research Fellowship 

TES transition-edge sensor 

TIP NIST Technology Innovation Program 

TNT Template Numerical Toolkit (software) 

TRC NIST Thermodynamics Research Center 

TV total variation 

UCLA University of California at Los Angeles 

UMBC University of Maryland Baltimore County 

URL universal resource locator 

VCCTL Virtual Cement and Concrete Testing Laboratory 

VRML virtual reality modeling language 

W3C World Wide Web Consortium 

X3D Extensible 3D 

XML Extensible Markup Language 

ZPE zero-point energy