NISTIR 7994

http://dx.doi.org/10.6028/NIST.IR.7994

Applied and Computational

Mathematics Division

Summary of Activities for Fiscal Year 2013

 

NISTIR 7994

Applied and Computational

Mathematics Division

Summary of Activities for Fiscal Year 2013

Ronald F. Boisvert, Editor

Applied and Computational Mathematics Division

Information Technology Laboratory

http://dx.doi.org/10.6028/NIST.IR.7994

March 2014

U.S. Department of Commerce 

Penny Pritzker, Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director
ii NIST Applied and Computational Mathematics Division

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 five 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 2012

through December 2013.

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: Slice along the z=0 plane of the fourth wave function characterizing the interaction 

of two nonreactive polar RbCs molecules. Results computed using the system PHAML developed by the 

NIST Applied and Computational Mathematics Division. See page 64.

Acknowledgements: Thanks to Catherine Graham and Ginger White for assisting in the compilation of

Parts III and IV of this document.

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 2013 iii

Contents

PART I: OVERVIEW...................................................................................................................................................... 1

Introduction............................................................................................................................................................ 3

Highlights................................................................................................................................................................ 5

Technical Accomplishments ................................................................................................................................ 5

Technology Transfer and Professional Activities................................................................................................ 8

Staff News............................................................................................................................................................ 9

Recognition........................................................................................................................................................ 14

PART II: FEATURES................................................................................................................................................... 15

Approximating the Ising Partition Function ..................................................................................................... 17

Compensating Operators and Stable Time Marching in Ill-Posed Nonlinear Evolution Equations............ 19

Single Photon Conversion Technology: Research to Commercialization ....................................................... 22

Analysis for Dynamic Metrology ........................................................................................................................ 26

A Framework for Reproducible Latent Fingerprint Enhancements............................................................... 29

PART III: PROJECT SUMMARIES ............................................................................................................................... 33

Mathematics of Metrology .................................................................................................................................. 35

Compensating Operators and Stable Time Marching in Ill-Posed Nonlinear Evolution Equations................. 35

Analysis for Dynamic Metrology....................................................................................................................... 35

A Framework for Reproducible Latent Fingerprint Enhancements.................................................................. 35

Improved Time Delay Estimation Method in the Frequency Domain ............................................................... 35

Applied Hierarchical Control............................................................................................................................ 36

Molecular Movies: Imaging Femtosecond Motion during Electrochemical Transitions.................................. 37

Stochastic Simulation in Chemical Spectroscopy.............................................................................................. 38

Computational Tools for Shape Measurement and Analysis............................................................................. 39

Computation of Shape Geodesics...................................................................................................................... 40

Traceable Simulation of Magnetic Resonance Imaging .................................................................................... 41

Modeling and Optimization in Cryobiology ...................................................................................................... 41

Equilibrium and Stability of Drops on a Conical Substrate .............................................................................. 42

Diffuse Interface Model Incorporating Interfacial Properties.......................................................................... 43

Spectral-Galerkin Scheme to Study Ferroelectric Liquid Crystal Properties ................................................... 44

Modeling Magnetic Fusion................................................................................................................................ 46

Development of a New Solver for HVAC Simulation ........................................................................................ 46

Sustainable Design of Reinforced Concrete Structures..................................................................................... 48

Modeling with Uncertainty Estimation of a Thickness-Shear MEMS Resonator.............................................. 48

Using Quadratic Functions over Lines in Evolutionary Optimization .............................................................. 49

Separating Signal from Noise via the SVD........................................................................................................ 50

The Metrology of Supernova Light Curves........................................................................................................ 50

Sparse Low-rank Nonnegative Approximation of Interval Matrices................................................................. 51

Advanced Manufacturing.................................................................................................................................... 52

Rheology of Dense Suspensions ........................................................................................................................ 52
iv NIST Applied and Computational Mathematics Division

Micromagnetic Modeling...................................................................................................................................52

OOF: Finite Element Modeling of Material Microstructures............................................................................53

Solving the Diffusion Equation in Microstructures............................................................................................54

Moving Grain Boundary Grooves under Stress.................................................................................................54

Morphological Stability .....................................................................................................................................55

Inverse Method for Estimating Shear Stress in Machining................................................................................55

Model Selection for Fracture and Fatigue Failure Data of Engineering Materials..........................................56

Structural Design Allowables for Composites...................................................................................................57

High Performance Computing and Visualization..............................................................................................59

A Dynamic Computational Phantom for RF Propagation in Body Area Networks...........................................59

Rheology of Dense Suspensions.........................................................................................................................59

Modeling and Visualization of Cement Paste Hydration and Microstructure Development.............................61

High Precision Calculations of Fundamental Properties of Few-Electron Atomic Systems.............................62

Nano-structures, Nano-optics, and Controlling Exciton Fine Structure ...........................................................63

Parallel Adaptive Refinement and Multigrid Finite Element Methods..............................................................64

Texture Compression Evaluation and Optimization ..........................................................................................65

Declarative 3D Graphics...................................................................................................................................66

Optical Characterization of Immersive 3D Displays.........................................................................................67

Visualization for Measurement Science for Complex Information Systems.......................................................68

Mathematical Knowledge Management.............................................................................................................70

Digital Library of Mathematical Functions.......................................................................................................70

Mathematical Knowledge Representation .........................................................................................................71

Visualization of Complex Functions Data .........................................................................................................72

Standard Reference Tables on Demand.............................................................................................................74

Digital Repository of Mathematical Formulae ..................................................................................................75

Eigenfunction Expansions for Special Functions and Orthogonal Polynomials ...............................................77

Quantum Information..........................................................................................................................................80

Single Photon Conversion Technology: Research to Commercialization .........................................................80

Quantum Information Science ...........................................................................................................................80

Quantum Computing Benchmarks .....................................................................................................................81

Quantum State Estimation Theory and Experiment...........................................................................................82

Random Number Generation based on Bell Inequality Violation......................................................................83

Tamper-Resistant Cryptographic Devices based on Quantum Mechanics........................................................84

Post-Quantum Cryptography.............................................................................................................................85

High-Speed Low Density Parity Codes for Quantum Key Distribution.............................................................85

Simulating Quantum Field Theories on Quantum Computers...........................................................................86

Circuit Obfuscation and Synthesis.....................................................................................................................87

Quantum Adiabatic Optimization ......................................................................................................................88

Foundations of Measurement Science for Information Systems......................................................................89

Systemic Risks/Benefits of Interconnectivity ......................................................................................................89

Examining the Gromov Curvature of Networks in Time....................................................................................90

An Improved Feedback Vertex Set Heuristic .....................................................................................................90

Broadcast and Spread of Information in Complex Networks.............................................................................91

An Algebraic Formulation for the Analysis and Visualization of Network Graphs...........................................92
Summary of Activities for Fiscal Year 2013 v

Security Risk Analysis of Enterprise Networks using Attack Graphs................................................................ 93

Combinatorial Testing....................................................................................................................................... 94

Coverage and Energy Optimization in Mobile Sensor Networks ...................................................................... 95

A Dynamic Computational Phantom for RF Propagation in Body Area Networks .......................................... 96

Evaluation and Mitigation Strategies for Cross-Interference between Multiple Body Area Networks............. 97

PART IV: ACTIVITY DATA .................................................................................................................................... 99

Publications ........................................................................................................................................................ 101

Appeared ......................................................................................................................................................... 101

Refereed Journals..................................................................................................................................... 101

Journal of Research of NIST ................................................................................................................... 102

Books.......................................................................................................................................................... 102

Conference Proceedings........................................................................................................................... 102

Technical Magazine Articles.................................................................................................................... 105

Technical Reports..................................................................................................................................... 105

Accepted .......................................................................................................................................................... 105

In Review ........................................................................................................................................................ 106

Invention Disclosures..................................................................................................................................... 106

Presentations ...................................................................................................................................................... 107

Invited Talks ................................................................................................................................................... 107

Conference Presentations............................................................................................................................... 110

Web Services....................................................................................................................................................... 112

Software Released .............................................................................................................................................. 112

Conferences, Minisymposia, Lecture Series, Courses..................................................................................... 112

MCSD Seminar Series.................................................................................................................................... 112

Courses/Shortcourses Taught ........................................................................................................................ 113

Conference Organization ............................................................................................................................... 113

Other Professional Activities............................................................................................................................. 115

Internal ........................................................................................................................................................... 115

External .......................................................................................................................................................... 115

Grants Awarded................................................................................................................................................. 117

External Contacts............................................................................................................................................... 117

PART V: APPENDIX .................................................................................................................................................. 119

Staff ..................................................................................................................................................................... 121

Glossary of Acronyms........................................................................................................................................ 124
vi NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2013 1

Part I: Overview

 Part I

Overview
2 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2013 3

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 and user facilities 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 ACMD 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 groups and external organizations 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 (Michael Donahue, 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; Isabel Beichl and Xiao 

Tang, Project Leaders)

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. 

Project descriptions in Section III of this document are organized according to these broad themes. 
4 NIST Applied and Computational Mathematics Division

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 measured

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 to critical measurement science applications. 

Advanced Manufacturing. Delivering technical support 

to the nation’s manufacturing industries as they strive to 

out-innovate and out-perform the international competition has always been a top priority at NIST. This has also 

emerged as a major White House priority in recent 

years, in which NIST is playing an increasingly central role. 

Mathematical modeling, computational simulation, and 

data analytics are key enablers of emerging manufacturing 

technologies. This is most clearly evident in the Materials 

Genome Initiative, an interagency program with the goal 

of significantly reducing the time from discovery to commercial deployment of new materials through the use of 

modeling, simulation, and informatics. ACMD’s role in 

advanced manufacturing centers on the development and 

assessment of modeling and simulation tools, with emphasis on uncertainty quantification, as well as support of 

NIST Laboratory efforts in such areas as nanomanufacturing, smart manufacturing, and materials modeling.

High Performance Computing and Visualization.

Computational capability is advancing rapidly, with the 

result 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 scientists rarely have. In addition, the 

hardware landscape is changing rapidly, so new algorithmic techniques must constantly be developed. We are 

developing and applying such facilities and expertise for 

application to NIST problems. Computations and laboratory experiments often 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.

Mathematical Knowledge Management We work 

with researchers in academia and industry to develop 

technologies, tools, and standards for representation, 

exchange, and use of mathematical data. Of particular 

concern are semantic-based representations which can 

provide the basis for interoperability of mathematical 

information processing systems. We apply this to the 

development and dissemination of reference data for 

applied mathematics. The centerpiece of this effort is the 

Digital Library of Mathematical Functions, a freely available interactive and richly linked online resource, providing 

essential information on the properties of the special 

functions of applied mathematics, the foundation of mathematical modeling in all of science and engineering.

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 engage in (a) theoretical studies to understand the 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. 

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 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 stability of our critical infrastructure is simply unknown. Measurement science has long provided a basis 

for the understanding and control of physical systems. 

Such deep understanding and insight is lacking for complex information systems. We seek to develop the 

mathematical foundations needed for a true measurement 

science for complex networked information systems.
Summary of Activities for Fiscal Year 2013 5

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 notable technical accomplishments with significant impact. Further details are provided in Part II 

(Features) and Part III (Project Summaries).

Mathematics of Metrology. An important focus of ACMD is the development of mathematical 

methods and tools of use in metrology, and their application to modeling and analysis problems at NIST. 

Our work in this area is very broad. The applications we considered this year range from the interpretation 

of data from measurements of femtosecond-scale electrochemical transitions to supernova light, and the 

modeling of phenomena from liquid crystals to building ventilation systems. In the process we develop 

fundamental mathematical tools such as novel time-delay estimation methods, stable time-marching 

methods for ill-posed nonlinear evolution equations, and special-purpose optimization methods.

Among the new metrological challenges that we are working on include dynamic metrology, the 

measurement of time varying quantities, which is requiring specialized approaches to signal analysis. 

While our efforts are focused on the measurement of time-varying waveforms for communications applications, the same mathematical issues are now turning up in the measurement of time-varying pressure, 

force, and torque (see page 26). Another novel measurand is shape, which is of interest in characterizing, 

for example, cell colonies in microscope images, cancer indicators in medical imagery, or microstructures 

in material micrographs. We are cooperating with the ITL Statistical Engineering Division in a NIST Innovations in Measurement Science (IMS) project to develop techniques and tools for shape metrology

with application to NIST problems (see pages 39 and 40).

Another growth area for ACMD is metrology for modeling and simulation. We seek to develop 

techniques and tools for verification, validation, and uncertainty analysis that enables a quantitative understanding of the uncertainty in results produced by computational simulation. Reference problems are 

an important tool for verification, enabling intercomparision of modeling codes. We continue to develop 

new such problems for the field of micromagnetics (see page 52), and this year we unveiled an online repository of reference problems useful for comparison of adaptive grid solvers for partial differential 

equations (see page 64). An important part of physical metrology is the concept of traceability of a measurement to a reference standard. This year we initiated a project to create SI1

-traceable simulations for 

magnetic resonance imaging (see page 41).

Advanced Manufacturing. NIST work in measurements, standards and technologies are an important enabler of innovation in the manufacturing sector. In the last few years NIST has been 

participating in the interagency Materials Genome Initiative (MGI) within the President’s Advanced 

Manufacturing Partnership unveiled in 2011. The MGI seeks to promote the widespread use of modeling 

and simulation and data informatics to greatly reduce the time and cost from materials discovery and deployment. ITL works closely with the NIST Material Measurement Laboratory to carry out NIST’s work 

under the MGI. ACMD’s role is principally in two areas: the development and assessment of modeling 

and simulation software, and the development of techniques and tools for the quantification of uncertainty 

in materials models and simulations. ACMD’s OOMMF (page 52) and OOF (page 53) projects are partially supported by MGI funding, for example. In addition, we have developed alliances with several 

external partners to advance Division engagement with the MGI. Researchers at the University of California at San Diego are developing a graphical processing unit (GPU) version of OOMMF to enable costeffective high resolution micromagnetics simulations. The Institute of Mathematics and Its Applications 

(IMA) at the University of Minnesota has undertaken a NIST-supported project on uncertainty quantifica-

 

1

International System of Units, see http://physics.nist.gov/cuu/Units/
6 NIST Applied and Computational Mathematics Division

tion (UQ) in molecular dynamics simulations of resins used in composite materials. As part of that work, 

the IMA has engaged a postdoc who is spending part of his tenure at Boeing, where he is learning industrial applications first-hand. On December 16-17, 2013, the IMA hosted a NIST-supported workshop entientitled Uncertainty Quantification in Materials Modeling2

; some 30 researchers representing both the 

UQ and materials modeling community attended. Follow-on is planned. 

Finally, on December 3, 2013 NIST announced3that it has selected a consortium led by Northwestern University to establish a new NIST-sponsored center of excellence for advanced materials 

research. The new Center for Hierarchical Materials Design (CHiMaD), whose other partners include the 

University of Chicago and Argonne National Laboratory, will be funded in part by a $25 million award 

from NIST over five years. We anticipate many opportunities to collaborate with CHiMaD researchers in 

the next few years.

High Performance Computing and Visualization. ACMD provides leadership within NIST in 

the application of high performance computers to the solution of metrology problems of importance to the 

NIST labs. A good example is our work in the modeling of the rheology of dense suspensions, in which 

our simulations, run on the Blue Gene/Q system at the Argonne National Laboratory Leadership Computing Facility, are being used to develop novel designs for rheometers as well as standard reference 

materials used to calibrate them (see page 59). 

ACMD continues to set new accuracy records for computations of non-relativistic ground state 

energies of few electron atomic systems. Fundamental understanding of atomic systems is necessary for a 

wide variety of applications including material design, drug discovery, and providing a testbed for quantum theory. Despite their small size, atomic systems present enormous challenges for scientists hoping to 

compute their properties from first principles. These difficulties have resulted in much of our computational infrastructure being predicated on simplifying assumptions. In ACMD we have taken a different 

approach. For several years we have invested in developing the foundational analytical and numerical 

machinery to solve the few-electron Schrödinger system with no approximations other than the truncation 

of infinite series. This investment has resulted in several extreme-accuracy firsts in the world of computational atomistics. In FY 2013, ACMD researchers computed the ground-state energy of the four-electron 

Beryllium atom to eight digits of accuracy using an expansion with 70000 unknowns to represent the solution. By extending these results we have been able to perform the most accurate computations ever done 

– eight digits of accuracy – of the entire isoelectronic series up through atomic number 113. The fourelectron case is particularly exciting as, due to the ACMD formalism, higher electron systems will present 

no new analytical difficulties. These results are being prepared for publication (see page 62).

Visual-based analysis is an indispensable tool for the interpretation of both large-scale simulation 

results and massive collections of measured data. For some time we have been working to develop 3D 

immersive visualization environments into virtual measurement laboratories. This requires a deep understanding of the uncertainty introduced by the visualization system itself. To this end we have undertaken a 

project with the NIST Physical Measurement Laboratory to perform optical characterization of immersive 

3D displays (see page 67).

Mathematical Knowledge Management. In a world where technical communication is increasingly 

done online, technologies, tools, and standards for the representation, exchange and use of mathematical 

data are critical. The current state-of-the-art is less than ideal, and we are trying to improve it. An important aspect is the generation of content that conforms to MathML, the W3C standard for the 

representation of math on the Web. LaTeXML, developed by ACMD, has become a popular tool for converting documents coded in the popular mathematical typesetting system LaTeX to MathML (see page 

71). This is a surprisingly challenging problem, for which ACMD has developed considerable expertise.

At NIST, the main application for LaTeXML has been the generation of content for the NIST 

Digital Library of Mathematical Functions (DLMF), an online reference work on the properties of the 

special functions of applied mathematics, which was released in 2010. Already a popular online resource, 

 

2

http://www.ima.umn.edu/2013-2014/SW12.16-17.13/?event_id=SW12.16-17.13

3

http://www.nist.gov/mml/coe-120313.cfm
Summary of Activities for Fiscal Year 2013 7

the DLMF is being actively maintained and continues to be developed. This year, for example, all of the 

interactive 3D visualizations of mathematical functions in the DLMF have been converted to WebGL, a 

JavaScript API for rendering interactive 3D graphics objects in a web browser without the use of a plugin 

(see page 72). The new visualizations will be released soon. Another capability under active development 

is a tool for generating tables on demand with carefully characterized uncertainty (see page 74). A major 

blow was dealt to the DLMF project this year with the passing of its esteemed Mathematics Editor, Frank 

W. J. Olver (see page 9). Considerable work has gone into the development of plans to ensure continued 

strong support for the project (see page 70).

Quantum Information. Our work in quantum information science is focused in three main areas: (a) 

theoretical understanding how quantum resources can be used to greatly increase our ability to perform 

information processing tasks, (b) techniques for characterizing the results of quantum-based measurements, e.g., quantum state tomography and quantum computer benchmarking, and (c) demonstration and 

characterization of systems for quantum communications. 

This year ACMD theorists developed new and effective analysis methods for determining the extent to which experiments violate classicality assumptions, thus verifying fundamental notions of 

quantum theory (see page 80). Such Bell tests are still extraordinarily difficult to perform; most require 

unwanted assumptions (“loopholes”) that cast doubt on their validity. ACMD is working with the NIST 

Physical Measurement Laboratory on a NIST Innovations in Measurement Science project, which will 

attempt to close such loopholes. Entangled photons violating the Bell test, which would certify that no 

one in the universe could have known their state before measurement, will be used as a physical source of 

randomness, ultimately feeding the NIST Random Number Beacon under development by the ITL Computer Security Division (see page 83). 

In another effort, we have developed new insight in the use of quantum mechanics to construct an 

important class of tamper-resistant devices called one-time memories. Such memories represent an important primitive that enables powerful applications in computer security, such as one-time programs. We 

find that one-time memories cannot exist in a world that is fully classical or fully quantum; but, surprisingly, one-time memories can be built in a world that is partly quantum (see page 84).

The need for reliable and efficient single photon detectors suitable for application in longdistance quantum communications has led ACMD scientists to create and improve single photon frequency upconversion technology. ITL is now a world leader in the development and application of this 

technique, as evidenced by the publication of a survey of the group’s work over the past five years in the 

highly cited journal Physics Reports. The team has also been successful in working to transfer ACMDdeveloped technology to small businesses through the NIST Small Business Innovative Research (SBIR)

Program. The team’s pioneering work is also providing the basis for a new initiative at the Defense Advanced Research Projects Agency (DARPA) (see page 22).

Foundations of Measurement Science for Information Systems. Abstract networks, also 

known in mathematics as graphs, provide an important basis for mathematical models in many fields, including computer science (information and software), engineering (the Internet and the power grid),

biology (protein interactions and food webs), and the social sciences (social networks). In ACMD, we are 

studying metrics for characterizing the structure of large networks, with the aim to understand how structure influences dynamics of processes operating on networks. This year our work in the development of 

computational algorithms for network problems yielded significant results for the study of fundamental 

models in physics. Using insights from combinatorics and graph theory we developed a completely new, 

and highly efficient, method for approximating the partition function of the Ising model (see page 17). 

While originally developed as a model of the statistical mechanics of magnetic systems, many difficult 

computational problems in material science, bioscience, and computer science can be formulated as special instances of the Ising model. 

For the last three years ACMD has had a collaboration with Bell Labs to study the geometrical 

properties of large-scale networks. The third of a series of workshops on this topic was held on October 
8 NIST Applied and Computational Mathematics Division

25, 2013. The Bell Labs – NIST Workshop on Large-scale Networks4, which took place in Murray Hill, 

NJ, had 28 participants (8 from NIST). Discussion topics included the measurement of key geometrical 

properties (e.g., dimension and curvature), characteristics of flow influenced by such features, and effective computation and approximation methods for such problems.

This year we forged a new alliance with the Santa Fe Institute (SFI) to help deepen our connection to the complex systems research community. With funding provided from a NIST grant, the SFI will 

be holding a series of workshops in the general areas of network science, biology-inspired computing, and 

computer security. The first such workshop, Structure, Statistical Inference, and Dynamics in Networks: 

From Graphs to Rich Data5, which was held on May 6-9, 2013 in Santa Fe, attracted 44 participants (5 

from ACMD). The second, Deep Computation in Statistical Physics6, held on August 8-10, 2013, had 22 

participants (3 from ACMD).

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 34 articles appearing in peer-reviewed journals and 44 papers in conference 

proceedings. Thirteen additional papers have been accepted for publication, while 22 others are undergoing review. Division staff members gave 66 invited technical talks and presented 49 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 (CY) 2013, the division web 

server satisfied more than 4.6 million requests for pages from more than 382,000 distinct hosts. In total, 

there have been more than 354 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 150 such papers published 

in CY 2013 alone (more than 1,590 such papers have been identified since 2001). 

Members of the Division are also active in professional circles. Staff members hold a total of 16 editorial positions in peer-reviewed journals. This year Isabel Beichl completed her second term as Editorin-Chief of the IEEE/AIP publication Computing in Science & Engineering. ACMD faculty appointee 

Dianne O’Leary serves at Editor-in-Chief of the SIAM Journal on Matrix Analysis and Applications. Staff 

members are also active in conference organization, serving on 25 organizing/steering/program committees. 

 

4

http://ect.bell-labs.com/who/iis/research/workshops/NIST-BellLabsWorkshopOct25-2013x.pdf

5

http://www.santafe.edu/gevent/detail/science/1175/

6

http://www.santafe.edu/gevent/detail/science/1176/

Table 1. Approximate number of downloads of selected division software packages during CY 2013

Package Description Downloads

JAMA Linear algebra in Java 23 700

OOMMF Modeling of nano-magnetic phenomena 11 000

TNT Linear algebra using C++ templates 2 800

OOF Modeling materials with complex microstructure 1 100

Ngraph Basic graph algorithms; web crawler 900

spblas Sparse basic linear algebra components 800

f90gl Fortran 90 interface to OpenGL graphics 675

PHAML Parallel adaptive solution of partial differential equations 360
Summary of Activities for Fiscal Year 2013 9

Service within professional societies is also prevalent among our staff. For example, Ronald Boisvert completed his third (and final) term as Co-Chair of the Publications Board of the Association for 

Computing Machinery (ACM). In this role he served as a member of the ACM Council, the association’s 

board of directors. In addition, staff members serve on committees of the IEEE Computer Society and the 

Mathematical Association of America. Staff members are also active in a variety of working groups. For 

example, Ronald Boisvert and Andrew Dienstfrey serve as members 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, Bruce Miller is a member of W3C’s Math Working Group, Kamran Sayrafian is a 

member of the IEEE 802.15 Working Group on Wireless Personal Area Networks, Vladimir Marbukh is a 

member of the Network Complexity Research Group of the Internet Research Task Force (IRTF), and 

Sandy Ressler is a member of the Declarative 3D for the Web Architecture Community 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. Robert Bohn is CoChair of the NITRD Program’s Faster Administration of Science and Technology Education and Research (FASTER) Community of Practice.

For further details, see Section IV, Activity Data.

Staff News

The past year saw many staffing changes. Among these are the following.

Arrivals

Sean Colbert-Kelly began his term as a NIST/NRC Postdoctoral Associate in ACMD in January 2013. 

Colbert-Kelly received a Ph.D. in Mathematics from Purdue University in 2012. At Purdue he undertook 

a theoretical and computational analysis of a Ginzburg-Landau type energy for Smectic C* Liquid Crystals. At NIST he will be continuing this work with Geoffrey McFadden studying dynamical properties of 

vortices.

Ginger White joined ACMD in February 2013 as Group Secretary for the Mathematical Modeling and 

Analysis and Mathematical Software Groups. White comes to ACMD from the National Library of Medicine at the NIH where she served as a library technician. She has had previous experience as a technical 

writer with the USDA and as a broadcast journalist with the US Army.

Formerly a senior research scientist at the Courant Institute of Mathematical Sciences at New York University, Zydrunas Gimbutas joined ACMD in Boulder in July 2013. Gimbutas, who received a Ph.D. in 

Applied Mathematics from Yale University in 1999, has more than 15 years of experience designing, analyzing and implementing fast numerical algorithms of applied analysis for computational acoustics and 

electromagnetics, quadratures for singular functions, and scientific computing. Before his appointment at 

Courant, Gimbutas served for five years as a research scientist at MadMax Optics, Inc.

In July 2013 Michael Cromer, a postdoctoral scholar at the University of California at Santa Barbara,

joined ACMD as a NIST/NRC Postdoctoral Associate. Cromer received a Ph.D. in Applied Mathematics 

from the University of Delaware in 2011, where he wrote a thesis on models of wormlike micellar mixtures. At NIST Cromer will work with Geoffrey McFadden on the modeling and simulation of shear 

thickening fluids.

Richard La, Associate Professor of Electrical and Computer Engineering and the Institute for Systems 

Research at the University of Maryland, began a Guest Researcher appointment in ACMD in July 2013. 

La, who received a Ph.D. in EECS from the University of California at Berkeley in 2000, will be conducting research in network science, with applications to computer security.

Paulina Kuo joined ACMD in September 2013 after spending two years with ACMD as a guest researcher supported by the Joint Quantum Institute. Kuo received undergraduate degrees in Physics and 

Materials Science from MIT. In 2008 she received a PhD in Applied Physics from Stanford University. 

She also served as a NIST/NRC Postdoctoral Associate in the NIST Physical Measurement Laboratory. 
10 NIST Applied and Computational Mathematics Division

An expert in nonlinear optics, Kuo will be contributing to the Division's experimental efforts in quantum 

communications.

Michael Mascagni, Professor of Computer Science at Florida State University, began a Faculty Appointment in ACMD in September 2013. Mascagni received Ph.D. in Applied Mathematics from the 

Courant Institute at NYU in 1987, and has held appointments at NIH, the Supercomputing Research Center and the University of Southern Mississippi. At FSU he holds joint appointments in the Mathematics 

and the Scientific Computing Departments. His research interests include computational science, numerical analysis, Monte Carlo methods, and random number generation. At NIST he will be contributing to 

efforts in materials modeling and parallel computing.

Yvonne Kemper began a stay in ACMD as a NIST/NRC Postdoctoral Associate in December 2013. She 

received a Ph.D. in mathematics from the University of California at Davis in 2013, where she wrote a 

thesis on structural measurements of simplicial complexes and convex polytopes. At NIST she will be 

working with Isabel Beichl on approximating flow and chromatic polynomials of big data networks. 

Departures

Agnes (Abbie) O’Gallagher of ACMD retired in November 2012 after 27 years of service at the NIST 

Boulder Labs. During her career at NIST O’Gallagher provided support for ACMD efforts in cryocooler

modeling, DNA sequence alignment, and CT scanner modeling. She was also an active member of ITL's 

Diversity Committee, where she organized the very successful ITL Diversity Book Club.

Adele Peskin, a long-standing member of ACMD’s High Performance Computing and Visualization 

Group in Boulder, has transferred to ITL’s Software and Systems Division. There she will continue work, 

started during her tenure in ACMD, on the analysis of imagery from biology and medicine.

Asha Nurse completed her term in ACMD as an ARRA Postdoctoral Fellow in February 2013. At NIST 

she worked with Geoffrey McFadden on an analysis of bubble motion and size variation during thermal 

migration with phase change, as well as the equilibrium and stability of drops on a conical substrate with 

application to tissue engineering. She continues her affiliation with NIST as a guest researcher.

Yong-Su Kim, who joined ACMD in March 2012 as a guest researcher from the Pohang University of 

Science and Technology in South Korea, returned to Korea in March 2013. An expert in quantum optics, 

Kim contributed his expertise to ITL’s quantum communications project in the area of frequency upconversion technology.

Elizabeth Moseman, former NIST/NRC Postdoctoral Associate, departed NIST for a permanent position 

at the National Security Agency in the spring of 2013. At NIST, Moseman worked on algorithms for 

computing properties of large-scale graphs.

Amada Streib and Noah Streib, NIST/NRC Postdoctoral Associates in ACMD departed in August 2013, 

accepting positions at the Institute for Defense Analysis’ Center for Computing Sciences in Bowie, MD. 

The Streibs each received Ph.D.’s in the Algorithms, Combinatorics and Optimization program at Georgia 

Tech. At NIST they worked with Isabel Beichl on novel graph theoretic methods for efficient simulation 

of the Ising model of computational physics. 

Ismet Sahin completed his term in ACMD as an ARRA Senior Fellow in April 2013. At NIST Sahin 

worked with Anthony Kearsley on evolutionary optimization algorithms, as well as applications to waveform time delay estimation algorithms that are used in seismology, radar, sonar, and biomedical science.

Daniel Kaslovsky, recipient of an NSF Postdoctoral Fellowship for Transformative Computational Science using CyberInfrastructure, who was carrying out his research in ACMD in Boulder, accepted a 

permanent position at Seagate Technology in Longmont, Colorado. 
Summary of Activities for Fiscal Year 2013 11

Students

During FY 2013 ACMD was able to support the work of 27 student interns, including 16 graduate students, eight undergraduates, and three high school students. See Table 2 for a complete listing.

ACMD staff members are quite active in the education of graduate students, serving both as Ph.D. 

advisers and as members of thesis committees. For a complete list, see page 116.

Three graduate students in physics at Colorado University in Boulder who carried out their research 

at the NIST Boulder Labs under the supervision of Manny Knill of ACMD received their Ph.D. degrees 

in 2013. Michael Mullan, who completed a thesis entitled Quantum Algorithms for Atomic Clocks, accepted a position with Northup Grumman. Following his thesis work on Randomized Benchmarking of 

Clifford Operators, Adam Meier moved on to the Georgia Tech Research Institute. Yanbao Zhang has 

relocated to Waterloo’s Institute for Quantum Computation following his work on Analysis of Tests of 

Local Realism.

Table 2. Student Interns in ACMD

Name Institution Type Mentor Project 

Philip Lenzini Univ. of Colorado G PREP E. Knill Statistics for quantum information

Adam Meier Univ. of Colorado G PREP E. Knill Quantum computer simulation

Rebecca Mitchell Univ. of Colorado G PREP B. Alpert Numerical linear algebra

Michael Mullan Univ. of Colorado G PREP E. Knill Quantum computing theory

James Van Meter Univ. of Colorado G PREP E. Knill Quantum measurement of space-time

Yanbao Zhang Univ. of Colorado G PREP E. Knill Tests of local realism

Hamza Attak ISIMA (France) G FGR J. Terrill Visualization algorithms

Martina Barbi U. Bologna (Italy) G FGR K. Sayrafian RF propagation in body-area networks

Styvens Belloge ISIMA (France) G FGR J. Terrill Visualization in computer security

Yannick Congo ISIMA (France) G FGR S. Langer Finite element analysis of microstructure

Deyan Ginev Jacobs U. (Germany) G FGR B. Miller Semantics of mathematical documents

Gregory Rami ISIMA (France) G FGR J. Terrill Impact of fire on building structures

Earl Bellinger SUNY Oswego G NPSC J. Terrill Data mining

Bryan Gard Louisiana State Univ. G NPSC E. Knill Quantum measurement analysis

Adam Keith Univ. of Colorado G NSF E. Knill Quantum measurement analysis

Michael Baume Univ. of Maryland G DGR S. Jordan Analysis of quantum algorithms

Rehab Al Ammary Montgomery College U SURF A. Gueye Identifying critical links in networks

Michael Baeder Harvey Mudd College U SURF H. Cohl Hypergeometric orthogonal polynomials

Kevin Keller Univ. of Maryland U SURF J. Terrill Analysis of early-age cement hydration

Andrea Rommal Muhlenburg College U SURF A. Mink Quantum randomness amplification

Rebekah Wheatley Johns Hopkins Univ. U SURF H. Cohl Functions in hyperspherical geometry

Janelle Williams Virginia State Univ. U SURF H. Cohl Web resources for special functions

Luis Catacora Univ. of Maryland U DGR J. Terrill Immersive visualization for HydratiCA 

Ajay Kannan Dartmouth College U Vol. S. Langer Image processing

Philbert Hwang Poolesville H. S. HS SHIP H. Cohl Hypergeometric orthogonal polynomials

Amolak Nagi Walt Whitman H. S. HS SHIP S. Ressler Web-based visualizations

Alicia Ouyang River Hill H. S. HS Vol. J. Terrill Information visualization using D3

 Legend G Graduate student PREP Professional Research Experience Program (Boulder)

U Undergraduate FGR Foreign Guest Researcher

HS High school NPSC National Physical Sciences Consortium Fellow

NSF National Science Foundation Fellow

DGR Domestic Guest Researcher

SURF Summer Undergraduate Research Fellowship

SHIP Summer High school Internship Program

Vol. Volunteer
12 NIST Applied and Computational Mathematics Division

Passings

Saul Gass, a consultant to NIST from 1976 to 2013—most recently a faculty appointee in ACMD—died 

of cancer on March 17, 2013 at the age of 87. A professor emeritus in the University of Maryland’s business school, he was an internationally respected expert in operations research (OR), a mathematics-based 

discipline that uses advanced analytical methods to help organizations make better decisions. 

Gass began his career in operations research in the field’s early years, working in the Pentagon in 

the early 1950s for George Dantzig. Dantzig was the principal developer of the simplex algorithm for linear programming, which is the cornerstone of the optimization methods that are among the most 

important tools in operations research. In 1958, Gass published the first-ever textbook on linear programming, a book that is currently in its fifth edition. 

Gass became one of the field’s leading practitioners, serving as president of the Operations Research Society of America, and working as a senior manager at IBM contributing to the space program’s 

Project Mercury. In the latter half of his career, he became a senior statesman for OR, writing and editing 

books chronicling the history of the field. “Everybody in the field of operations research knew Saul 

Gass,” said Ronald Boisvert, chief of ACMD. 

“Saul was one of the very last remaining grand pioneers of the relatively new field of operations research,” says Christoph Witzgall, a NIST researcher in the field of operations research from 1973 to 2003. 

“Beyond Saul’s impressive technical achievements, his role as a mentor, communicator, promoter, and 

organizer par excellence will be sorely missed.”

“It was a real privilege for us to have such a pioneer in our midst,” says Boisvert. “His encyclopedic knowledge of operations research was a great asset. Often when we had a ‘new’ and exciting problem 

to work on, we discovered that Saul had already made fundamental 

contributions to solving the problem years before. His advice was 

always thoughtful and helpful.”

The thread that runs through Gass’ NIST work was his evaluation of the ability of mathematical models to correctly guide 

critical decisions, adds Boisvert.

Although Gass had utilized NIST’s prototype computers in 

the 1950s while carrying out Air Force-funded projects, he first became a consultant to NIST in 1976 in order to aid the Operations 

Research Division of the Center for Applied Mathematics. In the 

early 1980s, Gass was offered the position of chief of NIST’s Operations Research Division, but he decided to stick with his full-time 

position teaching at the University of Maryland.

His work at NIST included evaluating oil and gas supply 

models for the Department of Energy, helping the Federal Emergency Management Agency prepare for national emergencies such 

as earthquakes and wars, improving the accuracy of 3-D coordinate 

measurement machines, and studying how the structure of computer 

networks and power grids contributes to their reliability.

Up until fall 2012, Gass continued to work at NIST one day 

per week, and his advanced age didn’t seem to slow him down. “An article about him in a leading operations-research journal was entitled ‘High-Octane Gass.’ Anyone who interacted with him understood that 

‘high-octane’ reference immediately. His energy and enthusiasm were boundless,” says Boisvert.

“He was also a kind and gentle man. He always took the time to say kind words to our support staff, 

and he was a favorite of theirs as a result. We will miss his sparkle and vitality.”

Gass’ hobbies included jogging (which he continued doing as recently as last year), gardening, and 

reading mystery novels. 

He is survived by his wife Trudy, their two children, and a granddaughter.

[A version of this article, which was developed by NIST Public Affairs, originally appeared on the 

NIST internal website.]

Figure 1. Saul Gass
Summary of Activities for Fiscal Year 2013 13

Frank W. J. Olver, a faculty appointee in ACMD, died on April 22, 2013 of complications following 

knee surgery. He was 88. Affiliated with NIST since 1961, Olver was a world-renowned applied mathematician and one of the most widely recognized contemporary scholars in the mathematical field of 

special functions, which are the bread-and-butter tools for creating mathematical models in all areas of 

science. He was working at NIST two days a week up until February 2013. 

Born in Croydon, England, Olver joined NIST’s staff as a mathematician, coming from the UK’s 

National Physical Laboratory (NPL), where he had been a founding member of the Mathematics Division and head of the 

Numerical Methods Section. NIST’s Milton Abramowitz recruited Olver to be the author of the chapter “Bessel Functions of 

Integer Order” in the Handbook of Mathematical Functions (M. 

Abramowitz and I. Stegun, eds., 1964), a publication which went 

on to become the most widely distributed and most highly cited 

publication in NIST’s history.

Olver is particularly known for his extensive work in the 

study of the asymptotic solution of differential equations, i.e., the 

behavior of solutions as the independent variable (or some parameter) tends to infinity, and in the study of the particular 

solutions of differential equations known as special functions 

(e.g., Bessel functions, hypergeometric functions, exponential 

integrals). His book Asymptotics and Special Functions (Academic Press, 1974) has become a classic. Having witnessed the 

birth of the computer age firsthand (as a colleague of the “father 

of computer science,” Alan Turing, at NPL, for example), Olver 

is also well known for his contributions to the development and analysis of numerical methods for computing special functions. 

In 2000, a 1,074-page commemorative volume Selected Papers of F.W.J. Olver was published by 

World Scientific Publishing Co. More than half of the 56 reprinted papers in the volume cite a NIST affiliation. In a review of that volume, Drexel University Professor Emeritus Jet Wimp said that the papers 

“exemplify a redoubtable mathematical talent, the work of a man who has done more than almost anyone 

else in the 20th century to bestow on the discipline of applied mathematics the elegance and rigor that its 

earliest practitioners, such as Gauss and Laplace, would have wished for it.” 

After leaving NIST’s staff in 1986, Olver became a professor in the University of Maryland’s 

mathematics department and in that university’s Institute for Physical Science and Technology. However, 

he continued to maintain a connection to NIST. Most notably, he served as the editor-in-chief and mathematics editor of the online NIST Digital Library of Mathematical Functions (http://dlmf.nist.gov) and its 

966-page print companion, the NIST Handbook of Mathematical Functions (Cambridge University Press, 

2010). Fitting capstones to Olver’s long career, these modern successors to the classic 1964 Abramowitz 

and Stegun handbook will extend its legacy well into the 21st century.

According to Digital Library of Mathematical Functions project lead Daniel Lozier, “Olver’s encyclopedic knowledge of the field, his clear vision for mathematical exposition, his keen sense of the needs 

of practitioners, and his unfailing attention to detail were key to the success of that project.” Olver himself 

was the author or coauthor of five of the 36 chapters. He continued editing work on the Digital Library

until the time of his death.

In 2011 Olver was honored with the Department of Commerce Gold Medal and was inducted into 

the NIST Gallery of Distinguished Scientists, Engineers and Administrators. He was also a Fellow and 

charter member of the UK’s Institute of Mathematics and Its Applications, as well as a foreign member of 

the Royal Swedish Academy of Sciences.

Among Frank’s hobbies was the game of tennis. One of his favorite stories was about the time he 

hit the winning shot in a playoff match that catapulted NIST’s team from the B league (lower division) 

into the A league (the best teams) of federal government inter-agency play for the first time ever.

Figure 2. Frank W. J. Olver
14 NIST Applied and Computational Mathematics Division

Olver produced an impressive mathematical progeny. His son Peter is head of the School of Mathematics at the University of Minnesota. And Peter’s son, Sheehan, is a lecturer in the School of 

Mathematics at the University of Sydney, Australia. Sheehan, a rising star in the field of numerical analysis, spent a summer as a NIST SURF student working on the Digital Library of Mathematical Functions

project. Frank is also survived by his wife Claire, and daughter Sally Sondergaard.

[A version of this article originally appeared on the NIST internal website.]

Recognition

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

below.

ACMD staff members and associates were honored in four of the six annual ITL awards presented in 

2013. Stephen Jordan received the Outstanding Journal Paper Award for his paper with Keith Lee and 

John Preskill entitled “Quantum Algorithms for Quantum Field Theories,” which appeared in Science on 

June 1, 2012. Raghu Kacker was cited, along with colleagues from the ITL Information Access Division, 

with the Outstanding Conference Paper Awards for “Data Dependency on Measurement Uncertainties in 

Speaker Recognition Evaluation,” published in the Proceedings of the 2012 SPIE Defense Security Sensing Conference. Andrew Dienstfrey and Ronald Boisvert received the Outstanding Contribution to ITL 

award for “pioneering efforts in the development and effective dissemination of research results and modern methodology advances in uncertainty quantification for scientific computing. And finally, Yu (Jeff) 

Lei, ACMD Guest Researcher from the University of Texas at Arlington, was tapped as ITL Associate of 

the Year, for “outstanding contributions to the combinatorial testing for software and systems project.”

Ronald Boisvert of ACMD completed an unprecedented three terms (9 years) as Co-Chair of the 

Publications Board of the Association for Computing Machinery (ACM) on June 30, 2013. With more 

than 100,000 members, ACM is the world’s largest educational and scientific society in the computing 

field. Its publications include more than 40 research journals, 8 magazines, 26 newsletters, as 

well as more than 450 conference proceedings volumes each year. The Publications Board develops 

editorial policies and procedures for the organization and appoints and oversees all of the volunteer 

Editors-in-Chief for ACM publications. In recognition of his service, the ACM Council, the 

organization’s governing body, passed the following resolution at its June 14, 2013 meeting: 

“Whereas Ron Boisvert is completing his service as 

co-Chair of the ACM Publications Board, after 

nine years of leading the Board with vision, judgment, discretion, and dedication; and Whereas 

ACM's publications program has been strengthened extensively through Ron's leadership, 

including extensive growth in journal publication 

and extensive improvements in the ACM Digital 

Library. Council expresses ACM's appreciation for 

Ron Boisvert’s exemplary and selfless service.” 

Figure 3. Ron Boisvert receives a certificate of appreciation from 

ACM President Vint Cerf at a meeting of the ACM Council in San 

Francisco in June 2013.
Summary of Activities for Fiscal Year 2013 15

Part II: Features

 

 Part II

Features
16 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2013 17

Approximating the Ising Partition Function 

The Ising model is a classical model in statistical mechanics of magnetization. Historically, this model has 

played a significant role in physics; the discovery of 

phase transitions within the model served as one of the 

first pieces of evidence supporting atomism, the claim 

that changes on an atomic scale could lead to large, 

observable changes. Due to its subtleties, the Ising 

model continues to be studied intensely by mathematicians, computer scientists, and physicists alike. The 

Ising model is very difficult to solve computationally. 

In fact, many difficult problems in materials science, 

bioscience and computer science can be formulated as 

special instances of the Ising model. 

The Ising model represents a magnet acted on by 

an external field. An estimate of the partition function

yields estimates for many important physical and thermodynamic quantities of the magnet and it is the

partition function that we strive to find. Unfortunately,

it has been proved that finding the partition function is 

very hard except for a few very restricted special cases,

and so approximation methods have been devised. 

These are still unsatisfactory because near certain critical temperatures, always where there is the most 

interest, the methods become extremely slow. We have 

designed a radically new method based on combinatorics and graph theory that physicists can use in 

practice. It combines a heuristic sampling method with 

graph theoretic and linear algebraic ideas to give a 

method that is independent of temperature.

Isabel Beichl

The Ising model is a classical model in statistical mechanics of magnetization. Historically, it has played a 

significant role in physics; the discovery of phase transitions within the model served as one of the first 

pieces of evidence in support of atomism, the claim 

that small changes on an atomic scale could lead to 

large, observable changes. Due to its subtle complexities, the Ising model continues to be studied intensely

by mathematicians, computer scientists, and physicists 

alike. In addition, the Ising model is a hard problem 

that is typical of many problems arising in materials 

science and bioscience. Other NP-hard problems can 

be formulated as instances of the Ising model [1].

The Ising model represents a magnet acted on by 

an external field. The magnet is represented by a graph 

G = (V,E), where the vertices V are the atoms in the 

magnet. The graph is accompanied by an assignment σ

of {±1} spins to each vertex, called a spin configuration, which represents the possible states of the atoms 

in the magnet. Each spin configuration appears in the 

model with a certain probability, which is governed by 

the temperature, the strength and direction of the external field, and the correlation of the spins between 

neighboring atoms. Given values for these parameters, 

the (Boltzmann) probability distribution on the 2|V|spin 

configurations is defined as: π(σ) = f(σ)/Z. The denominator Z, which is the sum of the f(σ) over all spin 

configurations, is called the partition function. Since an 

estimate of the partition function yields estimates for 

many important physical and thermodynamic quantities 

of the magnet, it is this function that we strive to find.

Unfortunately, finding Z is hard. Except for a few 

very-restricted special cases, the problem of determining Z exactly is #P-complete. Therefore, we desire to 

find approximation algorithms for Z that run quickly.

Currently, physicists use Markov chain methods that 

originated with the famous the Metropolis algorithm 

[5]. Although great improvements have been made to 

the basic Metropolis idea, all methods currently in use 

are known to be inefficient at low temperatures, and in 

fact, are not polynomial time algorithms. There is a 

Markov chain method of Jerrum and Sinclair [3], 

which they prove finds Z in polynomial time, but the 

order of the polynomial is large and so this algorithm is 

again too slow to use in practice.

Our aim has been to design an algorithm that physicists can use in practice. The algorithm that we created

does just that. It combines a heuristic sampling method 

of Chen [2] (which generalizes the pioneering work of 

Knuth [4]) with graph-theoretic and linear-algebraic 

tools. This is a novel method that is not based on the

Metropolis method, and which has not been previously 

investigated by the physics community. It brings the 

idea of Jerrum and Sinclair from complexity theory 

closer to the world of practical computation. We obtained a new insight into why computing near the 

critical point is slow and hard to do. It’s not the temperature all by itself, it’s the properties of the graph and 

how those properties are manifested when Z is evaluated near the critical temperature.

For fixed bond strength, computing Z is equivalent 

to counting the number of particular subgraphs of a 

graph G. Using the high temperature expansion, we can 

write Z and its derivatives as polynomials whose coefficients ck,e are the number of subsets of G with 2k

vertices of odd degree and e edges. It is these coefficients that we estimate. In the absence of an applied 

field, a special case of interest, the problem of estimating Z reduces to estimating c0,e

. It is simple to restrict 

our method to the case of no odd degree vertices, 

which significantly reduces the complexity.

Counting these subgraphs is equivalent to counting 

the leaves of a particular search tree. We count these 

leaves approximately using Chen’s stratified sampling. 

We construct a set of paths through the tree that identi-
18 NIST Applied and Computational Mathematics Division

fies a stratum on each of the nodes, and agglomerates 

nodes in the same stratum together with one representative of the stratum selected at random. This 

greatly reduces the tree size but still gives a leaf sampling with more information than a single path.

The tree itself is formed from subgraphs of G, the 

nodes of the tree being the subgraphs. The symmetric

difference of two subgraphs X1 and X2 written 

 , is the subgraph of G that contains precisely those

edges in exactly one of X1 and X2. One may consider 

this operation as addition of subgraphs over the 

field . Let be the set of even subgraphs, 

those subgraphs with no vertices of odd degree. Since 

the symmetric difference of two even subgraphs is 

again an even subgraph, we may view as a vector 

space over , called the cycle space of G. The dimension of the cycle space is m − n + 1, where m is the 

number of edges and n is the number of vertices. 

Hence, every set of m−n+1 linearly independent even 

subgraphs forms a cycle basis of G. Further, every 

even subgraph has a unique representation using the 

elements of , and | 

| 

 

. The symmetric 

difference of a graph with 2k odd vertices and an element of the cycle basis (which has 0 odd vertices) is 

still a graph with 2k odd vertices.

We generate a cycle basis for G which can be done 

in polynomial time and construct the desired search

tree by starting with a subgraph with the desired 2k odd 

vertices and at each level of the tree we take the symmetric difference with one of the basis cycles of 

, 

one cycle for each level. We estimate the number of 

vertices of this tree using the variation of Chen’s stratified sampling method described above, without

constructing the entire tree.

One of the problems with existing work on this 

problem is that near a critical temperature, the convergence become slower and slower. This new method is 

radically different in that it is temperature independent. 

A single run gets the partition function for all temperatures. The result is a fast and powerful code.

We have used this code to compute the coefficients of the partition function for the 2D and 3D Ising

model. We generate the 2D and 3D phase transition. 

We also discovered a binomial approximation with

great savings in computational cost. Three papers were 

written [6, 7, 8]. In Figure 4 and Figure 5, we show 

estimates of mean energy and specific heat after 

50 000 000 samples of our algorithm on a 16 × 16 grid 

as a function of β

−1. We are also able to estimate mean 

magnetic moment and magnetic susceptibility.

References

[1] A. Lucas, Ising Formulations of Many NP Problems, 

arXiv:1302.5843.

[2] P. Chen, Heuristic Sampling: a Method for Predicting 

the Performance of Tree Searching Programs, SIAM 

Journal on Computing 21 (1992), 295–315.

[3] M. Jerrum and A. Sinclair, Polynomial-time Approximation Algorithms for the Ising Model, SIAM Journal 

on Computing 22:5 (1993), 1087–1116.

[4] D. E. Knuth, Estimating the Efficiency of Backtrack 

Programs, in Selected Papers on Analysis of Algorithms, 

CSLI Publications, Stanford, CA, 2000.

[5] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. 

H. Teller and E. Teller, Equations of State Calculations 

by Fast Computing Machines, Journal of Chemical 

Physics 21:6 (1953), 1087–1092.

[6] A. Streib, N. Streib, I. Beichl and F. Sullivan, Stratified 

Sampling for the Ising Model, in review.

[7] A. Streib, N. Streib, I. Beichl and F. Sullivan, A Binomial Approximation Method for the Ising Model, in 

review.

[8] A. Streib and N. Streib, Cycle Basis Markov Chains for 

the Ising Model, in review.

Participants

Isabel Beichl, Amanda Streib, Noah Streib (NIST); 

Francis Sullivan (IDA Center for Computing Sciences).

Figure 4. Estimate of mean energy 50,000,000 samples on a 16 

×16 grid as a function of 1/β= kT.

Figure 5. Estimate of specific heat using 50,000,000 samples on a 

16 x 16 grid as a function of 1/β= kT.
Summary of Activities for Fiscal Year 2013 19

Compensating Operators and Stable Time Marching in Ill-Posed 

Nonlinear Evolution Equations

Reconstructing the past behavior of physical systems is 

of great interest in several environmental and geophysical contexts, such as pollution source identification [1, 

2]. In many cases, such systems are governed by coupled nonlinear hyperbolic-parabolic partial differential 

equations. The most desirable computational approach 

in such problems would seek the use of explicit time 

differencing to march backward in time from the 

known current state of the physical system. However, 

due to ill-posedness in time-reversed parabolic equations, such step by step backward in time marching 

would necessarily be unconditionally unstable and lead 

to explosive noise amplification. We have developed a 

novel stabilized time-marching procedure for computing nonlinear parabolic equations on 2D rectangular 

regions, backward in time. Very little is known either 

analytically, or computationally, about this class of 

exponentially ill-posed problems. To quench the instability, the procedure uses easily synthesized FFT-based 

compensating operators at every time step. A fictitious 

nonlinear image deblurring problem is used to evaluate the effectiveness of this computational approach. 

The method is compared with a previously introduced, 

global-in-time nonlinear Van Cittert iterative procedure. The latter is significantly more time consuming, 

and impractical on large problems.

Alfred Carasso

Little is known, either theoretically or computationally, about backward in time continuation in 

multidimensional nonlinear parabolic equations. Various examples discussed in [3-6] highlight the fact that 

only limited success is generally possible in such problems. This is a consequence of the Hölder-continuous 

stability inequalities that characterize ill-posed continuation [7]. Nevertheless, two novel and significant 

computational approaches are developed in [4] and [5] 

that open new doors for further fruitful exploration. 

The method in [4] is a global in time iterative procedure originally designed for solving linear convolution 

integral equations. The approach in [5] is a backward 

time marching scheme where compensating operators 

are applied at each time step to quench the instability.

2D Nonlinear Parabolic Equations in Rectangular 

Regions. The work in [4] and [5] deals with a class of 

nonlinear parabolic equations on the unit square Ω ≡ {0 

< x,y < 1} in the (x,y) plane, with homogeneous Neumann boundary conditions on ∂Ω. With fixed T >0, the 

following initial value problem is a typical example 

 ( ) ( ) 

( ) √| | ( ) ( )

 ( ) ( ),

where γ = 0.04, a = b = 0.5, r(w) = exp{cos2(w)}, and 

q(x,y,t) is given by

( ) ( ) 

 

( 

 

 )

 ( ) 

Instructive backward reconstruction experiments in 

such nonlinear equations result from the use of initial

data g(x,y) in the form of sharp 8-bit gray scale IM×

IM pixel images, with pixel values ranging between 0 

and 255. An explicit finite difference scheme is used to 

march the solution NT time steps ∆t forward in time, 

up to time T = NT ∆t. This results in a blurred version 

of the original sharp image. Reconstructing the initial 

data g(x,y) from these computed data at T = NT ∆t represents nonlinear image deblurring. A significant 

advantage of such experiments is that visual recognition provides immediate evaluation of the extent of 

useful recovery using the different computational approaches.

Given the fixed finite difference mesh parameters 

∆t = T/NT, ∆x = ∆y = 1.0/IM, denote by Λ

T

the forward 

in time nonlinear finite difference solution operator that 

transforms the initial image data w(x,y,0) = g(x,y) into 

the blurred image at time T, w(x,y,T) = f(x,y), through 

the above explicit scheme computation.

Thus

 

 ( ) ( )

i.e.,

 

 ( ) ( ).

The following iterative approach has been found useful 

in many examples similar to Eq. (1).

Nonlinear Van Cittert Iterative Procedure. Given 

the blurred image data f(x,y) at time T, fix λ such that 0 

< λ < 1. Let h

1

(x,y) = λ f(x,y), and consider

 

 

( ) 

 ( ) ( )   ( ) 

 .

Note that this involves repeated numerical solution of 

Eq. (1) using successive updated initial data h

m

(x,y).

While this iteration cannot converge, good reconstructions can often be obtained by terminating this process

after a finite number of iterations.
20 NIST Applied and Computational Mathematics Division

Compensated Backward Time Marching in Eq. (1). 

Let B denote the linear operator ‒∆p, where p is any 

real number with 2 < p < 3. In the present case of 2D 

problems in rectangular regions, the operator B can 

easily be synthesized using FFT algorithms. For problems in more general domains, the action ‒∆p

can be 

synthesized from knowledge of a sufficient number of 

eigenpairs of the Laplacian on that domain. Such 

eigenpairs can be acquired a priori. With small ε > 0, 

one can stabilize backward time marching in the explicit finite difference scheme for Eq. (1), by applying 

the compensating operator exp{‒ε |∆t| B} to the finite 

difference calculation after each time step. Here, the 

pair (ε, p) must be chosen interactively. However, there 

are infinitely many such useful pairs, and a good 

choice can generally be found after very few trials.

The present compensated marching approach differs from the quasi-reversibility method discussed in 

[7]. The latter method is restricted to linear parabolic 

problems 

 ( ) 

and it uses the modified equation

 ( ) 

 

( ) ( ) 

for backward continuation, where A* is the adjoint of 

the elliptic differential operator A. However, an adjoint 

operator is not easily defined in the nonlinear case.

Two Examples. Figure 6 is a 512×512 US Air Force 

Resolution image. Nonlinear blurring was achieved by 

using an explicit scheme in Eq. (1) with ∆x = ∆y = 

1/512, ∆ t = 1.5 × 10-7, and 600 time steps, to yield the 

blurred image at the final time T = 9.0 ×10-5. This blurring computation was accomplished in 3 minutes on a 

modest personal workstation. Due to the pronounced 

anisotropic character of q(x,y,t) in Eq. (2), the vertical 

sequence of numbers near the right edge has almost 

been erased. However, after 100 Van Cittert iterations 

in the rightmost image in Figure 6, that vertical sequence is partially restored, along with noticeable 

improvements in other parts of the image. As may be 

expected, that Van Cittert reconstruction required almost 5 hours, as it necessitated 100 successive 

nonlinear blurring computations, each lasting 3

minutes.

However, using ε = 3.5 × 10-4and p = 2.5 in the 

compensated backward explicit scheme produced the 

middle image in Figure 6. The vertical sequence of 

numbers near the right edge appears better defined in 

the middle image than in the rightmost Van Cittert image. However, certain other parts of the image are 

marginally better recovered in the Van Cittert restoration. The above choice of (ε,p) was arrived at after 

several interactive trials, each lasting 4 minutes. Clearly, on a parallel computer, several such pairs (ε,p) can 

be explored simultaneously.

Figure 7 is a 256 × 256 satellite image. Here the 

blurring computation required 20 seconds, and very 

useful reconstruction is achieved after 100 Van Cittert 

iterations and 2000 seconds, as shown in the rightmost 

image in Figure 7. Again, interestingly, after a few 25

second interactive trials, equally good results can be 

achieved using the compensated backward explicit 

scheme with ε = 6.5 × 10-4and p = 2.35.

Concluding Remarks. Only limited success is generally possible in solving nonlinear backward parabolic 

equations. In many cases, compensated marching 

schemes can produce useful reconstruction in large 

Figure 6. In 512×512 resolution chart image, stabilized backward time-marching with ε = 3.5 × 10-4, p = 2.5, competently recovers vertical 

sequence of numbers near image right edge in relatively little computing time, while the Van Cittert iteration is computationally impractical on 

large problems.
Summary of Activities for Fiscal Year 2013 21

sized problems for which a global in time iterative procedure is computationally impractical. 

References

[1] J. Atmadja and A. C. Bagtzoglou, Pollution Source 

Identification in Heterogeneous Porous Media, Water 

Resources Research 37 (2001), 2113-2125

[2] C. Bagtzoglou and J. Atmadja, Mathematical Methods 

for Hydrologic Inversion: The Case of Pollution Source 

Identification, Chapter 5 in Handbook of Environmental

Chemistry, (2005), 65-96.

[3] A. S. Carasso, Reconstructing the Past from Imperfect 

Knowledge of the Present: Effective Non-uniqueness in 

Solving Parabolic Equations Backward in Time, Mathematical Methods in the Applied Sciences 6:3 (2012), 

249-261.

[4] A. S. Carasso, Hazardous Continuation Backward in 

Time in Nonlinear Parabolic Equations, and an Experiment in Deblurring Nonlinearly Blurred Imagery, JourJournal of Research of the NIST 118 (2013), 199-217.

[5] A. S. Carasso, Compensating Operators and Stable 

Backward in Time Marching in Nonlinear Parabolic 

Equations, NIST Internal Report, NISTIR 7967, (November 2013).

[6] A. S. Carasso, A Stable Marching Scheme for an Illposed Initial Value Problem, in Improperly Posed Problems and their Numerical Treatment, (G. Hammerlin 

and K. H. Hoffman, eds.), Birkhauser-Verlag, Boston, 

1983.

[7] R. J. Knops, Logarithmic Convexity and Other Techniques Applied to Problems in Continuum Mechanics, in 

Symposium on Non-Well-Posed Problems and Logarithmic Convexity, (R. J. Knops, ed.), Lecture Notes in 

Mathematics 316, Springer-Verlag, New York, 1973.

[8] R. Lattes and J. L. Lions, The Method of QuasiReversibility, American Elsevier, New York, 1969.

Participants

Alfred Carasso

Figure 7. Stabilized backward time-marching with ε = 6.5 × 10-4, p = 2.35, produces a reconstructed Satellite image comparable in visual 

quality to that resulting from the computationally intensive Van Cittert iteration.
22 NIST Applied and Computational Mathematics Division

Single Photon Conversion Technology: Research to 

Commercialization

In a properly designed nonlinear optical device, single 

photons can be converted from one wavelength to another with near 100% efficiency. This technology has 

found numerous applications because of its ability to 

manipulate the frequency (that is, color) of nonclassical light while preserving its quantum properties. In 

the past few years, we have adapted this technology to

develop highly efficient and sensitive single photon 

detectors for use in quantum communications. In addition, we have performed significant studies to optimize 

their use for advanced measurement science. 

Continuing these developments, in FY 2013 the 

team proposed and demonstrated another technique 

called frequency-correlated bi-photon spectroscopy, 

which is potentially very important in cases where the 

spectral measurement can only be performed locally 

while the object is far away or somehow inaccessible. 

Additionally, the team jointly developed a more practical dual-channel single-photon up-conversion detector 

in collaboration with a team of Stanford University

researchers. In such a dual-channel device, two detectors may be used at the same time so that the overall

achievable data rate is doubled, which is advantageous

in advanced communication systems. 

Some of the techniques proposed by our team are 

being transferred to US industry via the NIST Small 

Business Innovative Research (SBIR) program. 

DARPA has also seen great promise for this technology; their most recent SBIR solicitation cited three 

publications from our team. Furthermore, highefficiency frequency conversion is one of the building 

blocks needed for the development of quantum repeaters, which are necessary to move quantum-based 

cryptographic key exchange beyond point-to-point 

communications. 

Xiao Tang

Light consists of a huge number of individual photons, 

each with a unique color. Single photon conversion 

technology can change the color, or in technical terms 

change the frequency, of a single photon of light using

nonlinear optics. In a nonlinear optical device, two 

photons at lower frequencies can be combined into one 

photon of a higher frequency in a process called frequency up-conversion. Alternatively, a single photon at 

a high frequency can be converted to a pair of photons 

at lower frequencies, which is called frequency downconversion. The quantum properties of the initial photon are preserved in the conversion process. This 

technology, known as "quantum frequency conversion" 

(QFC), has found numerous applications because of its 

ability to manipulate the frequency of nonclassical 

light. For example, advanced optical communications 

applications, including single-photon quantum communications and quantum information processing for 

provably secure data links, can benefit from operating

in both the visible and the near-infrared (NIR) wavelengths. In principle, QFC provides a way to coherently 

convert between visible photons (best for photon processing, storage, and detection) and NIR photons (best

for long-haul transmission through fiber at commercial 

telecommunication bands). 

Previous work. By using the up-conversion technique, 

near-infrared light can be converted to light in the visible or near visible range where it can be detected by 

low-cost commercially available detectors with lownoise and high efficiency. In recent years, ITL’s quantum communication research team has developed upconversion single photon detectors in the NIR range by 

using long-wavelength pump light. These detectors 

were used in NIST quantum key distribution (QKD) 

systems at an operating wavelength of 1310 nm, significantly increasing the operating distance over existing 

systems while maintaining very high speed [1]; this 

work won an R&D 100 Award in 2007. 

Due to conservation of energy, the frequency of 

the pump light varies, and only signal photons at the 

corresponding frequency can be converted and detected. In this way, the spectrum of the signal photon can 

be measured if we vary the wavelength of the pump 

light. In 2009 we developed an up-conversion specFigure 8. Paulina Kuo (right) and Oliver Slattery of ACMD work 

on a single photon conversion device.
Summary of Activities for Fiscal Year 2013 23

trometer based on this principle [2], which can be used 

to measure the spectrum of extremely weak, singlephoton-level optical signals. Its sensitivity is three orders of magnitude higher than any existing commercial 

spectral instrument. 

Our team has used these single photon upconversion detectors and spectrometer in a variety of 

research projects including

a) implementation of a high-speed quantum key distribution system;

b) demonstration of a detector with a temporal resolution better than the jitter-limited resolution of 

commercial single photon detectors; 

c) characterization of an entangled photon pair 

source, including a direct spectrum measurement 

for photons generated in spontaneous parametric 

down-conversion; 

d) characterization of single photons from quantum 

dots including the measurement of carrier lifetime 

with high accuracy, and the demonstration of 

preservation of non-classical features of the converted photons; 

e) observation of 2nd, 3rd and 4th order temporal 

correlations of near infrared single photons from 

coherent and pseudo-thermal sources following 

frequency up-conversion; 

f) study of the time-resolving measurement capability of up-conversion detectors using a short pulse 

pump; and

g) evaluation of the modulation of a single photon 

wave packet for better interfacing of independent 

sources. 

These efforts by the ITL quantum communication team 

were summarized in a comprehensive review article 

published in Physics Reports [3]. This article demonstrates that the team is a world leader in research and 

development in this field. 

Recent Developments. In FY 2013 we have undertaken work to improve the performance of the devices, 

and to expand their application. Three such efforts:

“Frequency Correlated Bi-Photon Spectroscopy,” “Dual-channel Single-photon Upconversion,” and “Twophoton Interference with Coherent Pulses” are described below. In addition, the team continues to work 

to transfer their technology to US industry for commercialization.

Frequency Correlated Bi-Photon Spectroscopy. Our

demonstration of frequency correlated bi-photon spectroscopy is based on combining the ITL up-conversion 

spectrometer and the ITL correlated photon pair 

source. The photon pair source generates correlated 

photon pairs using a frequency down-conversion technique; one photon of the pair is in the 

telecommunication band (~1310 nm, useful for longhaul transmission) and the other is in the near visible

range (~895 nm, useful for storage in the Cesium atomic system). These correlated photons are similar to 

twins; they were born at same time and their characteristics are also correlated with each other. For example, 

once the wavelength (or frequency) of one photon is 

determined, the wavelength of the other is also known 

by energy conservation. The photons at one wavelength can be sent as a probe to interact with a remote 

or inaccessible object. In principle, the spectral funcFigure 9. With the pump beams at different colors (wavelengths), the signal photon pulses are converted to different wavelengths. They can 

be separated by a grating and detected by detectors (one for each wavelength). The detected data can be restored at a multiplied rate, beyond 

the intrinsic data rate limitation. 
24 NIST Applied and Computational Mathematics Division

tion of the remote object can be determined by locally 

measuring the correlated ‘twin’ photon at another 

wavelength using an up-conversion detector and monitoring the coincidence of the twin photon pairs. The 

ITL quantum communication team proposed and 

demonstrated this technique. The results were published in Laser Physics Letters [4]. This technique is 

potentially very important in cases where the spectral 

measurement can only be performed locally while the 

object to be measured is far away or inaccessible. 

Frequency correlated bi-photon spectroscopy provides a new way to measure spectral properties of

remote objects. However its functionality and performance can be further improved. For example, it is 

important to have high spectral resolution in the spectrum measurement. In the current experimental 

configuration, the spectral resolution is determined by 

the spectral response function of the frequency conversion process in the device. In order to improve the 

spectral resolution, the ITL team carefully investigated 

the relationship of the spectral response function, pump 

condition, and other parameters in the device. In this 

way, optimized operating conditions can be predicted 

and achieved for better spectral resolution. A detailed 

analysis was published in Optics Express [5]. 

Dual-channel Single-photon Upconversion. The data 

transmission rate of a quantum communication system 

using silicon based single-photon detectors is limited 

by the jitter in the detectors. In FY 2010 the team proposed and experimentally demonstrated a multiwavelength pumping technique that multiplied the data 

rate of such systems beyond their intrinsic jitter limitation [6]; see Figure 9. Based on this idea, the team 

recently developed a more practical dual-channel single-photon up-conversion detector in collaboration 

with Stanford University researchers [7]. In a regular 

single channel up-conversion detector, signal photons 

in the telecommunication band can be converted to a 

wavelength (λ1) in the visible range by using a pump 

beam at another wavelength using the up-conversion 

technique. In the dual channel device, if two pump 

beams alternate at slightly different wavelengths, the 

signal photons can be converted to two slightly different wavelengths (λ1, λ2) in the visible range. These

converted photons can in turn be separated by a dispersion element and then detected by two separate photon 

detectors. The data from the two detectors can then be 

combined into one data steam. In such a dual channel 

device, the data rate in each channel is still intrinsically 

limited by the jitter of the detector, but the combined 

data rate is doubled. This technology provides an important solution for the higher data rate requirements in 

advanced communication systems. 

For further improvement in noise reduction, the 

team carefully investigated a variety of spectral filtering techniques with this dual channel up-conversion 

detector and found that volume Bragg gratings are the 

best choice for up-conversion single photon detectors 

for simultaneously achieving low noise and high conversion efficiency [8]. 

Two-photon Interference with Coherent Pulses.

Photon interference is one of the most fascinating topics in optical physics. Photon interference studies aim 

to understand the nature of the phenomenon, as well as 

its application in quantum information science. In FY 

2013, the team observed photon interference with coherent pulses [12]. This is the first step in the 

preparation for the future development of a quantum 

repeater.

Technology Transfer. The team has also worked to 

enable the transfer of its technology to US industry to 

enable commercialization. In particular, US companies 

AdvR and Lepton Technology received funding from 

the NIST SBIR Program to develop technology based 

on the NIST up-conversion device described earlier 

[1]. Phase 1 and Phase 2 of this SBIR project were 

successfully completed in FY 2013. Soon after, another NIST SBIR project was initiated to enable US 

Company Gener8 to further develop the NIST technique of using a Bragg grating embedded on a nonlinear single photon source for enhanced narrowband 

photon pair creation [9]. 

Additional development and commercialization of 

ITL’s technology is now being spearheaded by

DARPA, who recently announced an SBIR solicitation

[10] based mainly on the technology developed at 

NIST. Three articles by the ITL team [2, 6, 11] were 

cited in the solicitation. 

Future Plans. One of the ITL team’s long-term goals 

is the development of quantum repeaters. Current 

quantum communication technology can only be done 

by point-to-point communication. The distance in 

which this can be done is limited by signal attenuation 

in the transmission medium, e.g., optical fiber or the 

atmosphere. In classical telecommunications, “repeaters” read an incoming digital signal, restore its fidelity

and retransmit it to the next node along a path to its 

ultimate destination. Quantum repeaters have the same 

function, but they must operate in a different way. Due 

to the no-cloning rule of quantum mechanics, the incoming qubits cannot be directly read, lest their 

information content be lost. Instead, the incoming 

quantum state must be purified and enhanced to restore 

its fidelity and then passed to the next node without 

being directly read by using a sophisticated technique 

based on entanglement swapping. This is quite challenging; a quantum repeater is, in essence, a special 

purpose quantum computer.

The quantum frequency conversion described 

above is one of the building blocks needed for the development of quantum repeaters. The ITL team is 

working on other elements for this long-term goal as 

well. For example, the ITL team has started the effort 
Summary of Activities for Fiscal Year 2013 25

to design and implement entangled photon pair 

sources. This is part of a collaborative NIST Innovation 

in Measurement Science (IMS) project, entitled “Quantum Randomness as a Secure Resource”. In addition, 

the team recently initiated collaboration with Washington University to develop narrow-band entangled 

photon pair sources based on micro-toroids. Entangled 

photon pair sources are important building blocks, not 

only for quantum repeaters, but also for quantum randomness required for secure communications. 

Another example is to further study photon interference phenomenon based on the observation of

photon interference with coherent pulses [12]. The 

team recently started a project to observe photon interference from independent single photon sources. 

Another critical device, called a quantum interface, 

has been designed and is in the process of implementation in the lab. It will convert photons in the telecom 

wavelength band to an atomic transition wavelength,

while preserving their non-classical features. Such a 

capability would connect telecom photons (for transmission) with atomic quantum systems (for storage). 

Furthermore, the team initiated a quantum memory 

project, which is a core component of the quantum 

repeater. Each of these ambitious and challenging research tasks is a necessary building block that will see

final integration into a future 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 15:12, (2007), 7247.

[2] L. Ma, O. Slattery and X. Tang, Experimental Study of 

High Sensitivity Infrared Spectrometer with Waveguidebased Up-conversion Detector, Optics Express 17:16

(2009), 14395.

[3] L. Ma, O. Slattery and X. Tang, Single Photon Frequency Up-conversion and its Applications, Physics Reports, 

521:2 (2012), 69-94.

[4] O. Slattery, L. Ma, P. Kuo, Y.-S. Kim and X. Tang, 

Frequency Correlated Bi-Photon Spectroscopy using a

Tunable Up-Conversion Detector, Laser Physics Letters

10 (2013), 075201. 

[5] P. S. Kuo, O. Slattery, Y.-S. Kim, J. S. Pelc, M. M. 

Fejer and X. Tang, Spectral Response of an Upconversion Detector and Spectrometer, Optics Express 21:19

(2013), 22523.

[6] Lijun Ma, Joshua C. Bienfang, Oliver Slattery and Xiao 

Tang, Up-conversion Single-photon Detector using Multi-wavelength Sampling Techniques, Optics Express

19:6 (2011), 5470. 

[7] J. S. Pelc, Paulina S. Kuo, Oliver Slattery, Lijun Ma, 

Xiao Tang, and M. M. Fejer, Dual-channel, Singlephoton Upconversion Detector at 1.3 μm, Optics Express 20:17 (August 2012), 19075. 

[8] P. S. Kuo, J. S. Pelc, O. Slattery, Y.-S. Kim, M. M. 

Fejer, and X. Tang, Reducing Noise in Single-photon 

Frequency Conversion, Optics Letters 38:8 (April 

2013), 1310.

[9] L. Yan, L. Ma, and X. Tang, Bragg-grating-enhanced 

Narrowband Spontaneous Parametric Downconversion, 

Optics Express 18:6 (March 2010), 5957.

[10] See DARPA SBIR solicitation SB133-001, Title: Efficient quantum frequency conversion for advanced 

optical communications7. 

[11] J. S. Pelc, C. R. Phillips, Q. Zhang, C. Langrock, O. 

Slattery, X. Tang, M. M. Fejer, Long-wavelengthPumped Upconversion Single-photon Detector at 1550 

nm: Performance and Noise Analysis, Optics Express 19

(2011), 21445.

[12] Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, Conditions for Two-photon Interference with Coherent Pulses, 

Physical Review A 87 (2013), 063843. 

Participants

Xiao Tang, Paulina Kuo, Lijun Ma, Oliver Slattery, 

Yong-Su Kim, Alan Mink and Barry Hershman

(ACMD); Joshua Bienfang (NIST PML); Martin Fejer 

and Jason Pelc (Stanford University); Li Yan (University of Maryland Baltimore County)

 

7

http://www.acq.osd.mil/osbp/sbir/solicitations/sbir20133/darpa133.htm
26 NIST Applied and Computational Mathematics Division

Analysis for Dynamic Metrology

Diverse measurement contexts require estimates of 

time-varying quantities. Ideally the measurement device responds to signal variations significantly more 

rapidly than the modulation of the underlying signal. If 

so, then well-developed techniques may be used for the 

calibration and analysis of the measurement system. By 

contrast, as the characteristic timescales for signal 

modulation and measurement response become commensurate, the situation becomes more complicated; 

directly measured quantities may require correction 

for the finite bandwidth of the measurement system 

response. Toward this goal heuristic estimation rules 

have evolved over time and are now widely used. We 

rederive one common rule of thumb, and present sufficient conditions for its validity. Furthermore, we 

investigate its quantitative performance in cases for 

which these conditions are violated and encounter surprisingly poor results. While our work is directly 

relevant to high-speed communication systems, the fact 

that the analysis structures are universal to any linear, 

time-invariant system may serve as a cautionary tale 

for new research initiatives focusing on dynamic metrology ongoing at counterpart metrology institutes.

Andrew Dienstfrey

In collaboration with NIST PML, we are providing 

precision calibration and measurement services for 

waveforms as required by high-speed data systems. 

Figure 10 provides a representative example of the 

problem. The figure shows an eye-diagram, a standard

diagnostic for digital waveform generators. The procedure superimposes a random bit stream such that all 

possible binary transitions appear. A mask region defines a pass/fail test for the generator as a signal falling 

within this region confounds the determination of the 

bit: 0 or 1. In Figure 10, the generator on the left passes 

the test while the generator on the right fails. The issue

here is that these eye diagrams represent the same generator; the difference is in the oscilloscope used to 

measure the signal! Which measurement is correct? 

Private communications with industry representatives 

indicate that measurement ambiguity results in significant overhead costs.

The source of the problem lies with the dynamic 

response characteristics of the oscilloscope relative to 

the underlying signal. High-speed pattern generators 

are designed to deliver binary transitions on the order 

of 10 picoseconds (ps) or less, yet the fastest oscilloscopes available have impulse response functions with

full-width-half-max times of 4 ps to 7 ps, only marginally faster. For situations requiring high accuracy, the 

measurement system cannot be considered ideal and 

the directly measured signal must be corrected for finite bandwidth effects.

Unfortunately, implementing these corrections 

correctly incurs significant costs in the form of increased measurement and analysis requirements. Rules 

of thumb have been developed over time as shorthand

to avoid this penalty. In the following we present an

elementary derivation of one of these heuristics, and 

demonstrate that it rests on shaky ground as a quantitative tool. Even more, the foundational assumptions 

about the qualitative nature of the correction turn out to 

be unfounded. Details can be found in [1] and [2]. 

Waveforms Parameters and Analysis. We assume 

that the measurement can be modeled as a linear, timeinvariant system in which case its analysis is cast as a

convolutional equation,

 ( ) ∫ ( ) ( ) 

 

. (1)

Here a(t) is the system response function, x(t) the 

noise-free input waveform, and y(t) is the noise-free 

output. Estimation of any one of these functions in a 

noisy measurement context arises as a canonical problem. For convenience, here we restrict attention to the

scenario in which x(t) is an impulse waveform. A practical example of this could be using a high-speed 

oscilloscope to measure the impulse response function 

of a photodiode used to convert optical signals to electrical. Measurement of digital waveforms proceeds

analogously once technical difficulties are resolved 

related to the lack of a Fourier transform.

Given a time-varying waveform, x(t), different 

metrics are used to quantify its speed of variation. The 

speed of an impulse response function is routinely 

quantified by its full duration at half maximum, denoted by τF(x). For step-like waveforms this role is played

Figure 10. The “eye-diagram'” diagnostic for a digital signal generator depends on the dynamic response of the measurement. The 

generator on the left passes the test while the generator on the right 

fails. The problem is that this test applies to the same generator as 

measured by two different oscilloscopes!
Summary of Activities for Fiscal Year 2013 27

by the transition durations between states, usually 10 % 

to 90 % denoted by τR. In addition to τF, an alternative 

definition of response has been proposed:

 ∫ ( ) (2a)

 ( ) 

 

 

∫ ( ) (2b)

 

 

( ) 

 

 

∫( )

 ( ) (2c)

Of course Eq. 2 assumes that the moments exist and 

that the total integral is not zero; this can be verified for 

the impulse-response functions relevant to our work. 

The final equation Eq. 2c defines an alternative characterization of the speed of an impulse-like waveform 

that while not in wide use, has been advocated in some 

contexts. More importantly Eq. 2 plays a central role 

in motivating the next idea.

Returning to our measurement problem, a detailed 

analysis involves: (1) obtaining an estimate of a(t), for 

example by a separate calibration experiment; (2) making a measurement of y(t); and (3), inversion of Eq. 1 

for x(t). In addition to the substantial measurement 

burden required to characterize time-dependent functions, the final step is complicated and delicate as 

deconvolution is generically an ill-posed problem requiring regularization to stabilize the inversion in the 

presence of noise.

Across the wide-ranging landscape of heuristic 

analyses developed as an alternative, the most common 

conventional wisdom is that the finite bandwidth of the 

measurement system results in a measured waveform

that is slower than the true signal. If nothing else, it 

follows that the speed of x(t) should be corrected for 

this effect. The formula that is nearly universally used 

to estimate this correction is

 ( ) √ ( )

 ( ) (3)

We will refer to this approximate correction as rootsum-of-squares or RSS. The advantages of RSS over 

the convolutional analysis are obvious but bear repeating. For one, RSS only requires estimates of a single 

parameter representing waveform speeds, in place of 

the complete characterization of all waveforms as a 

function of time. Furthermore, in contrast to the issue 

of regularization, RSS inversion is easy to implement 

and analyze.

Despite the widespread use of RSS, we have been 

unable to find a derivation that includes clear conditions for its validity. Here we offer one. The definition 

of τσ is reminiscent of the definition of variance of a 

random variable. In this analogy the role of the probability density function is played by x(t). While the 

scaling by 1/A normalizes the integral mass to be one, 

x(t) generally oscillates and is not of one sign. Despite 

this, a simple computation shows that the analog to the 

additivity of variance law nevertheless follows. More 

precisely, assuming the measurement model, Eq. 1, and 

that the quantities in Eq. 2 exist, one may show that

 

 

( ) 

 

( ) ( )

 

.

Thus we have the desired RSS 

relationship, only written with 

respect to the dubious quantities τσ

as opposed to τF. Introducing a

constant as the ratio between these 

two waveform parameters,

 

 

( ) ( )

 ( ), we can 

state the following sufficient conditions for RSS.

Fact 1. Given the convolutional 

relation Eq. 1, if 

( ) 

 

( ) ( ), then ( )

 

 

( )

 

( )

 

.

A similar constant, kR, may be 

defined with respect to step waveforms, and likewise the constancy 

of this constant serves as a sufficient condition for an RSS 

formula involving τR.

Figure 11 shows the constants

(kF, kR) for a variety of waveforms. 

The red x's show the values of the 

constants for three classical lowpass filters (Chebyshev, Butterworth, and Bessel-Thompson) of 

orders two through six. The blue 

Figure 11. Values of the ratios (kF, kR) for elementary filters (red x's) and their pairwise convolutions (blue dots). The non-constancy of these ratios results in a corresponding violation of a 

simple RSS relationship for τF.
28 NIST Applied and Computational Mathematics Division

dots show all possible pairwise convolutions over a 

wide range of relative bandwidths. The first observation is that the time ratios (kF, kR) cannot be considered 

universal. It follows that the desired quantitative RSS 

relationship for τF is dubious. Even more striking is the 

fact that the ratios can be negative, suggesting that the 

finite bandwidth effects of measurement can result in a 

waveform that appears faster than the underlying input. 

Additional numerical experiments have confirmed this 

fact. In summary, not only does RSS fail to provide 

quantitative estimates of dynamic correction, the deeper and more foundational qualitative assumption that a 

measured waveform is slower than its input can also be 

erroneous.

Dynamic Metrology. For communications applications, the need to correct measurements for finite 

bandwidth effects has been understood for some time. 

One (perhaps simplistic) explanation is that the insatiable thirst for greater bandwidth results in the scenario 

that devices to generate, receive, and measure communications waveforms are based on nearly

commensurate technologies. Increasingly, the dynamic 

paradigm is becoming relevant for measurements that 

heretofore were analyzed under static considerations. 

For example, in the automotive industry, precise, detailed measurements of the time-varying pressure 

inside combustion chambers are desired to improve 

fuel efficiency. Under normal operation, pressure can 

vary significantly over times on the order of tens of 

microseconds, yet until recently, SI8traceable calibration of pressure sensors has been performed 

exclusively for static loads. In response, several European metrology institutes have embarked upon an 

extensive and coordinated re-evaluation of their measurement services for time-varying pressure, force, and 

torque [3, 4, 5].

Following [6], we define a dynamic measurement

as one in which the measurand varies in time sufficiently fast relative to the response of the measurement 

system that corrections for finite bandwidth effects are 

required to achieve the desired accuracy. This definition makes clear that it is neither the absolute timescale 

nor physical application that is relevant for the designation. Rather, the common characteristics are the 

essential time-varying nature of the measurand, and the 

commensurability of the timescale of this variation

relative to the response time of the measurement device. It follows that while the physical details of 

dynamic measurements may be very different, elements of the measurement analysis are shared. We 

expect that future collaborations across these application areas will serve to identify foundational concepts 

for the calibration and analysis of dynamic measurement systems.

 

8

International System of Units, http://www.bipm.org/en/si/

References

[1] A. Dienstfrey and P. D. Hale, Colored Noise and Regularization Parameter Selection for Waveform Metrology, 

IEEE Transactions on Instrumentation and Measurement, to appear.

[2] A. Dienstfrey and P. D. Hale, Analysis for Dynamic 

Metrology, Measurement Science and Technology, to

appear.

[3] T. Bruns, Publishable JRP Summary Report for JRP 

IND09 (Dynamic) Traceable Dynamic Measurement of 

Mechanical Quantities, European Association of National Metrology Institutes (EURAMET), Technical 

Report JRP-IND099, Nov. 2012.

[4] T. Esward, C. Matthews, S. Downes, A. Knott, S. 

Eichstädt and C. Elster, Uncertainty Evaluation for 

Traceable Dynamic Measurement of Mechanical Quantities: A Case Study in Dynamic Pressure Calibration, in

Advanced Mathematical and Computational Tools in 

Metrology and Testing IX (F. Pavese, M. Bär, J.-R. 

Filtz, A. B. Forbes, L. Pendrill, and K. Shirono, eds.), 

World Scientific Publishing Company, 2012, 143-150.

[5] C. Bartoli, M. F. Beug, T. Bruns, C. Elster, T. Esward, 

L. Klaus, A. Knott, M. Kobusch, S. Saxholm and C. 

Schleger, Traceable Dynamic Measurement of Mechanical Quantities: Objectives and First Results of the 

European Project, International Journal of Metrology

and Quality Engineering 3:3 (January 2012), 127-135.

[6] T. J. Esward, C. Elster and P. Hessling, Analysis of 

Dynamic Measurements: New Challenges Require New 

Solutions, in Proceedings of the XIX IMEKO World 

Congress, Lisbon, Portugal, September 6-11, 2009, 

2307-2310.

Participants

A. Dienstfrey (ACMD); Paul Hale (NIST PML)

 

9

http://www.euramet.org/_leadmin/docs/EMRP/JRP/JRP_Summaries

_2010/IND09_Publishable_JRP_Summary.pdf
Summary of Activities for Fiscal Year 2013 29

A Framework for Reproducible Latent Fingerprint 

Enhancements

Fingerprint evidence is routinely used to convict offenders of crimes, but such evidence is of highly variable quality, suffering from incompleteness, pressure 

gradations, and background variability. Due to the low 

signal quality of the fingerprint, these images are not 

suitable for input into fingerprint identification software. Because of this, the forensics community 

currently uses a variety of image processing tools to 

improve the quality of these images before attempting 

to identify a match. As dramatic and essential as these 

transformations are, no research exists to characterize 

this step of the evidentiary analysis chain. Fundamental questions about reproducibility, traceability, and 

quantification of accuracy remain. The aim of this 

work is to develop independent, systematic, and easily 

reproducible alternatives to forensic image preprocessing that can yield fingerprint enhancements of 

comparable quality. Such alternative approaches provide a valuable frame of reference that may be helpful 

in informing, complementing, and possibly validating 

exiting methodology.

Alfred Carasso

In recent years, the reliability of fingerprint evidence has come under increased scrutiny, [1-5]. One 

area of concern involves the digital enhancement of 

latent fingerprints left unintentionally at a crime scene. 

Such prints are generally smudgy, with poorly defined 

ridge impressions that may be partially obscured by 

background structural detail, together with superimposed random noise. There may also be overlapping 

prints. A key step in obtaining latent print enhancements that has been stressed by numerous researchers 

involves isolating ridge impressions from such backgrounds. In a recent comprehensive NIST study [6, 

Chapter 4], the possibility of misleading artifacts in 

digital enhancements is discussed, with guidelines proposed for the proper evaluation and acceptance of 

enhanced images. These guidelines include validation 

of the enhancement technology, along with maintenance of an audit trail of the digital procedures used.

Photoshop10 processing is the preferred methodology among law enforcement forensic analysts for the 

enhancement of latent fingerprint images. Aiming to 

meet the requirements of automated fingerprint identi-

 

10 The commercial software products IDL, Matlab, Photoshop and 

PV-WAVE are identified in order to specify experimental procedure 

adequately. Such identification is not intended to imply recommendation or endorsement NIST, nor is it intended to imply that the 

software identified are necessarily the best available for the purpose.

fication systems (AFIS), forensic Photoshop enhancements typically strive to achieve an image exhibiting 

black ridge impressions over a quasi-uniform light grey 

background. A variety of “dodge and burn” and 

“brush” tools are typically applied to lighten or darken 

selected areas within the image, and remove unwanted 

background information. The multiplicity and diversity of the individual steps used in this process are not 

fully documented, and the procedure may not be reproducible. Viewing such enhancements without some 

frame of reference cannot allay the apprehension that 

potentially significant information may have been inadvertently eliminated, or artifacts possibly introduced, 

by overzealous application of image tools more appropriately used for retouching photographs, removing 

wrinkles, or darkening gray hair. These are some of the 

reasons why such fingerprint enhancements have occasionally been challenged.

Alternative Latent Fingerprint Enhancements. As 

shown in Figure 12, it is possible to achieve fully reproducible enhancements, comparable in visual quality 

to AFIS-ready forensic Photoshop enhancements, using 

scientific image analysis software tools that are independent of Photoshop. In [7] and [8], several 

alternative fingerprint enhancement approaches are 

discussed, along with the software routines necessary 

to implement them. All of these methods aim at bringFigure 12. Four distinct enhancements of latent fingerprint 1. 

Possibly significant background structures are suppressed in 

Forensic Photoshop and MATLAB contrast adjusted images. IDL 

Histogram images produce better defined ridge impressions, along 

with considerable background information. Such background 

detail can be attenuated by reproducible fractional diffusion 

smoothing, as shown in the next figure.
30 NIST Applied and Computational Mathematics Division

ing into better visual range potentially significant structures that are present in the image, but not easily 

discernible. Each of these enhancement methods is 

based on the use of a single command from such widely used scientific image analysis packages as 

MATLAB [9], IDL [10], and PV-WAVE [11]. Such 

enhancement commands are applied to the whole image at once, are executed in seconds, and are obviously 

reproducible. In addition, [12] provides a thorough 

discussion of the theory underlying these techniques. 

Progressive Levy Smoothing of Histogram Equalized Latent Fingerprints. Of particular interest in 

latent print enhancement are the IDL commands that 

produce Histogram Equalization, and Adaptive Histogram Equalization, respectively. These two distinct 

IDL techniques generally exhibit better-defined ridge 

structure, along with considerably more background 

detail than is the case in forensic Photoshop enhancements. However, while some of this detail may be 

valuable contextual information in certain cases, there 

is also typically a great deal of noise and background 

clutter that can obscure useful ridge impressions. As 

shown in Figure 13, an effective smoothing technique, 

previously used successfully in nanoscale imaging 

[13], can be applied to gradually attenuate background 

detail while preserving ridge information.

The success of this smoothing technique hinges on 

two significant factors. First, the smoothing diffusion

equation involves the Laplacian operator raised to a 

low fractional power, such as p=0.2 for example. This

leads to significantly milder smoothing of high frequency information than would occur with classical 

Gaussian smoothing where p=1. Second, the progressive time evolution of the diffusion process can be 

monitored, and the “slow motion” suite of gradually 

smoother images, such as Figure 13 can be stored. This 

provides an audit trail that allows retrieving possibly 

useful information that might have been lost in transit 

to the user-selected optimal image. Different values of 

the exponent p can be explored.

As shown in Figure 14, such independent and fully reproducible enhancements provide a valuable frame 

of reference that may be helpful in informing, complementing, and possibly validating the forensic 

Photoshop methodology.

This work was sponsored by the 2012 NIST Forensic Measurement Challenges grant, “Metrics for 

Manipulation and Enhancement of Forensic Images.” 

A NIST Invention Disclosure covering this work was 

filed by the NIST Technology Partnership Office in 

May 2013.

Figure 13. Progressive smoothing of IDL Histogram Equalized latent fingerprint 2, by solving Levy stable fractional diffusion equation from 

time t=0 to time t=0.5. Smoothed image at time t=0.4 appears to be optimal visually.
Summary of Activities for Fiscal Year 2013 31

References

[1] J. L. Mnookin, A Blow to the Credibility of Fingerprint 

Evidence, Boston Globe, February 2, 2004.

[2] J. L. Mnookin, The Achilles Heel of Fingerprints, Washington Post, May 29, 2004.

[3] F. McRoberts and S. Mills, Digitized Prints Can Point 

Finger at the Innocent, Chicago Tribune, January 3,

2005.

[4] F. McRoberts and S. Mills, US Seeks Review of Fingerprint Techniques, Chicago Tribune, February 21, 2005.

[5] J. L. Mnookin, The Courts, the NAS, and the Future of 

Forensic Science, Brooklyn Law Review 75 (2010),

1209-1241. 

[6] Latent Print Examination and Human Factors: Improving the Practice through a Systems Approach, Report of 

the Expert Working Group on Human Factors in Latent 

Print Analysis, US Department of Commerce, National 

Institute of Standards and Technology, (February 2012).

[7] A. S. Carasso, Alternative Methods of Latent Print Enhancements and Metrics for Comparing Them, NIST 

Internal Report 7910, January 2013.

[8] A. S. Carasso, The Use of “Slow Motion” Levy Stable 

Fractional Diffusion Smoothing in Alternative Methods 

of Latent Finger Print Enhancements, NIST Internal Report 7932, April 2013.

[9] Image Processing Toolbox User's Guide (2012), The 

MathWorks, Inc. Natick, MA 0176.

[10] ITTVIS Interactive Data Language (IDL), 

http://www.exelisvis.com/IDL.aspx.

[11] PV-Wave 7.5 Image Processing Toolkit User's Guide, 

Visual Numerics, Inc. Houston, TX 77042.

[12] W. K. Pratt, Digital Image Processing, WileyInterscience, New York, 2012.

[13] A. S. Carasso and A. E. Vladar, Fractional Diffusion, 

Low Exponent Levy Stable Laws, and “Slow Motion” 

Denoising of Helium Ion Microscope Nanoscale Imagery, Journal of Research of the National Institute of 

Standards and Technology 117 (2012). 

Participants

A. Carasso (ACMD)

Figure 14. Viewed on-line on high resolution monitor, smoothed IDL images complement and inform the forensic Photoshop image. Leftmost 

IDL Adaptive Histogram image shows writing near top, streaks near bottom left edge, and horizontal left to right smearing of lower print near 

lower right corner, in addition to well-defined ridge structure. To a lesser extent, these features are also present in the rightmost IDL Histogram image. However, when the Photoshop image is viewed in isolation, the smearing in the lower print is not immediately evident. Also, the 

streaks are faint in the middle image, and the writing near the top appears to have been erased.
32 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2013 33

Part III: Project Summaries

 Part III

Project Summaries
34 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2013 35

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 to critical measurement science applications. 

Compensating Operators and Stable 

Time Marching in Ill-Posed 

Nonlinear Evolution Equations

Alfred Carasso

See feature article, page 17.

Analysis for Dynamic Metrology

Andrew Dienstfrey

Paul Hale (NIST PML)

See feature article, page 26.

A Framework for Reproducible

Latent Fingerprint Enhancements

Alfred Carasso

See feature article, page 29.

Improved Time Delay Estimation 

Method in the Frequency Domain

Anthony J. Kearsley

Ismet Sahin (University of Maryland)

Marwan Simaan (University of Central Florida)

Time-delay estimation is crucial in many applications 

such as in seismology, radar, sonar systems, and biomedical sciences [1]. In these applications, multiple 

noisy copies of a reference waveform are recorded at 

different times, and time-delay amounts between these 

recordings provide important information about the 

underlying system. For instance, in seismology, timedelays between multiple seismic waveforms indicate 

depths of reflections and propagation velocities of 

seismic signals through different layers of the earth.

These, in turn, reveal structural properties of the subsurface layers [2]. In sonar and radar systems, timeshifts between transmitted and received waveforms 

provide estimated location and velocity of an aircraft or 

an underwater vehicle [1]. In biology, estimation of 

time delays between multiple potential waveforms is 

the first step for accurately quantifying amplitude and 

latencies of brain responses to visual stimuli [3]. Such

amplitude and latency measurements are important for 

diagnosing medical problems such as multiple sclerosis 

and optic neuritis.

Methods that involve processing signals either in 

the time domain or in the frequency domain for estimating the time delays have been investigated 

extensively in the past. Our interest centers on a frequency domain method that has been proven to be very 

successful in estimating time delays to within a fraction 

of the sampling period. This method formulates and 

Figure 15. Contours of the cost function for a 2-dimensional timedelay estimation problem. The cost functions with the contours 

shown in (a), (b), (c), and (d) are successively minimized in this 

order. Notice the gradual reduction in the basin of attraction. 

The minimizer of the previous cost function is used as the best 

initial guess for the current minimization at hand. In (d) the 

square marker represents the initial guess, the triangle represents 

the minimizer of the original cost function and the circle represents the minimizer obtained by successive minimizations.
36 NIST Applied and Computational Mathematics Division

minimizes a frequency domain cost function which 

takes into account spectral differences between the 

phase-shifted discrete Fourier transforms (DFTs) of all 

pairs of the available signals [2]. A limiting factor in 

this approach is its sensitivity to the initial guesses of 

time-delays which are provided to the optimizers. Optimization methods tend to diverge for initial guesses 

that are not near to the minimizer due to the narrow 

basin of attraction of the cost function.

Since a good initial guess may not be available for 

many applications, we aim to find approaches that are 

in general not sensitive to the choice of initial guesses. 

To this end, we derive the analytic Hessian of the cost 

function and obtain a condition guaranteeing the positive definiteness of the Hessian, and therefore 

convergence of second order optimization algorithms 

such as Newton’s algorithm [4]. This condition motivates us to construct multiple modified cost functions,

minimizing them successively in order to have larger 

basins of attraction at the beginning, and then gradually 

reducing the size of the basin.

Figure 15 illustrates this process. Figure 15 (a) has 

the largest basin of attraction whose minimization from 

far-initial points leads to a convergence to a point that

is in the basin of the true minimizer. The converged 

point becomes the initial guess for the next minimization task involving the cost contours in Figure 15 (b). 

Proceeding this way, we converge to the true minimizer represented by the circle marker in Figure 15 (d)

from the initial square point. Note that minimization of 

the original cost function shown in Figure 15 (d) would 

result in convergence to the nearest local minimizer 

shown by the triangle marker, which is far from the 

global optimum.

We are planning to develop more efficient numerical algorithms in order to improve scalability of this 

approach for large dimensional time-delay estimation 

problems in a future work.

[1] G. Clifford Carter, Coherence and Time Delay Estimation: An Applied Tutorial for Research, 

Development, Test, and Evaluation Engineers, IEEE 

Press, 1993. 

[2] M. Simaan, A Frequency-Domain Method for TimeShift Estimation and Alignment of Seismic Signals,

IEEE Transactions on Geoscience and Remote Sensing GE-23:2 (March 1985), 132 –138. 

[3] I. Sahin and N. Yilmazer, A Discrete Fourier Transform Method for Alignment of Visual Evoked 

Potentials, in Proceedings of the IEEE Symposium on 

Computational Intelligence in Bioinformatics and 

Computational Biology (CIBCB), May 2010, 1-3. 

[4] I. Sahin, M. Simaan, and A. J. Kearsley, A GloballyConvergent Time Delay Estimation Method in Frequency Domain, in review.

Applied Hierarchical Control

Anthony J. Kearsley

Very often systems governed by partial differential 

equations (PDE) can be controlled (e.g., through 

boundary control or distributed control). One has the 

ability to select boundary conditions or prescribe state 

equation variables to behave in a particular way. These 

problems are particularly challenging when the PDE 

are time dependent. These types of problems abound 

in applications, especially those in measurement science. Efficient numerical methods for the solution of 

these problems have been the subject of significant 

research [1]. Recently, specialized numerical methods 

have been developed for application-specific problems. 

Such is the case with, for example, calibration of spectrometry instruments. 

Motivated by specific scientific and engineering 

applications, such as those arising in calibrating and 

optimizing instrument performance, we investigate a 

means of formulating a class of optimal control problems in which desired behavior of solutions or 

“targets” can be partitioned into categories of increasing relative importance. For example, one might want 

to find instrument settings that reduce the signal-tonoise in a portion of a spectrum, while simultaneously 

optimizing a known absolute molecular mass distribution. These instrument response function problems are 

notoriously difficult, and casting them as hierarchal

control problems, problems with multiple objectives, 

appears to be a fruitful research direction. 

There is no unique mathematical formulation of 

these types of problems; indeed, different formulations can generate completely different “optima.” 

In one formulation, the problem is posed as the minimization of a weighted sum of the deviations from the 

targets with weights corresponding to an established 

priority among the targets (see [6]). Another formulation, sometimes referred to as goal programming,

insists that a set of preferred targets be satisfied to 

within certain tolerances and the others be reduced as 

much as possible within these constraints (see [5]). 

Both of these approaches involve the choice of a set of 

weights or tolerances for which there may be little theoretical guidance.

An instance of this problem occurs, for example, 

in calibrating a matrix-assisted laser desorption/ionization time-of-flight (MALDI/TOF) mass 

spectrometer when one knows the total amount of 

compound present in a sample, suggesting that one 

minimize a least squares or distance regression function while simultaneously maximizing the signal to 

noise ratio. Motivated by this application, and others,

we seek to formulate this problem as a collection of 

nested optimization problems in which the solutions of 

the inner problems are determined using the variables 
Summary of Activities for Fiscal Year 2013 37

in the outer problems as parameters. This approach, 

which is based on the work of von Stackelberg [4] in 

an economics context, requires that the deviations from 

the least important targets, called the “follower” targets, be decreased only after the deviations from the 

most important targets, called the “leader” targets, satisfy prescribed bounds. This type of optimal control 

problem has been termed hierarchical control [2]. One 

way of formulating this type of problem is in terms of a 

nested optimization structure in which, in an “inner 

minimization,” the follower targets are minimized subject to fixed values of certain of the control variables,

and then an “outer minimization” is performed over the 

remaining control variables to obtain optimal leader 

target satisfaction [3]. The resulting accuracy on the 

follower targets is therefore determined by, and is subordinate to, the optimization over the leader targets. In 

the case of MALDI/TOF calibration, matching known 

experiment parameters would be a primary objective,

and maximizing signal to noise a secondary or “follower” objective. 

Recently we have derived optimality conditions 

for a linear differential equation [7] and are very close 

to extending our results to a more general reaction diffusion equation [8]. This work constitutes significant 

steps towards the ultimate goal of robustly and reproducibly optimizing instrument performance for 

multiple objectives.

[1] R. Glowinski, J. L. Lions and J. He, Exact and Approximate Controllability for Distributed Parameter 

Systems: A Numerical Approach, Cambridge University 

Press, 2008. 

[2] J. L. Lions, Hierarchical Control, Proceedings of the 

Indian Academy of Sciences (Mathematical Sciences)

104:1 (February 1994), 295-304.

[3] L. Vicente and P. Calamai. Bilevel and Multilevel Programming: A Bibliography Review, Journal of Global 

Optimization 6 (1994), 1–16.

[4] H. von Stackelberg, Marktform und Gleichgewicht,

Springer, Vienna, 1934.

[5] J. P. Ignizio, Goal Programming, Lexington Books, 

Lexington MA, 1976 

[6] J. Koski, H. Eschenaur and A. Osycka, Multicriteria 

Design Optimizaiton, Springer-Verlag, Berlin, 1990. 

[7] A. J. Kearsley Optimality Conditions for the Hierarchical Control of a Linear Partial Differential Equation, 

in Proceedings of the 2nd IEEE Conference on Instrumentation, Control and Automation, November 2011.

[8] A. J. Kearsley, Hierarchical Control of a Reaction Diffusion Equation, International Journal on Applied 

Mathematics and Statistics 35:5 (2013), 5–19.

Molecular Movies: Imaging 

Femtosecond Motion during 

Electrochemical Transitions

Bradley Alpert

Joel Ulom (NIST PML)

Chris Cromer (NIST PML)

Ralph Jimenez (NIST PML)

Vital to the development of next-generation nanomaterials, including photovoltaics and industrial 

catalysts, is an understanding gained through measurement of electron release, transport, and transfer in 

engineered nanostructures. This project, supported for 

the past three years by a NIST Innovations in Measurement Science (IMS) grant, 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 JILA11, with 

transition-edge sensor (TES) microcalorimeter spectroscopy, developed and refined in the NIST Quantum 

Electronics and Photonics 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 0.1 K to room temperatures.

Wiener filtering, long used among astronomers for 

estimating amplitudes of pulses of known shape contaminated with noise of known 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. 

This year progress occurred in the following areas:

1. Alpert's method for computing filters in the time 

domain, rather than the frequency domain, allowing for orthogonality to prior pulse tails, and its 

evaluation on gamma-ray data, was published [1]. 

It is being implemented at Los Alamos National 

 

11 JILA is a physics research institute jointly operated by NIST and 

Colorado University at Boulder.
38 NIST Applied and Computational Mathematics Division

Laboratory to accelerate an extensive data collection being taken to evaluate the effectiveness of 

microcalorimeters, as an alternative to high-purity 

germanium detectors, for determining isotopic 

composition of nuclear materials. It is also being 

implemented at NASA Goddard Space Flight Center to evaluate as a processing technique for X-ray 

spectroscopy data. Consultations with both of 

these external groups are ongoing.

2. An extensive data collection from special preparations by Japanese collaborators of several different 

elements (Ti, Cr, Mn, Fe, Co in one set) was made 

at NIST of X-ray emissions from electronic transitions, with more than 100 detectors operating in 

parallel, with multiplexing, to further evaluate processing and calibration challenges. One issue that 

rose in prominence is the dependence of photon 

pulse shape on subsample arrival phase and the 

corresponding filtering sensitivity to pulse arrival 

phase. Alpert has worked with Joe Fowler of the 

NIST Physical Measurement Laboratory to propose and evaluate new processing techniques to 

cope with this issue.

The new experimental apparatus that couples the 

pulsed x-ray laser with a large microcalorimeter 

array has, over the past year, been used to collect 

extensive data sets. As anticipated, several new 

processing issues have become prominent, including detector crosstalk, detector nonlinearity, and 

non-Gaussian noise patterns. For some of these, it 

appears most expedient to treat them with new 

processing methods yet to be developed.

[1] B. K. Alpert, R. D. Horansky, D. A. Bennett, W. B. 

Doriese, J. W. Fowler, A. S. Hoover, M. W. Rabin and 

J. N. Ullom, Operation of Gamma-Ray Microcalorimeters at Elevated Count Rates using Filters with 

Constraints, Review of Scientific Instruments 84:5

(2013), 056107.

[2] B. K. Alpert, W. B. Doriese, J. W. Fowler and J. N. 

Ullom, Predicted Energy Resolution of a Running-Sum 

Algorithm for Microcalorimeters, Journal of Low Temperature Physics 167:5-6 (2012), 582-587.

[3] W. B. Doriese, B. K. Alpert, J. W. Fowler, G. C. Hilton, 

A. S. Hojem, K. D. Irwin, C. D. Reintsema, D. R. 

Schmidt, G. M. Stiehl, D. S. Swetz, J. N. Ullom and L. 

R. Vale, Optimization of the TES-Bias Circuit for a 

Multiplexed Microcalorimeter Array, Journal of Low 

Temperature Physics 167:5-6 (2012), 595-601.

[4] D. A. Bennett, R. D. Horansky, D. R. Schmidt, A. S. 

Hoover, R. Winkler, B. K. Alpert, J. A. Beall, W. B. Doriese, J. W. Fowler, C. P. Fitzgerald, G. C. Hilton, K. D. 

Irwin, V. Kotsubo, J. A. B. Mates, G. C. O'Neil, M. W. 

Rabin, C. D. Reintsema, F. J. Schima, D. S. Swetz, L. R. 

Vale and J. N. Ullom, A High Resolution Gamma-Ray 

Spectrometer Based on Superconducting Microcalorimeters, Review of Scientific Instruments 83:9 (2012), 

093113.

Stochastic Simulation in Chemical 

Spectroscopy

Anthony Kearsley

William Wallace (NIST MML)

Yutheeka Gadhyan (University of Houston)

In the data analysis of chemical spectra a collection of

deterministic numerical schemes are used together to 

predict chemical information. Very often linear regression or “binning” of data is used in conjunction with a 

derivative checker that finds peaks and troughs. This 

process is fraught with difficulties, and is very often 

performed by a technician by eye. This is, of course 

simply impossible in many applications (e.g., medicine, forensics) where an automated procedure is 

necessary for the instrument output to be credible. 

Recently we have begun examining the use of stochastic differential equations (SDE) to model and build 

regression simulations of chemical spectra. Very loosely, one can construct an SDE that has two components,

a drift component that captures the signal, and a diffusion term that captures the noise. In so doing, the SDE 

naturally (and automatically) can split the “instrument 

output” into noise and true signal. Once this has been 

accomplished, one can find peaks, examine structures,

measure the area under structures, etc. These techniques are quite often used in financial modeling, albeit 

in a different way. 

This year we developed such a scheme and analyzed its convergence and statistical properties. Using a 

first order Euler-Maruyama discretization, one can 

build an inexpensive numerical scheme to regress on 

chemical spectra accurately. In addition, statistical information about the noise estimation can be calculated 

inexpensively. To validate these ideas we derived and 

analyzed the SDE, implemented a simple numerical 

integration, together with associated convergence analFigure 16. Regression applied to a data spectrum from a MALDITOF mass spectrometry study of a narrow-polydispersity synthetic 

polymer.
Summary of Activities for Fiscal Year 2013 39

ysis, which suggested a time-stepping scheme. We 

applied the regression to a data spectrum from a 

MALDI-TOF mass spectrometry study of a narrowpolydispersity synthetic polymer. Polystyrene, with an 

average molecular mass of 9100 g/mol, was analyzed 

using all-trans-retinoic acid as a matrix, and silver trifluoracetate as a cationizing agent, as detailed in [1]. 

Early results appear promising (see Figure 16); the 

regression certainly follows the instrument output well,

and it succeeds in automatically separating noise from 

signal.

Because this regression provides a statistical estimate of the noise, one has the ability to interrogate 

peaks in the spectrum, that is, to examine the estimated 

noise in a neighborhood of a peak that was identified 

by, for example, the peak peaking software from the 

instrument. In Figure 17 we see an interesting example 

where off-the-shelf peak-picking software found four 

peaks very close to each other. The magnitude of these 

peaks was suspiciously low. Examining the noise estimate produced by the SDE approach, three of the four 

identified peaks were below the level of the noise, suggesting that the off-the-shelf software incorrectly 

identified them as peaks. However, one of the peaks 

was above the estimated noise level. Surprisingly, this 

fourth peak was a true peak, thus illustrating the potential benefit of our SDE regression approach. A 

preliminary manuscript is being prepared [2].

[1] C. M. Guttman, K. M. Flynn, W. E. Wallace and A. J. 

Kearsley, Quantitative Mass Spectrometry and Polydisperse Materials: Creation of an Absolute Molecular 

Mass Distribution Polymer Standard, Macromolecules

42 (2009), 1695–1702. 

[2] Y. Gadhyan, A. Kearsley and W. Wallace, Stochastic 

Regression Modelling of Chemical Spectra, in preparation.

Computational Tools for Shape 

Measurement and Analysis

Gunay Dogan

The main goal of this project is to develop efficient and 

reliable computational tools to detect geometric 

structures and to evaluate and compare them in a 

quantitative manner. Such structures include curves, 

regions and boundaries obtained from given direct and 

indirect measurements, such as microscope images or 

tomographic measurements. This is important in many 

areas of science and engineering, such as the analysis 

of microscopy images for cell biology or micro-CT 

(computed tomography) images of microstructures in 

material science.

We have been developing image segmentation 

algorithms based on energy minimization principles, 

which leads to shape optimization formulations. In this 

approach, the user starts the segmentation algorithm 

with some initial estimate of the sought region 

boundaries, which is then deformed or evolved 

iteratively towards minimal energy configurations, 

which are, by design, the right segmentations. An 

example of such a process is shown in Figure 18.

Segmentation of different image classes requires

different model energies specially designed for each 

class. For example, a two-phase-material image can be 

segmented by the Chan-Vese segmentation energy, 

which decomposes the image into a background and 

some foreground objects. This was implemented 

previously as part of this project. In this fiscal year, this 

model was extended to handle multiphase images as 

well. Images with well-defined edges, on the other 

hand, can be segmented with the Geodesic Active 

Contour (GAC) model, also implemented as part of this 

project. The GAC model is sensitive to the choice of 

image interpolation and image derivatives. To ensure 

robustness and efficiency, B-splines were incorporated 

into the image definition. Moreover, a diffusion process 

was implemented on the image grid to obtain smooth 

image features to be used by the segmentation models. 

An anisotropic version of the GAC model was also 

developed. This takes local orientation of the candidate 

boundaries into account to improve alignment with the 

target boundaries. New geometric function definitions 

were implemented to support definitions of the new 

energies mentioned, as well as future energies.

Significant efforts have gone into increasing the 

efficiency and robustness of the shape optimization 

framework. Ideally, the segmentation algorithm should

terminate successfully in a short amount of time and 

not require a lot of user tuning. In order to reduce 

computation time, judicious caching was introduced for 

both shape energies and mesh functions, so that 

numerical quantities would be computed only at the 

mesh locations needed and only when they were new 

Figure 17. Results of off-the-shelf peak picking software.
40 NIST Applied and Computational Mathematics Division

and needed to be refreshed. Additionally, sophisticated 

line search algorithms were implemented to reduce 

both the number of iterations and energy evaluations. 

Finally, automatic stopping criteria were developed to 

avoid premature termination and superfluous iterations 

once the segmentation is achieved.

Some preliminary work to address the case of 

indirect measurements (tomography) was carried out. 

Such reconstructions can be also formulated as a shape 

optimization, which fits our framework. A simple proof 

of concept for the case of x-ray tomography was 

implemented to demonstrate viability. A potential 

application is reconstruction of microstructure 

interfaces from micro-CT measurements.

Computation of Shape Geodesics

Gunay Dogan

Javier Bernal

Charles Hagwood (NIST ITL)

Shape, a natural and intrinsic attribute of geometric 

structures and objects, is a very good comparator. Its 

use in applications, e.g., object recognition, cluster and 

classification analyses, computational biology, analysis 

of microstructure grains, and other areas, attests to its 

significance for modern technology. Many years of 

work on shape analysis by contributors such as Bookstein, Kendal, Grenander, Younes, and Mumford, 

culminated in work by Srisvastav et al. [1], who derived a presentation of shape as an object in a 

Riemannian manifold. With such a representation, geometric objects can be compared in a quantitative

manner based on their geodesic distance. 

The development of a fast algorithm for computing shape geodesics is under way. Such an algorithm 

is essential for large-scale comparisons. For this purpose, proper optimality conditions have been derived 

for the minimization problem at the heart of the shape 

geodesics computation. Using this formulation, unnecessary steps in Srivastava’s algorithm have been

removed. This has resulted in savings in computation 

time on synthetic examples. Moreover, geodesic distance values on these synthetic examples have been 

improved. These results are preliminary, but encouraging, confirming that the work in this area is moving in 

the right direction. See Figure 19.

[1] E. Klassen, A. Srivastava, W. Mio and S. Joshi. Analysis of Planar Shapes using Geodesic Paths on Shape 

Spaces, IEEE Pattern Analysis and Machine Intelligence

26:3 (March 2004), 372-383.

Figure 18. The segmentation of a microstructure image using the algorithms developed in this project. The top left image shows the final 

result of our segmentation, which produces well-defined regions and boundaries. It compares favorably with the result on top right, which was 

obtained by thresholding, a very common technique used for image segmentation. Thresholding does not work well for such noisy images and 

produces many misclassified pixel labels, i.e. black dots in white areas and white dots in black areas. This is not a problem for our algorithm. 

The bottom row shows some intermediate steps of the iterative segmentation process. The curves on the left image are the starting curves. The 

algorithm deforms them gradually as shown in the intermediate steps, and it stops when the curves are aligned with region boundaries as 

shown in the last image of the bottom row.
Summary of Activities for Fiscal Year 2013 41

Traceable Simulation of Magnetic 

Resonance Imaging

Zydrunas Gimbutas

Andrew Dienstfrey

Steve Russek (NIST PML)

Katy Keenan (NIST PML)

Karl Stupic (NIST PML)

Magnetic resonance imaging (MRI) is maturing as a 

quantitative biomedical imaging technology. For example, imaging facilities routinely report tumor 

volumes in units of mm3, blood perfusion in units of ml 

g

-1 min-1

, apparent diffusion coefficient in mm2s

-1

, and 

temperature in K. However, as of a few years ago the 

use of SI units for these technologies was potentially 

unwarranted as SI traceability chains supporting these 

MRI measurement modalities were unclear and, in 

many cases, non-existent. More recently NIST and

partner institutions have made substantial investments 

to develop such traceability chains. NIST now supports 

several phantoms, as standard reference artifacts are 

referred to in the medical community, enabling SItraceable calibration for MRI scanners.

MRI is predicated on established physical principles. It follows that predictive quantitative simulation 

of this imaging modality is possible, and a growing 

number of computer codes are available which claim to 

do just this. Virtual prototyping is highly desirable to

improve the fundamental understanding of MRI capabilities, with expectations for significant reductions in 

time and costs by comparison with use of physical 

scanners. While nearly all agree on the potential for

quantitative MRI simulation, neither NIST nor any 

other national metrology institution is currently positioned to verify the accuracy of such claims.

In 2013 we initiated a new project 

to create SI-traceable simulations for 

magnetic resonance imaging. Under this 

project we will develop quantitative 

analysis of MRI simulation side-by-side 

with the ongoing MRI phantom development projects at NIST. This past year 

we obtained, compiled, and executed a 

number of MRI simulation codes. These 

are large codebases developed principally within academic and industrial

research labs, and they carry minimal 

documentation. Regardless, we can 

now execute a number of the most highly-cited MRI simulation tools: ObjectOriented Development Interface for 

NMR (ODIN) [2], SIMRI [1], and 

JEMRIS [3]. 

In the next year we will continue to explore the 

quantitative capabilities of each code in isolation, as 

well as identify MRI measurement scenarios that will 

allow cross-comparison of the numerical outputs. In 

tandem, we will collaborate with NIST researchers 

performing MRI measurements to begin comparing 

computational to experimental results. In the longterm, we hope to further enable simulation-based innovations in MRI imaging and future phantom design, 

while maintaining traceability to NIST physical measurements, and the International System of Units.

[1] H. Benoit-Cattin, G. Collewet, H. Saint-Jaimes and C. 

Odet, The SIMRI Project: a Versatile and Interactive 

MRI Simulator, Journal of Magnetic Resonance 173:1

(March 2005), 97-115.

[2] T. H. Jochimsen and M. von Mengershausen. ODIN -

Object-oriented Development Interface for NMR, Journal of Magnetic Resonance 170:1 (Sept. 2004), 67-78.

[3] T. Stöcker, K. Vahedipour and D. Pugfelder, HighPerformance Computing MRI simulations, Magnetic 

Resonance in Medicine 64:1 (July 2010), 186-193.

Modeling and Optimization in 

Cryobiology

Anthony Kearsley

Daniel Anderson (George Mason University)

James Benson (Northern Illinois University)

Adam Higgins (Oregon State University)

Mathematical modeling plays an important role in understanding the behavior of cells, tissues, and organs 

undergoing cryopreservation. Uses of these models 

range from explanation of phenomena, exploration of 

potential theories of damage or success, development 

of equipment, and refinement of optimal cryopreservation and cryoablation strategies. Cryopreservation 

Figure 19. Left: fluorescence image of multiple DLEX-p46 cells. Right: A geodesic 

distance comparison matrix showing distances between 3 cell shapes. In real comparison problems, 100 x 100 geodesic matrices or larger are required. This is why 

improved computation speed is needed.
42 NIST Applied and Computational Mathematics Division

procedures permit cells to be stored indefinitely using 

extremely cold temperatures, suspending metabolic 

activities, and preserving the cell and its function. 

Loosely speaking, there are two main types of cryopreservation procedures: equilibrium (conventional 

slow freezing) and non-equilibrium or ultra-rapid 

freezing (vitrification). Both procedures employ the use 

of cryoprotectants, chemicals behaving like antifreeze. 

Cryoprotectants prevent cellular damage during the 

freezing process. After proper freezing, cells should be 

able to be stored for an indefinite amount of time. This 

can be done, for example, by immersing them in liquid 

nitrogen, an extremely cold fluid with an approximate 

temperature of -196o C. Cryoprotectants must be removed during the thawing process; slowly the water 

balance in the cell is restored and normal activity in the 

cell should return. 

Procedures exist for the freezing of single cells, 

tissue comprised of many cells and entire organs. Size, 

amount of cytoplasm (or fluid), and structural complexity change the freezing procedures employed. For 

example, cells with less cytoplasm, like sperm cells, 

are generally considered to be less difficult to freeze 

than those cells with more cytoplasm, like eggs. Slow 

freezing or equilibration has been successfully employed to freeze and store a wide range of cells but 

research is ongoing to optimize the process. 

Recently we studied the use of optimization techniques to determine or improve the equilibration of 

cryoprotectant. We considered the case of cells and 

tissues with high concentrations of permeating chemicals known as cryoprotective agents, or CPAs. Despite 

their protective properties, CPAs can cause damage as 

a result of osmotically-driven cell volume changes, as 

well as chemical toxicity. In this study, data was used 

to determine a toxicity cost function, a quantity that 

represents the cumulative damage caused by toxicity. 

We then used this cost function to define and numerically solve the optimal control problem for CPA 

equilibration, using human oocytes as a representative 

cell type with high clinical relevance. The resulting 

optimal procedures are predicted to yield significantly 

less toxicity than conventional procedures. 

Results showed that toxicity is minimized during 

CPA addition by inducing the cell to swell to its maximum tolerable volume and then loading it with CPA 

while in the swollen state. This counterintuitive result 

is considerably different from the conventional stepwise strategy, which involves exposure to successively 

higher CPA concentrations in order to avoid excessive 

shrinkage. The procedures identified are a first step 

deriving procedures that significantly reduce damage 

due to toxicity. 

Over the last half century there has been a considerable amount of work in bio-heat and mass-transport, 

and these models and theories have been readily and 

repeatedly applied to cryobiology with much success. 

However, there are significant gaps between experimental and theoretical results that suggest that there are 

missing links in models. One source for these potential 

gaps is that cryobiology is at the intersection of several 

very challenging aspects of transport theory: it couples 

multi-component, moving boundary, multiphase solutions that interact through a semipermeable elastic 

membrane with multicomponent solutions in a second 

time-varying domain, during a two-hundred Kelvin 

temperature change with multi-molar concentration 

gradients and multi-atmosphere pressure changes. 

We have been developing mathematical and computational models built on first principles to describe 

coupled heat and mass transport in cryobiological systems in an effort to account for these various effects. 

Our efforts have advanced along three fronts: (1) we 

have examined concentration variable relationships, 

their impact on choices Gibbs energy models, and their 

impact on chemical potentials, (2) we have subsequently developed heat and mass transport models that are 

coupled through phase-change and biological membrane boundary conditions, and (3) we have developed 

numerical methods for solving these multi-species multiphase free boundary problems. 

[1] D. M. Anderson, J. D. Benson and A. J. Kearsley, Foundations of Modeling in Cryobiology, in preparation.

[2] J. D. Benson, A. J. Kearsley and A. Z. Higgins, 

Mathematical Optimization Procedures for 

Cryoprotectant Equilibration using a Toxicity Cost 

Function, Cryobiology 64:3 (2012), 144-151. 

Equilibrium and Stability of Drops 

on a Conical Substrate

Asha Nurse, 

Sean Colbert-Kelly 

Geoffrey McFadden

Sam Coriell (NIST MML)

In some applications of tissue engineering, biological 

cells in solution show a tendency to self-assemble into 

a spherical cluster, a configuration that minimizes the 

surface area of the assembly. If the cells are situated in 

the bottom of a scaffold that contains a conical pillar, 

they can instead be forced to form a toroidal cluster at 

the base of the pillar as shown in Figure 20.

Depending on the size of the cluster, the cells are 

sometimes observed to climb the side of the pillar, in 

the direction opposed to gravity, eventually reaching 

the apex of the cone and falling off. A dynamical model of this process has been developed by A. Nurse et al. 

[1, 2], in which the motion results from the competition 

between the effects of gravity and surface energy of the 

cluster. In a toroidal geometry with given volume, the 

cluster can reduce its total surface area by decreasing 
Summary of Activities for Fiscal Year 2013 43

its major radius, which it can do if it climbs the side of 

the pillar. This motion reduces the net surface energy at 

the expense of the gravitational potential energy, which 

tends to oppose the upward motion.

We have continued this modeling effort by studying the equilibrium and stability of toroidal liquid 

drops on a conical substrate, taking into account the 

effects of gravity and surface energy. Axisymmetric 

configurations can be computed by minimizing an appropriate energy functional that depends on the shape 

of the drop, resulting in a nonlinear ordinary differential equation coupled to a volume constraint. The 

solution depends on the cone geometry, the contact 

angle of the drop on the substrate, the drop volume, 

and the ratio of gravitational to capillary forces as 

measured by the Bond number Bo = g R2/, where 

is the drop density, g is the gravitational acceleration, R 

is the radius of a sphere of equal volume, and  is the 

surface energy. Examples of equilibrium shapes are 

shown in Figure 21.

Rather surprisingly, increasing the Bond number 

(stronger gravity) results in drops that are higher on the 

cone, not lower. This results from the requirement of 

an equilibrium force balance: a larger capillary force is 

produced if the drop moves up and reduces its major 

radius. Conservation of volume produces an increase in 

the drop's minor radius as the major radius decreases.

Axisymmetric toroidal drops can also be subject to

instabilities that can cause “fluting'” in the azimuthal 

direction that are analogous to the Raleigh instability of 

a liquid jet, which can lead to breakup of the jet via 

droplet formation. We have therefore also formulated 

the associated stability problem, which involves a solution of the equations for the second variation of the 

energy functional. We find that the drops are subject to 

a non-axisymmetric instability to perturbations that can 

cause tilting and distortion of the drop.

[1] A. Nurse, L. B. Freund and Jacquelyn Youssef, A Model 

of Force Generation in a Three Dimensional Toroidal 

Cluster of Cells, Journal of Applied Mechanics 79

(2012), 051013.

[2] J. Youssef, A. Nurse, L. B. Freund and Jeffrey R. Morgan, Quantification of the Forces Driving Self-Assembly 

of Three-Dimensional Microtissues, Proceedings of the 

National Academy of Sciences 108 (2011), 6993-6998.

Diffuse Interface Model 

Incorporating Interfacial Properties

Sean Colbert-Kelly

Geoffrey McFadden

Frederick Phelan, Jr. (NIST MML)

Surfactants are chemical compounds that lower interfacial tension between two liquids or a liquid and a solid. 

Surfactants have important applications in detergents, 

droplet break-up, reducing the risk from bubbles 

formed in blood due to rapid decompression and prevention of lung collapse at the end of expiration [1, 

3].This research project studies the transition that occurs between two immiscible fluids with surfactant at 

the interface between the two fluids. 

Discontinuities in fluid properties at the interface, 

as well as properties such as surface energy and surface 

viscosity associated with the interface itself, tend to 

complicate the computation of flow near the interface. 

Utilizing a diffuse interface model can be useful in 

investigating the dynamics near the interface. The mixing properties of the two fluids affect the interface 

shape’s dynamics. Surfactants migrate to the fluid interface in a binary mixture due to the amphiphilic 

nature of these molecules [1]. The presence of the surfactant produces dramatic changes in the interfacial 

Figure 20. Side view of a toroidal cell cluster climbing the side of 

a conical pillar.

Figure 21. Equilibrium cross-sections of three axisymmetric 

liquid drops on the side of a conical pillar with half-angle  = 57o

at the apex of the cone. The drops have contact angles of  = 143o

on the conical substrate. Drops corresponding to three different 

Bond numbers Bo are shown, where the Bond number is the ratio 

of gravitational to capillary forces.
44 NIST Applied and Computational Mathematics Division

properties of the fluid mixture, and therefore greatly 

alters the stability, equilibrium properties, and the 

droplet dynamics of the mixture. An initial effect of the 

surfactant is a lowering of the surface tension. However, gradients in the surfactant concentration on the drop 

surface under flow give rise to Marangoni forces that 

alter drop shape, breakup and coalescence dynamics, as 

well as giving rise to flow induced migration [2]. An 

additional effect of the surfactant is that they give rise 

to shear and dilational interfacial viscosities. Along 

with surface tension, the interfacial viscosities play a 

crucial role in coalescence dynamics, therefore governing the long time stability of emulsions. Current 

models do not accurately model the dramatic effects of 

surfactants on emulsion properties and dynamics.

Following previous work, this project intends to 

develop a description of the mixture of two immiscible 

fluids with surfactants where mixing can occur near the 

interface, while incorporating interfacial properties that 

many diffuse interface models (DIM) tend to ignore. 

Previous research has employed a mixing rule to incorporate interfacial viscosity [4]. However, this project 

will consider alternative approaches using a diffuse 

interface description. The research project will consider 

the situation of a droplet in a particular medium that 

follows a Stokes flow. The two liquids are considered 

Newtonian and incompressible, where in the interfacial 

region this assumption may not hold. In addition to 

developing a diffuse interface model, this project will 

study the limiting problem of the diffuse interface 

model, to determine if a sharp interface model is recovered in letting the interfacial region get arbitrarily

thin. It will also be of benefit to study the deformation 

of the droplet, and determine if the droplet will remain 

spherical in shape.

Currently, we are comparing various free energy 

formulations to determine which one is to be utilized 

[1, 3] based on the representation of the system of interest and computational ease. From what has been 

gathered, the common elements of the free energy are:

 Cahn-Hilliard free energy: The bulk energy density drives the system into distinct phases 

corresponding to its minimum values. The gradient energy term penalizes steep gradients 

characterized by the constant multiplying this 

term.

 Entropy for ideal mixing of surfactant: This term 

governs the kinetics of surfactant adsorption and 

also incorporates the saturation of surfactant at the 

interface, governing the entropy decrease of mixing the surfactant with the bulk phase [1].

 Surfactant-interface coupling energy: This term 

describes the adsorption behavior of the surfactant 

near the binary fluid interface [3].

 Energy for excess surfactant in the pure regions:

This term penalizes the free energy if there is free 

surfactant in the bulk region of the system. It can 

also be regarded in some models as the bulk solubility [1]. Some models incorporate the 

penalization of free surfactant in the pure phases in 

the surfactant-interface coupling energy term [3].

[1] S. Engblom, M. Do-Quang, G. Amberg and A.-K. Tornberg, On Diffuse Interface Modeling and Simulation of 

Surfactants in Two-Phase Fluid Flow, Communications 

in Computational Physics 14:4 (2013), 879-915.

[2] J. T. Schwalbe, F. R. Phelan, Jr., P. M. Vlahovska and S. 

D. Hudson, Interfacial Effects on Droplet Dynamics in 

Poiseuille Flow, Soft Matter 7 (2011), 7797–7804.

[3] C.-H. Teng, I.-L. Chern and M.-C. Lai, Simulating Binary Fluid-Surfactant Dynamics by a Phase Field Model, 

Discrete and Continuous Dynamical Systems Series B

17:4 (2012) 1289-1307.

[4] W. Yu and C. Zhou, The Effect of Interfacial Viscosity 

on the Droplet Dynamics Under Flow Field, Journal of 

Polymer Science Part B: Polymer Physics 46:14 (2008), 

1505-1514.

Spectral-Galerkin Scheme to Study 

Ferroelectric Liquid Crystal

Properties

Sean Colbert-Kelly

Geoffrey McFadden

Daniel Phillips (Purdue University)

Jie Shen (Purdue University)

This project considers the effect of introducing defects 

into a ferroelectric liquid crystal thin film. The liquid 

crystal film of interest is chiral smectic c (SmC*), 

which has a spontaneous polarization field [1]. Such 

films are composed of layers of liquid crystal molecules. The local average of the molecular long axes at a 

point in the layer, the director field n, is tilted at a constant angle 0 < θ < π/2 from the normal to the layers. 

Hence, each layer in a thin film of SmC* can be represented as a two-dimensional liquid [2], with u

representing the normalized projection of n onto the 

2D layer.

If a particle is introduced into a thin film SmC* 

liquid crystal, then an island will form, several layers 

thicker than the surrounding thin film, around the defect [3]. These islands are disk-like and u is tangential

counterclockwise on the island’s outer edge, resulting 

in a vector field of degree 1. Its initial orientation is 

tangential. However, increase in the island’s size or 

external forces can cause distinct textural transformations in the director field. The pattern can remain 

unchanged or transform to a simple spiral, tangential 

counterclockwise on the boundary and approximately 

radial at the smoke particle boundary [3].
Summary of Activities for Fiscal Year 2013 45

The free energy of this system in the island can be 

described by a relaxed energy

 

( ) 

 

 

∫ ( 

( )

 ( ) )

 

 

 

 

 

 

( | |

 )

 

 

where ks, kb are the splay and bend constants for the 

liquid crystal, is the radius of the defect core and u is 

no longer restricted to having length 1. Due to the polarization vector field, u is given boundary conditions, 

i.e., u = g when |x| = 1, ks ≠ kb, and g has degree d > 0. 

For each , a minimizing vector field exists and as 

 

 

. 

 has d degree 1 singularities, and 

near a singularity, a, 

 behaves locally as

 

 

 

| |

where for ks < kb and for kb < ks

[4].

The purpose of this project is to develop a spectral-Galerkin numerical method to solve the EulerLagrange equations for 

, when is small, so as to 

capture the experimental observations and analytical 

results described above. Many numerical methods deal 

with the case ks = kb, resulting in the Allen-Cahn equation. Our method will also simulate the case ks ≠ kb [5, 

6]. We develop a gradient flow stabilized scheme to 

solve the Euler-Lagrange equations and let the solutions stabilize to an equilibrium state. This is done due 

to the non-linear terms in the equations. We discretize 

the Euler-Lagrange equation as a first-order semiimplicit stabilized scheme. The equation is then converted into a polar geometry representation. With this 

representation we can approximate the solution with a 

Fourier expansion in the angle variable using the FFT 

and then approximate the Fourier coefficients using 

Chebyshev polynomials in the radius variable, giving 

the form of the approximation

 ∑ ∑ ( ̂ ) 

 

 

| | 

 

 

( ) 

 

This scheme has been shown to be unconditionally 

stable. Using MATLAB R2012a version 7.14.0.739, 

we tested the scheme with various boundary conditions 

having degree one and two. Figure 23 plots the minimum vector field orientation 

, given the values of ks,

kb and the boundary data g. We see that in the case ks < 

kb, the vector field is nearly radial near the origin. 

When kb < ks, the vector field is nearly tangential near 

origin. This follows what was shown analytically. The

plot in the case ks < kb follows what was seen experimentally as well. In the case where ks < kb and the

vector field is tangential at the 

boundary, either clockwise or 

counterclockwise, the stable 

vector field is a simple spiral.

In the case of degree two 

boundary conditions, 

 

, 

the simulations suggest 

uniqueness of the location for 

the two degree one vortices. 

They seem to migrate to the 

real axis in the case ks < kb and

to the imaginary axis in the 

case kb < ks, lying symmetrically about the origin, as depicted 

in Figure 22. This result is independent of where the initial 

vortices where located or 

whether the vortices are degree 

1 or 2. Further analysis of this 

result needs to be done, in 

terms of analyzing the energy 

in a renormalized state, expressed in terms of the 

vortices, boundary data, and 

the vector field in the domain.

Lee, Konovalov, and 

Meyer [3] note that the size of 

the island also affects the transformation of the vector field. If 

the island is of small size, i.e. 

small radius, then the pure 

 

 ( ( 

 

 

)) ( )

Figure 23. Stable vector fields to the free energy.

 

 ( ) ( )

Figure 22. Stable vector fields to the free energy.
46 NIST Applied and Computational Mathematics Division

bend patterns rarely transform to a simple spiral. This 

would be a test that could be done on the simulation to 

determine if we obtain similar results.

[1] J.-B. Lee, R. A. Pelcovits, and R. B. Meyer, Role of 

Electrostatics in the Texture of Islands in Free-standing 

Ferroelectric Liquid Crystals, Physical Review E 75

(2007), 051701.

[2] R. B. Meyer, L. Liébert, L. Strzelecki and P. Keller, 

Ferroelectric Liquid Crystals, Le Journal de Physique 

Lettres 36:3 (1975), L69-L71.

[3] J.-B. Lee, D. Konovalov, and R. B. Meyer, Textural 

Transformations in Islands on Free Standing Smectic-C* 

Liquid Crystal Films, Physical Review E 73 (2006), 

051705.

[4] S. Colbert-Kelly and D. Phillips, Analysis of a Ginzburg-Landau Type Energy Model for Smectic C* Liquid 

Crystals with Defects, Annales de l'Institut Henri Poincare (C) Non Linear Analysis 30:6 (2013), 1009-1026.

[5] J. Shen, Efficient Spectral-Galerkin Methods III: Polar 

and Cylindrical Geometries, SIAM Journal on Scientific 

Computing 18:6 (199), 1583-1604.

[6] J. Shen and X. Yang, Numerical Approximations of 

Allen-Cahn and Cahn-Hilliard Equations, Discrete and 

Continuous Dynamical Systems. Series A 28:4 (2010), 

1669-1691.

Modeling Magnetic Fusion

Geoffrey McFadden

Antoine Cerfon (New York University)

A potential source of commercial energy is based on 

the confinement of hot plasma of hydrogen isotopes by 

a strong magnetic field in a toroidal geometry so the 

ions fuse to form helium and release energetic neutrons. A number of computational methods to model 

magnetic fusion devices have been developed by researchers at New York University (NYU) and 

elsewhere to allow effective numerical simulations of 

the most essential features of modern tokomak and 

stellarator experiments. G. McFadden and colleagues at 

NYU are currently participating in a benchmarking 

exercise to compare the simulation results produced by 

a number of codes that are in use by the fusion community. The benchmark is based on the DIII-D 

tokomak experiment at General Atomics in San Diego, 

California. The NSTAB equilibrium and stability code 

developed by Paul Garabedian and Mark Taylor at 

NYU [1] uses a variational formulation of the equations of magneto-hydrodynamics to compute plasma 

equilibria that exhibit a family of nested flux surfaces 

that enable plasma containment [2]. A typical NSTAB 

calculation is shown in Figure 24, illustrating a crosssection of the axisymmetric DIII-D geometry. The 

benchmarking exercise is being organized by researchers at the Princeton Plasma Physics Laboratory and 

Oak Ridge National Laboratory.

[1] M. Taylor, A High Performance Spectral Code for Nonlinear MHD Stability, Journal of Computational Physics

110 (1994), 407-418.

[2] P. R. Garabedian and G. B. McFadden, Design of the 

DEMO Fusion Reactor Following ITER, Journal of Research of the National Institute of Standards and 

Technology 114 (2009), 229-236.

Development of a New Solver for 

HVAC Simulation

Anthony Kearsley 

Amanda Pertzborn (NIST EL)

Jin Wen (Drexel University)

Shokouh Pourarian (Drexel University)

Dan Veronica (NIST EL)

Buildings account for 82 % of the electrical energy 

consumption in the US [1]. Furthermore, approximately 80 % of the life cycle energy use of a building is 

associated with its operation rather than material and 

construction costs [2]. Thus, optimal building operational decisions are crucial to energy efficiency. The 

imminent need for buildings to interact with a smart 

electric grid adds new opportunities to move optimal 

decision making for each building into the realm of 

Figure 24. Magnetic flux surfaces in a three-dimensional model 

of the DIII-D tokomak computed by using the NSTAB equilibrium 

code [1]. A cross-section of the toroidal geometry is shown, with 

the axis of symmetry to the left of the surfaces.
Summary of Activities for Fiscal Year 2013 47

automated cyber-physical systems governed by artificial intelligence. For example, information provided to 

the building control system by the smart grid, such as 

real-time electricity pricing, can be used to make decisions about whether to use power generated by solar 

panels in the building itself or sell it to the utility. Development of algorithms needed to provide this 

intelligence requires a robust simulation testbed.

HVACSIM+, the current simulation test bed, was 

developed at NIST in the 1980s for the simulation of 

heating, ventilating, and air conditioning (HVAC) systems [3]. A specialized solver was developed for 

HVACSIM+ at NIST. At the time this was an advanced program, but now the limitations of 

HVACSIM+ are apparent: the size of the problems that 

can be solved is limited, it is too sensitive to initial 

guess values for the state of the system, and the user 

must be adept at formulating the problem in order to 

achieve a good solution. 

Two examples of the sensitivity of HVACSIM+ to 

the initial guess values are shown in Figure 25 and 

Figure 26, which are based on examples taken from 

[4]. The model that produced Figure 25 includes a 

heating coil, controller, several valves, and lengths of 

pipe; this is a very simple model. The temperature at 

one point in the pipe over time is shown in the figure. 

The base case is the solution suggested in [4]; the 1 % 

case was calculated by randomly perturbing some of 

the initial values used in the base case between -1% 

and 1 %; the 5 % case was calculated similarly. When 

the perturbation is only 1 %, the solution changes only 

slightly, but when the perturbation increases to 5 %, the 

solution changes noticeably. 

Figure 26 was generated by a system including a 

single zone (for example, a room in a building) 

supplied with conditioned air by an air handler that 

includes a cooling coil. It is a relatively simple model 

as compared to what exists in an actual building. The 

base case was calculated following the steps described 

in [4] to generate a good set of guess values. The 1% 

line was calculated using guess values generated by 

randomly perturbing the initial conditions for the base 

case by -1% or +1 %. This small perturbation in the 

guess values caused the solution to diverge within the 

first 3 seconds of the simulation. A tool that is this 

sensitive to guess values that are by their nature 

uncertain has limited utility for the problems we 

envision needing to model.

Dr. J. Wen and S. Pourarian at Drexel University 

have been investigating the causes of this instability as 

part of a grant [5]. A. Kearsley has been working closely with them to develop a new, more stable solver 

based on the Levenberg-Marquardt method. A. Pertzborn and D. Veronica have been working to integrate 

this new solver into the existing program for testing.

Additional work remains to update HVACSIM+ 

and turn it into a tool that can be applied to the effort to 

fully integrate embedded intelligence with smart grid in 

commercial buildings. This effort requires a solver that 

is not only robust and stable, but is also capable of enforcing constraints to maintain the solution in a 

physically realistic space, handle large scale models, 

and reformulate a poorly designed problem.

[1] Buildings Energy Data Book, US Department of Energy, Table 6.1.112

, downloaded 12/6/2013.

[2] Transforming the Market: Energy Efficiency in Buildings

13

, World Business Council for Sustainable 

Development.

[3] D. Clark, HVACSIM+ Building Systems and Equipment 

Simulation Program Reference Manual, National Bureau 

of Standards, NBSIR 84-2996, 1984.

[4] D. Clark and W. May, HVACSIM+ Building Systems 

and Equipment Simulation Program – Users Guide, National Bureau of Standards, NBSIR 85-3243, 1985.

 

12 http://buildingsdatabook.eren.doe.gov/TableView.aspx?table= 

6.1.1

13 http://www.wbcsd.org/Pages/EDocument 

/EDocumentDetails.aspx?ID=11006

Figure 25. Temperature calculated by HVACSIM+ at one point in 

a basic heating coil control loop for three sets of initial guess 

values.

0 500 1000 1500 15

20

25

30

35

40

Time (s)

Temperature (°C)

Base case

1%

5%

Figure 26. Flow rate calculated by HVACSIM+ for a single zone 

air handler with cooling coil for two sets of initial guess values.
48 NIST Applied and Computational Mathematics Division

[5] NIST Grant, Number 60NANB10D243, Tools for Evaluating Fault Detection and Diagnostic Methods for 

HVAC Secondary Systems of a Net Zero Building.

Sustainable Design of Reinforced 

Concrete Structures

Florian A. Potra 

Dong Hun Yeo (NIST EL)

Emil Simiu (NIST EL)

Traditionally, the objective of structural engineering 

has been to achieve construction that is safe and disaster-resilient on the one hand and economical on the 

other. It is only recently that the scope of structural 

engineering has been expanded to include sustainability. According to studies conducted by the 

Organization for Economic Cooperation and Development (OECD), the residential and commercial building 

sectors are responsible for approximately 30% of primary energy consumed and of greenhouse gas 

emissions in OECD countries. 

The contribution of reinforced concrete construction to embodied energy is significant, and modern 

structural design methods can help to achieve important reduction of this contribution. In spite of the 

use of additives such as fly ash, reinforced concrete 

structures, which are large consumers of cement, are 

responsible for a sizable proportion of worldwide carbon emissions. These emissions can be reduced 

significantly by using optimization techniques to devise a more efficient use of both concrete and steel. 

Modern optimization tools now make it possible to 

perform large volumes of calculations applicable to a 

wide variety of structural engineering problems. 

This project presents an optimization approach developed with a view to allowing decision-makers to 

balance sustainability and economic objectives. To 

illustrate this approach a reinforced concrete frame 

under gravity and lateral loads was considered. The 

optimization with respect to the CO2 footprint results in 

an increase in the relative amount of steel within the 

members’ cross sections; however, the requisite ductility is assured via constraints specified in the 

optimization process. The reduction of the footprint 

achieved by optimizing the design to obtain minimum 

carbon emissions, as opposed to optimizing the design 

to achieve minimum cost, is of the order of 5% to 15%, 

depending upon the parameter values being assumed. 

In addition, an investigation was performed into 

the effects of concrete compression strength on the 

optimization effectiveness. As the concrete strength 

increases, the difference between the costs of the costoptimized and the footprint-optimized frames decreases, while the difference between the CO2 footprints of 

the cost-optimized and the CO2-optimized frames increases. Thus, for higher strength concrete, the 

optimization is very effective. The initial results of this 

project are contained in [1]. 

The reduction can be smaller for low-structures 

and other structures with predominantly tensioncontrolled members. However, for structures whose 

members predominantly experience large compressive 

forces, such as high-rise buildings, the reduction may 

be more significant. This may also be true of certain 

pre-tensioned or post-tensioned concrete members. 

Additional research aimed at ascertaining the extent to 

which this is the case is warranted. Although footprintoptimized reinforced steel construction is slightly more 

expensive, this situation may change in the future.

Large and significant segments of American industry (e.g., Exxon, Shell, General Electric, and many 

others) are now accepting and including into their plans 

the concept of adding carbon emissions taxation to 

their business expenses. Including such taxes in the 

total construction costs makes it possible to optimize 

construction from the point of view of both cost and 

emissions. It is anticipated that the approach developed 

in this project will be incorporated into engineering 

practice via manuals of practice, standards and codes, 

and contribute significantly to the reduction of global 

carbon emissions and to a greener economy. Future

research will continue with a view to rendering the 

approach developed so far increasingly practical and 

user-friendly, and attempting to incorporate it in common “green structural engineering” practice.

[1] D. Yeo and F. A. Potra, Sustainable Design of Reinforced Concrete Structures through CO2 Emission 

Optimization, Special Issue on “Sustainable Building 

Structures,” Journal of Structural Engineering-ASCE, 

to appear. 

Modeling with Uncertainty 

Estimation of a Thickness-Shear 

MEMS Resonator 

Jeffrey T. Fong

Ward L. Johnson (NIST MML)

Pavel Kabos (NIST PML)

T. Mitchell Wallis (NIST PML)

Li Ma (NIST MML)

N. Alan Heckert (NIST ITL)

James J. Filliben (NIST ITL)

Pedro V. Marcal (MPACT Corp)

Johnson, et al. have recently conducted experiments at 

the NIST Boulder laboratory on excitation and detection of thickness-shear modes of vibration in a microelectro-mechanical system (MEMS) resonator due to a 

Lorentz force produced by a current in a thin-film 
Summary of Activities for Fiscal Year 2013 49

waveguide in the presence of a static magnetic field. 

The experiments produced two results of interest, 

namely, (1) a vibrationally trapped thickness-shear 

MEMS device with Lorentz force transduction was 

shown to be experimentally feasible, and (2) measurable signals were not detected in the fabricated devices 

for acoustic resonances. The second result was disappointing, because the investigators were looking for 

resonances that offer the potential of providing ultrahigh resolution for sensing gas and liquid-borne molecules in health care, environmental, water quality, 

homeland security, and defense. 

An earlier attempt by Heyliger, Flannery and 

Johnson to estimate the first thickness-shear mode resonance frequency using a two-dimensional finiteelement model and a series of ad hoc simplifying assumptions resulted in a prediction of 412 MHz [2]. 

However, no such measurement evidence was found in 

subsequent experiments [1]. 

The goal of this finite element modeling project is 

to develop a fully three-dimensional finite element

model using two commercially-available general purpose software packages, ABAQUS and COMSOL, for 

a variety of device designs to answer three questions: 

(a) Why did the prediction of the earlier finite element

model fail in experiments? (b) What changes in device 

design are likely to yield an experimentally verifiable 

prediction? (c) How does simulation uncertainty match

the uncertainty in experiments?

[1] W. L. Johnson, T. M. Wallis, P. Kabos, E. Rocas, E. 

Collado, L.-A. Liew, J.-Y. Ha, A. V. Davydov, A. 

Plankis and P. Y. Heyliger, A Thickness-shear MEMS 

Resonator Employing Electromechanical Transduction 

through a Coplanar Waveguide.

[2] P. Y. Heyliger, C. M. Flannery and W. L. Johnson, 

Nanotechnology 19 (2008), 145707.

Using Quadratic Functions over 

Lines in Evolutionary Optimization 

Anthony J. Kearsley

Ismet Sahin (University of Maryland)

Population-based metaheuristic optimization algorithms aim to find an extremum of a given function 

defined on a region of interest. The ease with which 

they can be implemented and applied to problems has 

resulted in an increase in their use and development [1,

2]. They are often employed when the cost function 

does not have derivative information (gradient or Hessian) readily available, perhaps due to its complexity, 

discontinuity, or nonnumeric structure. While other 

approaches exist for these types of problems such as 

direct search methods [3] or simulated annealing methods [4], this project focuses on a population set-based 

algorithm. Population-based algorithms create an initial 

generation of vectors where each vector is an approximation to the minimizer of the given function, and then 

apply evolutionary operations in order to produce new 

generations with improved approximations. The mutation and crossover evolutionary operations produce 

variations in the generation, and the selection operation 

chooses the variational points yielding smaller function 

values. 

Even though many evolutionary algorithms have 

been proposed in the literature, their mutation operations are limited in using mathematical models that can 

predict the cost function surface. A recent study introduced the Random Lines (RL) algorithm, which uses

quadratic function models in its mutation operation and 

achieves improved robustness and efficiency in finding 

the minimizer. However, its use of concave quadratics 

can be improved substantially as it now simply assigns

the maximizer of the model as the mutated point.

In this project, we are motivated to develop new 

schemes to handle the concave cases more efficiently 

[6]. Figure 27 demonstrates 3 convex and 2 concave 

quadratic models over five randomly selected lines, 

where clearly minimizers of the convex models lead to 

the regions with smaller function values. Based on the 

concave models, the proposed schemes choose search 

directions away from the maximizers along the line. 

The step sizes are determined based on the distances 

between the points of the current generation. We 

demonstrate that these schemes improve robustness 

and efficiency substantially compared to the original 

RL algorithm and other evolutionary optimization algorithms. In a future work, we are planning to extend 

this algorithm for constrained optimization problems.

Figure 27. Contours of two dimensional cost function f(x) specified in the title of the plot and five randomly selected lines. Three 

points are chosen over each line and a quadratic model is fit to 

these points. The extrema of these models are indicated by the red 

diamond markers. Two quadratics over the lines passing through 

(x3,x5) and (x2, x4) are concave for which we propose new schemes 

to produce mutated points in this project. Other three quadratic 

models are convex and their minimizers are used as mutated 

points for corresponding lines.
50 NIST Applied and Computational Mathematics Division

[1] A. Torn, Global Optimization, Springer-Verlag, 1989.

[2] D. G. Luenberger and Y. Ye, Linear and Nonlinear 

Programming, Springer, 2008.

[3] T. G. Kolda, R. M. Lewis and V. Torczon, Optimization 

by Direct Search: New Perspectives on Some Classical 

and Modern Methods, SIAM Review 45:3 (2003), 385-

482.

[4] S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Optimization by Simulated Annealing, Science 220:4598 (1983), 

671-680.

[5] I. Sahin, Random Lines: a Novel Population Set-based 

Evolutionary Global Optimization Algorithm, in Genetic 

Programming (S. Silva, et al., eds.), Lecture Notes in 

Computer Science 6621 (2011), Springer, 97-107.

[6] I. Sahin and A. J. Kearsley, Using Quadratic Functions 

over Lines in an Evolutionary Optimization Algorithm, 

submitted.

Separating Signal from Noise via the 

SVD

Bert W. Rust

Cubic splines are often used to estimate the signal in

noisy measured data. One approach imposes a smoothness constraint on the equations used for calculating an

interpolating spline and requires the specification of a

smoothing constant to determine the amount of 

smoothing imposed. Another approach uses a regression spline with fewer knots than the number of 

observations, and requires the specification of the 

number and locations of those knots. 

B. J. Thisse and his colleagues [1, 2] have developed an algorithm that determines the optimal number 

and distribution of knots. But these results can be improved still further by solving the resulting linear 

regression problem by a variant of the truncated singular value decomposition method which truncates the

singular vector expansion rather than the singular value

distribution [3]. This method is a variant of principal

components regression which does not use the singular

values to choose the principal components. It produces

residuals which are closer to uncorrelated white noise

than are those obtained from smoothing spline approximations.

[1] B. J. Thijsse, M. A. Hollanders and J. Hendrikse, A 

Practical Algorithm for Least-Squares Spline Approximation of Data Containing Noise, Computers in Physics

12 (1998), 93-399.

[2] B. J. Thijsse, J. Barend and B. W. Rust, Freestyle Data 

Fitting and Global Temperatures, Computing in Science 

& Engineering (January/February 2008), 49-58.

[3] B. W. Rust, Truncating the Singular Value Decomposition for Ill-Posed Problems, NISTIR 6131, July 1998.

The Metrology of Supernova Light 

Curves

Bert W. Rust

Katharine M. Mullen (UCLA)

We model the Type Ia supernova light curve as the 

superposition of three luminosity pulses: an initial 

pulse generated by the deposition of 56Ni followed by 

the sub-sequent pulses generated by the radioactive 

decays 56Ni → 

56Co →56Fe. We assume that the two 

radioactive decays occur in a stable environment with 

density and temperature so high that the two decay 

rates are accelerated by the same factor. We use a three 

parameter Weibull probability density function to 

model the 56Ni deposition so that the model can be 

written as a linear combination of the Ni-deposition 

pulse and the solutions to two coupled ordinary differential equations with four adjustable nonlinear 

parameters, specifying the time of the onset of Nideposition, the shape and the scale of the deposition 

pulse, and the acceleration factor for the two decay 

rates. The three linear parameters specify the energies 

associated with the three processes and enable the estimation of the energy/nucleon emitted by the Nideposition. 

Fitting the model to the measured light curves for 

a sample of relatively nearby supernovae gave fits that 

explained more than 99 % of the total variance in every 

case. Such high fidelity to the measured data indicates 

that the fitted light curves may give more precise estimates of important parameters like the maximum 

luminosity and the time at which it occurs, the rise time 

to maximum luminosity, and the decline rate of the 

luminosity in the tail of the curve. 

Such improved precision should prove very beneficial in calibrating the extragalactic distance scale and 

performing cosmological tests with very distant supernovae. For the small sample that has been analyzed 

thus far, the average of the estimates for the energy/nucleon in the Ni-deposition pulse is slightly greater 

than the binding energy of 56Ni.

[1] B. W. Rust, M. Leventhal and S. L. McCall, Evidence 

for a radioactive decay hypothesis for supernova luminosity, Nature 262 (1976), 118-120.

[2] B. W. Rust and K. M. Mullen, The Metrology of Supernova Light Curves, poster, 223rd Meeting of the 

American Astronomical Society, Washington D.C., Jan. 

8, 2014.
Summary of Activities for Fiscal Year 2013 51

Sparse Low-rank Nonnegative 

Approximation of Interval Matrices

Dianne P. O'Leary

Yi-Kai Liu

John M. Conroy (IDA CCS)

Daniel Samarov (NIST ITL)

Data often has a simple underlying structure that is 

obscured by measurement error or missing values. For 

example, in spectroscopy, the true spectrum is a 

weighted sum of some dictionary spectra corresponding to the components in the sample. Similarly, in 

classifying a set of documents, the values in a matrix 

might represent the importance of each term in each 

document, but some values might be missing and others are quite noisy, obscuring the underlying dictionary 

of topics. The same problem arises in other matrix 

completion problems, where, for example, the preference of each customer for each product should be 

estimated from an incomplete set of preferences.

Each of these matrix approximation or matrix 

completion problems has the same structure. The idea 

is to approximate a given matrix A, which we don’t 

know with certainty, by a nonnegative low-rank matrix.

Previous approaches to these problems minimize 

the difference between the noisy measurements A and 

the computed low-rank matrix.

Our approach is different: we assume that we are 

given upper and lower bounds on each entry of the true 

matrix. These bounds are determined from the measured values and their uncertainties. This defines an 

interval in which the true unknown matrix lies. We 

minimize the difference between the computed lowrank matrix and the closest matrix that lies within the 

interval. We also allow weights in measuring this difference; for example, if we have no information about 

a particular element of A, we might set the corresponding weight to zero. As in previous approaches, we can 

add a penalty term to enhance sparsity in the approximation.

We developed an alternating minimization algorithm to solve this problem and tested it on problems in 

document classification and (simulated) spectral analysis. On data from NIST's 2004 Document 

Understanding Conference (DUC-04) competition, our 

new approach improved the performance measure 

known as adjusted mutual index from 0.70 to 0.82, 

where 1.00 indicates that all documents were classified 

correctly. We are extending the approach to tensor approximation.

[1] J. Conroy, S. T. Davis, J. Kubina, Y.-K. Liu, D. P. 

O’Leary and J. D Schlesinger, Multilingual Summarization: Dimensionality Reduction and a Step towards 

Optimal Term Coverage, in Proceedings of the Workshop on Multilingual Multi-document Summarization 

(MultiLing 2013), Sofia, Bulgaria, August 2013, 55-63.
52 NIST Applied and Computational Mathematics Division

Advanced Manufacturing

Delivering technical support to the nation’s manufacturing industries as they strive to out-innovate and out-perform 

the international competition has always been a top priority at NIST. This has also emerged as a major White House 

priority in recent years, in which NIST is playing an increasingly central role. Mathematical modeling, computational simulation, and data analytics are key enablers of emerging manufacturing technologies. This is most clearly 

evident in the Materials Genome Initiative, an interagency program with the goal of significantly reducing the time 

from discovery to commercial deployment of new materials through the use of modeling, simulation, and informatics. ACMD’s role in advanced manufacturing centers on the development and assessment of modeling and 

simulation tools, with emphasis on uncertainty quantification, as well as support of NIST Laboratory efforts in such 

areas as nonmanufacturing, smart manufacturing, and materials modeling.

Rheology of Dense Suspensions

William George

Steven Satterfield

Marc Olano

Judith Terrill

Nicos Martys (NIST EL)

Edward Garboczi (NIST EL)

Pascal Hebraud (CNRS/ESPCI, France)

See page 59.

Micromagnetic Modeling

Michael Donahue

Donald Porter

Robert McMichael (NIST CNST)

June Lau (NIST MML)

http://math.nist.gov/oommf/

Advances in magnetic devices such as recording heads, 

field sensors, spin torque oscillators, and magnetic 

nonvolatile memory (MRAM) 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. 

ACMD 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 its basic functionality. OOMMF also serves as a fully functional 

micromagnetic modeling system, handling both two 

and three-dimensional problems, with sophisticated 

extensible input and output mechanisms. In FY 2013 

alone, the software was downloaded more than 11,000 

times, and use of OOMMF was acknowledged in some

150 peer-reviewed journal articles. OOMMF has become an invaluable tool in the magnetics research 

community.

Key new developments over the last year include:

a) Derivation of new equations for cell-to-cell demagnetization tensor values that produce fourth 

order precision with respect to cell edge length.

b) Enhancement of robustness against data loss with 

pre-loading of code that manages error handling 

and improved logging of data archiving operations.

c) Creation of a new application to manage and manipulate tables of output quantities.

Ongoing work includes collaboration with the University of California, San Diego on porting OOMMF 

calculations to massively parallel graphical processing 

units (GPUs) with Materials Genome Initiative support.

OOMMF is part of a larger activity, the Micromagnetic Modeling Activity Group (muMAG), 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. ACMD staff members are involved in development of the standard problem suite as well. Ongoing 

work includes the development of new OOMMF capabilities and data processing utilities to facilitate the 

collection and reporting of points of comparison defined in standard problems.

In addition to the continuing development of 

OOMMF, the project also does collaborative research 

using OOMMF. Recent work has applied OOMMF to 

the investigation of the structure and periodicity of 

cross-tie walls in thin magnetic strips. A new contributed extension from Laboratoire de Physique des 

Solides (Universite Paris Sud) adds calculation of the 

Dzyaloshinskii-Moriya interaction (DMI) to OOMMF 
Summary of Activities for Fiscal Year 2013 53

simulations, enabling the study of skyrmions, a subject 

of widespread current interest. The availability of the 

OOMMF source played a key role in a new understanding of the effect of boundary conditions on the 

DMI. 

The ACMD micromagnetic project produced two 

conference presentations this past year.

[1] M. J. Donahue, “Structure and Periodicity of Cross-tie 

Walls in Thin Magnetic Strips,” 12th Joint 

MMM/Intermag Conference, Chicago, IL, Jan. 16, 2013.

[2] D. G. Porter, “Scaling Tcl Data Structures,” 20th Annual 

Tcl/Tk Conference, New Orleans, LA, Sept. 26, 2013.

OOF: Finite Element Modeling of 

Material Microstructures

Stephen A. Langer

Andrew C.E. Reid (MML)

Günay Doğan (Theiss Research)

Faical Yannick Palingwende Congo (ISIMA)

http://www.ctcms.nist.gov/oof/

The Object Oriented Finite Elements (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.

The OOF development team consists of two NIST 

staff, Steve Langer and Andrew Reid, and two guest 

researchers, Gunay Doğan and Yannick Congo. Langer 

works on OOF full time, and Reid splits his time between OOF and other duties in MML. Doğan works on 

OOF and shape metrology. Congo works full time on 

the OOF test suite and comes to NIST from Burkina 

Faso, by way of ISIMA and Université Blaise-Pascal in 

France.

The currently available version of OOF is OOF2, 

which solves two dimensional time-dependent problems based on two dimensional micrographs. Version 

2.1.8 was released this year, but since it only fixed a 

few rarely encountered bugs and added a couple of 

specialized features requested by users, it was released 

quietly, without an official announcement. The specialized features were modifications to the build script 

to allow the program to be run on some uncommon 

computer configurations and the addition of a “Pause”

button to control prerecorded demonstrations of the 

software, making it more useful as a pedagogical tool. 

As a diagnostic test, at one point OOF2 was ported to 

the popular Raspberry Pi credit-card-sized computer. 

This highly resource-constrained environment revealed 

a bug in the allocation of memory at start-up time, 

which has now been fixed.

OOF2 continues to be used in the materials science 

community. The source code was downloaded more 

than 1 100 times during FY 2013. The program can 

also be run on-line at nanoHUB14, where it was used in 

more than 2 500 sessions this year.

A large part of the development effort this year 

went toward OOF3D, the soon to be released three 

dimensional version of OOF. OOF3D will read three 

dimensional microstructural datasets from experiments 

or simulations and perform fully three dimensional 

computations on them.

Work has been centered on the test suites, the development of which has revealed numerous bugs and 

missing features. The goal is to ensure that before the 

first version of OOF3D is released, all of its critical 

features are implemented and tested. It must be able to 

solve a full problem, from microstructure to postprocessing analysis, and must be able to do so in a 

manner that is not too laborious for the user. Some 

features can be copied directly from OOF2 (e.g., command and control infrastructure), some require various 

degrees of modification from their OOF2 versions 

(e.g., addition of groups of faces to the existing element, segment, and node groups), and some are 

completely new (e.g., detecting whether a set of element faces forms an orientable surface on which 

boundary conditions can be applied).

An interesting discovery this year was that the 

OOF3D GUI (graphical user interface) tests were sensitive to the choice of a window theme on some 

computers. A test script recorded on one computer 

with one windowing system would fail when replayed 

on a different computer. Changing the GUI theme 

would change the size of the labels on GUI buttons and 

other widgets, which would slightly change the space 

allocated for the OOF3D graphics canvas, which would 

slightly change the position of objects drawn in the 

canvas, which would drastically change the interpretation of mouse clicks on the canvas. The solution was 

to add information about the canvas size to the GUI log 

script, in addition to information about window size 

changes.

At the end of FY 2013 only two major features 

still needed to be added to OOF3D before it could be 

released: Neumann boundary conditions and postprocessing of output. Neumann boundary conditions 

can be implemented in the same general way as they 

are in OOF2, but require methods for integrating over 

 

14 http://www.nanohub.org/
54 NIST Applied and Computational Mathematics Division

surfaces and specifying locations on surfaces that are 

new to 3D. (They are not conceptually difficult, but 

require care in their implementation to ensure correctness, flexibility, and maintainability.) Post-processing 

likewise will mostly involve copying code from OOF2, 

but must be extended to handle different ways of specifying the domain of the post-processing commands. 

For example, in 3D there are both linear and planar 

cross sections, and it's not possible to choose the left or 

right side of a linear cross section the way it is in 2D.

Other development efforts will benefit both OOF2 

and OOF3D. Andrew Reid completed evaluation of a 

constitutive rule for solid-state deformation scenarios 

where the system remains permanently deformed after 

the applied loads are removed. Once implemented in 

OOF, this will allow it to contribute to studies of metal 

forming of interest to the Materials Genome Initiative.

Image segmentation, namely, identification of 

phases or regions and their boundaries in given microstructure images, is a critical step in both OOF2 and 

OOF3D. Once the distinct regions forming the microstructure have been identified, users can generate 

computational meshes conforming to the regions for 

different materials and simulate various physics using 

these meshes. In this fiscal year, Gunay Doğan worked 

to improve and extend previously developed segmentation models to be able to handle more diverse imaging 

scenarios in an efficient and robust manner. The main 

focus of this work was region-based and edge-based 

segmentation models. To ensure consistent and reliable 

performance in difficult situations, such as low-contrast 

or high-noise images, he implemented various improvements to the underlying shape optimization 

algorithms. The details of this work are given in the 

section for Computational Tools for Shape Measurement and Analysis (see page 39).

Future goals for the OOF project include:

 Merging the OOF2 and OOF3D code bases so that 

future improvements can be made to both programs simultaneously. A lot of code is already 

shared between the two, but many changes in 

OOF2 have not been made in OOF3D and vice 

versa.

 Providing an easily extensible platform for two

and three dimensional plasticity calculations.

 Providing advanced image segmentation tools

within OOF2 and OOF3D.

 Parallelizing the time-critical code, especially in

OOF3D.

Solving the Diffusion Equation in 

Microstructures

Javier Bernal

Nicos Martys (NIST EL)

Scott Jones (NIST EL)

Software is being implemented for solving the diffusion equation in microstructures that represent cracked 

concrete. This software will be utilized to predict the 

influence of cracks on the service life of concrete. The 

microstructures will be meshed using a Voronoi construct in order to provide a realistic representation of 

the crack/pore interface. The Voronoi construct should 

allow for the development of a multiscale representation of the cracked microstructure in a way that will 

improve computational efficiency and accuracy.

Moving Grain Boundary Grooves 

under Stress

Geoffrey McFadden

William Boettinger (NIST MML)

Robert Sekerka (Carnegie Mellon University)

Grain boundaries are the interfaces that separate individual grains of a crystalline material that have 

different orientations of the crystal axes in each grain. 

Grain growth occurs by grain boundary motion, which 

is subject to energetic driving forces from effects such 

as surface tension, which tends to minimize net surface 

energy, and elastic forces, which tend to minimize 

strain energy. In thin films of polycrystalline material, 

the presence of lateral compressive or tensile stresses 

can cause migration of a grain boundary with an associated deformation of the nearby solid-vapor interface 

at the film surface. These features are commonly observed in thin films under compression, and have been 

conjectured to lead to the formation of crystalline 

“whiskers” that can bridge gaps between electronic 

components and lead to electrical failure. 

Models of grain boundary motion when the slope 

of the solid-vapor interface is small have been developed by Mullins and co-workers in a variety of 

contexts [1, 2]. In work completed this fiscal year we 

have extended the model to finite slopes. In a sample 

with two-dimensional geometry this results in a system 

of nonlinear fourth-order ordinary differential equations in a coordinate system that moves with the 

velocity of the grain boundary. We have computed 

finite-amplitude solutions to the governing equations 

that extend the small-amplitude theory, and have also 

improved the model in [2] by formulating conditions 
Summary of Activities for Fiscal Year 2013 55

that maintain the equality of chemical potential at the 

trijunction [3].

[1] W. W. Mullins, The Effect of Thermal Grooving on 

Grain Boundary Motion, Acta Metallurgica 6 (1958), 

414-427.

[2] F. Y. Genin, Effect of stress on grain boundary motion 

in thin films, Journal of Applied Physics 77 (1995) 

5130–5137.

[3] R. F. Sekerka, W. J. Boettinger and G. B. McFadden, 

Surface Morphologies due to Grooves at Moving Grain 

Boundaries Having Stress-Driven Fluxes, Acta Materialia 61 (2013) 7216-7226.

Morphological Stability

Geoffrey McFadden

Sam Coriell (NIST MML)

Robert Sekerka (Carnegie Mellon University)

In the production of metallic or semiconductor alloy 

crystals it is usually desirable that the concentration 

distributions be spatially uniform, as heterogeneous 

alloy concentrations can seriously degrade material 

performance. Crystal growth is therefore usually performed under highly controlled conditions to achieve 

high levels of homogeneity. A common technique is 

Bridgman growth, in which the crystal in grown “directionally” in a one-dimensional temperature gradient 

that in principle produces a planar interface separating 

the cooler growing solid phase from the hotter molten 

phase. If the solutes are uniformly distributed in the 

melt at the solid-liquid interface, the resulting crystal 

has the desired levels of homogeneity. 

In practice the system can be subject to instabilities that produce non-planar interfaces, which result in 

associated non-uniform concentration distributions in 

the growing crystal. The study of such instabilities has 

therefore been an area of fundamental importance in 

materials processing, dating back to the early days of 

the development of semiconductor technology. A 

landmark contribution to the field was the theoretical 

work published in 1964 [1] by W. W. Mullins and R. F. 

Sekerka that has become known as the theory of morphological stability. They explained how the 

temperature and concentration gradients at the solidliquid interface can lead to “constitutional supercooling” instabilities that are analogous to the instabilities 

commonly observed when freezing a pure material that 

has been cooled to temperatures below the material’s 

melting point. A large literature has been since produced on the theory of morphological stability and on 

related aspects of this phenomenon during materials 

processing. In particular, this has been an important 

area of research at NIST, where R. F. Sekerka has been 

an active consultant since the 1970's. 

A 72 page review article on morphological stability was written by S. R. Coriell and G. McFadden in 

1993 [2] for the three volume Handbook of Crystal 

Growth. The article covers the technical aspects of the 

theory in some detail, including the discussion of a 

number of extensions of the theory, with 242 references to the literature. 

That article has been well received, but because of 

the continuing activity in the field over the ensuing 

twenty years it is now somewhat dated due to the appearance of subsequent work. A second edition of the 

handbook is now in preparation, and a revised version 

of this review article has been written by R. F. Sekerka, 

S. R. Coriell, and G. B. McFadden [3]. This article is 

intended to include recent references to the subject, and 

to present the theory at a level that is accessible to the 

non-expert. The article has been submitted to the 

handbook editor, and will appear in the second edition 

of the Handbook.

[1] W.W. Mullins and R.F. Sekerka, Stability of a planar 

interface during solidification of a dilute binary alloy, 

Journal of Applied Physics 35 (1964) 444-451.

[2] S. R. Coriell and G. B. McFadden, Morphological Stability, Chapter 12 in Handbook of Crystal Growth, 

Volume 1b. Transport and Stability, (D. T. J. Hurle, 

ed.), North-Holland, Amsterdam, 1993, 785-857.

[3] R. F. Sekerka, S. R. Coriell, and G. B. McFadden, Morphological Stability, in Handbook of Crystal Growth,

2nd edition (T. Nishinaga, ed.), North-Holland, Amsterdam, to appear.

Inverse Method for Estimating 

Shear Stress in Machining

Timothy Burns

Steven Mates (NIST MML)

Richard Rhorer (NIST EL)

Eric Whitenton (NIST EL)

Debasis Basak (Orbital Sciences Corporation)

A major reason for the lack of predictive capability of 

finite-element based machining models is the lack of 

good constitutive response models for the flow stress in 

the chip material during a rapid material removal process. The conditions of rapid and very large shearing 

deformation, heating rates as high as one million degrees C per second, resulting in enormous temperature 

gradients, and peak temperatures on the order of 

1000 C in the thin primary shear zone where cutting 

takes place, and in the secondary shear zone, the thin 

boundary layer region where the work material continues to deform as it moves along the cutting edge of the 

tool (see Figure 28), are much more extreme than the 

conditions that most current materials testing laboratories can reproduce, control, and measure accurately. 
56 NIST Applied and Computational Mathematics Division

We have developed an inverse method for estimating the flow stress in the chip in the region of chip-tool 

contact along the rake face of the tool, during orthogonal machining. The method gives a formula for the 

peak stress in the chip on the rake face, that is based on 

an estimate of the temperature of the work material as 

it exits the primary shear zone, an experimental measurement of the peak temperature in the work material 

along the tool-chip interface, and a two-zone empirically based contact model for friction along this interface. 

We have also shown how the method can be generalized to provide an estimate of the stress in the chip on 

the rake face, and in the primary shear zone, given experimentally determined cutting force measurements 

and a discrete set of steady-state temperature measurements along the cutting edge of the tool, even when no 

friction model is specified. In the latter case, the inverse problem of determining the shear stress in the 

chip along the tool rake face can be interpreted as a 

problem requiring the deconvolution and unfolding of a 

Volterra integral equation of the first kind [1]. 

We are in the process of applying our method to 

estimate the flow stress during high-speed machining 

of the titanium alloy Ti–6Al–4V, using cutting force 

and temperature data that have been obtained using the 

new instrumented transparent yttrium aluminum garnet 

(YAG) tool that has recently been developed by Menon 

and Madhavan [2]. Ti–6Al–4V is a material that is

widely used in aircraft manufacture. It is difficult to 

machine, because it has a low heat capacity and heats 

up very rapidly, leading to tool breakage, shear localized chips, and other difficulties. The goal of our work 

is to provide improved machining process simulation 

capabilities.

[1] T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. Whitenton, 

and D. Basak. Inverse method for estimating shear stress 

in machining, in review.

[2] T. Menon and V. Madhavan. High accuracy full-field 

infrared thermography of the chip-tool interface through 

transparent cutting tools while machining Ti-6Al-4V, in 

review.

Model Selection for Fracture and 

Fatigue Failure Data of Engineering 

Materials

Jeffrey T. Fong

N. Alan Heckert (NIST ITL)

James J. Filliben (NIST ITL)

Stephen W. Freiman (NIST MML)

Pedro V. Marcal (MPACT Corporation)

One of the most hotly-debated questions in engineering 

design and failure analysis is how best to fit a set of 

fracture and fatigue failure data. In an ASTM recommended standard practice for advanced ceramic 

materials [1], it is assumed that a two-parameter 

Weibull distribution with a zero location parameter will 

“best” fit the data. This leads to a physically unrealistic 

and highly conservative assumption that among all 

possible samples of an engineering material, one will 

fail a uniaxial tensile strength test at zero load. Also 

unduly conservative will be the so-called A- and Bbasis design allowables for failure strength at 95% confidence when the location parameter is assumed to be 

zero at origin of the axis.

In this work, we take a brute-force and somewhat 

“exhaustive” approach by developing a validation tool 

to answer the question how “best” a given set of univariate strength data will fit a distribution without 

assuming a zero location parameter. We select two 

methods of parameter estimation and apply four criteria 

of goodness-of-fit to more than 60 commonly-known 

distributions to see how they rank among themselves 

according to each of the eight combinations of parameter-estimation method plus goodness-of-fit criterion. 

We then develop a composite index for the eight individual rankings and order all 60+ distributions in a list 

for selecting the most “appropriate” distribution for the 

given data set. 

The two parameter estimation methods are: 

1. Maximum Likelihood Method [2]. 

2. Probability Plot Correlation Coefficient Method 

The four goodness-of-fit criteria are: 

1. Kolmogorov-Smirnov Criterion [4]

2. Anderson-Darling Criterion [5, 6]

3. Akaike-Burnham-Anderson Criterion [7, 8]

Figure 28. Schematic of orthogonal cutting, showing primary and 

secondary shear planes; shear angle φ; rake angle α; force between tool face and chip R; force between workpiece and chip 

along primary shear plane R; cutting velocity vc; shearing velocity vs; and chip velocity vf.
Summary of Activities for Fiscal Year 2013 57

4. Probability Plot Correlation Coefficient Criterion 

[3]

Using the public-domain statistical analysis software 

DATAPLOT [9], we developed a model selection validation tool, and demonstrated its feasibility by 

applying it to six sets of data: a glassy material, two 

steels, two ceramic materials, and aluminum oxide 

[10]. We also wrote a PYTHON-based management 

code to automate the complex series of data analysis 

tasks including an input module linked to Excel [10].

[1] ASTM, Standard Practice for Reporting Uniaxial 

Strength Data and Estimating Weibull Distribution Parameters for Advanced Ceramics, ASTM Designation: 

C 1239-07, Committee C28 on Advanced Ceramics, 

West Conshohocken, PA, 2008.

[2] J. Aldrich, R. A. Fisher and the Making of Maximum 

Likelihood 1912–1922, Statistical Science 12: 3 (1997), 

162–176.

[3] J. J. Filliben, The Probability Plot Correlation Coefficient Test for Normality, Technometrics 17:1 (1975), 

111-117.

[4] F. J. Massey, Jr., The Kolmogorov-Smirnov Test for 

Goodness of Fit, Journal of the American Statistical Association 46 (1951), 68-78.

[5] T. W. Anderson and D. A. Darling, Asymptotic Theory 

of Certain ‘Goodness of Fit’ Criteria based on Stochastic 

Processes, Annals of Mathematical Statistics 23 (1952), 

193-212.

[6] T. W. Anderson and D. A. Darling, A Test of Goodness 

of Fit, Journal of the American Statistical Association

49 (1954), 765-769.

[7] H. Akaike, A New Look at the Statistical Model Identification, IEEE Transactions on Automatic Control 19:6

(1974), 716-723.

[8] K. P. Burnham and D. R. Anderson, Multimodel Inference: Understanding AIC and BIC in Model Selection,

Sociological Methods and Research 33 (2004), 261-304.

[9] J. J. Filliben and N. A. Heckert, Dataplot: A Statistical 

Data Analysis Software System15, NIST, Gaithersburg, 

MD, 2002.

[10] J. T. Fong, A. N. Heckert, J. J. Filliben, P. V. Marcal, 

and S. W. Freiman, A Multi-Distribution and MultiGoodness-of-Fit-Criterion Method of Finding the Most 

Probable Underlying Distribution for a Given Set of 

Univariate Data, in preparation.

 

15 http://www.itl.nist.gov/div898/software/dataplot.html

Structural Design Allowables for 

Composites 

Jeffrey T. Fong

N. Alan Heckert (NIST ITL)

James J. Filliben (NIST ITL)

J. D. Daniel Melo (Federal University of Rio Grande 

do Norte, Brazil)

Carlos A. Cimini, Jr. (Federal University of Minas 

Gerais, Brazil) 

Stephen W. Tsai (Stanford University)

The purpose of this work is to evaluate a 2002 study 

[1] on a comparison of 12 composites failure theories 

with 14 experiments using only point estimates of 

mean values. We conclude that “the designer wishing 

to estimate the ultimate failure strength of a multidirectional laminate can at best hope for accuracy of 

+/- 50 % in the majority of cases.” 

In our work, we propose an alternative approach of 

testing theories against experiments by using interval 

estimates and the associated concept of uncertainty. 

For each given failure criterion, we first apply the classical law of error propagation [2] to estimating the 

uncertainty of the failure stress (and/or strain) as a 

function of the uncertainties of the material parameters. 

We then apply the concepts of “coverage” and “tolerance limits” to estimate the A- and B-basis allowables 

[3, 4] for multi-directional laminate design against failure. To illustrate our uncertainty-based approach [5], 

we introduce two failure criteria, one uniaxial and the 

other bi-axial, both of which are derived from the composites failure theories of Tsai and Wu [6], Hashin [7], 

and Christensen [8], to obtain results that refute the 

2002 study [1].

[1] M. J. Hinton A. S. Kaddour and P. D. Soden, A Comparison of the Predictive Capabilities of Current Failure 

Theories for Composite Laminates, Judged Against Experimental Evidence, Composites Science and 

Technology 62 (2002), 1725-1797.

[2] H. H. Ku, Notes on the Use of Propagation of Error 

Formulas, NBS Journal of Research 70C:4 (1966), 263-

273.

[3] Composite Materials Handbook – Polymer Matrix 

Composites Guidelines for Characterization of Structural Materials16

, MIL-HDBK-17/1 Rev. F, June 2002, 

(Vol. 1 of 5), U.S. Department of Defense Handbook,

Chapter 8 – Statistical Methods.

[4] J. T. Fong, C. Cimini, D. Melo, J. J. Filliben and N. A. 

Heckert, Theoretical Failure Envelopes of Open Hole 

Composite Laminates with A- and B-bases Allowables 

Estimated from Smooth Specimen Properties, in Proceedings of 2013 International Conference on 

Composites Design, Montreal, Canada, July 2013.

 

16 http://snebulos.mit.edu/projects/reference /MIL-STD/MIL-HDBK-17-

1F.pdf
58 NIST Applied and Computational Mathematics Division

[5] J. T. Fong, J. J. Filliben and N. A. Heckert, Composites 

Failure Criteria, Uncertainty Propagation, and Estimation of the A- and B-basis Design Allowables, in 

preparation.

[6] S. W. Tsai and E. M. Wu, A General Theory of Strength 

for Anisotropic Materials, Journal of Composite Materials 5 (1971), 58-80

[7] Z. Hashin, Failure Criteria for Unidirectional Fiber 

Composites, Journal of Applied Mechanics 47 (1980), 

329-334.

[8] R. M. Christensen, Stress Based Yield/Failure Criteria 

for Fiber Composites, International Journal of Solids

and Structures 34 (1997), 529-543.
Summary of Activities for Fiscal Year 2013 59

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, and 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.

A Dynamic Computational Phantom 

for RF Propagation in Body Area 

Networks

John Hagedorn

Kamran Sayrafian

Martina Barbi

Judith Terrill

See page 96.

Rheology of Dense Suspensions

William George

Judith Terrill

Steven Satterfield

Marc Olano

Nicos Martys (NIST EL)

Edward Garboczi (NIST EL)

Pascal Hebraud (CNRS/IPCMS, Strasbourg, France)

Understanding the mechanisms of dispersion or 

agglomeration of particulate matter in complex fluids, 

such as suspensions, is of technological importance in 

many industries such as pharmaceuticals, coatings, and 

construction. These fluids are disordered systems 

consisting of a variety of components with disparate 

properties that can interact in many different 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 (EL), we have developed an 

application, called QDPD [1] (Quaternion-based 

Dissipative Particle Dynamics), which is capable of 

performing large-scale simulations of dense 

suspensions. This simulator uses a modified version of 

the DPD technique [2] for the simulation of Newtonian 

fluids, and the Smoothed Particle Hydrodynamics 

technique (SPH) [3] for the simulation of nonNewtonian fluids.

QDPD is highly parallel and has been shown to 

efficiently scale up to at least 32 000 processors when 

running on the DOE supercomputer Intrepid (IBM 

Blue Gene/P) at the Argonne National Laboratory. Our 

goal in this project is to advance our understanding of 

the flow properties of a specific material, fresh 

concrete, a dense suspension composed of cement, 

water, sand, and rocks.

We are currently using this computational 

approach in the development of standard reference 

materials (SRMs) for the calibration of vane 

rheometers used to measure the flow properties of fresh 

concrete. While concrete flow measurements, using 

different existing concrete rheometers, can be found to 

correlate, they usually do not provide results in 

fundamental units. This is a consequence of the 

Figure 29. A snapshot from a QDPD simulation of a 4-blade 

rheometer with a view from the bottom of the rheometer. From this 

view, the blades are rotating clockwise. The suspended spheres are 

color-coded by their starting quadrant.
60 NIST Applied and Computational Mathematics Division

complex flow patterns that develop in the vane 

rheometer combined with the non-Newtonian behavior 

of the mortar or concrete. This results in complex local 

stress and strain/strain rate fields making it difficult to 

express measurement data in terms of fundamental 

rheological parameters. By modeling the flow of an 

SRM in a vane rheometer we are able to predict what 

should be measured by an experimentalist, and further, 

our simulations are designed to enable us to map out 

many details of the local flow, such as stress/strain 

fields in 3D, and bring insight into the vane rheometer 

measurement process.

Most research on suspensions has made the 

simplifying assumption that the matrix fluid, that is, the 

fluid supporting the suspended particle, is Newtonian. 

With the use of high-performance computing, we have 

been able to extend this research to include the 

simulation of suspensions with non-Newtonian fluid 

matrices, which includes most suspensions of interest 

to industry. One result of our studies has been to show 

that the viscosity versus shear rate curves for 

suspensions having various volume fractions can be 

collapsed onto a single universal curve parameterized 

by the properties of the underlying non-Newtonian 

matrix fluid [4]. This, along with other results from 

our studies, has advanced our basic understanding of 

the flow of dense suspensions [5-6].

Building on this research, we have begun using 

simulation in the design process for new SRMs, as 

described earlier, which will be used for calibrating 

mortar and concrete rheometers. The first such SRM 

will be a mortar SRM, which is expected to be released 

in early 2014. Our simulations of this SRM were 

completed in 2012-2013. The second SRM to be 

developed will be a concrete SRM, for which we will 

begin simulations in 2014.

Along with the development of these SRMs, in 

2014 we will also be extending QDPD to simulate 

rheometers with new blade geometries. Our simulator 

currently assumes that the rheometer has a simple vane 

design consisting of either four or six flat blades

(Figure 29 and Figure 31). As we begin this study we 

will add to this a new double helix blade design (Figure 

30), and possibly others such as a screw blade.

Novel rheometer blade designs suggested by the

simulations will be constructed at NIST using additive 

manufacturing techniques for polymers and metals, and 

NIST experimental results will compared to the 

simulation results. 

To support this study, in June of 2013 we 

submitted a proposal for supercomputer time to the 

DOE INCITE program (Innovative and Novel 

Computational Impact on Theory and Experiment17). 

As a result of this proposal we have been awarded 40 

million CPU-hours of supercomputer time for calendar 

year 2014 on the IBM Blue Gene/Q, Mira, at the 

Argonne Leadership Computing Facility. Mira is 

currently ranked 5th on the Top 500 list of 

 

17 http://www.doeleadershipcomputing.org/

Figure 31. A snapshot from a QDPD simulation of a 6-blade 

rheometer with a view from the bottom of the rheometer. From 

this view, the blades are rotating clockwise. The suspended 

spheres are color-coded by their starting quadrant.

Figure 30. A design drawing for a proposed “double helix” 

rheometer.
Summary of Activities for Fiscal Year 2013 61

supercomputer installations18 and will thus enable us to 

perform a suite of detailed simulations.

[1] N. Martys, Study of a Dissipative Particle Dynamics 

Based Approach for Modeling Suspensions, Journal of 

Rheology 49:2 (2005).

[2] P. J. Hoogerbrugge and J. M. V. A. Koelman, Simulating 

Microscopic Hydrodynamic Phenomena with 

Dissipative Particle Dynamic, Europhysics Letters 19

(1992), 155-160.

[3] J. J. Monaghan, Smoothed Particle Hydrodynamics, 

Reports on Progress in Physics 68 (2005), 1703–1759.

[4] N. Martys, M. Liard, P. Hebraud, W. George, Universal 

Scaling Law for the Flow of non-Newtonian Colloidal 

Suspensions, Society of Rheology 85th Annual Meeting, 

Montreal, Canada, October 2013.

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

Hebraud, Stress Propagation in a Concentrated Colloidal 

Suspension under Shear, The European Physical Journal

E 35:3 (2012).

[6] P. Hebraud, D. Lootens, and N. Martys, Stress

Organization in an Attractive Concentrated Colloidal 

Suspension under Flow, XVIth International Conference 

on Rheology, Lisbon, Portugal, Aug-2012.

Modeling and Visualization of 

Cement Paste Hydration and 

Microstructure Development

William George

Steven Satterfield

Judith Terrill

Terence Griffin

Wesley Griffin

Kevin Keller (University of Maryland)

Earl Bellinger (SUNY Oswego)

Alicia Ouyang (River High School)

Jeffrey Bullard (NIST EL)

Edward Garboczi (NIST EL)

Paul E. Stutzman (NIST EL)

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

When cement powder is mixed with water, the hydration process that transforms the paste from a fluid

suspension into a hardened solid involves complex 

chemical and microstructural changes. Understanding 

and predicting the rates of these changes is a longstanding goal, which could lead to the development and 

deployment of chemical admixtures for controlling 

early stage properties of concrete. 

Computational modeling of this hydration process

is challenging because it involves a large number of 

coupled nonlinear rate equations that must be solved in 

 

18 http://www.top500.org

a highly irregular three-dimensional domain. To address these challenges we are applying a new 

computational model called HydratiCA, which has

several advantages. HydratiCA uses stochastic cellular 

automata algorithms to simultaneously model reaction 

and transport phenomena in 3D. This allows us to track 

the detailed kinetics and equilibria that occur in a diverse range of cementious systems.

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. Over the course of the simulation time, a series of 

data volumes is produced at the time values of interest. 

Visualization of the output is important both for validation and to understand the results.

This year we submitted a proposal to NSF for 

computer time and were awarded 100 000 hours on the

Texas Advanced Computing Center’s Dell PowerEdge 

C8220 Cluster with Intel Xeon Phi coprocessors 

(Stampede). We set up and validated HydratiCA on 

Stampede. We made modifications to the code to make 

it more efficient. We also made progress on checkpointing. We developed an extendable tool for 

analyzing the output files. It takes a directory of output 

files and runs a variety of user selected analyses in parallel on the files. One of the analyses generates

percolation paths, for which we created an automatic 

3D visualization. We have been exploring the use of 

D319 as an additional analysis tool for this project. In 

particular, we have developed the infrastructure to 

connect javascript based web apps to the immersive 

environment to enable interactive analyses using D3.

We also upgraded the physics in the model to include a more general rate law for mineral dissolution in 

water, with the result applied to simulate the hydration 

and microstructure development of tricalcium silicate, 

the most important mineral phase in Portland cement. 

Dissolution rates obtained from this simulation were in

excellent agreement with recent experimental measurements reported in the literature. In addition, the new 

rate law provides a much better agreement between the 

simulations and experimental measurements of the 

time-dependent chemical composition of the aqueous 

solution during hydration.

With this improved accuracy, we have begun to 

model the influence on tricalcium silicate hydration of

sulfate and carbonate components in solution. This is 

an important but poorly understood area that has an 

impact on the well-known effects of gypsum additives 

and calcite fillers to modify the hardening process. 

Understanding the mechanisms of optimized gypsum 

and the filler effect will help enable the rational design 

of sustainable infrastructure materials with a more be-

 

19 http://d3js.org/
62 NIST Applied and Computational Mathematics Division

nign environmental footprint, lower embodied energy, 

and more efficient integration of industrial byproducts.

A new visualization approach was also implemented this year. Solid components are represented by

GPU-rendered sphere glyphs with diameters representing the local volume fraction. The sphere glyphs are 

displayed at their locations and their diameters are animated over the simulation time. Multiple interactive 

probes have been implemented to obtain volume data:

 Print a table of all solution and solid component 

values at that location and time.

 Continuously display the solution components 

concentration fraction (SCC) value for a selected 

component while plotting SCC values vs. time.

 Define two end points of an interactive 3D line 

segment and dynamically plot SCC values along 

the line segment.

 Use an interactive line segment sweep to identify a 

sub-volume, and then click a menu item to compute and display total, average and standard 

deviation for local data items. See Figure 32.

In the coming year we will expand the computations to include larger systems with more realistic

particle size and shape distributions. These simulations 

are important for understanding the possible effects of 

space filling by solid hydration 

products on the kinetics of hydration and rate of hardening of

concrete binders.

[1] L. Valentini, J. W. 

Bullard, G. Artioli, S. G. Satterfield, J. E. Terrill and M. Magistri, 

Role of Sulfate Incorporation in CS-H during Cement Hydration: 

Results from Numerical Modeling 

of the System C3S + Gypsum, in 

preparation.

[2] G. W. Scherer, J. W. 

Bullard and J. J. Thomas, Supersaturation of C-S-H during Hydration 

of Cement, in preparation.

[3] J. Stoian, T. Oey, J. 

Huang, A. Kumar, J. W. Bullard, 

M. Balonis, S. G. Satterfield, J. E. 

Terrill, N. Neithalath and G. Sant, 

Prehydration of Ordinary Portland 

Cement and its Mitigation using 

Limestone: New Insights from 

Experiments and Simulations, in 

preparation. 

[4] T. Oey, A. Kumar, J.W. 

Bullard, N. Neithalath and G. Sant, 

The Filler Effect: the Influence of 

Filler Content and Surface Area on 

Cementitious Reaction Rates, Journal of the American Ceramic 

Society 96 (2013), 1978-1990.

High Precision Calculations of 

Fundamental Properties of FewElectron Atomic Systems 

James S. Sims

Stanley Hagstrom (Indiana University)

M. B. Ruiz (University of Erlangen)

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

as the atomic properties of elements 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 accomplish 

this for few-electron atomic systems. 

The mathematical intractability of the Schrödinger 

equation has 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 

Figure 32. Example of the probe defining a sub-volume and computed total, average, and standard deviation for data items in the selected sub-volume. Tricalcium silicate particles (blue), were 

hydrated in a lime solution for 20 hours. The particles partially dissolved and are covered with a 

0.6-micrometer overgrowth layer of a calcium silicate hydrate product (red). Portlandite (green) 

nucleates and grows in the adjacent solution. 
Summary of Activities for Fiscal Year 2013 63

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. 

The essential flaw in theoretical methods is their 

inability to correctly describe the behavior of manybody 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 the 

theoretical development of our hybrid Hylleraas-CI 

(Hy-CI) wave function method to solve the electron 

cusp problem and bring sub-chemical accuracy to 

atomic systems with more than two electrons. 

Our method has been employed over the past few 

years to explore its utility for both three electron

lithium systems and the four electron beryllium atom. 

In the case of lithium, we have computed the lowest 

four excited state energies of the lithium atom to two 

orders of magnitude more accurately than has been 

done before [4]. At the four electron level, we have 

demonstrated the ability of Hy-CI calculations to

achieve 0.1 microhartree accuracy for beryllium. This 

represents one of the highest levels of accuracy ever 

achieved in quantum computations with more than 

three electrons. 

Familiar chemical electron affinities and ionization 

energies involve these nonrelativistic energies. To get 

truly accurate chemical properties like these it is 

important to go beyond the 0.1 microhartree accuracy 

to somewhere close to the nanohartree level we were 

able to achieve for lithium. To enable Hy-CI 

calculations to do this, we have been investigating 

more flexible atomic orbital basis sets, better

configuration state function filtering techniques to 

control expansion lengths, and improved four electron

integral techniques. Progress to date has included 

improving our beryllium accuracy an order of 

magnitude, and we have computed the non-relativistic 

energy of not only beryllium, but many members of its 

isoelectronic series to 8 significant digit accuracy. With 

these results and a least squares fit of the calculated 

energies, we have been able to compute the entire 

beryllium isoelectronic sequence and are in the final 

stages of preparing a paper on this work.

[1] T. Kato, On the Eigenfunctions of Many-particle Systems in Quantum Mechanics, Communications in Pure 

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

[2] R. T. Pack and W. B. Brown, Cusp Conditions for Molecular Wavefunctions, Journal of Chemical Physics 45

(1966), 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), 4484-4508.

[4] 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), 052507.

[5] J. S. Sims and S. A. Hagstrom, Hylleraas-Configuration 

Interaction Study of the Singlet S Ground State of Beryllium., Physical Review A 83 (2011), 032518.

[6] James S. Sims and Stanley A. Hagstrom, Hylleraasconfiguration-interaction Nonrelativistic Energies for 

the Singlet S Ground States of the Beryllium Isoelectronic Series up through Z = 113, in preparation.

Nano-structures, Nano-optics, and 

Controlling Exciton Fine Structure 

James S. Sims

Wesley Griffin

Garnett W. Bryant (NIST PL)

Jian Chen (University of Maryland Baltimore County)

Research and development of nanotechnology, with 

applications ranging from smart materials to quantum 

computation to biolabs on a chip, is an important national priority. Semiconductor nanoparticles, also 

known as nanocrystals and quantum dots, are one of 

the most intensely studied nanoscale systems. Nanoparticles are typically 1 nm to 10 nm in size, with 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 the bulk and from 

small clusters. As a result of enhanced quantum confinement effects, nanoparticles act as artificial, 

manmade atoms with discrete electronic spectra that 

can be exploited as light sources for novel enhanced 

lasers, discrete components in nanoelectronics, qubits 

for quantum computers, and enhanced ultrastable fluorescent labels for biosensors to detect, e.g., 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, 

as well as to develop immersive visualization techniques and tools to enable analysis of highly complex 

computational results of this type. The electrical and 

optical properties of semiconductor nanocrystals and 

quantum dots are studied. In the most complex structures, this entails modeling structures with on the order 

of a million atoms. Highly parallel computational and

visualization platforms are critical for obtaining the 

computational speeds necessary for systematic, comprehensive studies.

This year our work, which was focused on modulating and controlling the optical properties of selfassembled quantum dots using electric fields [1], culminated in a paper published in Physical Review B [2].
64 NIST Applied and Computational Mathematics Division

Calculations were carried out on NIST’s 7,892-

processor Linux cluster. In addition to the electric field 

work, we have also added a parameter to the code 

which handles the imaginary part of the magnetic field 

parameters (electric field parameters are real), and 

there are now data input files for strain, electric fields, 

and magnetic fields. Magnetic fields are an invaluable 

tool that allows for the implementation of two-level

systems in quantum dots, with the control of spin needed for applications in quantum information. A fully 

atomistic theory has been shown to be essential for a 

full description of exciton states in quantum dots in 

strain and electric fields. We have implemented an atomistic, tight-binding theory for excitons in quantum 

dots with an applied magnetic field. A talk was given 

on this work at the 13th Annual International Conference of Optics of Excitons in Confined Systems [3].

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. In the coming year we will continue to 

focus on modulating and controlling the optical properties of self-assembled quantum dots via external 

magnetic fields using this new feature of our codes.

We have been working on visualizing new data 

sets as part of a recent NIST cooperative agreement 

with the University of Maryland Baltimore County in 

which Dr. Jian Chen and her students will explore new 

methods for data visualization in 3D immersive virtual 

environments. The results of this work should provide 

insight into quantum dots and electron spin distribution. Additionally, since this new data is a 3D vector 

field, the tools we develop should be useful for vector 

field data in the future.

Going forward, our plan is to develop Dr. Chen’s 

preliminary visualizations into a 3D immersive visualization application that can be used on a workstation 

and in the RAVE. We also plan to submit a paper on 

this work to the 2014 IEEE VIS Conference.

[1] G. W. Bryant, N. Malkova and J. S. Sims, “Electric-field 

Control of Exciton Fine Structure: Atomic Scale Manipulation of Exchange Splitting,” American Physical 

Society Annual March Meeting, Baltimore, MD, March, 

2013.

[2] G. W. Bryant, N. Malkova and J. S. Sims, Mechanism 

for Controlling the Exciton Fine Structure in Quantum 

Dots using Electric Fields: Manipulation of Exciton Orientation and Exchange Splitting at the Atomic Scale, 

Physical Review B 88 (2013), 161301(R) .

[3] G. W. Bryant and J. S. Sims, “Magnetoexcitons in 

Quantum Dots: Atomistic Theory of g-factors, Diamagnetic Shifts and Spin Mixing”, 13th International 

Conference on Optics of Excitons in Confined Systems, 

Rome, Italy, Sept 9-13, 2013.

Parallel Adaptive Refinement and 

Multigrid Finite Element Methods

William F. Mitchell

Marjorie A. McClain

Eite Tiesinga (NIST PML)

Paul Julienne (NIST PML)

John Villarrubia (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 (PDEs). 

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 on parallel computers. 

The expertise and software developed in this project 

are useful for many NIST laboratory programs, including material design, semiconductor device simulation,

the quantum physics of matter, and simulation of scanning electron microscopes.

Recently we completed a study of the performance 

of 13 proposed hp-adaptive strategies in terms of accuracy vs. degrees of freedom [3]. This year we extended 

the experiment to include a comparison based on accuracy vs. computation time [1]. For this experiment we 

gathered a collection of 12 test problems, most of 

which came from the numerical results section of papers on hp-adaptive refinement. These problems 

contain a variety of difficulties including singularities, 

sharp peaks, wave fronts, oscillations and boundary 

layers. Most of them are parameterized to adjust the 

strength of the difficulty. We found that which strategy is most effective depends on the type of difficulty, 

and the accuracy requirements. The so-called reference

solution methods performed well in terms of accuracy 

vs. degrees of freedom, but are very expensive computationally. In terms of accuracy vs. computation time,

the use of a priori knowledge is best for problems with 

known singularities and no other significant feature, 

while the method based on the decay rate of the coefficients of the p-hierarchical basis seems to be the best 

general purpose strategy.

The 12 test problems used in the study are all twodimensional linear elliptic PDEs. We believe it would 

be useful to create a collection of standard benchmark 

PDEs, appropriate for adaptive mesh refinement, of 

other types, including 3D, parabolic, hyperbolic, and 

nonlinear equations. We have begun work on a web 
Summary of Activities for Fiscal Year 2013 65

site20 to make such a collection available to the adaptive finite element research community [2].

The development and application of PHAML continues to be of prime importance. PHAML was 

originally developed to solve elliptic partial differential

equations in two spatial dimensions. We are now extending it to three dimensions, in support of 

collaborations with PML. This year we extended the 

code to include high order tetrahedral elements, but 

have not yet included hp-adaptivity with those elements.

There are two major collaborative efforts with 

PML that apply PHAML to their physical models.

 In collaboration with Eite Tiesinga and Paul Julienne, we are using PHAML to study the 

interaction of atoms and molecules held in an optical trap. Previously we calculated the bound 

states, scattering properties and dynamics of two 

dipolar molecules held in a cylindrically symmetric trap, a 2D problem [4]. We are currently 

extending these simulations to a 3D model without 

the assumption of cylindrical symmetry. We validated PHAML’s high order 3D elements using the 

harmonic oscillator problem, for which the exact 

wave function is known. Using 4th order elements 

we were able to get six-digit accuracy in a few 

minutes. We are now attempting to solve a much 

more difficult problem, a model of two nonreactive polar RbCs molecules in an optical lattice site.

 

20 http://math.nist.gov/amr-benchmark

 We are collaborating with John Villarrubia to apply PHAML to the modeling of scanning electron 

microscope images of samples that contain a mixture of conducting and insulating regions. 

Villarrubia has a code that models electron scattering in materials, secondary electron production, 

and detection. We have coupled this code with 

PHAML to determine the electric fields that affect 

the image.

Future work will continue to enhance PHAML with 

additional capabilities, robustness and efficiency, implement and study some recently proposed hp-adaptive

strategies, develop a new hp-adaptive strategy that attempts to capture the essential aspects of the reference

solution strategies without computing the expensive 

reference solution, complete the extension of PHAML 

to 3D problems, and continue collaborations that use 

PHAML in NIST applications.

[1] W.F. Mitchell and M.A. McClain, A Comparison of hpAdaptive Strategies for Elliptic Partial Differential 

Equations, ACM Transactions on Mathematical Software, to appear.

[2] W.F. Mitchell, A Collection of 2D Elliptic Problems for 

Testing Adaptive Algorithms, Applied Mathematics and 

Computation 220 (2013), 350-364.

[3] W.F. Mitchell, Performance of hp-Adaptive Strategies 

for Elliptic Partial Differential Equations, in Proceedings of the 4th International Congress on Computational 

Engineering and Sciences (FEMTEC 2013), May 2013.

[4] T.M. Hanna, E. Tiesinga, W.F. Mitchell and P.S. Julienne, Resonant Control of Polar Molecules in an 

Optical Lattice, Physical Review A 85:2 (2012).

Texture Compression Evaluation 

and Optimization

Wesley Griffin

Marc Olano (Univ. of Maryland Baltimore County)

Texture compression is widely used in real-time rendering to reduce storage and bandwidth requirements. 

Hardware-based texture compression has not fundamentally changed since its introduction in 1999. 

Recently, however, interest has grown in improving 

texture compression. We are exploring new techniques 

for reducing the bit rate for the current fixed bit rate 

algorithms as well as new variable bit rate algorithms 

that can be efficiently decoded in graphics hardware.

In evaluating texture compression, the most common approach is to use some combination of the mean 

square error, peak signal-to-noise ratio, or visual image 

inspection of the compressed texture. In [1] we show 

that this approach for evaluating texture compression 

does not properly account for the two ways in which 

Figure 33. Slice along the z=0 plane of the fourth wave function 

from a 3D simulation of the interaction of two nonreactive polar 

RbCs molecules.
66 NIST Applied and Computational Mathematics Division

textures are used in rendering images, and present a 

method that evaluates compression artifacts on final 

rendered images using perceptually rigorous objective 

image quality assessment metrics.

One of the more interesting conclusions in our paper is that current hardware compression algorithms are 

too conservative. Further reductions in bit rate can reduce the compressed size of textures while having only 

a small impact on image quality. This result benefits 

the real-time rendering community by showing that 

individual textures can be more highly compressed,

thus saving on bandwidth and asset load times.

Going forward, we plan to turn our evaluation 

framework into an optimization function for texture 

compression. By developing an optimization method

we can enable real-time rendering asset pipelines to 

automatically optimize texture compression rates and 

quality. This will further benefit the real-time rendering 

community by removing the highly subjective and 

time-consuming task of finding the right compression 

algorithm settings for textures.

[1] W. Griffin and M. Olano, Objective Image Quality Assessment of Texture Compression, in Proceedings of the 

2014 ACM SIGGRAPH Symposium on Interactive 3D 

Graphics and Games, to appear.

Declarative 3D Graphics

Sandy Ressler

Kyle Leber (Lock Haven University)

Web pages exist as large collections of hierarchical 

elements that are rendered to the page. All content is 

organized via the Document Object Model (DOM). A 

huge collection of tools has been created to allow programmers to manipulate the DOM. In particular, tools 

and frameworks based on JavaScript have become the 

go-to language for Web development. Declarative 3D 

Graphics is a method of representing graphics in a declarative manner (as opposed to imperative) that makes 

3D graphics a first class citizen of the web page. Placing 3D graphics in the DOM, therefore, allows these 

same JavaScript tools to access and manipulate 3D 

graphics, even though they were not specifically designed for 3D graphics.

We use anthropometry, the measurement of humans, as a testbed application, to experiment with 

declarative 3D capabilities and techniques. This application enables us to visualize several hundred whole 

body laser scans complete with the 3D landmarks that 

were captured as part of an anthropometric survey. 

Over the last 18 months we have extended this application to let us take direct measurements, interactively, 

on the surface of the visualized bodies. We plan on 

extending the capabilities of JavaScript libraries, such 

as jQuery, to provide a useful set of capabilities for the 

use of anthropometric databases. 

Of note is the fact that we do not need to develop 

yet another entirely new set of user interface techniques; we can simply use the commonly understood 

vocabulary of web pages. The illustration demonstrates 

use of our application in a typical web browser. This 

demonstrates that current declarative 3D technology is 

viable for the development of larger scale applications 

using the infrastructure that already exists for web application development. We hope to extend the visual 

measurement capabilities to more dimensions such as 

the ability to take and measure cross sections through 

the body and volumetric measurements.

[1] J. Jankowski, S. Ressler, J. Behr, Y. Jung, K. Sons and

P. Slusallek, Declarative Integration of Interactive 3D 

Graphics into the World-Wide Web: Principles, Current 

Approaches, a Research Agenda in Web3D ‘13: Proceedings of the 18th International Conference on 3D 

Web Technology, San Sebastian, Spain, June 20-22, 

2013, 39-45.

[2] S. Ressler and K. Leber, Web Based 3D Visualization 

and Interaction for Whole Body Laser Scans, in Proceedings of the 4

th International Conference and

Exhibition on 3D Body Scanning Technologies, Long 

Beach CA, Nov. 19-20, 2013.

Figure 34. Testbed application for declarative 3D graphics on the 

web.
Summary of Activities for Fiscal Year 2013 67

Optical Characterization of 

Immersive 3D Displays

S. Satterfield

J. E. Terrill

J. Penczek (NIST PML)

P. A. Boynton (NIST PML)

T. Scheitlin (NCAR)

Many things influence a visualization of a dataset. 

These include the nature of the data itself and its uncertainties, the visual representation space, the 

visualization algorithms used for implementation, as 

well as algorithmic simplifications. Another factor impacting the final visualization is how accurately the 

images are rendered by the display system. We seek to 

develop a deeper understanding of each part of this 

process. In the current work we are studying the impact 

of the display on stereo visualizations. 

Every display technology has its own inherent performance limitations. The non-ideality of the display 

introduces constraints on what information can actually 

be observed by the viewer. By characterizing the optical performance of the display system, we can 

quantitatively determine what visual information may 

be impaired. The operators of the display facility can 

use the results to evaluate how the visual characteristics that are important to them are affected, understand 

the visual limitations of their system, and use the performance data to drive improvements. The display 

performance data also informs the scientists that create 

the visualization data how much of that data can actually be realized/observed. For example, the display may 

exhibit sufficient 3D crosstalk that small spatial features are washed out due to a lack of contrast. If the 

scientists are aware of this limitation, they can modify 

their visualization to work around that limitation. A 

careful characterization of the display system can also 

predict if the display is prone to inducing visual fatigue 

or headaches.

This past year we leveraged our prior work to develop a suite of tests for the optical characterization of 

immersive 3D displays [1-3]. A set of 23 image pairs 

and a custom detector gimbal alignment structure were 

created to support this study. A precision spectroradiometer (Photo Research PR-740) with a 1-degree

aperture, and a 4 nm bandwidth, was used to measure 

radiometric, photometric, and colorimetric data on two 

immersive stereo display systems. One was a rearprojection system, the other a front-projection system. 

The optical characteristics measured on these systems 

included: luminance and color difference between left 

and right eye, contrast ratio between left and right eye, 

crosstalk between left and right eye, viewing direction 

dependence, head tilt dependence, luminance and color 

uniformity, and shutter glasses characteristics. A relative photometric camera was also used to evaluate the 

spatial distribution of some of these characteristics. 

The 2D maps captured by the camera can provide an 

intuitive and comprehensive description of how these 

characteristics behave across the viewing area [4]. 

An example of this is given in Figure 35 for the 

case of 3D crosstalk from the display system at the 

NIST Boulder Visualization Lab. The image on the left 

illustrates what the viewer can observe for an intended 

black image at the left eye, with a white unintended 

image in the right eye. In an ideal 3D display, only a 

pure black image should be observed in the left eye. 

However, real displays will exhibit some light leakage 

from the white unintended image to the black intended 

image. The images in Figure 35 demonstrate how the 

light leakage is distributed over the screen, and serves 

to degrade the performance of the display. The 2D map 

on the right quantifies the 3D crosstalk over the entire 

display. Further measurements revealed that the “X” 

crosstalk pattern rotates with a corresponding head tilt, 

suggesting, therefore, that much of this crosstalk is 

 

Figure 35. Left image shows view of 3D display observed through left lens of eye glasses. The right image is a map of the 3D crosstalk over the 

active area of the display.
68 NIST Applied and Computational Mathematics Division

related to the imperfections of the eye glasses.

The first display tested was the NIST Powerwall 

display in Boulder, Colorado. This was a rear projection display with a Christie Mirage 2000 projector, an 

8.75 m × 6.79 m active screen, with 1280×1024 resolution, and Crystal Eyes3 active glasses. In most cases, 

the viewers of this display stand about 1.2 m in front of 

the screen and wear the active 3D glasses. The same 

viewing conditions were replicated for the measurements by placing the detector at the same eye location. 

Our investigation revealed that the Boulder system had 

a relatively low luminance, which limited the contrast 

of the data and required a dark room for viewing. The 

eye glasses were the dominant cause of the 3D crosstalk, had poor optical transmission, and blue-shifted the 

colors. The display system also exhibited a perceptible 

flicker, which increased the propensity for eye fatigue 

and headaches with prolonged viewing.

The second display system investigated was at the 

National Center for Atmospheric Research (NCAR) 

Visualization Lab. The laboratory uses the display system to present 3D datasets on climate research, and as 

an educational outreach tool. This front projection system had a Christie Mirage HD6 projector with 

1920×1080 resolution, a 3.78 m × 2.13 m active screen 

area, and used Macnaughton active 3D glasses. The 

screen was mounted on a wall at the front of a conference room, with the viewers seated around a U-shaped 

table centered in front of the screen. Given the wide 

range of viewing angles, the detector was nominally 

positioned normal to the screen and 5.4 m from the 

screen center, which approximated the average viewing 

conditions. The display exhibited brighter images than 

the NIST Boulder system, which contributed to substantial improvements in the visibility of features. The 

eye glasses were still the dominant cause for the 3D 

crosstalk, but to a much lesser degree. The glasses also 

had better optical transmission, yet still produced a 

color shift. In addition, the open front-projection configuration of the NCAR system allowed us to 

characterize the relative contribution of the projector, 

screen, and eye glasses to the final viewing experience. 

Some limiting characteristics were identified and quantified. The room lighting conditions were also 

evaluated and shown to have a dramatic impact on how 

much visual information could be observed.

The preliminary findings of this investigation were 

provided to both Visualization Lab supervisors. It is 

expected that this information will be used to direct 

future improvements to these facilities. In the coming 

year, a more detailed analysis of this investigation will 

be submitted to a relevant journal in order to raise 

awareness of the practical limitations of rendering 

complex visual information. We also intend to extend 

this work to multi-screen immersive displays, such as a 

four-sided Cave Automatic Virtual Environment 

(CAVE) display system. This is a more immersive virtual reality environment, which also poses a more 

complex rendering and measurement challenge.

[1] Information Display Measurements Standard21, International Display Metrology Committee, Society of 

Information Display. 

[2] E. F. Kelley, K. Lang, L. D. Silverstein and M. H. Brill, 

Methodology for Estimating the Luminous Flux Based 

upon Color Primaries from Digital projection Displays, 

NISTIR 6657, January 2009.

[3] E. F. Kelley, K. Lang, L. D. Silverstein and M. H. Brill, 

Projector Flux from Primaries, Society of Information 

Display Symposium Digest of Technical Papers 40

(2009), 224-227.

[4] J. Penczek, P. A. Boynton, E. F. Kelley, Measuring 3D 

Crosstalk Uniformity and its Influence on Contrast Ratio, Journal of the Society of Information Display 21

(June 2013), 225-230.

Visualization for Measurement 

Science for Complex Information 

Systems

Sandy Ressler

Kevin Mills (NIST ITL)

Chris Dabrowski (NIST ITL)

James Filliben (NIST ITL)

We aim to develop and evaluate a coherent set of 

methods to understand behavior in complex information systems, such as the Internet, computational 

grids and computing clouds. ACMD is providing visualizations of simulation results that are being 

undertaken as part of this effort. One key goal is to 

produce these visualizations as rapidly as possible in 

order to provide insight to the researchers early enough 

in development to positively affect the research. On 

several occasions we have, in fact, been instrumental in

identifying bugs in the simulation system.

For example, we produced an animation illustrating the progression of “fitness” of a model evolved 

using a genetic algorithm applied to the Koala cloud 

computing simulation system. The animation uses 

shape, size and color as a method to illustrate the settings of three variables in the simulation. Each 

generation, from the 500 total, corresponds to a single 

frame of the animation. See Figure 36.

In addition, the researchers are beginning to study

a network based on the 2001 configuration of the Autonomous System portion of the Internet (see Figure 

37). The graph consists of approximately 11000 nodes 

and 47 000 edges. Using an off-the-shelf open source 

tool (gephi) we produced visualizations that helped 

 

21 http://icdm-sid.org/
Summary of Activities for Fiscal Year 2013 69

identify structure in the network which was completely 

unknown previously. Each color is a particular cluster 

of nodes is computed according to the “modularity” 

network metric.

[1] K. Mills, C. Dabrowski, J. Filliben and S. Ressler, Using 

Genetic Algorithms and Simulation to Search for Failure 

Scenarios in System Models, in Proceedings of the Fifth 

International Conference on Advances in System Simulation (SIMUL 2013), October 27 - November 1, 2013, 

Venice, Italy.

Figure 37. Internet autonomous system graph circa 2001.

Figure 36. Frame from an animation illustrating the effect of 

settings from 3 variables on the fitness of the individuals. The gray 

snake like line illustrates the quickly increasing fitness.
70 NIST Applied and Computational Mathematics Division

Mathematical Knowledge Management

We work with researchers in academia and industry to develop technologies, tools, and standards for 

representation, exchange, and use of mathematical data. Of particular concern are semantic-based 

representations which can provide the basis for interoperability of mathematical information processing 

systems. We apply this to the development and dissemination of reference data for applied mathematics. The 

centerpiece of this effort is the Digital Library of Mathematical Functions, a freely available interactive and 

richly linked online resource, providing essential information on the properties of the special functions of 

applied mathematics, the foundation of mathematical modeling in all of science and engineering.

Digital Library of Mathematical 

Functions

Daniel Lozier

Frank Olver

Bruce Miller

Bonita Saunders

Marjorie McClain

Howard Cohl

Ronald Boisvert

Charles Clark (NIST PML)

Brian Antonishek (NIST ITL)

Adri Olde Daalhuis (University of Edinburgh)

http://dlmf.nist.gov/

Math and science go hand in hand. Purely mathematical developments find application in practical problemsolving in all fields of science as well as engineering, 

while cutting-edge science is a major driver of mathematical research. Often the mathematical objects at the 

intersection of math and science are mathematical 

functions. Effective use of these tools requires ready 

access to their many intricate properties. This need was 

capably satisfied for 50 years by the Handbook of 

Mathematical Functions [1]. Twenty-first century 

needs, greatly enlarged since 1964, are being met by 

the NIST Digital Library of Mathematical Functions22

(DLMF) and its print companion, the NIST Handbook 

of Mathematical Functions [2]. The new handbook 

contains more than twice as many formulas as the old 

one, coverage of more functions, and an up-to-date list 

of references. Collectively, the new handbook and 

website are called the DLMF. The website covers everything in the handbook and much more: additional 

formulas and graphics, interactive search, live zooming 

and rotation of 3D graphs, internal links to symbol definitions and cross-references, and external links to 

online references and sources of software.

Today’s DLMF is the product of many years of effort by more than 50 expert contributors. But its 

appearance in 2010 was not the end of the project. Corrections to confirmed errata, bibliographic updates, and 

 

22 http://dlmf.nist.gov/

addition of important new material all need to be made, 

and new chapters covering emerging subject areas need 

to be added, so as to assure the continued vitality of the 

DLMF deep into the 21st century. Related developments currently in progress at NIST include DLMF 

Tables, an on-demand table generation web service for 

special functions, and the DRMF (Digital Repository 

of Mathematical Formulae), a listing of mathematical 

formulas taken with permission from respected publications such as Gradshteyn and Ryzhik’s Tables of 

Integrals, Series and Products.

Just one update appeared on the website in the past 

year. It introduced several improvements that affect 

display of math and graphics. A short list of corrections 

and other changes are scheduled for the next release, 

expected in early 2014. The complete record of changes since original release is given online23

.

The DLMF project has been led by senior editors 

with the expert assistance of associate editors, chapter 

authors, and chapter validators. With the passage of 

time some of these experts, for various reasons, have 

reduced or ended their commitment to the project. A 

major blow to the project was the death of the Mathematics Editor, Frank Olver, in April 2013; fortunately, 

Adri Olde Daalhuis had already been named as a second Mathematics Editor. Another recent death was 

Bille Carlson, long-time professor at Iowa State University and author of the chapter on Elliptic Integrals.

As a result of these developments, leadership of 

the DLMF project is being reconstituted into three 

newly defined categories: the editorial board, a small 

group of senior leaders with ultimate responsibility and 

final authority for the content and presentation of the 

DLMF, senior associate editors, senior leaders in the 

community with special interest in special functions, 

mathematical handbooks, and the presentation of mathematics on the web who will advise the editorial board 

on the future development of the DLMF, and associate 

editors, experts in the mathematics of special functions 

who will assist the Mathematics Editor with the 

maintenance and development of the technical content 

of the DLMF. All former associate editors, authors, and 

validators have received a letter signed by ITL Director 

 

23 http://dlmf.nist.gov/errata
Summary of Activities for Fiscal Year 2013 71

Charles Romine describing the new editorial structure. 

The recipients were asked if they wish to offer to continue their participation in one of these new categories. 

They were asked also if they know of mathematicians 

whom they would recommend to serve in one of the 

categories. An upcoming editorial meeting will be devoted to reviewing responses to the letter and filling in 

the new categories of leadership.

The NIST Information Services Office has conducted a citation analysis to measure the penetration of 

the DLMF into the user community in comparison to 

the old 1964 Abramowitz-Stegun handbook, which the 

DLMF is intended to replace. The analysis covers the 

years 2007-2012, roughly 3 years before and 3 years 

after publication of the DLMF. The data shown in Figure 38 combines the handbook and website citations 

for the DLMF (It was reported in the study that 17% of 

the citations over the 3-year period were to the online 

version.) It can be seen from the figure that citations to 

the DLMF began immediately to increase steadily from 

year to year, while citations to the old handbook, which 

had been increasing, began a steady decrease in 2010. 

In percentage terms, by the end of 2012 citations to the 

DLMF handbook and website had grown to about 8% 

of the total number of citations to both handbooks.

[1] M. Abramowitz and I. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs and 

Mathematical Tables, Applied Mathematics Series 55, 

National Bureau of Standards, Washington, DC, 1964.

[2] F. Olver, D. Lozier, R. Boisvert and C. Clark, eds., NIST 

Handbook of Mathematical Functions, Cambridge University Press, 2010.

Mathematical Knowledge 

Representation

Bruce Miller

Deyan Ginev (Jacobs University, Germany)

Although we became involved in Mathematical 

Knowledge Management (MKM) to support the development of the Digital Library of Mathematical 

Functions (DLMF), the release of the latter in 2010 

hardly signified an end to our activities. Simply maintaining the DLMF [1] requires continued enhancement 

of the tools and techniques as well as tracking the technologies involved. Applying what we’ve learned to 

other projects is an even more powerful motivator.

Mathematics Markup Language (MathML) is at 

the core of delivering mathematics on the web, and the 

current mixed situation illustrates some of our challenges. MathML defines markup for both Presentation

(for displaying mathematics) and Content (for encoding its meaning). We participate in the Math Working 

Group of the World Wide Web Consortium (W3C), 

which recently released version 3 of the MathML specification. This version greatly improves the 

expressiveness of the Content format. Yet, it is quite 

difficult to convert markup meant for human consumption, such as LaTeX intended for high-quality 

typesetting, into fully disambiguated Content MathML.

While Content MathML is essential for reusing 

mathematics for computation, the more easily generated Presentation MathML at least provides quality 

display, is scalable, accessible and can be supported by 

assistive technologies. Consequently, several recent 

standards, in particular version 5 of HTML (HTML5), 

the markup used for web pages, and ePub, a standard 

for electronic books, have both adopted MathML as an 

integral part of their markup. Furthermore, at World 

Wide Web Consortium’s encouragement, the Math 

Working group is preparing a 2nd Edition of the 

MathML 3 specification and will submit it this spring 

to ISO to become an international standard.

In spite of this, some major browser developers are 

still reluctant to expend the effort implement MathML; 

only one browser has essentially full, native support. 

However, a portable JavaScript library called MathJax 

can display MathML on most browsers with high 

quality, albeit quite slowly, while preserving accessibility.

Thus MathML support, one way or another, is 

much more widespread than it was when DLMF was 

initially released. The spring 2014 update of DLMF 

will employ HTML5 as the default format rather than 

using images for math. This will include MathML; 

MathJax will be used as the fallback for browsers 

without native support. Although it may be slower than 

images in some cases, it will look better, be more scalFigure 38. Citations to the original Abramowitz and Stegun 

Handbook and the DLMF compared.
72 NIST Applied and Computational Mathematics Division

able and accessible and will increase the visibility of 

MathML (hopefully in a positive way).

In this context, much of this year's work has been 

in development [2], rather than research. The LaTeXML software, used to convert LaTeX to XML 

(HTML, HTML5, MathML, etc.) moves towards a 

long overdue release. Portability, 

code quality, robustness and 

coverage have 

been major concerns, as well as encompassing a larger 

set of standards. Generation of HTML5 has already 

been mentioned. Prototype support for ePub has also 

been completed. Some of the graphics libraries commonly used in LaTeX (tikz, pgf) can now be used to 

produce Scalable Vector Graphics (SVG), a standard 

for 2D graphics also included in HTML5.

Ongoing progress in generating Content MathML, 

particularly for DLMF, has enabled extensibility, allowing us to employ more sophisticated parsers. Some 

groundwork in representing inherently ambiguous 

markup has also been achieved [3].

In the meantime, the software is being used in the 

infrastructure of several other projects such as: Planet 

Math24; it continues to be used to process arXiv25 [4], 

in particular to generate test-data for research in mathematical search; and in the Digital Repository of 

Mathematical Formulas (see page 71).

[1] B. R. Miller, Three Years of DLMF: Web, Math and 

Search, Lecture Notes in Computer Science 7961, 

Springer, Heidelberg (2013), 288-295.

[2] B. R. Miller, D. I. Ginev, LaTeXML 2012 - A Year of 

LaTeXML, Lecture Notes in Computer Science 7961, 

Springer, Heidelberg (2013), 335-338.

[3] D. Ginev, The Structure of Mathematical Expressions, 

Master’s Thesis, Jacobs University, 2011.

[4] H. Stammerjohanns, M. Kohlhase, D. Ginev, C. David, 

B. Miller, Transforming Large Collections of Scientific 

Publications to XML, Mathematics in Computer Science

3:3 (2010), 299-307.

 

24 http://planetmath.org

25 http://arxiv.org

Visualization of Complex Functions 

Data 

Bonita Saunders

Brian Antonishek (NIST ITL)

Qiming Wang

Bruce Miller

Sandy Ressler

Daniel Lozier

While complex function data visualization can be a 

powerful tool for researchers studying mathematical or 

physical phenomena, problems with accessibility can 

severely limit its usefulness. Currently, interactive 3D 

visualizations in the NIST Digital Library of Mathematical Functions (DLMF) are rendered using two 

common technologies, VRML and X3D, which require 

users to download a plugin based on their operating 

system. This is inconvenient not only for users, but 

also for those maintaining the site, since updates of the 

plugin, web browser, and even the operating system 

can affect the quality of the visualization. To remedy 

this problem we have been working on the conversion 

of the DLMF 3D graphics to a WebGL format. 

WebGL is a JavaScript API (application programming interface) for rendering 3D graphics in a 

web browser without the use of a plugin. Our WebGL 

code is based on the X3DOM framework which allows 

the building of the WebGL application around X3D, an 

XML based graphics code. WebGL visualizations are 

visible on Windows, Mac, and Linux platforms in most 

HTML5 compatible browsers. Microsoft had originally 

indicated that they would not support WebGL because 

of security concerns, but they have now relented and 

are touting it as a feature of their latest browser, Internet Explorer 11 under Windows 8.1. Our preliminary 

tests and research indicate that there may be some 

problems with their implementation, but we will continue to monitor this. On the other hand, while we 

never found a VRML/X3D plugin that would successfully render our complex visualizations in Linux, we 

have had no problem rendering our WebGL versions of 

the visualizations in Linux using common web browsers such as Firefox and Chrome.

We have spent the last few months integrating the 

new visualizations into the DLMF. Figure 39 shows a 

WebGL visualization of the Riemann zeta function 

embedded in a DLMF web page. The WebGL renderings of the DLMF visualizations are superior in overall 

quality to the VRML/X3D versions. Color maps are 

more vibrant, cutting plane curves clearer, and the interactive movement of surfaces faster and smoother. 

However, we noticed that WebGL is more particular 

about the quality of the underlying computational grid. 

A few color map anomalies not seen in the 

VRML/X3D visualizations were traced to slight overlaps of grid lines. Subsequently we regenerated several 
Summary of Activities for Fiscal Year 2013 73

grids and boundary contours, greatly improving surface 

color maps and clipping in some WebGL visualizations. We hope the adaptive grid generation work now

in progress will help us eliminate minor imperfections 

still apparent on some surfaces, especially those containing several poles. The WebGL visualizations will 

appear in the next update of the DLMF web site as the 

default, but for this first release, users will still be able 

to choose VRML/X3D visualizations if preferred.

[1] B. Saunders, Q. Wang and B. Antonishek, Adaptive 

Composite B-Spline Grid Generation for Interactive 3D 

Visualizations, in Proceedings of MASCOT/ISGG 2012, 

Las Palmas de Gran Canaria, Spain, October 22-26, 

2012, submitted.

[2] B. Saunders and Q. Wang, Tensor Product B-Spline 

Mesh Generation for Accurate Surface Visualizations in 

the NIST Digital Library of Mathematical Functions, 

Mathematical Methods for Curves and Surfaces, Lecture 

Notes in Comp. Science 5862 (2010), Springer, 385-393. 

[3] B. Saunders and 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, SV.3.

[4] 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, Volume 6, 2007 (Supplement on the Proceedings of the 20th International 

CODATA Conference, Beijing, China, October 2006), 

pp. S146- S154. 

[5] B. Saunders and 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, 235-243.

Figure 39. DLMF webpage with embedded visualization of Riemann zeta function.
74 NIST Applied and Computational Mathematics Division

Standard Reference Tables on 

Demand

Bonita Saunders

Bruce Miller

Marjorie McClain

Daniel Lozier

Chris Schanzle

Annie Cuyt (University of Antwerp)

Stefan Becuwe (University of Antwerp)

Franky Backeljauw (University of Antwerp)

Tables of elementary and special functions values have 

been used by mathematical software designers, numerical analysts and other researchers in the mathematical 

and physical sciences for many years. Reliable reference values are invaluable, for example, when testing 

new software implementations. Today several libraries 

and systems produce high quality function values, but 

most offer limited information about the accuracy of 

their computations. One notable exception is the work 

of Annie Cuyt and colleagues at the University of 

Antwerp [1, 2, 3], whose multiprecision software provides strict error bounds for the accuracy of its 

computations.

Software designed by the Antwerp group was used 

to develop CFHB Live26, an online system that uses 

series and continued fraction representations to obtain 

function values and error bounds with negligible added

cost. We are collaborating with the Antwerp group to 

build an online system that allows users to create their 

own tables of special function values with an error certification [4] for integration within the NIST Digital 

Library of Mathematical Functions (DLMF). At NIST 

we are building the front end user interface to work 

with a back end computational engine based on the 

MPIeee library. 

During the past few months we have focused on 

the launch of a prototype system at Antwerp. The top 

level structure is similar to the DLMF. As shown in 

Figure 40, the table of contents lists names corresponding to chapters found in the DLMF. After a chapter 

and function are selected, a user may request a tabulation of function values to user-specified precision, or 

comparison to user-uploaded function values. Each 

output line of a tabulation that contains the function 

value and numbers representing an interval bounding 

the error. Currently, the output of a comparison shows 

function values computed by the system alternated with 

corresponding values from the table of data provided 

by the user, but discussions are ongoing concerning the 

best output format. There appears to be a consensus 

that relative errors should be shown along with some 

indication of digits that are possibly in error as illus-

 

26 http://www.cfsf.ua.ac.be/

trated in Figure 41. The prototype can be viewed at the 

University of Antwerp website27.

Several talks were presented about the project this 

year. Bonita Saunders presented the work at the Mathematical Association of America (MAA) MD-DC-VA 

Section Meeting at Salisbury University on April 13, 

2013. Daniel Lozier presented a minisymposium talk 

and announced the Antwerp site at the Society for Industrial and Applied Mathematics (SIAM) Annual 

Meeting in July 2013. 

Our current focus includes increasing the number 

of functions offered, inserting more user documentation, and adding functionality, for example, offering 

users a choice of rounding modes for tabulations and 

comparisons. Other issues under discussion include 

more extensive documentation for experts, integration 

with the DLMF site, and strenuous testing of inputs to 

catch potential vulnerabilities. Of course, as some issues are addressed, others are revealed. Consequently, 

another important job is prioritizing the work so that 

the NIST site is ready before the end of this fiscal year. 

 

27 http://cantlive.ua.ac.be/dlmftables/

Figure 40. Sample table of contents for DLMF Tables website.

Figure 41. Output for comparison of DLMF Tables computations 

with table of function values submitted by user.
Summary of Activities for Fiscal Year 2013 75

[1] A. Cuyt, V. B. Petersen, B. Verdonk, H. Waadeland and 

W. B. Jones, Handbook of Continued Fractions for Special Functions. Springer, New York, 2008.

[2] F. Backeljauw, A Library for Radix-independent Multiprecision IEEE-compliant Floating-point Arithmetic, 

Technical Report 2009-01, Department of Mathematics 

and Computer Science, Universiteit Antwerpen, 2009.

[3] M. Colman, A. Cuyt and J. Van Deun, Validated Computation of Certain Hypergeometric Functions. ACM 

Transactions on Mathematical Software 38:2 (January 

2012), Article 11.

[4] F. Backeljauw, S. Becuwe, A. Cuyt, J. Van Deun, and 

D. Lozier, Validated Evaluation of Special Mathematical Functions, Science of Computer Programming 10

(2013), 1016.

Digital Repository of Mathematical 

Formulae

Howard S. Cohl

Marjorie A. McClain

Bruce R. Miller

Bonita V. Saunders

Deyan Ginev (Jacobs University Bremen)

Janelle C. Williams (Virginia State University)

http://drmf.mathweb.org

The purpose of this project is to create a communitydriven digital knowledge base for mathematical formulae, equations, and objects associated with special 

functions and orthogonal polynomials. The original 

suggestion for this came from Dmitry Karp in an issue 

of OPSF-Net [1], with follow-up comments by Daniel 

Lozier [2] and Tom Koornwinder [3, 4]. The project 

has been ongoing since April 2013, and had a first aim 

of creating a proof-of-concept deployment. A demonstration will then be presented to the special functions 

and orthogonal polynomials mathematical community 

for a first round of feedback. We refer to our deployment, built with the publishing platform used by 

Wikipedia, namely MediaWiki, as the Digital Repository of Mathematical Formulae (DRMF).

The DRMF is focused on the needs of mathematicians performing research in the field of special 

functions who wish to (a) disseminate recent research 

results, and (b) interact with other researchers interested in these results. (In the field of special functions, 

new results are most often embodied in mathematical 

formulae.) We also hope that the DRMF will serve as a 

laboratory providing insight on successfully developing 

and curating such a resource.

On the technical front, we have built on the experience of the DLMF project28 [5], as well as the 

 

28 http://dlmf.nist.gov/

Planetary and MediaWiki publishing platforms. Each 

feature of the publishing process is modelled as a separate general-purpose MediaWiki extension, and pubpublished on GitHub for redistribution. The first 

demonstration provides experimental extensions for (1) 

formula interactivity, (2) formula pages, (3) centralized 

bibliography and (4) mathematical search. At its foundation, DRMF shares the core technologies of the 

DLMF, based on community-recognized open standards (TeX, HTML+MathML), as integrated by the 

LaTeXML converter. We incorporate some of the 

high-quality components used in Planetary (the 

JOBAD interactivity framework), as well as those designed for MediaWiki (such as the MathSearch and 

Math extensions). Examples of formula interactivity 

include:

 a clipboard for mathematics, allowing easy 

copy/paste of a formula's source, presentation or 

content MathML representations;

 on-demand summary of constraints and substitutions applicable to a formula;

 on-demand consulting with external web services 

(e.g., Wolfram Alpha) and local computer algebra 

systems (e.g., Mathematica, Maple).

The DRMF's first vision of a repository for mathematical formulas is to treat any notable expression as 

a primary object of interest, describing it in its own 

“formula page.” See Figure 42. Currently, formula 

pages contain a description of the formula itself, open 

section for proofs, bibliographic citations, a glossary of 

special DLMF symbols used in the formula and a link 

to the formula in the DLMF, whenever applicable. 

Optionally, one may also enter relevant constraints, 

substitutions, notes, the formula name, as well as links 

to formula generalizations and specializations. For each 

formula page there is a corresponding talk page where 

discussions about the formula and its page may take 

place. We are currently developing a strategy for handling the insertion of formula errata.

We are also exploring a variety of search strategies 

within our MediaWiki deployment. A key asset in our 

development of search capabilities is the use of DLMF 

macros in writing the TeX markup of formulas. LaTeXML (see page 71) uniquely translates the macros 

for specific special functions, orthogonal polynomials 

and general mathematical objects into Content 

MathML symbols, which in turn fuel structural search 

engines, such as MathWebSearch, to return results with 

very high accuracy.

Next, we present an early overview of the 

shortlisted resources which we plan to incorporate. We 

have been given permission to seed the DRMF with 

data from the NIST Digital Library of Mathematical 

Functions; Koekoek, Lesky and Swarttouw's (KLS) 

book Hypergeometric Orthogonal Polynomials and 
76 NIST Applied and Computational Mathematics Division

Their q-Analogues [6], as well as the Bateman Manuscript Project (BMP) [7, 8].

We are in active communication with other publishers to get permission for other proven sources of

mathematical formulae. Our current focus is on seeding the DRMF with DLMF data, and we have 

completed this for DLMF Chapter 25 on Zeta and Related Functions. Future near-term efforts will focus on 

seeding the rest of the DLMF data as well as the KLS 

data with DLMF macros incorporated. Efforts to upload BMP data will rely on mathematical optical 

character recognition software to produce LaTeX 

source for these formulae, and this effort is currently 

under consideration.

Figure 42. Sample DRMF formula page.
Summary of Activities for Fiscal Year 2013 77

[1] D. Karp, Knowledge Base of Formulas, OP-SF NET

18:4 (2011), Topic 5.

[2] D. Lozier, Comment 1 on Dmitry Karp’s Proposal, OPSF NET 18:4 (2011), Topic 6.

[3] T. Koornwinder, Comment 2 on Dmitry Karp’s proposal, OP-SF NET 18:4 (2011), Topic 7.

[4] T. Koornwinder, Additions to formulas in KoekoekLesky-Swarttouw, OP-SF NET 18:6 (2011), Topic 3.

[5] F. W. J. Olver, D. W. Lozier, R. F. Boisvert and C. W. 

Clark, The NIST Digital Library of Mathematical Functions, Cambridge University Press, 2010.

[6] R. Koekoek, P. A. Lesky and R. F. Swarttouw, Hypergeometric Orthogonal Polynomials and their qAnalogues, Springer Monographs in Mathematics, 

Springer-Verlag, Berlin, 2010.

[7] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, Vols. I, II, III, 

Robert E. Krieger Publishing Co. Inc., Melbourne, FL, 

1981.

[8] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms, Vols. I and II, 

Robert E. Krieger Publishing Co. Inc., Melbourne, FL, 

1954.

Eigenfunction Expansions for 

Special Functions and Orthogonal 

Polynomials

Howard S. Cohl

Hans Volkmer (University of Wisconsin-Milwaukee)

Roberto S. Costas-Santos (University of Alcalá)

Rebekah M. Wheatley (Johns Hopkins University)

Michael A. Baeder (Harvey Mudd College)

Connor MacKenzie (Westminster College)

Philbert Hwang (Poolesville High School)

The concept of a function expresses the idea that one 

quantity (the input) completely determines another 

quantity (the output). Our research concerns special 

functions and orthogonal polynomials. A special function is a function that has appeared in the mathematical 

sciences so often that it has been given a name. Green's 

functions (named after the British mathematician 

George Green, who first developed the concept in the 

1830s) describe the influence of natural phenomena 

such as electromagnetism, gravity, heat and waves. 

For example, in electrostatics, a Green’s function describes the influence of a point charge, called the 

source, over all of space. The inputs for Green’s functions are all of space (with the exception of a singular 

region), and the output is the “force” exerted from the 

point throughout space. Green's functions are fundamental to the study of partial differential equations and 

are powerful in that they provide a mechanism for obtaining their solutions. 

We study the properties of Green’s functions in 

spaces which are curved, and in particular, those spaces 

which locally look the same in every direction, i.e., 

those that are isotropic. Orthogonal polynomials and 

the special functions associated with them occupy a 

natural location in the study of these spaces. We focus 

on their behavior. Such a study is fundamental to the 

mathematical understanding of the universe, which as 

Einstein showed is curved. In particular, we compute 

eigenfunction expansions for fundamental solutions of 

multi-dimensional linear elliptic partial differential 

equations in separable coordinate systems on highly 

symmetric Riemannian manifolds. These iterated expansions are computed in the natural eigenfunctions 

produced by the method of separation of variables for 

elliptic partial differential equations on these manifolds. These iterated expansions are often connected 

by addition theorems to simpler expansions in fewer 

discrete and continuous eigenmode variables. We utilize classical analysis on these manifolds in order to 

obtain new special addition theorems that identify fundamental expansions through specialization and 

generalization in a geometrical context.

In Euclidean space, fundamental solution expansions can be given in terms of the harmonics expressed 

in separable coordinate systems. With H. Volkmer, we 

have an ongoing investigation of these expansions. It is 

our goal to develop eigenfunction expansions for a 

fundamental solution of Laplace’s equation in threedimensions in parabolic cylinder, elliptic cylinder, rotationally-invariant cyclidic (fourth order), asymmetric 

quadric (second order) and asymmetric cyclidic coordinate systems. In connection with this effort, in [1], 

we compute new definite integrals using orthogonality 

and integral transforms. These integrals originate from 

eigenfunction expansions for a fundamental solution of 

Laplace’s equation in three-dimensional Euclidean 

space in separable, rotationally-invariant coordinate 

systems. These expansions had been previously computed in [2] and an erratum [3] has been recently 

published. In [4], we analyzed summation and integration expansions for a fundamental solution of Laplace’s 

equation in three-dimensional Euclidean space in parabolic cylinder and elliptic cylinder coordinates. These 

expansions are given in terms of parabolic cylinder 

functions and Mathieu functions, the special functions 

which arise in these separable coordinate systems for 

Laplace’s equation. In [5] (see also [6]), we performed 

a global analysis of solutions for Laplace's equation on 

three dimensional Euclidean space in one of the most 

general orthogonal asymmetric confocal cyclidic coordinate systems which admit solutions through 

separation of variables. We refer to this coordinate 

system as five-cyclide coordinates since the coordinate 

surfaces are given by two cyclides of genus zero which 

represent the inversion at the unit sphere of each other, 

a cyclide of genus one, and two disconnected cyclides 
78 NIST Applied and Computational Mathematics Division

of genus zero. This coordinate system is obtained by 

stereographic projection of sphero-conal coordinates on 

four-dimensional Euclidean space. The harmonics in 

this coordinate system are given by products of solutions of second-order Fuchsian ordinary differential 

equations with five elementary singularities. The Dirichlet problem for the global harmonics in this 

coordinate system is solved using multiparameter spectral theory in the regions bounded by the asymmetric 

confocal cyclidic coordinate surfaces. H. Volkmer and 

H. Cohl have submitted a second paper on the topic of 

asymmetric cyclidic harmonics [12]. In this paper we 

compute external harmonics for the asymmetric cyclidic separable harmonic five-cyclide coordinate system, 

as well as expansions for a fundamental solution of 

Laplace's equation in these harmonics.

On highly symmetric manifolds, fundamental solution expansions are often given in terms of angular 

harmonics which are represented in terms of Fourier, 

Gegenbauer, and Jacobi polynomials. In practice, 

these expansions are often expressible using generating 

functions for these orthogonal polynomials. We have 

developed a technique for generalizing generating 

functions for hypergeometric orthogonal polynomials 

which has been useful in developing fundamental solution expansions. In [7], a generalization of the 

generating function for Gegenbauer polynomials is 

derived which allows one to expand this generating 

function in terms of Gegenbauer polynomials with arbitrary order. This Gegenbauer polynomial expansion 

allows one to expand powers of the distance between 

two points in d-dimensional Euclidean space in Vilenkin's polyspherical coordinates. In [8], we describe 

two methods for computing azimuthal Fourier expansions for a logarithmic fundamental solution of the 

polyharmonic equation in d-dimensional Euclidean 

space. In [9], we compute a generalization of the generating function for Gegenbauer polynomials extended 

to Jacobi polynomials. The expansion with Chebyshev 

polynomials of the first kind is used to compute Fourier 

expansions for a power-law fundamental solution of 

the polyharmonic equation in d-dimensional Euclidean 

space in rotationally-invariant coordinate systems. In 

[9], addition theorems for the Fourier coefficients of a 

power-law fundamental solution of the polyharmonic 

equation in d-dimensional Euclidean space in Vilenkin's polyspherical coordinates are computed. We also 

develop addition theorems for Fourier coefficients of 

fundamental solutions for linear elliptic partial differential equations on highly symmetric Riemannian 

manifolds. With 2013 Summer Undergraduate Research Fellowship (SURF) student, Rebekah Wheatley, 

we derived Fourier and Gegenbauer expansions for a 

fundamental solution of Laplace's equation in hyperspherical geometry. Under Cohl’s supervision, 

Wheatley computed Fourier and Gegenbauer expansions and corresponding addition theorems for a 

fundamental solution of Laplace's equation in ddimensional hyperspherical geometry.

Furthermore, we have developed specializations 

and generalizations of generating functions for orthogonal polynomials in the Askey scheme for generalized 

hypergeometric orthogonal polynomials. For instance, 

in [10], we present an interesting extension of the generating function for Gegenbauer polynomials to Jacobi 

polynomials, and re-expresses Gauss hypergeometric 

functions in terms of more elementary functions for 

certain generating functions for classical orthogonal 

polynomials. We also produce corresponding definite 

integrals using orthogonality. In [11] (joint with H. 

Volkmer and 2012 SURF student Connor MacKenzie) 

we generalize generating functions for hypergeometric 

orthogonal polynomials, namely Jacobi, Laguerre and 

Wilson polynomials. These generalizations are determined using connection relations with one free 

parameter for these hypergeometric orthogonal polynomials. The coefficients of these expansions are 

given in terms of generalized hypergeometric functions. We then produce corresponding definite integrals 

using orthogonality. With 2013 SURF student Michael 

Baeder, we extend the work presented in [11] to other 

generating functions for hypergeometric orthogonal 

polynomials, such as Wilson, continuous Hahn, continuous dual Hahn and Meixner-Pollaczek polynomials. 

We are also extending this investigation to include discrete orthogonal polynomials such as Racah 

polynomials. Akin to [11], with 2013 Summer High 

School Internship Program (SHIP) student Philbert 

Hwang and with Roberto Costas-Santos, we compute 

generalizations of generating functions for basic hypergeometric orthogonal polynomials in the q-Askey 

scheme.

[1] H. S. Cohl and H. Volkmer, Definite Integrals using 

Orthogonality and Integral Transforms, Symmetry, Integrability and Geometry: Methods and Applications 8 

(2012), 077.

[2] H. S. Cohl, J. E. Tohline, A. R. P. Rau and H. M. Srivastava, Developments in Determining the Gravitational

Potential using Toroidal Functions, Astronomische Nachrichten 321:5/6 (2000), 363-372.

[3] H. S. Cohl, Erratum: “Developments in Determining the 

Gravitational Potential using Toroidal Functions,” Astronomische Nachrichten 333:8 (2012), 784-785.

[4] H. S. Cohl and H. Volkmer, Eigenfunction Expansions 

for a Fundamental Solution of Laplace’s Equation on R

3

in Parabolic and Elliptic Cylinder Coordinates, Journal 

of Physics A: Mathematical and Theoretical 45:35

(2012), 355204.

[5] H. S. Cohl and H. Volkmer, Separation of Variables in 

an Asymmetric Cyclidic Coordinate System, Journal of 

Mathematical Physics 54:6 (2013), 06351.

[6] H. S. Cohl and H. Volkmer, Publisher's Note: “Separation of Variables in an Asymmetric Cyclidic Coordinate 

System,” Journal of Mathematical Physics 54:7 (2013),

079904.
Summary of Activities for Fiscal Year 2013 79

[7] H. S. Cohl, On a Generalization of the Generating Function for Gegenbauer Polynomials, Integral Transforms 

and Special Functions 24:10 (2013), 807-816.

[8] H. S. Cohl, Fourier Expansions for Logarithmic Fundamental Solutions of the Polyharmonic Equation, Journal 

of Classical Analysis 2:2 (2013), 107-127.

[9] H. S. Cohl, Fourier, Gegenbauer and Jacobi Expansions 

for a Power-law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems, 

Symmetry, Integrability and Geometry: Methods and 

Applications 9 (2013), 042.

[10] H. S. Cohl and C. MacKenzie, Generalizations and Specializations of Generating Functions for Jacobi, 

Gegenbauer, Chebyshev and Legendre Polynomials with 

Definite Integrals, Journal of Classical Analysis 31

(2013), 17-33. 

[11] H. S. Cohl, C. MacKenzie and H. Volkmer, Generalizations of Generating Functions for Hypergeometric 

Orthogonal Polynomials with Definite Integrals, Journal 

of Mathematical Analysis and Applications 407:2

(2013), 211-225. 

[12] H. S. Cohl and H. Volkmer, Expansions for a Fundamental Solution of Laplace's Equation on R

3

in Fivecyclidic Harmonics, in review.
80 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. 

Single Photon Conversion 

Technology: Research to 

Commercialization

Xiao Tang

Lijun Ma

Paulina Kuo

Oliver Slattery

Yong-Su Kim

Alan Mink

Barry Hershman

Joshua Bienfang (NIST PML)

Martin Fejer (Stanford University)

Jason Pelc (Stanford University)

Li Yan (University of Maryland Baltimore County)

See feature article, page 22.

Quantum Information Science

Scott Glancy

Emanuel Knill

Adam Keith

Adam Meier

Jim van Meter

Mike Mullan

Yanbao Zhang

Kevin Coakley (NIST ITL)

Sae Woo Nam (NIST PML)

B. Eastin (Northrop Grumman)

E. Cobanera (Indiana University)

G. Ortiz (Indiana University)

The traditional information units of classical computing are 0/1-valued bits, which may be realized as 

distinguishable states of physical systems. Quantum 

information science investigates the properties and 

applications of quantum bits. Formally, quantum bits 

have pure states defined as superpositions of two distinguishable states. Quantum bits promise to be powerful information processing units whose potential is 

realized when they are coupled by means of quantum 

gates, which generalize classical circuit elements. Applications include efficient algorithms for factoring 

integers and for physics simulation, protocols for secure communication, and significantly improved 

measurement precision. In addition, there is the potential for illuminating the foundations of physics, in 

particular the universality of quantum mechanics and 

field theory. In the last few years, there has been tremendous experimental progress demonstrating longlived quantum bits in diverse systems, including individually trapped atoms, superconducting circuit 

elements and various other solid state devices. Thus, 

we currently expect that quantum information processing will eventually be realized on large scales.

Our work in quantum information science aims to 

contribute to our understanding of the power and limitations of quantum physics as it relates to information 

extraction and processing. In this spirit, we investigate 

a broad range of subjects. In the current reporting period, we determined effective analysis methods for 

certifying that experiments violate classicality assumptions, we obtained new criteria for showing that timetagged detections violate such assumptions, and we 

initiated an investigation of quantum measurements of 

properties of curved space-time.

The principle of local realism (LR) asserts that 

states of spatially separate systems can be described as 

probability distributions over states where each system 

is in a definite state. Quantum mechanics violates this 

principle. Experimental demonstrations of this violation usually involve measuring a so-called Bell 

quantity and showing that the measured value violates 

a bound satisfied by LR. While violations have been 

found in many experiments, these experiments have so 

far been subject to various loopholes. That is, they require additional, unwanted assumptions to conclude 

that local realism fails. We are involved in experiments 

that aim to “close” these loopholes and apply the prop-
Summary of Activities for Fiscal Year 2013 81

erties of the violating quantum systems to deviceindependent random number generation, a protocol 

enabled by quantum mechanics. We therefore improved the analysis of LR violation so that an 

unambiguous statement of statistical significance is 

obtained. Our method is highly robust in that it is compatible with arbitrary strategies for stopping the 

experiment and can be used to compare the violation 

between disparate experiments. For our applications, it 

provides a strong certificate of performance, a necessity for protocols such as random number generation. 

This research is the main contribution of Yanbao 

Zhang's PhD thesis [2], completed this year. Yanbao is 

continuing to work in this area at the Institute for 

Quantum Computing in Waterloo, Canada.

Recent experiments to close the loopholes when 

demonstrating the failure of LR involved observations 

consisting of series of time tagged detections of photon 

pairs at various measurement settings. Traditional Bell 

inequalities work only for one photon pair at a time, 

requiring that each photon pair can be unambiguously 

identified in the data. Because of jitter in the recorded 

detection times and high rates of pair emission, this 

identification is not assured. As a result, the Bell inequalities can be violated by an LR source taking 

advantage of this effect. We developed a general theory 

of Bell quantities and inequalities for time tag sequences [3], integrated it with the analysis methods of the 

previous paragraph, and applied it successfully to experimental data from two external groups.

Looking further ahead, we are interested in how 

one can best measure properties of and discover new 

features of any quantum system. It is in this spirit that 

we have contributed to the study of non-abelian dualities for better understanding unconventional condensed 

matter systems [1].

While quantum effects are actively exploited for 

extremely precise measurements of time (atomic 

clocks) and space (interferometry for gravitational 

wave measurements), how properties of quantum field 

theory in space-time will affect these measurements is 

not well explored. We are investigating how these 

properties result in deviations from expectations based 

on non-relativistic quantum mechanics and at what 

level of precision these deviations become significant. 

Our initial focus is on Heisenberg-uncertainty-like limitations on measurements of the space-time metric. 

There is not yet an agreement on the best framework 

for analyzing such limitations. So far we have found 

that with respect to local quantum field theory on 

curved space times, there are issues with several existing arguments, including the lack of coordinate 

independence.

[1] E. Cobanera, G. Ortiz and E. Knill, The Non-Abelian 

Duality Problem, in review.

[2] Y. Zhang, Analysis of Tests of Local Realism, Ph.D.

Thesis, University of Colorado, Boulder, 2013.

[3] Y. Zhang, S. Glancy and E. Knill, Efficient Quantification of Experimental Evidence Against Local Realism, 

Physical Review A 8 (2013), 052119.

Quantum Computing Benchmarks

Emanuel Knill

Adam Meier

Michael Mullan

Dietrich Leibfried (NIST PL)

David Wineland (NIST PL)

David Pappas (NIST PL)

While the potential benefits of quantum information 

processing are tremendous, there are significant obstacles in realizing these benefits. Perhaps the most 

challenging obstacles are to experimentally construct 

multi-qubit systems whose quantum states are both 

stable and robustly manipulatable by quantum gates. 

One reason the two requirements are difficult to meet is 

that stability requires good isolation from the environment, but manipulatability involves interaction with an 

external controller. There is a proliferation of experimental systems that aim to meet these requirements 

with a few qubits and that hope to eventually scale up 

to many qubits. To evaluate such systems without regard to experimental details, we develop benchmarks, 

which are standardized processes and measurements 

that quantify the quality and scale of the experimental 

quantum system for information processing. 

Over the past few years we have developed and 

implemented a randomized benchmarking strategy that 

has been widely adopted. At NIST it has been implemented with trapped ion-qubits. The benchmarking 

procedures used and experimental analysis applied 

were the main contributions of Adam Meier's PhD thesis [1], completed this year. Adam is continuing this 

work at the Georgia Tech Institute.

A simple strategy for testing an experimental twoqubit gate is to prepare a maximally entangled state and 

measure each qubit in various bases. The fidelity of the 

state measurement can then be inferred from the data. 

This strategy has been used for characterizations of 

spin-spin iterations in ion-trap experiments at NIST

[3]. A recent version of this experiment brought to light 

several issues with this technique. The first is that the 

measurements need to be calibrated using similar 

measurements on known states. The instruments must 

be stable during the calibration and the subsequent 

measurements for this to work. Since perfect stability is 

unachievable, this requires additional tests to bound the 

contributions due to instability. At least one data set 

thought to be good turned out to suffer from this issue. 

The quality of the calibration becomes particularly 

important as the precision of the fidelity measurement 

improves or the fidelity approaches its maximum value 
82 NIST Applied and Computational Mathematics Division

of 1. For example, at the moment it is not clear whether we could confidently claim fidelity better than (say) 

0.995 in such an experiment. Traditionally, the data of 

the ion-trap experiments involve decomposing detection-count histograms as a mixture of reference 

histograms, where the latter are calibrated beforehand. 

Our analysis now bypasses the need for a full determination of reference histograms by using linear 

functionals of histograms to estimate the fundamental 

quantities from which the fidelity can be computed. We 

hope to integrate the new techniques into the control 

and data acquisition system in NIST’s ion-trap labs.

A general theme of this project is to develop better 

measurement strategies involving general quantum 

systems. In this spirit, we are formulating the theory 

and implementing algorithms and simulations for actively estimating the current time with passive atomic 

clocks, particularly the so-called quantum logic clocks. 

This work constitutes the PhD Thesis of Mike Mullan

[2], completed this year, and is being developed further 

by Adam Keith. So far we have successfully demonstrated improvements in timekeeping with simulated 

clocks subject to memory-less local oscillator noise. A 

goal is to demonstrate our strategies on an experimental system such as trapped beryllium ions.

[1] A. M. Meier, Randomized Benchmarking of Clifford 

Operators, PhD Thesis, University of Colorado, Boulder, 2013.

[2] M. Mullan, Quantum Algorithms for Atomic Clocks, 

PhD Thesis, University of Colorado, Boulder, 2013.

[3] A. C. Wilson, Y. Colombe, K. R. Brown, E. Knill, D. 

Leibfried and D. J. Wineland, Entangling Spin-Spin Interactions of Ions in Individually Controlled Potential 

Wells, in review.

Quantum State Estimation Theory 

and Experiment

Scott Glancy 

Emanuel Knill 

Konrad Lehnert (NIST PML) 

Will Kindel (University of Colorado) 

Hsiang-Sheng Ku (University of Colorado) 

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 certain am I that it has prepared that state?”

Full quantum state estimation can be a demanding 

task, requiring a large number of different measurements to be performed on (independently prepared 

copies) of the quantum state and requiring large 

amounts of computation to estimate the state. One 

method for reducing these costs is to exploit preexisting knowledge about the state being measured. For example, the state could be restricted to a 

smaller sub-set of all quantum states, such as those 

states that have Gaussian probability distributions for 

measurement results. ACMD developed an algorithm 

for estimating these Gaussian states that is 

orders of magnitude faster than full quantum state estimation and can be applied to data sets that are much 

too large to be analyzed with full quantum state estimation. ACMD’s new algorithm will be useful to many 

experiments on quantum optics and nano-mechanical 

resonators. 

ACMD continues the collaboration with the JILA 

laboratory of Konrad Lehnert through the Defense Advanced Research Projects Agency (DARPA) project 

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 2013 

the laboratory prepared an entangled state of quantum 

microwaves. ACMD developed methods to calibrate 

the measurements, analyze the entangled state using a 

phenomenological model and using Gaussian state estimation, and quantify the amount of 

entanglement. After demonstrating entanglement in 

this system, the experiment will progress to achieving 

the increased measurement efficiency required for 

quantum teleportation and optimizing the teleportation 

protocols for this system.
Summary of Activities for Fiscal Year 2013 83

Random Number Generation based 

on Bell Inequality Violation

Scott Glancy

Stephen Jordan

Emanuel Knill

Paulina Kuo

Yi-Kai Liu

Alan Mink

Xiao Tang

Lawrence Bassham (NIST ITL)

Joshua Bienfang (NIST PML)

Michaela Iorga (NIST ITL)

Alan Migdall (NIST PML)

Sae Woo Nam (NIST PML)

Rene Peralta (NIST ITL)

Andrea Rommal (Muhlenburg College)

Andrew Rukhin (NIST ITL)

Random number generation is a key step in almost all 

cryptographic protocols. For cryptographic applications 

one needs to know that the random numbers used could 

not have been known prior to their generation. There 

are no empirical tests on classical data that can certify 

this. However, using counterintuitive aspects of quantum mechanics, it is possible to empirically verify the 

generation of random numbers that could not have 

been known prior to their measurement without violating fundamental laws of physics. This can be achieved 

using modern variants of Einstein’s “spooky action at a 

distance” thought experiment, known as Bell tests. 

Recently, advances in quantum optics technology have 

moved these tests from the realm of thought experiments into the laboratory. A current NIST Innovations

in Measurement Science project involving several 

members of ACMD seeks to implement an optical Bell 

experiment and use it to produce random numbers certifiably secure for use in cryptographic applications. 

Despite technological advancements, implementing Bell tests remains challenging. Work has been 

ongoing at NIST to integrate fast, highly-efficient photon detectors, high-speed optical switching, and lowloss photon transmission into a Bell experiment whose 

data analysis can be carried out with minimal assumptions. Within ACMD, efforts have focused on 

developing tools for data analysis, analyzing alternative 

architectures for the experiment, and developing hardware and software infrastructure for the informationtheoretic and cryptographic aspects of the project, such 

as post-processing algorithms to evaluate and extract 

the attained randomness. 

On July 21-26, 2013 several members of ACMD 

met in Boulder for an intensive workshop on Bellbased randomness. Several protocols for processing 

random numbers using Bell experiments have been 

proposed in the quantum information theory literature. 

All of them require some initial seed of random numbers. Randomness expansion protocols start with a 

small seed and expand it via Bell experiments into a 

larger supply of random bits. Randomness amplification protocols start with an imperfect private seed and 

amplify it into an almost perfectly private supply of 

random numbers. A significant outcome of the workshop was a survey of the theoretical protocols and the 

corresponding hardware requirements for each.

The Bell experiment needs several additional ingredients to become a useful cryptographic resource. 

These include: a source of random numbers to use as 

the initial seed, software for analyzing the outcomes of 

the experiment to certify the presence of fresh randomness, software for distilling the data produced by the 

experiment into nearly-uniformly-random strings of 

bits, and technology to publish these strings over the 

Internet. Over the past year, ACMD has made progress 

in the development of each of these.

A prototype “randomness beacon” serving time

stamped, digitally-signed random bit strings over the 

Figure 43. Architecture of Bell experiment random number generator implementation.
84 NIST Applied and Computational Mathematics Division

internet, developed by the ITL Computer Security Division, is currently operational29

. The prototype beacon 

uses a conventional hardware random number source

not based on Bell experiments. Although the unpredictability of these random numbers is not certifiable 

by direct appeal to the laws of physics, the beacon can 

serve as a testbed for the various beacon-based cryptographic protocols for e-commerce and privacy 

protection that have been proposed in the cryptographic 

theory literature.

ACMD has developed an architectural model for 

Bell based randomness, as shown in Figure 43. Plans 

are to implement that model using field programmable 

gate arrays (FPGAs) at Bob and Alice to capture and 

timestamp detector events, as well as to generate supplemental supplies of random numbers for 

measurement basis selection and Trevisan extractor 

seeds.

Many Bell experiments generate entangled photon 

pairs randomly in time, and the detectors used to measure the photons suffer from timing jitter. These effects 

can create confusion in the “time-tag” measurement 

record that could allow a hacker to secretly control the 

random numbers output by the experiment. ACMD has 

developed new analysis tools for these experiments that 

can detect any such hacking attempt. After certifying 

the impossibility of local hidden variable models for 

the output data, the next step is to distill the output data 

into a string of almost perfectly uniform random bits. 

This is achieved by a software tool called a randomness 

extractor. We have now implemented, tested, and debugged a version of the Trevisan randomness extractor 

and have additionally identified theoretical improvements to that extractor. 

Although Bell experiments expand or amplify initial supplies of random numbers, it is of course 

desirable for these initial supplies to be of as high a 

quality as possible. Ideally, the initial random numbers 

should be unpredictable and produced at high rate and 

with low latency. Several methods for generating the 

initial supply of random numbers have been investigated, and one has now been implemented, specifically a 

random number generator based on a chaotic analog 

circuit implemented within an FPGA.

 

29 https://beacon.nist.gov/home

Tamper-Resistant Cryptographic 

Devices based on Quantum 

Mechanics 

Yi-Kai Liu

In recent years there has been growing interest in building tamper-resistant cryptographic devices, for 

applications such as software copy-protection and digital rights management. For example, many video game 

consoles use tamper-resistant chips to prevent unauthorized software from being loaded onto the system. 

Tamper-resistant chips can also be useful in preventing 

side-channel attacks, where an adversary tries to gain 

extra information about a computation by measuring 

physical characteristics of the hardware, such as timing 

and power consumption.

Can one make use of quantum mechanics to build 

better tamper-resistant cryptographic devices? One 

may hope that this is possible, because information 

behaves in surprising ways when it is encoded into the 

state of a quantum mechanical object. For instance, an 

unknown quantum state cannot be copied perfectly, 

and most measurements of the state will damage it. On 

the other hand, entangled quantum states can exhibit 

correlations that are impossible in a classical world, 

and can be used to perform novel tasks such as deviceindependent quantum key distribution. 

We are developing a quantum-based approach to 

construct an important class of tamper-resistant devices 

called “one-time memories.” Roughly speaking, a onetime memory is a device that stores two messages, in 

such a way that a user can retrieve either the first message or the second message, but not both. One-time 

memories are relatively simple to construct, yet they 

are known to be extremely powerful. In particular, they 

can be used to build “one-time programs,” which have 

the following behavior: a user can run the program 

exactly once, but the program hides its internal state (as 

if it were an oracle or “black box”), and after one execution the program becomes unusable (as if it had 

“self-destructed”).

We find that one-time memories cannot exist in a 

world that is fully classical or fully quantum; but, surprisingly, one-time memories can be built in a world 

that is partly quantum. More precisely, one-time memories can be built from “isolated qubits,” which are a 

quantum resource (qubits that can be prepared and 

measured in superposition states) combined with a 

classical restriction (that it is impossible to perform 

entangling operations on pairs of qubits). This is interesting from a theoretical perspective, as it touches on 

fundamental questions in quantum information theory, 

concerning the power of local operations and classical 

communication, and the phenomenon of “nonlocality 

without entanglement.” It is also interesting from a 
Summary of Activities for Fiscal Year 2013 85

practical perspective, as there are plausible experimental realizations of isolated qubits, using nuclear 

spins in solid-state materials.

The next step will be to improve the security and 

efficiency of our constructions for one-time memories. 

In particular, our present constructions have a number 

of drawbacks: they are purely information-theoretic, 

not computationally efficient, and the security guarantees we have shown are not strong enough to support t

he construction of one-time programs. We believe that 

improvement in all of these areas should be possible.

[1] Y.-K. Liu, Building One-Time Memories from Isolated 

Qubits, Proceedings of ITCS 2014: Innovations in Theoretical Computer Science, to appear.

Post-Quantum Cryptography

Stephen Jordan

Yi-Kai Liu

Lily Chen (NIST ITL)

Dustin Moody (NIST ITL)

Rene Peralta (NIST ITL)

Ray Perlner (NIST ITL)

Daniel Smith-Tone (NIST ITL)

The development of quantum computers creates new 

challenges and new opportunities for cryptography. If 

large-scale quantum computers are ever built, they 

would break many of the cryptosystems that are currently used to protect communications on the Internet, 

such as RSA, Diffie-Hellman and elliptic curve cryptosystems. Thus, there is now considerable interest in 

designing so-called “post-quantum” cryptosystems that 

would be secure against quantum attacks. We have 

been investigating this area, with a view to developing 

future standards for public key cryptography.

Some proposals for quantum-resistant cryptosystems include lattice-based cryptosystems (such as 

NTRU), code-based cryptosystems (such as McEliece), 

multivariate cryptosystems (such as HFE and unbalanced oil-vinegar), hash-based signatures (such as 

Merkle trees), and key exchange protocols based on 

elliptic curve isogenies. However, all of these proposals face significant open questions regarding their 

security and practical feasibility.

In the past year we have examined these issues in 

greater detail. In particular, we have compiled a list of 

evaluation criteria for post-quantum encryption and 

signature schemes, covering issues such as security, 

performance and compatibility with existing applications. We have also studied the feasibility of 

integrating these post-quantum cryptographic primitives into higher-level protocols such as TLS 

(Transport Layer Security) and IPSec (Internet Protocol Security); this indicates a potential need for postquantum key exchange protocols, in addition to encryption and signature schemes.

We have surveyed a number of different approaches to evaluating the security of post-quantum 

cryptosystems, including empirical studies of the performance of known cryptanalytic attacks, proofs of 

security based on conjectures in computational complexity theory, and formal analysis that upper-bounds 

the power of certain common classes of attacks. In particular, we have surveyed recent work on lattice basis 

reduction, quantum algorithms for finding isogenies of 

elliptic curves, Grobner basis attacks on code-based 

cryptosystems, and differential attacks on multivariate 

cryptosystems. Finally, we have been keeping up with 

recent progress in lattice-based signature schemes.

We have discussed some research questions with 

technical staff from the Trusted Systems Research 

Group at the National Security Agency. We also participated in a conference on Quantum-Safe Cryptography

organized by the European Telecommunications 

Standards Institute (ETSI), where we presented talks 

on “Practical Impacts of Quantum Computing” and 

“Evaluating the Security of Post-Quantum Cryptosystems.” 

High-Speed Low Density Parity 

Codes for Quantum Key 

Distribution

Alan Mink 

Anastase Nakassis (NIST ITL)

Quantum information science incorporates quantum 

mechanics into information technology. It is an emerging field thought to have the potential to cause 

revolutionary advances. One promising early area is 

quantum cryptography, specifically Quantum Key Distribution (QKD), which is a protocol that uses a pair of 

unsecured communication channels, a quantum channel and a classical channel, to establish a shared secret 

between two parties, Alice and Bob. This shared secret 

is then used to encrypt messages between Bob and Alice. QKD has been proven information theoretically 

secure, unlike classical key distribution that relies on 

computational complexity.

There are four stages to the QKD protocol. The 

first stage involves quantum mechanics, while the other 

three use classical processing. Stage 1 is the transmission of randomly encoded single photons over a lossy 

quantum channel to be measured by Bob. Stage 2 is 

where Alice and Bob exchange information over the 

classical channel to “sift” their bit sequences to achieve 

a common sequence. But since that sequence may have 

errors, in Stage 3 Alice and Bob exchange information 

over the classical channel to correct errors in their bit 
86 NIST Applied and Computational Mathematics Division

sequences without exposing the value of their bits. 

Stage 4 is where Alice and Bob amplify the privacy of

their now identical bit sequences through the application of a hash function to eliminate any leaked 

information, yielding a smaller set of secret bits between Alice and Bob. The last two stages are referred 

to as post-processing.

There is a large body of information about error 

correction (EC) codes, but QKD presents a different 

environment than conventional communication. For 

example, expected QKD error rates (1% to 11% vs. 

0.1% or below) are higher, error correction information 

is sent separately over an error free channel, the 

amount of information that the EC code leaks about the 

data must be minimized and kept below a given limit to 

enable the extraction of a secret, and quantum data 

retransmission is not possible. 

Researchers are pursuing the next generation of 

QKD systems, ones that can attain higher speeds and 

longer distances. Our focus is on speed; moving from 

the current Mb/s to the Gb/s secure key generation rate

will require highly optimized and parallel implementations of QKD post processing algorithms. One-way EC 

algorithms, such as low density parity check (LDPC) 

and Polar codes, tend to be coarse grained computations in that a given data set does not need to 

communicate until a solution is obtained. Such algorithms are amenable to parallel implementation. Each 

data set can be assigned to a separate computation engine, which would operate independently in parallel, 

but each result must be collected sequentially to maintain the required synchronization between Alice and 

Bob’s bits. Also a single communication round trip 

reduces delays, a benefit as the distance between Alice 

and Bob increases.

We have shown [1] that bit error estimation can be 

combined with the EC algorithm to avoid extra communication and time delays and that the size of the data 

block for EC and privacy amplification doesn’t need to 

be the same. In general, it is advantageous to size those 

blocks for the specific algorithms, usually EC in smaller blocks, and then combine the data into larger blocks,

using actual error rate for privacy amplification.

Although previous QKD implementations have relied heavily on field programmable gate arrays 

(FPGAs) to attain the Mb/s current operating range, we 

have found that FPGAs are not suited for Gb/s post 

proceeding operations. This is mainly due to their relatively limited memory resources. One-way EC 

algorithms require an order of magnitude more 

memory than the original class of Cascade EC algorithms, limiting opportunities for parallel instantiation

on an FPGA, and thus overall speed-up. Furthermore, 

speeding-up a given instantiation requires an n-port 

memory, which allows parallel simultaneous memory 

accesses to attain higher throughput, which FPGAs 

have even smaller amounts of. These memories can be 

designed into ASICs, and as a result Gb/s LDPC EC 

has been achieved for 10 Gigabit Ethernet operations. 

Alternatively, less expensive LDPC implementations 

on graphical processing units (GPUs) have reported 

operations in the 100 Mb/s range, and the new generation of GPUs claim to be an order of magnitude faster.

Our experiments [1] have shown that CPU and 

FPGA implementations of LDPC for QKD can achieve 

a few Mb/s of throughput, while initial implementations, on an older GPU, has performed an order of 

magnitude faster. Throughput of LPDC algorithms 

depend on the data error rate and the proximity to the 

Shannon limit, thus impacting the amount of entropy 

one can extract in privacy amplification. We have 

evaluated the EC performance of our LDPC implementations over the QKD operating range and found that 

throughput diminishes as the Shannon limit is approached. Our plans are to optimize our GPU 

implementation to achieve another order of magnitude 

of performance that could translate to Gb/s throughput 

on the newer generation of GPUs.

[1] A. Mink and A. Nakassis, Practical Strategies for QKD 

Key Production, in Proceedings of the SPIE 8749 (April 

2013), Defense Security and Sensing, Baltimore, MD, 

840009.

Simulating Quantum Field Theories 

on Quantum Computers

Stephen Jordan

Keith Lee (University of Waterloo and Perimeter Inst.) 

John Preskill (Caltech)

Hari Krovi (BBN Technologies)

Quantum field theories arose as a way to make quantum mechanics compatible with special relativity. 

Today, they are a central tool in physics, used to describe both the behavior of high energy particles and of 

condensed-matter systems such as superconductors and 

semiconductors. In particular, the most fundamental 

theory of physics to have passed experimental test is 

the Standard Model of particle physics that describes 

all known forces except gravity within a unified 

framework of quantum field theory.

Like all quantum theories, quantum field theories 

are computationally difficult to simulate because the 

dimension of the state space scales exponentially with

the number of degrees of freedom. Quantum field theories present the additional difficulty that the set of 

degrees of freedom is formally infinite. It is worth noting that familiar classical field theories such as 

Maxwell’s equations for electromagnetism also suffer 

from a formally infinite set of degrees of freedom. The 

standard approach for simulating both quantum and 

classical field theories is to truncate to a finite set of 
Summary of Activities for Fiscal Year 2013 87

degrees of freedom through discretization. However, in 

the case of quantum field theories there is a surprising 

and nontrivial interplay between quantum effects and 

discretization effects known as renormalization.

One of the key challenges in this project is using 

the theory of renormalization to analyze the errors incurred by discretizing a quantum field theory to make it 

suitable for simulation on a quantum computer. The 

simulation of discretized quantum field theories on 

conventional supercomputers is also a well-studied 

topic. However, conventional supercomputers are only 

able to solve what might be termed statics problems in 

quantum field theory, such as estimating binding energies of nuclei. Dynamics problems, such as simulating 

relativistic scattering processes as studied in particle 

colliders, become rapidly intractable for even the most 

powerful conventional supercomputers as the number 

of particles increases. For such problems, our analysis 

shows quantum computers to be capable of achieving 

exponential speedup over classical computers [1].

In addition to discretization, two further aspects of 

the simulation problem demanded particular attention. 

The first is preparation of physically realistic initial 

states, and the second is simulation of detectors. These 

tasks unfortunately turn out to be strongly dependent 

on the details of the underlying quantum field theory. 

Our initial work [1] showed how to simulate relativistic scattering of massive bosons. Our recent work 

has focused on extending our state preparation techniques to handle massive fermions, and to optimizing 

our techniques for simulating detectors. The ultimate 

goal is to simulate bosons and fermions in both the 

massive and massless cases. This would show that the 

full Standard Model can be efficiently simulated on 

quantum computers and would imply that, excluding 

gravity, the known constituents of our universe are not 

capable of computational power beyond that offered by 

quantum computers.

Lastly, we are seeking to encode universal quantum computations into idealized particle scattering 

processes. Such an encoding would imply that if a polynomial-time classical algorithm is ever discovered for 

simulating particle scattering in quantum field theory, 

then classical computers could efficiently emulate everything that quantum computers are capable of doing. 

There is significant evidence (though no mathematical

proof) that quantum algorithms are, for certain problems such as integer factorization, exponentially faster 

than classical algorithms. Thus, our embedding could 

be thought of as evidence that the problem of simulating particle scattering processes in quantum field 

theories is in fact exponentially hard for classical computers.

[1] S. P. Jordan, K. S. M. Lee and J. Preskill, Quantum 

Algorithms for Quantum Field Theories, Science 336

(2012), 1130-1133.

Circuit Obfuscation and Synthesis

Stephen Jordan 

Gorjan Alagic (Caltech)

Stacey Jeffery (University of Waterloo)

Aniruddha Bapat (Caltech)

Logic gates, for both classical and quantum computation, obey various identities and can be treated as an 

algebraic system. Algebraic manipulation of logic circuits has many applications, which include automated 

synthesis of optimized circuits, testing equivalence of 

circuits, and obfuscation of circuits. Obfuscation is 

perhaps the most exotic and least familiar of these applications. Roughly speaking, a circuit obfuscator is an 

algorithm that applies circuit identities to scramble a 

circuit, thereby making it difficult to reverse-engineer 

while preserving its functionality. Aside from its obvious applications to protecting intellectual property, 

obfuscation is known to be a powerful primitive from 

which numerous other cryptographic protocols can be 

constructed. 

One way to obfuscate circuits is to reduce them to 

a canonical form uniquely determined by the circuit's 

truth table. This erases all information about the circuit’s original implementation. This has been achieved 

for certain limited classes of circuits, but it is provably 

impossible to reduce general logic circuits to a canonical form in polynomial time. Interestingly, the 

feasibility of a slight variant of this idea remained an 

open question until recently. Specifically, motivated by 

physical considerations including quantum mechanics, 

a notion of reversible circuits has been introduced, in 

which no data is ever erased. The problem of reduction 

to canonical form is significantly different for reversible circuits than for conventional logic circuits. 

Nevertheless, we recently proved that this is also impossible to achieve by any efficient (i.e., polynomialtime) algorithm [2].

In light of no-go theorems such as the above, one 

can seek to satisfy weaker, but still useful, security 

definitions. In a recent breakthrough, Garg et al. have 

found a polynomial-time algorithm which, under plausible cryptographic assumptions, produces obfuscated 

circuits such that circuits with the same truth table are 

not reduced to forms that are identical, but rather are 

(in a certain precise sense) computationally indistinguishable. Our current work includes the investigation 

of ways to adapt these new techniques to quantum circuits. We have also proposed an alternative way of 

weakening the notion of obfuscation, which we call 

partial-indistinguishability obfuscation [1]. The idea is 

that by culling the list of circuit identities one can make 

the reductions to canonical form tractable.

A polynomial-time algorithm is known for reducing words in the braid group to canonical form. 

Therefore, circuits composed from logic gates that
88 NIST Applied and Computational Mathematics Division

obey the identities of the braid group generators can be 

efficiently obfuscated in a way that satisfies our “partial-indistinguishability” definition. Satisfying the 

identities of the braid group generators may appear to 

be a rather peculiar property for a set of logic gates to 

possess. However, in the quantum world this arises 

quite naturally—the braiding of certain exotic quasiparticles called anyons can achieve a complete set of 

quantum logic operations. Furthermore, using ideas 

from quantum physics, classical logic gates satisfying 

the relations of the braid group generators have also 

been discovered.

Motivated by applications to circuit obfuscation, 

we have been investigating more efficient ways to 

translate circuits into gate-sets that obey the braid 

group relations. In particular, the best published 

scheme for braid-based classical computation does not 

use logic gates acting on bits, but rather on 60-state 

“dits”. We have reduced this to 44 states. We have also 

performed computer searches that suggest that classical 

braid-based computing using dits of 5 states or fewer is 

impossible. In addition, we have proven that braidbased quantum computation with standard 2-state 

qubits is impossible.

Aside from obfuscation, one of the main applications of algebraic techniques to circuit design is circuit 

optimization. There are many metrics that one can seek 

to optimize. One metric of particular importance in 

optimizing quantum circuits is the number of qubits 

used as working memory. Recently, we have discovered a group-theoretic construction showing that a 

much more general class of quantum circuits can be 

implemented “in-place” than was known previously. 

Specifically, other than the input qubits, no additional 

workspace is needed to implement quantum gates controlled by arbitrary Boolean formulas. The previous 

best construction achieved this for the special case 

where the Boolean formula was composed only from 

logical AND.

[1] G. Alagic, S. Jeffery and S. P. Jordan, Partialindistinguishability Obfuscation using Braids, 

arXiv:1212.6458, December 2012.

[2] S. P. Jordan, Strong Equivalence of Reversible Circuits 

is coNP-Complete, arXiv:1307.0836, July 2013.

Quantum Adiabatic Optimization

Stephen Jordan

Michael Jarret (University of Maryland)

In quantum systems, the allowed energies are often 

quantized into a discrete set of values. For many applications, the energy gap between the lowest allowed 

energy and the second-lowest energy is the key property. In particular, a class of quantum algorithms called 

adiabatic algorithms has been proposed for optimization problems. The runtime of such adiabatic 

algorithms is determined by this energy gap.

Despite much effort, the energy gaps characterizing proposed adiabatic algorithms have proven very 

difficult to analyze theoretically. One of the intuitions 

behind adiabatic algorithms is the idea that adiabatic 

algorithms are similar to simulated annealing, except 

that quantum systems can escape from local energy 

minima via tunneling instead of by thermal excitation. 

Implicit behind this reasoning is arguably the idea that 

quantum adiabatic algorithms have no difficulty finding the global energy minimum if there are no other 

local minima to get trapped in. One result from this 

project has been the discovery of a counterexample to 

this intuition. Specifically, we discovered a fairly simple optimization problem on a graph with no local 

energy minima, which nevertheless has an exponentially small eigenvalue gap.

On the positive side, we have proven that in certain highly regular graphs, such as the path and 

hypercube graphs, this intuition is correct. That is, the 

energy gap cannot be small unless there are local energy minima. In fact, our lower bounds for the 

eigenvalue gaps associated with convex energy landscapes on path graphs is precisely tight and constitutes 

a discrete analogue to the recently proven fundamental 

gap theorem regarding Schrödinger operators on R.
Summary of Activities for Fiscal Year 2013 89

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 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 stability of our critical infrastructure is simply unknown. Measurement science has long 

provided a basis for the understanding and control of physical systems. Such deep understanding and insight 

is lacking for complex information systems. We seek to develop the mathematical foundations needed for a 

true measurement science for complex networked information systems.

Systemic Risks/Benefits of 

Interconnectivity

Vladimir Marbukh

Assane Gueye

Iraj Saniee (Alcatel Lucent Bell Laboratories)

O. Narayan (University of California at Santa Cruz)

Technological advances combined with economic advantages drive systems towards interconnectivity. This 

trend has already produced highly interconnected 

world-wide infrastructures, which are essential for U.S. 

industrial competitiveness and economic security. 

However, recent systemic failures of communication, 

power, financial and other large-scale infrastructures 

have demonstrated that the economic and social benefits of large scale and interconnectivity come with 

inherent systemic risks of cascading failures, as well as 

undesired and malicious behavior. This project concentrates on developing systemic risk metrics that can be 

used for prediction and mitigation of undesirable system behavior of this type.

In the last several years numerous research centers, 

think tanks, and working groups have been chartered to 

address various aspects of systemic risk. The motivation for ACMD’s decision to contribute to these 

interdisciplinary efforts, which encompass areas of 

complex systems, physics, economics, biology, computational sciences, etc., is twofold. First, ACMD is well 

positioned due to synergy among existing ITL and 

NIST programs on complex systems, cyber security, 

cloud computing, communication networks, smart grid, 

big data, etc. Second, and more importantly, ITL and 

NIST must develop competency in these areas due to 

clear national needs to understand and mitigate systemic risks in critical infrastructures. Our current efforts lie 

in the following three overlapping areas.

The first area is understanding, prediction and mitigation of cascading overload in the large-scale 

infrastructures of shared resources. Dynamic resource 

sharing has both positive and negative effects on system performance, with the positive effect resulting 

from the statistical multiplexing gain, and the negative 

effect resulting from unavoidable overhead, e.g., due to 

coordination or delays in accessing distant resources. 

Motivated by large-scale cloud computing infrastructures, [1] makes a case for the Perron-Frobenius 

eigenvalue of the mean-field equations linearized about 

the “operational” system equilibrium to be viewed as a 

measure of the systemic risk of cascading overload in 

complex loss resource sharing systems. Draft [2] extends [1] to more realistic service models allowing 

queuing of requests. In the future we plan to investigate 

practical applicability and the possibility of real-time

estimation of this risk measure.

The second area is quantification and mitigation of 

networked system performance deterioration due to 

attack by an intelligent adversary or adversaries. Paper

[3] proposes and discusses a game-theoretic framework 

for (a) evaluating security vulnerability, (b) quantifying 

the corresponding Pareto optimal vulnerability/cost 

tradeoff, and (c) identifying the optimal operating point 

on this Pareto optimal frontier. The vulnerability metric 

is determined by the Nash equilibrium payoff of the 

corresponding game. Paper [4] analyses the economics 

of network vulnerability reduction by considering the 

tradeoff between system redundancy and component 

hardening. Our analysis suggests that due to the effect 

of diminishing return, the optimal vulnerability reduction strategy depends on the specific system 

cost/preference structure.

Finally, the third area is effect of system information availability on the system performance under 

normal and adversarial conditions. Routing is the most 

basic function of a networked system. In the extreme 

case when global system information is locally available, the routing performance is optimized by

“minimum cost routing” with the appropriately defined 

cost function. In another extreme case when no global 

information is locally available, i.e., due to high network volatility, random walk routing is the only 

choice. Paper [5] derives an analytical expression for 
90 NIST Applied and Computational Mathematics Division

the mean load at each node of an arbitrary undirected 

graph for the uniform multicommodity flow problem 

under random walk routing. Our analysis shows that 

the mean load is proportional to the nodal degree with 

a common multiplier equal to the sum of the inverses 

of the non-zero eigenvalue of the graph Laplacian. 

Using this explicit expression for the mean load, [5] 

gives asymptotic estimates for the load on a variety of 

graphs with known spectral densities. For graphs with 

unknown spectral densities [5] gives numerical estimates for the mean load.

[1] V. Marbukh, Perron-Frobenius Measure of Systemic 

Risk of Cascading Overload in Complex Clouds: Work 

in Progress, in Proceedings of the 6th IFIP/IEEE 

International Workshop on Distributed Autonomous 

Network Management Systems, Ghent, Belgium, May 

2013.

[2] V. Marbukh, Economic Efficiency vs. Systemic Risks in 

the Cloud Computing Model: Towards Quantitative 

assessment, in preparation.

[3] A. Gueye and V. Marbukh, A Game-theoretic 

Framework for Network Security Vulnerability 

Assessment and Mitigation, Lecture Notes in Computer 

Science 7638 (2012), Decision and Game Theory for 

Security, 186-200.

[4] A. Gueye and V. Marbukh, A Cost/Benefit Analysis of 

Network Vulnerability Reduction: Element Hardening 

vs. Adding Redundancy, in Proceedings of WPIN+NetEcon 2013: The Joint Workshop on Pricing 

and Incentives in Networks and Systems, Pittsburgh, PA, 

June 21, 2013.

[5] O. Narayan, I. Saniee and V. Marbukh, Congestion Due 

to Random Walk Routing, arXiv:1309.006.

Examining the Gromov Curvature 

of Networks in Time

Brian Cloteaux

Vladimir Marbukh

As various networks evolve in time, it has been 

observed that various characteristics (such as density

and diameter) change in some unexpected ways [2]. 

For instance, if we were to randomly add nodes to 

some network model, we would expect to see the 

diameter of the network increase in time. Instead, for 

various complex networks, we see that the diameter 

does not grow in time, and many times it actually 

shrinks. Explanations for this phenomenon are

necessary to be able to model and measure these 

networks.

In looking for an explanation for these 

observations, we are interested in how the Gromov 

hyperbolicity of a network changes as the network 

evolves. Intuitively, Gromov hyperbolicity is a 

measurement of how close a network is to resembling a 

tree. We are interested in seeing whether hyperbolicity 

changes can account for the network observations.

A difficulty with this type of experiment is that 

naive computation of Gromov hyperbolicity requires 

O(n

4

) steps. This makes it too expensive to compute for 

large networks, and is the reason that this simple type 

of experiment has not been tried before. We are 

currently using and extending the algorithms produced 

by INRIA [1] for this type of measurement. We are 

also working on new approaches to computing this 

value including fast approximations.

[1] N. Cohen, D. Coudert, and A. Lancin, Exact and 

Approximate Algorithms for Computing the 

Hyperbolicity of Large-scale Graphs, INRIA Research 

Report RR-8074, September 2012.

[2] J. Leskovec, J. Kleinberg and C. Faloutsos, Graphs over

Time: Densification Laws, Shrinking Diameters and 

Possible Explanations, in Proceedings of the 11th ACM 

SIGKDD International Conference on Knowledge 

Discovery and Data Mining, 2005.

An Improved Feedback Vertex Set 

Heuristic

James M. Shook

Isabel Beichl

To recover from deadlock it is sometimes necessary to 

end processes so that availability of resources can be 

restored. The trick is to accomplish this by ending the 

fewest possible processes. To help with these decisions, the relationships between processes can be 

represented by a directed graph called a dependency 

graph. If the dependency graph has a cycle, then deadlock has occurred and we need to end a process on that 

cycle. A feedback vertex set (FVS) is a set of vertices 

or processes that hits every cycle in the dependence 

graph. Finding the smallest FVS was shown to be NPhard in [2]. Thus, research has focused on finding an 

efficient heuristic for the FVS problem.

In [3], the authors presented a method that finds an 

FVS, F, with a running time of O( |F| n

2.376), where n is 

the number of vertices in the graph. Evidence was given that their algorithm is superior to other existing 

heuristics. Using an observation made in [1], and relating it to disjoint cycle unions, we designed a method 

that has a running time of about O( |F| log(n) n

2

). We 

found that our method is not only faster than previous 

heuristics, but the size of our FVS is significantly improved over other methods. We give a detailed analysis

of our method in a soon to be finished paper.

[1] I. Beichl and F. Sullivan, Approximating the Permanent 

via Importance Sampling with Application to the Dimer 

Covering Problem, Journal of Computational Physics

149:1 (1999), 128-147.
Summary of Activities for Fiscal Year 2013 91

[2] R. Karp, Reducibility among Combinatorial Problems, 

in Complexity of Computer Computations (R. Miller and 

J. Thatcher, eds.), Plenum Press, 1972, 85-103.

[3] M. Lemaic and E. Speckenmeyer, Markov-chain-based 

Heuristics for the Minimum feed-back Vertex Set Problem, Technical Report, 2009. 

Broadcast and Spread of 

Information in Complex Networks

Fern Y. Hunt

We are studying the optimal spread of information in 

networks where communication and coordination are 

autonomous and distributed. In a model of such communication, nodes receive information (function 

values) from their neighbors and broadcast back a 

weighted average of these values. The issues arising 

from this research are particularly relevant to control of 

large networks of nodes with limited communication 

resources. Examples include sensor networks for energy and water supply, propagation of influence in social 

networks, and the study of gene regulatory networks. 

Following the work of Borkar et al. [1], information spread is studied in terms of a dual process, a 

random walk on an (assumed strongly connected) 

graph of the network. A random walk is initiated at a 

node, i.e., a vertex outside a pre-determined set of target nodes, and is halted upon first arrival to that set.

The effectiveness of the set is then measured by the 

sum of the expected times random walkers first arrive 

starting from outside the set. We can find the most effective target set by minimizing the sum of the 

expected arrival times over all sets with the same or 

smaller cardinality. The optimal target set is also optimal for the dual process of spreading. So, if 

information must be communicated to a large network 

but resources limit the number of nodes that can be 

directly contacted, then the quickest way to communicate is to inform the nodes of the optimal target set. 

The work of Clark et al. [2] also shows that the target 

nodes are analogous to leader nodes in a leaderfollower consensus model. We can demonstrate that a 

set of effective leaders is also a set of effective target 

nodes in the random walk model.

The objective function in all these minimizations 

is a supermodular set function. Most existing results on 

the computation and approximation of optimal sets are 

based on the application of the greedy algorithm, a 

long standing technique for optimizing submodular 

(supermodular) functions [1, 2]. Unfortunately it is not 

hard to find examples of graphs where the set constructed by the greedy algorithm fails to be optimal. 

However the supermodularity of the objective function 

is used in [1] and [2] to guarantee that the constructed 

set is in some sense within (1-1/e) of the optimal, and 

theoretical work suggests that this is the best possible 

result. Interestingly, Krause et al. [6] report that “online 

computations (problem instance dependent)” can reach 

within 95% of the optimal solution in a sensor placement problem. 

 Led by our own computations, we reformulated 

the problem so that optimal or near optimal sets can be 

constructed. Here, near optimality of a set is defined in 

terms of its objective function value, which must be 

bounded above by a constant. Rather than starting with 

just the graph and the desired cardinality of an unknown set, our method is based on generating vertex 

covers for the graph. A vertex cover is a set of vertices 

with the property that every edge of the graph is incident to a vertex in the cover. These sets are optimal 

spreaders for their cardinality and can be efficiently 

generated by the greedy algorithm for a maximal 

match. Since vertex covers frequently contain optimal 

sets as subsets, one idea is to restrict the search to these 

sets. Not every maximal match has optimal subsets,

however. 

Our principal contribution this year is the construction of a subset of optimal and near optimal sets 

that are the feasible sets for a greedoid. This method 

may be extendable to general isotone supermodular 

functions. The properties of this structure imply that 

near optimal (and possibly optimal) sets can be constructed in a stepwise fashion. The degree of optimality 

can be specified in advance and all feasible vertex covers of sufficient size (which depends on the degree of 

optimality) contain near optimal (and possibly optimal) 

sets. Greedoid properties also permit the construction 

of a greedoid graph whose nodes are optimal, and near 

optimal, feasible sets, so it may be possible to improve 

approximations by local searches in the vicinity of an 

initial estimate. 

The framework sketched here allows the problem 

Figure 44. The figure shows a graph with 6 vertices and two 

distinct (non-automorphic) vertex covers. Vertices of the respective covers are colored. On the right, the vertex cover solves the 

optimal target (or spread) problem for K=4. It contains sets that 

solve the optimal target problem for K=1 ({3} or {4}), K=2, 

({3,4}), and K=3 ({1,3,4}). The vertex cover on the left is a solution of the optimization problem for K=4, but it contains no 

optimal sets as proper subsets. Our research seeks to identify 

vertex covers like those on the right with a view towards searching 

for optimal subsets of a desired cardinality.
92 NIST Applied and Computational Mathematics Division

of optimal spread to be considered in the context of the 

topology of the graph of optimal and near optimal sets. 

How can they be efficiently computed? Understanding 

the relationship between the topology of the network 

graph and the greedoid graph is an important next step 

to answering this question and is a topic of future research.

[1] V. Borkar, J. Nair and N. Sanketh, Manufacturing Consent, in Proceedings of the 48th Annual Allerton 

Conference, 2010, 1550-1555.

[2] A. Clark, L. Bushnell and R. Poovendran, Leader Selection for Minimizing Convergence Error in LeaderFollower Systems: A Supermodular Optimization Approach, in Proceedings of the 10th International

Symposium on Modeling and Optimization in Mobile Ad 

Hoc and Wireless Networks (WiOpt), 2012, 111-115.

[3] F. Hunt, Optimal Spread in Network Consensus Models, 

in review.

[4] F. Hunt, The Structure of Optimal and Nearly Optimal 

Target Sets in a Random Walk Model of Spread in a 

Network, in preparation.

[5] B. Korte, L. Lovasz and R. Schrader, Greedoids, 

Springer Verlag, 1991.

[6] A. Krause, J. Leskovec, C. Guestrin, J. Van Briessen 

and C. Faloutsos, Efficient Sensor Placement Optimization for Securing Large Water Distribution Networks, 

Journal of Water Resources Planning and Management

134 (2008), 516-526.

An Algebraic Formulation for the 

Analysis and Visualization of 

Network Graphs

Roldan Pozo

Understanding the topological structure of large graphs 

remains an important problem in network science. 

While it is straightforward to visualize small networks 

of hundreds or a few thousands of vertices and edges 

using conventional graph visualization packages, attempting to render large real networks is nearly 

impossible. This is particularly true for information 

networks and social networks, where the graph sizes 

number into the millions and billions. And with the 

amount of data being generated and gathered from 

large social media sites ever increasing, the challenge 

of characterizing larger and larger networks is only 

getting greater.

Conventional algorithms for graph visualization 

typically render such networks as a solid blot of color 

in which is difficult to see meaningful information. 

This difficulty is strongly influenced by the presence of 

high-degree nodes (hubs) that entangle many parts of 

the graph with itself, together with the sheer volume of 

nodes and edges that makes rendering into a reasonable 

image size for viewing and printing impractical.

An alternate approach is to visualize important 

network properties, rather than the actual network itself. For example, such network portraits might 

attempt to capture interesting attributes of a large 

graph, such as degree distribution, or its connective 

properties. In our work, we focus on a particular type 

of information: the distribution of “fringe” communities: small connected components of a graph, in the 

absence of high-degree hubs. In a social science context, for example, they represent independent or rogue 

groups, which are highly connected amongst themselves, but which are often lost with the inclusion of 

more popular nodes.

Consider, for example, a web graph, where nodes 

are individual web pages, and edges are directed hyperlinks between two web pages. Figure 45, for example, 

illustrates connected components of the 

math.nist.gov web graph, where nodes of degree greater than 25 have been removed. The image reveals 

various structures, such as ladders, stars, and cluster 

patterns representing tightly coupled web pages. These 

form the nucleus of fringe communities of web pages, 

and by varying the degree parameter we can select the 

size and granularity of groups revealed. As the degree 

threshold is increased from 1 to the largest degree in 

the original graph, we can form a connected component 

size distribution, which can be encoded as a row of a 

matrix. This sparse matrix may still be too large to 

view directly, but can be compactly rendered by projecting its nonzero values onto the z-axis and 

displaying it as a three-dimensional structure, as shown 

in Figure 46.

Figure 45. Non-trivial components of math.nist.gov web graph, 

restricted to nodes with combined degree less than or equal to 25.
Summary of Activities for Fiscal Year 2013 93

The Q-matrix of a network, in its fundamental 

formulation, is a connected component size distribution 

matrix for a series of degree-limited subgraphs of the 

original network (or weakly-connected component for 

directed networks.) Thus, Q(i,j) is the number of connected components of size j in a subgraph where the 

maximum degree is equal to or less than i. 

The Q-matrix of a graph can be considered as a 

generalization of its degree-distribution. However, it 

encodes other properties, such as the formation and 

growth of its giant component, its connected subparts, 

as well as its size parameters. In fact, common network metrics (e.g., degree distribution, number of 

connected components, number of vertices and edges) 

can be extracted from the Q-matrix using simple linear 

algebra operations.

Among the interesting characteristics of the Qmatrix formulation is that network graphs from similar 

application areas (e.g., social networks, email networks, web graphs, peer-to-peer networks, road 

networks, citation graphs) share similar visual characteristics, creating a potential framework for network 

identification and classification. Indeed, we have used 

the Q-matrix formulation to generate meaningful 

thumbnail images for network data collections. Finally, 

the computation of the Q-matrix is highly efficient. 

Graphs with millions of vertices and edges can be processed in seconds on common desktop computers. 

We are extending research of Q-matrix theory to 

generalized vertex orderings beyond that of node degree, such as PageRank, eigenvalue centrality, 

betweeness centrality, and k-core numbers. Furthermore, we are investigating the use of Q-matrix analysis 

to specific problems in the area of microbiology (genomic networks) and economics (financial market 

networks).

[1] R. Pozo, Efficient Q-matrix Computation for the Visualization of Complex Networks, in Proceedings of 

Complex Networks Workshop, Eighth International Conference on Signal Image Technology and Internet Based 

Systems, Sorrento, Italy, Nov. 25-29, 2012, 762-767.

Security Risk Analysis of Enterprise 

Networks using Attack Graphs

Anoop Singhal (NIST ITL)

S. Jajodia (George Mason University)

Lingyu Wang (Concordia 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 the nation. Vulnerabilities are 

regularly discovered in software applications that are 

exploited to stage cyber-attacks. Currently, management of security risk of an enterprise network is more 

an art than a science. System administrators operate by 

instinct and experience rather than relying on objective 

metrics to guide and justify decision making. 

The objective of this research is to develop a 

standard model for security risk analysis of computer 

networks. A standard model will enable us to answer 

questions such as “Are we more secure now 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 allow users, vendors, and researchers to evaluate 

methodologies and products for network security in a 

coherent and consistent manner.

In this project, we have approached the challenge 

of network security analysis by capturing vulnerability 

interdependencies and measuring security in the exact 

way that real attackers penetrate the network. Our 

methodology for security risk analysis is based on the 

model of attack graphs. We analyze all attack paths 

through a network, providing a probabilistic metric of 

the overall system risk. Using this metric, we analyze 

trade-offs between security costs and security benefits.

Computer systems are vulnerable to both known 

and previously unknown (zero day) attacks. Handling 

zero day vulnerabilities is inherently difficult due to 

their unpredictable nature. In FY 2013, we attempted 

to assess the risk of unknown attack patterns. We developed a new model “k-zero day safety” for zero day 

attacks. Existing algorithms for computing this metric 

are not scalable as they assume that a complete zero 

day attack graph has been generated. We have proposed a set of polynomial time algorithms for 

estimating k-zero day safety. Our paper on this topic 

[1] received the Best Paper award at the 10th International Conference on Security and Cryptography.

Figure 46. Q-matrix plot of math.nist.gov webgraph (29K vertices, 62K edges) showing the component size distribution of 

degree-limited subgraphs.
94 NIST Applied and Computational Mathematics Division

Measuring the mean time to compromise of a network provides important insights for understanding a 

network’s vulnerability to attacks. We have proposed a 

unified framework for measuring a network’s mean 

time to compromise by considering both known and 

zero day attacks. This approach was published in a 

paper in the IEEE Symposium on Reliable and Distributed Systems [2]. We have also shown an application 

of this framework to network hardening.

In FY 2014, we plan to apply attack graphs to 

study the effect of diversity for network defense. We 

also plan to publish the results as a NIST report and as 

white papers in conferences and journals.

[1] M. Albanese, S. Jajodia, A. Singhal, and L. Wang, An 

Efficient Approach to Assessing the Risk of Zero-day 

Vulnerabilities, in Proceedings of the 10th International 

Conference on Security and Cryptography (SECRYPT 

2013), Reykjavik, Iceland, July 29-31, 2013.

[2] W. Nzoukou, L. Wang, S. Jajodia and A. Singhal, A 

Unified Framework for Measuring a Network’s Mean 

Time-to-compromise, in Proceedings of the 32nd IEEE 

International Symposium on Reliable Distributed Systems (SRDS 2013), Braga, Portugal, September 30 -

October 3, 2013.

[This research was sponsored in part by ACMD.]

Combinatorial Testing

Raghu Kacker

D. Richard Kuhn (NIST ITL)

Yu Lei (University of Texas at Arlington)

James Lawrence (George Mason University)

Combinatorial testing (CT) is an approach to detect 

combinatorial interaction faults, which may cause a 

software based system to fail when certain values of 

some factors occur together. Combinatorial testing is 

based on the insight, referred to as the interaction rule, 

that while the behavior of a software system may be 

affected by a large number of factors, only a few factors are involved in a failure-inducing fault. Many 

critical system failures in recent times have been traced 

to interaction faults in the underlying software. Studies 

of actual faults reveal that most involve only one or 

two factors, though some may involve up to six. 

NIST has taken the lead to advance software testing technology from pair-wise to higher strength 

testing, to make tools and techniques available to US 

industry, and to help promote its effective use. As a 

result of these efforts, CT is being increasingly used in 

a wide spectrum of industries and taught in colleges. 

CT is a versatile and broadly applicable methodology 

that is helping to reduce testing costs and efforts in 

software based systems for science, commerce, defense 

and security, and electronic medical systems, and is 

increasingly used in hardware testing as well. A recent 

paper from the US Lockheed Martin Company reports 

20% savings in test efforts.

ACTS is a NIST/UTA (University of Texas at Arlington) tool to generate high strength test suites for 

CT. A key feature of ACTS is support of constraints 

among factor and test values. We have filled more than

1600 requests for ACTS, and the tutorial has been 

downloaded more than 26000 times. 

CCM is a new NIST tool to determine combinatorial coverage of a test suite that was not developed 

from a CT viewpoint. The latest version of CCM supports constraints and has a greatly improved graphical 

depiction of combinatorial coverage. A parallel processing version of CCM is also available. 

Combinatorial deficiency of a test suite can be remedied by including additional tests, so CCM can help a 

test suite satisfy combinatorial requirements. 

A book on CT entitled, Introduction to Combinatorial Testing, by D. R. Kuhn, R. N. Kacker and Y. Lei 

was published by the CRC Press in 2013.

This year we demonstrated the effectiveness of CT 

for conformance testing and interoperability testing of 

portable healthcare devices. The ISO/IEEE 11073 is a 

set of standards for interoperability of personal 

healthcare devices. We developed a framework and a 

research tool for conformance and interoperability testing to the IEEE 11073 standards. Testing using these 

methods detected two faults, one of which was a new 

discovery.

We organized the second International Workshop 

on Combinatorial Testing (IWCT) in conjunction with 

6th IEEE International conference of software testing 

(ICST) in Luxembourg to bring together researchers, 

developers, users, and practitioners to exchange ideas 

and experiences with CT methods and tools. Seventeen 

excellent papers were selected by the Program Committee and were presented in talk or poster format. The 

Figure 47. Combinatorial coverage for a test suite of 79 factors 

(seventy five with 2 test settings, two with 4 test setting and two 

with six test settings); horizontal-axis indicates fractions of the 2-

way, the 3-way, and the 4-way combinations and vertical-axis 

shows corresponding percent covered with 7489 tests in a project 

of Johns Hopkins University Applied Physics Laboratory.
Summary of Activities for Fiscal Year 2013 95

third IWCT is scheduled for March 31, 2014 in Cleveland, Ohio. We also organized the First Asian 

Workshop on Combinatorial Testing for Complex 

Computer Systems (AWCTCCS) in conjunction with 

18th IEEE International Conference on Engineering of 

Complex Computer Systems (ICECCS) on July 19, 

2013 at the National University of Singapore. It consisted of six presentations and one discussion session.

A joint presentation with NASA employees demonstrating effectiveness of CT was made at NASA’s 

Annual Workshop on Independent Verification and 

Validation of Software, Sept. 10-12, 2013. 

A team of four students from the Carnegie Mellon 

University is working with NIST on a master’s degree 

project to develop a tool that enhances the ability of 

testers to define an input model, and streamline the 

testing process. This will make CT easier to use and 

should improve results, since testers will have a better 

understanding of system characteristics.

Working with the NIST Computer Security Division and representatives and contractors of the General 

Services Administration, the team is developing a set 

of test specifications for the Personal Identity Verification (PIV) cards used throughout government. The 

objectives are to improve interoperability testing with 

fewer tests, and to develop procedures for computing 

the number of tests required for various PIV card specifications. 

Our research and tool development continues on 

input space modeling for CT, integration of test generation tools in large testing infrastructure and on 

automating determination of expected output for each 

test case. We continue to explore opportunities of application of CT in defense and security, electronic 

healthcare IT systems, and cloud computing systems.

[1] D. R. Kuhn, R. N Kacker and Y. Lei, Introduction to 

Combinatorial Testing, CRC Press, 2013.

[2] R. N. Kacker, D. R. Kuhn, Y. Lei and J. F. Lawrence, 

Combinatorial Testing for Software: an Adaptation of 

Design of Experiments, Measurement 46 (2013), 3745-

3752.

[3] L. Yu, Y. Lei, R. Kacker and D. R. Kuhn, R. Sriram and 

K. Brady, A General Conformance Testing Framework 

for IEEE 11073 PHD’s Communication Model, in Proceedings of 6th International Conference on Pervasive 

Technologies Related to Assistive Environments

(PETRA), Greece, May 29-31, 2013.

[4] L. Yu, Y. Lei, R. Kacker and D. R. Kuhn, ACTS: A 

Combinatorial Test Generation Tool, in Proceedings of 

Sixth IEEE International Conference on Software Testing, Verification and Validation (ICST-2013), 

Luxembourg, March 18-22, 2013.

[5] L. Yu, M. N. Borazjany, Y. Lei, R. N. Kacker and D. R. 

Kuhn, An Efficient Algorithm for Constraint Handling 

in Combinatorial Test Generation, in Proceedings of 

Sixth IEEE International Conference on Software Testing, Verification and Validation (ICST-2013), 

Luxembourg, March 18-22, 2013.

[6] M. N. Borazjany, L. S. G. Ghandehari, Y. Lei, R. Kacker and D. R. Kuhn, An Input Space Modeling 

Methodology for Combinatorial Testing, in Proceedings 

of Sixth IEEE International Conference on Software 

Testing, Verification and Validation (ICST-2013), Luxembourg, March 18-22, 2013.

[7] L. S. G. Ghandehari, M. N. Borazjany, Y. Lei, R. Kacker and D. R. Kuhn, Applying Combinatorial Testing to 

the Siemens Suite, in Proceedings of Sixth IEEE International Conference on Software Testing, Verification 

and Validation (ICST-2013), Luxembourg, March 18-

22, 2013.

[8] D. R. Kuhn, I. Dominguez Mendoza, R. N. Kacker and

Y. Lei, Combinatorial Coverage Measurement Concepts 

and Applications, in Proceedings of Sixth IEEE International Conference on Software Testing, Verification and 

Validation (ICST-2013), Luxembourg, March 18-22, 

2013.

[9] R. Kacker, D. R. Kuhn, Y. Lei and J. Lawrence, Combinatorial Testing for Software used in Metrology, in 

Proceedings of XX IMEKO World Congress, Busan, 

Republic of Korea, September 9-14, 2012.

Coverage and Energy Optimization 

in Mobile Sensor Networks

Vladimir Marbukh

Kamran Sayrafian

Amir Aghdam (Concordia University)

Hamid Mahboubi (Concordia University)

Kaveh Moezzi (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 target(s) and event(s) as well as their ability to communicate this information to the intended 

recipient(s). The information acquisition needs, which 

require proximity to the target(s), often compete with 

the communication needs, which require proximity to 

the recipient(s) of the sensor information. Inherent 

traits of MSN such as lack of centralized control, variety of performance criteria, operational uncertainties, 

possibilities of MSN topology change and sensor trapping in suboptimal locations make MSN optimization 

an exceedingly challenging problem. 

Our previous publications proposed aligning sensor mobility with the overall MSN goals by assuming 

that (a) sensing and communication are optimized 

much faster than sensors relocate, and (b) sensor relocations are governed by cost/benefit analysis where 

“cost” of sensor battery energy expenditure for sensor 

relocation is weighed against projected performance 

gains due to new sensor locations. Practicality of this 
96 NIST Applied and Computational Mathematics Division

framework depends on overcoming numerous challenges with the (inherently) distributed nature of MSN 

being the most critical. An intelligent sensor may be 

able to estimate its current life expectancy from its 

battery energy level and depletion rate affected by the 

surrounding terrain as well as sensor information acquisition and transmission capabilities. However, a 

sensor typically has no direct knowledge of the effect 

of its relocation on the rest of the MSN. Current research attempts to address some of these issues.

We have studied target monitoring using a network of collaborative mobile sensors in [1]. The 

objective is to compute the desired sensing and communication radii of the sensors as well as their 

locations at each time instant, such that a set of prescribed specifications is met. These specifications 

include end-to-end connectivity preservation from the 

target to a fixed destination, while longevity of sensors 

is maximized and the overall energy consumption is 

minimized. The problem is formulated as a constrained 

optimization problem, and a procedure for solving this 

problem is presented. Simulation results demonstrate 

the effectiveness of the proposed techniques.

Efficient sensor deployment strategies developed 

to increase coverage in wireless mobile sensor networks have been investigated in [2]. The sensors 

identify coverage holes within their Voronoi polygons, 

and then relocate to minimize these coverage holes. 

Novel edge-based and vertex based relocation strategies have been proposed, and their performances are 

compared with existing strategies. The proposed sensor relocation strategies are based on the distances for 

each sensor between the points inside the Voronoi polygon and the edges or vertices of the polygon. It is 

shown that the methods introduced in [2] outperform 

existing strategies. Simulations confirm the effectiveness of our deployment algorithms and their superiority 

to the techniques reported in the literature. Figure 48

demonstrates sample evolution of coverage area (along 

with the corresponding Voronoi regions) under an 

edge-based strategy. 

Continuing this work, we plan to investigate joint 

sensor motion and coverage radius optimization as an 

example of a cyber-physical system that involves codesign of physical and cyber components. 

[1] H. Mahboubi, A. Momeni, A.G. Aghdam, K. Sayrafian 

and V. Marbukh, An Efficient Target Monitoring 

Scheme with Controlled Node Mobility for Sensor 

Networks, IEEE Transactions on Control Systems 

Technology 20:6 (November 2012), 1522-1533.

[2] H. Mahboubi, K. Moezzi, A. Aghdam, K. Sayrafian, and 

V. Marbukh, Distributed Deployment Algorithms for 

Improved Coverage in a Network of Wireless Mobile 

Sensors, IEEE Transactions on Industrial Informatics, 

accepted.

A Dynamic Computational Phantom 

for RF Propagation in Body Area 

Networks

John Hagedorn

Kamran Sayrafian

Martina Barbi

Judith Terrill

A body area network (BAN) is a radio communication 

and networking protocol for short range, low power 

and highly reliable wireless connectivity for use inside 

or around a human body. It includes radio frequency 

(RF) enabled devices that could be implanted, worn or 

located adjacent to the body. Radio-enabled implantable sensor nodes offer a revolutionary set of 

applications, among which are smart pills for precision 

drug delivery, glucose monitors, blood pressure monitors, and eye pressure sensors for glaucoma patients. At 

the same time, wearable sensor nodes can enable remote wireless monitoring of electrocardiogram (ECG), 

Figure 48. Movement of sensors as well as the Voronoi polygons and sensing circles (a) Initial configuration (b) Configuration after the 

first round. (c) Final configuration.
Summary of Activities for Fiscal Year 2013 97

temperature, respiration, and heart rate. While BAN is 

poised to be a promising technology with novel uses in 

pervasive healthcare, there are still many technical, 

commercial and regulatory challenges, including usability, interoperability, energy source, miniaturization, 

security, and privacy. A prerequisite for the safe and 

effective design of such systems is an understanding of 

RF propagation around and inside the body. 

Efficient transceiver design for implants or wearable devices requires in-depth understanding of the 

propagation media, i.e., the human body. Due to the 

difficulties of performing experiments with human 

subjects, obtaining sufficient amounts of measurement 

data for such use-cases is extremely difficult or in some 

cases nearly impossible. So we have developed a 

unique 3D modeling and visualization platform that 

allows virtual RF propagation experiments to be performed using a posable human body computational 

phantom [1, 2]. 

As body motion could significantly impact the 

wireless communication between implants and wearable medical sensors, a dynamic computational phantom 

capable of emulating human motion would be a valuable tool to study and understand this impact. Our 

objective in this project is to create a dynamic computational phantom as an extension to our existing static 

body model. The dynamic phantom would be capable 

of emulating human motion such as walking, rolling in 

a bed, twisting/turning, and bending. To accomplish 

this, we have developed computational methods for 

deforming the 3D body model (including the internal 

body organs) into various poses. We have used these 

methods to create a sequence of poses to describe motion such as walking. Figure 49 shows four walking 

poses [2]. The posed body models will be used as the 

basis for a series of simulations. 

We plan to use our system to study the effects of 

body pose and motion on RF propagation in BAN. This 

is referred to as dynamic channel and it is a more realistic scenario of operation of wearable and implantable 

sensors in a human body. Through collaborative efforts 

with other research institutes, we compare the results of 

our simulations with experimental results. We anticipate that these efforts will accelerate the commercial 

development of BAN technology along with its related 

standards.

[1] K. Sayrafian-Pour, J. Hagedorn, W. Yang and J. Terrill, 

“A Virtual Reality Platform to Study RF Propagation in 

Body Area Networks,” 3rd IEEE International Conference on Cognitive Infocommunications, Kosice, 

Slovakia, December 5, 2012.

[2] J. Hagedorn, K. Sayrafian and J. Terrill, “A Dynamic 

Human Body Computational Phantom for RF Propagation Study,” 4th International Workshop on 

Computational Phantoms, Zurich, Switzerland, May 

2013.

Evaluation and Mitigation Strategies

for Cross-Interference between 

Multiple Body Area Networks 

Kamran Sayrafian

Martina Barbi

Vladimir Marbukh

John Hagedorn

Judith Terrill

Mehdi Alasti (Time Warner Cable)

Body Area Networks (BANs) consist of multiple wearable (or implantable) sensors that can establish twoway wireless communication with a controller node 

that could be either worn or located in the vicinity of 

the body. Considering the mobile nature of BANs 

along with their proposed operational frequency bands, 

these networks are expected to coexist with other wireless devices that are operating in their proximity. 

Therefore, interference from coexisting wireless networks or other nearby BANs could create problems on 

the reliability of the network operation.

Assuming that a single BAN uses a Time Division 

Multiple Access protocol to establish communication 

among its controller and body sensors, there will be no 

simultaneous transmission, and therefore no interference among nodes of a single BAN. However, when 

several BANs are within close proximity of each other, 

interference may occur since no coordination across 

separate networks exists in general. Hence, the increasing number of such BANs in short proximity of each 

other could result in performance degradation of one or 

several communication links. Even when there is a 

small number of adjacent body area networks, the received signal strength from nearby interfering BANs 

may be too high, resulting in overwhelming of the desired signal within a particular BAN, therefore causing

performance degradation in detecting or decoding the 

transmitted data.

The complexity associated to BAN communication channels [1, 5] along with the mobility of the 

subjects wearing BANs could create various compliFigure 49. Sequence of poses emulating walking in the human 

body model.
98 NIST Applied and Computational Mathematics Division

cated scenarios where inter-BAN interference has a 

negative impact on the reliable reception of data within 

one BAN. Figure 50 illustrates this point with a simple 

scenario involving two people who are wearing multiple sensors on the front and back sides of their bodies. 

When the bodies are face-to-face (i.e., Figure 50a), the 

line-of-sight channel among the two sensors located on 

their chests might lead to a strong cross-interference. 

As they cross each other, the shadowing created by the 

bodies would remove the interference on the chest sensors; however, line-of-sight among the back sensors 

(Figure 50b) could lead to interference at that location.

We have developed a simulation platform that allows for statistical evaluation of interference in multiBAN scenarios [2]. Figure 51 shows a typical scenario 

where multiple BANs (represented by circles) can be 

distributed in a virtual room. Each BAN, including a 

coordinator and several sensor nodes, can move in a 

given direction. This is meant to represent random 

walking of people (wearing BANs) inside a room. Initial position and speed of all BANs are programmable. 

Statistical knowledge of the amount and characteristics of the inter-BAN interference in various 

scenarios would be essential information to have in 

order to study communication link reliability in a body 

area network. So far, few studies have been done of the 

impact of such inter-BAN interference. A comprehensive study would eventually require an extensive 

measurement campaign with networks that have been 

implemented according to the BAN standard. Until 

then, a simulation platform that can allow researchers

to gain more information about the impact of interference would be an extremely valuable tool. In addition, 

such a platform could be used to study the performance 

of various interference mitigation techniques such as link 

adaptation and coordinated (or 

un-coordinated) transmission 

scheduling algorithms [3]. By 

distributing simultaneous (i.e.,

colliding) multi-BAN transmissions across several time slots, 

inter-BAN interference can be 

mitigated to some extent [4]. 

This study is currently underway. We also plan to use this 

platform to better understand the 

effectiveness of link layer adaptation in mitigating interference. 

[1] R. Chávez-Santiago, K. Sayrafian, A. Khaleghi, K. Takizawa, J.

Wang, I. Balasingham and H.-B. Li, 

Propagation Models for IEEE 802.15.6 Standardization 

of Implant Communication in Body Area Networks,

IEEE Communications 51:8 (2013), 80-87. 

[2] K. Sayrafian, J. Hagedorn, M. Barbi, J. Terrill and M. 

Alasti, A Simulation Platform to Study Inter-BAN 

Interference, in Proceedings of the 4

th IEEE 

International Conference on Cognitive Infocommunications, Budapest, Hungary, December 2-5, 2013.

[3] M. Alasti, M. Barbi, K. Sayrafian and R. Verdone, InterBAN Interference Evaluation & Mitigation: A 

Preliminary Study, in Proceedings of COST IC1004

TD(13)08060, Ghent, Belgium, September 25-27, 2013.

[4] V. Marbukh, K. Sayrafian and M. Alasti, Link-layer 

Adaptation in Body Area Networks: Balancing 

Reliability and Longevity, in Proceedings of the 24th

Annual IEEE International Symposium on Personal 

Indoor and Mobile Radio Communications (IEEE 

PIMRC 2013), London, UK, September 2-5, 2013.

[5] K. Sayrafian, J. Hagedorn, W.-B. Yang and J. Terrill, A 

Virtual Reality Platform to Study RF Propagation in 

Body Area Networks, in Proceedings of the 3rd IEEE 

International Conference on Cognitive Infocommunications, Kosice, Slovakia, December 2-5, 2012.

 (a) (b)

Figure 50. Cross-interference instances among two BANs.

Figure 51. Sample multi-BAN scenario in a 4 m x 4 m rectangular 

room.
Summary of Activities for Fiscal Year 2013 99

Part IV: Activity Data

 Part IV

Activity Data
100 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2013 101

Publications

Note: Names of (co-)authors with a Division affiliation 

during this reporting period are underlined.

Appeared 

Refereed Journals

1. B. K. Alpert, R. D. Horansky, D. A. Bennett, W. 

B. Doriese, J. W. Fowler, A. Hoover, M. W. Rabin

and J. N. Ullom, Operation of Gamma-Ray Microcalorimeters at Elevated Count Rates Using Filters 

with Constraints, Review of Scientific Instruments

84 (2013), 056107.

2. F. Backeljauw, S. Becuwe, A. Cuyt, J. Van Deun

and D. Lozier, Validated Evaluation of Special 

Mathematical Functions, Science of Computer 

Programming 10 (2013), 1016.

3. B. D. Bookatz, S. P. Jordan, Y.-K. Liu and P. 

Wocjan, Quantum Nonexpander Problem Is Quantum-Merlin-Arthur-Complete, Physical Review

A 87 (2013), 042317.

4. G. W. Bryant, N. Malkova and J. S. Sims, Mechanism for Controlling the Exciton Fine Structure in 

Quantum Dots using Electric Fields: Manipulation 

of Exciton Orientation and Exchange Splitting at 

the Atomic Scale, Physcal Review B 88 (2013), 

161301(R).

5. M. Campanelli, R. N. Kacker and R. Kessel, Variance Gradients and Uncertainty Budgets for 

Nonlinear Measurement Functions with Independent Inputs, Measurement Science and Technology

24 (2013), 025002.

6. R. Chávez-Santiago, K. Sayrafian, A. Khaleghi, K.

Takizawa, J. Wang, I. Balasingham and H.-B. Li,

Propagation Models for IEEE 802.15.6 Standardization of Implant Communication in Body Area 

Networks,” IEEE Communications Magazine 51:8

(Aug. 2013), 80-87. 

7. H. S. Cohl, Erratum: Developments in Determining The Gravitational Potential Using Toroidal 

Functions, Astronomische Nachrichten 333:8

(2012), 784-785.

8. H. S. Cohl and H. Volkmer, Definite Integrals 

Using Orthogonality and Integral Transforms, 

Symmetry, Integrability and Geometry Methods 

and Applications 8 (2012), 077. 

9. H. S. Cohl, Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution 

of the Polyharmonic Equation and Polyspherical 

Addition Theorems, Symmetry, Integrability and 

Geometry Methods and Applications 9 (2012), 

042.

10. H. S. Cohl, Fourier Expansions for a Logarithmic 

Fundamental Solution of the Polyharmonic Equation, Journal of Classical Analysis 2:2 (2013),

107-127.

11. H. S. Cohl and H. Volkmer, Separation of Variables in an Asymmetric Cyclidic Coordinate 

System, Journal of Mathematical Physics 54:6 

(2013), 063513.

12. H. S. Cohl, C. MacKenzie and H. Volkmer, Generalizations of Generating Functions for 

Hypergeometric Orthogonal Polynomials with 

Definite Integrals, Journal of Mathematical Analysis and Applications 407:2 (2013), 211-225. 

13. H. S. Cohl and H. Volkmer, Publisher's Note: Separation Of Variables in an Asymmetric Cyclidic 

Coordinate System, Journal of Mathematical 

Physics 54:7 (2013), 079904.

14. H. S. Cohl, On a Generalization of the Generating 

Function for Gegenbauer Polynomials, Integral 

Transforms and Special Functions 24:10 (2013),

807-816.

15. H. S. Cohl and C. MacKenzie, Generalizations 

And Specializations Of Generating Functions for 

Jacobi, Gegenbauer, Chebyshev and Legendre 

Polynomials with Definite Integrals, Journal of 

Classical Analysis 3:1 (2013), 17-33.

16. D. G. Harris, I. Beichl and F. Sullivan, Fast Sequential Importance Sampling to Estimate the 

Graph Reliability Polynomial, Algorithmica 68 

(2014), 916-939, (published online Nov. 8, 2012).

17. R. L. Jacobsen, R. D. Johnson III, K. K. Irikura

and R. N. Kacker, Anharmonic Vibrational Frequency Calculations are not Worthwhile for Small 

Basis Sets, Journal of Chemical Theory and Computation 9 (2013), 951-954.

18. R. N. Kacker, D. R. Kuhn, Y. Lei and J. F. Lawrence, Combinatorial Testing For Software: An 

Adaptation Of Design Of Experiments, Measurement 46 (2013), 3745-3752.

19. R. Kessel, R. N. Kacker and K. D. Sommer, Uncertainty Budgeting For Range Calibration, 

Measurement 45 (2012), 1661-1669.

20. A. J. Kearsley, Constrained Hierarchical Control 

of a Diffusion Equation, International Journal of 

Applied Mathematics and Statistics 35:5 (2013), 

5–19.

21. Y.-S. Kim, O. Slattery, P. S. Kuo and X. Tang, 

Conditions For Two-Photon Interference with Co-
102 NIST Applied and Computational Mathematics Division

herent Pulses, Physical Review A 87 (2013),

063843. 

22. P. S. Kuo, O Slattery, Y.-S. Kim, J. S. Pelc, M. M. 

Fejer and X. Tang, Spectral Response of an Upconversion Detector and Spectrometer, Optics 

Express 21:19 (2013), 22523. 

23. P. S. Kuo, J. S. Pelc, O. Slattery, Y.-S. Kim, M. M. 

Fejer and X. Tang, Reducing Noise in Singlephoton Frequency Conversion, Optics Letters 38:8

(2013), 1310.

24. L. Ma, O. Slattery and X. Tang, Single Photon 

Frequency Up-Conversion and its Applications,

Physics Reports, 521:2 (2012), 69-94.

25. F. Maggioni, F. A. Potra and M. Bertocchi, Optimal Kinematics of a Looped Filament, Journal of 

Optimization Theory and Applications 159 (2013), 

489-506.

26. H. Mahboubi, W. Momeni, A. Aghdam, K. Sayrafian-Pour and V. Marbukh, An Efficient Target 

Monitoring Scheme with Controlled Node Mobility For Sensor Networks, IEEE Transactions on 

Control 20:6 (2012), 1522-1532.

27. L. A. Melara and A. J. Kearsley, The Radius of 

Attraction for Newton’s Method and TVMinimization Image Denoising, Applied Mathematics Letters 25:12 (2012), 2417–2422. 

28. W. Mitchell, A Collection of 2D Elliptic Problems 

for Testing Adaptive Grid Refinement Algorithms,

Applied Mathematics and Computation 220

(2013), 350-364.

29. A. Nurse, G. McFadden and S. Coriell, Bubble 

Motion and Size Variation during Thermal Migration with Phase Change, Physics of Fluids 25

(2013), 013302.

30. D. P. O’Leary and B. W. Rust, Variable Projection 

for Nonlinear Least Squares Problems, Computational Optimization and Applications 54 (2013), 

579-593.

31. K. Pahlavan, G. Bao, Y. Ye, S. Makarov, U. Khan, 

P. Swar, D. Cave, A. Karellas, P. Krishnamurthy 

and K. Sayrafian, RF Localization for Wireless 

Video Capsule Endoscopy,” International Journal 

of Wireless Information Networks 19:4 (December 

2012), 326-340.

32. R. Sekerka, W. Boettinger and G. McFadden, 

Surface Morphologies due to Grooves at Moving 

Grain Boundaries having Stress-Driven Fluxes,

Acta Materialia 61 (2013), 7216-7226.

33. O. Slattery, L. Ma, P. Kuo, Y.-S. Kim and X.

Tang, Frequency Correlated Bi-Photon Spectroscopy using a Tunable Up-Conversion Detector, 

Laser Physics Letters 10 (2013), 075201. 

34. Y. Zhang, S. Glancy and E. Knill, Efficient Quantification of Experimental Evidence Against Local 

Realism, Physical Review A 88 (2013), 052119.

Journal of Research of NIST

1. A. S. Carasso and A. E. Vladar, Fractional Diffusion, Low Exponent Levy Stable Laws and ‘Slow 

Motion’ Denoising of Helium Ion Microscope Imagery, Journal of Research of the NIST 117

(2012), 199-142.

2. A. S. Carasso, Hazardous Continuation Backward 

in Time in Nonlinear Parabolic Equations, and an 

Experiment in Deblurring Nonlinearly Blurred Imagery, Journal of Research of the NIST 118

(2013), 199-217.

Books

1. D. R. Kuhn, R. N. Kacker and Y. Lei, Introduction 

to Combinatorial Testing, Chapman & Hall/CRC 

Innovations in Software Engineering and Software 

Development Series, Taylor & Francis Group, Boca Raton Florida, 2013.

Conference Proceedings

1. M. Alasti, M. Barbi, K. Sayrafian and R. Verdone, 

Inter-BAN Interference Evaluation & Mitigation: 

A Preliminary Study, in Proceedings of the Cooperative Radio Communications for Green Smart 

Environments Meeting (IC1004) TD (13)08060, 

Ghent, Belgium, Sept. 25-27, 2013.

2. M. N. Borazjany, L. S. G. Ghandehari, Y. Lei, R. 

N. Kacker and D. R. Kuhn, An Input Space Modeling Methodology for Combinatorial Testing, in 

Proceedings of Sixth IEEE International Conference on Software Testing, Verification and 

Validation (ICST), Luxembourg, March 2013, 

Second International Workshop on Combinatorial 

Testing (IWCT-2013), paper 2.

3. B. Cloteaux, Limits in Modeling Power Grid Topology, in Proceedings of the IEEE Network 

Science Workshop, West Point, NY, April 2013, 

16-22.

4. J. Conroy, S. T. Davis, J. Kubina, Y.-K. Liu, D. P. 

O’Leary and J. D Schlesinger, Multilingual Summarization: Dimensionality Reduction and a Step 

towards Optimal Term Coverage, in Proceedings 

of the Workshop on Multilingual Multi-document 

Summarization (MultiLing 2013), Sofia, Bulgaria, 

August 2013, 55-63.
Summary of Activities for Fiscal Year 2013 103

5. C. F. Ferraris, N. Martys and W. L. George, Development of Standard Reference Materials for 

Cement-Based Materials, in Proceedings of 

SCC2013, Fifth North American Conference on 

the Design and Use of Self-Consolidating Concrete, Chicago, IL, May 12-15, 2013. 

6. C. Flynt, P. Brooks and D. G. Porter, Characterizing and Back-Porting Performance Improvement, 

in Proceedings of the 20th Annual Tcl/Tk Conference, New Orleans, LA, September 2013, 53-64.

7. J. T. Fong, J. J. Filliben and A. N. Heckert, A Stochastic and Local Theory of Fatigue for Aging 

Pressure Vessels and Piping, in From Failure to 

Better Design, Manufacture and Construction, 

Proceedings of 2012 International Symposium on 

Structural Integrity (ISSI2012), S. T. Tu, Z. D. 

Wang, and G. C. Sih, Eds., Jinan, China, October 

31 – Nov. 2, 2012, 19-31.

8. J. T. Fong, W. F. Guthrie, J. J. Filliben and A. N. 

Heckert, A Bayesian Quantitative Nondestructive 

Evaluation (Q-NDE) Approach to Estimating Remaining Life of Aging Pressure Vessels and 

Piping, in Proceedings of the 2012 Quantitative 

Nondestructive Evaluation Conference, Denver, 

CO, July 2012.

9. J. T. Fong, C. Cimini, D. Melo, J. J. Filliben and 

A. N. Heckert, Theoretical Failure Envelopes of 

Open Hole Composite Laminates with A- and Bbases Allowables Estimated from Smooth Specimen Properties, in Proceedings of 2013 

International Conference on Composites Design, 

Montreal, Canada, July 2013.

10. J. T. Fong, W. F. Guthrie, A. N. Heckert and J. J. 

Filliben, A Bayesian Quantitative NDE Approach 

to Estimating Remaining Life of Aging Pressure 

Vessels and Piping, in Proceedings of 2013 International Conference on Structural Mechanics in 

Reactor Technology (SMiRT-22), San Francisco, 

CA, August 2013, Paper 991.

11. L. S. G. Ghandehari, M. N. Borazjany, Y. Lei, R. 

N. Kacker and D. R. Kuhn, Applying Combinatorial Testing to the Siemens Suite, in Proceedings 

of Sixth IEEE International Conference on Software Testing, Verification and Validation (ICST), 

Luxembourg, March 2013, Second International 

Workshop on Combinatorial Testing (IWCT2013), paper 4.

12. A. Gueye and V. Marbukh, A Game-theoretic 

Framework for Network Security Vulnerability 

Assessment and Mitigation, Lecture Notes in 

Computer Science 7638 (2012), Decision and 

Game Theory for Security, 186-200.

13. A. Gueye and V. Marbukh, A Cost/Benefit Analysis of Network Vulnerability Reduction: Element 

Hardening vs. Adding Redundancy, in Proceedings of the Joint Workshop on Pricing and 

Incentives in Networks and Systems (WPIN+NetEcon), Pittsburgh, PA, June 21, 2013.

14. J. Hagedorn, K. Sayrafian and J. Terrill, A Dynamic Human Body Computational Phantom for 

RF Propagation Study, in Proceedings of the 

Workshop on Computational Phantoms for Radiation Protection, Imaging, and Radiotherapy, 

Zurich, Switzerland, May 20-22, 2013.

15. J. Jankowski, S. Ressler, J. Behr, Y. Jung, K. Sons 

and P. Slusallek, Declarative Integration of Interactive 3D Graphics into the World-Wide Web: 

Principles, Current Approaches, a Research Agenda, in Web3D ‘13: Proceedings of the 18th 

International Conference on 3D Web Technology, 

San Sebastian, Spain, June 20-22, 2013, 39-45. 

16. R. N. Kacker, D. R. Kuhn, Y. Lei and J. F. Lawrence, Combinatorial Testing for Software used in 

Metrology, in Proceedings of XX IMEKO World 

Congress, Busan, Republic of Korea, September 

2012.

17. D. R. Kuhn, I. Dominguez-Mendoza, R. N. Kacker

and Y. Lei, Combinatorial Coverage Measurement 

Concepts and Applications, in Proceedings of 

Sixth IEEE International Conference on Software 

Testing, Verification and Validation (ICST), Luxembourg, March 2013, Second International 

Workshop on Combinatorial Testing (IWCT2013), paper 7.

18. P. S. Kuo, J. Bravo-Abad and G. S. Solomon, 

Demonstration of Second-harmonic Generation by 

4-bar-Quasi-Phasematching in a GaAs Microdisk 

Cavity, in Proceedings of Nonlinear Optics, Kohala Coast, HI, July 21-26, 2013, OSA Technical 

Digest, Optical Society of America, 2013, paper 

NF1A.1.

19. P. S. Kuo, J. S. Pelc, O. Slattery, Y.-S. Kim, M. M. 

Fejer and X. Tang, Efficient, Low-noise, Singlephoton Frequency Conversion, in Proceedings of 

CLEO: Science and Innovations, San Jose, CA, July 9-14, 2013, OSA Technical Digest, Optical 

Society of America, paper JTh2A.86.

20. P. S. Kuo, J. S. Pelc, O. Slattery, Y.-S. Kim and X. 

Tang, Entangled Photon Generation in a Phasemodulated, Quasi-phase Matched Crystal, Proceedings of SPIE 8875, 887508-1. 

21. A. Lazska and Assane Gueye, Quantifying All-toOne Network Topology Robustness Under Budget 

Constraints, in Proceedings of W-PIN+NetEcon 

2013: The Joint Workshop on Pricing and Incen-
104 NIST Applied and Computational Mathematics Division

tives in Networks and Systems, Pittsburgh, PA, 

June 21, 2013.

22. A. Lazska and A. Gueye, Quantifying Network 

Topology Robustness Under Budget Constraints,

in Proceedings of the 4th Conference on Conference on Decision and Game Theory for Security, 

Dallas, TX, November 11-12, 2013.

23. H. Mahboubi, J. Habibi, A. G. Aghdam and K. 

Sayrafian, Distributed Coverage Optimization in a 

Network of Static and Mobile Sensors, in Proceedings of the 2013 IEEE American Control 

Conference (IEEE ACC 2013), Washington, DC, 

USA, June 17-19, 2013.

24. V. Marbukh, Perron-Frobenius Measure of Systemic Risk of Cascading Overload in Complex 

Clouds: Work in Progress, in Proceedings of the 

6th IFIP/IEEE International Workshop on Distributed Autonomous Network Management 

Systems, Ghent, Belgium, May 2013.

25. V. Marbukh, K. Sayrafian-Pour and M. Alasti, 

Link Layer Adaptation in Body Area Networks: 

Balancing Reliability and Longevity, in Proceedings of the 24th IEEE International Symposium on 

Personal, Indoor and Mobile Radio Communications (PIMRC 2013), London, UK, September 8-

11, 2013.

26. W. Masoudimansour, H. Mahboubi, A. G. Aghdam and K. Sayrafian, Maximum Lifetime 

Strategy for Target Monitoring in Mobile Sensor 

Networks in Presence of Obstacles, in Proceedings

of 51st IEEE Conference on Decision and Control, 

Maui, HI, December 2012.

27. B. R. Miller and D. I. Ginev, LaTeXML 2012 - A 

Year of LaTeXML, in Proceedings of the Conference on Intelligent Computer Mathematics, Bath, 

UK, July 8-12, 2013, (J. Carette, et al. Eds), Lecture Notes in Computer Science 7961 (2013), 335-

338.

28. B. R. Miller, Three Years of DLMF: Web, Math 

and Search, in Proceedings of the Conference on 

Intelligent Computer Mathematics, Bath, UK, July 

8-12, 2013, (J. Carette, et al. Eds), Lecture Notes 

in Computer Science 7961 (2013), 288-295.

29. K. Mills, C. Dabrowski, J. Filliben and S. Ressler,

Using Genetic Algorithms and Simulation to 

Search for Failure Scenarios in System Models, in 

Proceedings of the Fifth International Conference 

on Advances in System Simulation (SIMUL 2013), 

Venice, Italy, Oct 27 - Nov 1, 2013.

30. A. Mink and A. Nakassis, Practical Strategies for 

QKD Key Production, Proceedings of SPIE 8749

(2013), 840009-1. 

31. A. Mink and J. Bienfang, QKD on a Board Limited by Detector Rates in a Free-Space 

Environment, in Proceedings of 7th International 

Conference on Quantum, Nano and Micro Technologies, Barcelona, Spain, August 25-31, 2013, 

28-33. 

32. R. Pozo, Efficient Q-matrix Computation for the 

Visualization of Complex Networks, in Proceedings of Complex Networks Workshop, Eighth 

International Conference on Signal Image Technology and Internet Based Systems, Sorrento, 

Italy, November 25-29, 2012, 762-767.

33. K. Sayrafian, J. Hagedorn, W.-B. Yang and J. Terrill, Virtual Reality Platform to Study RF 

Propagation in Body Area Networks, in Proceedings of the 3rd IEEE International Conference on

Cognitive Info-communications (CogInfoCom’12), 

Kosice, Slovakia, December 2-5, 2012.

34. K. Sayrafian, J. Hagedorn, M. Barbi, J. Terrill and

M. Alasti, A Simulation Platform to Study InterBAN Interference, in Proceedings of the 4th IEEE 

International Conference on Cognitive Infocommunicaitons (CogInfoCom’13), Budapest, 

Hungary, December 2-5, 2013.

35. O. Slattery, L. Ma, P. Kuo, Y.-S. Kim and Xiao 

Tang, Tunable Up-conversion Detector for Single 

Photon and Bi-photon Infrared Spectroscopic Applications, Proceedings of SPIE 8726 (2013), 

8726OY-1. 

36. V. Stanford, L. Diduch, A. Fillinger and K. Sayrafian, Connecting Medical Devices Through 

ASTM-2761-09 Standard: Implementation Issues 

and Lessons Learned, in Proceedings of the Wireless Health Conference, Baltimore, MD, Nov. 

2013.

37. J. C. Wu, A. F. Martin, C. S. Greenberg and R. N. 

Kacker, Data Dependency on Measurement Uncertainties in Speaker Recognition Evaluation, in 

Proceedings of the SPIE Defense, Security, and 

Sensing Conference 8382, Baltimore Maryland, 

April 2012, 83820D.

38. J. C. Wu, A. F. Martin, C. S. Greenberg, R. N. 

Kacker and V. M. Stanford, Significance Test in 

Speaker Recognition Data Analysis with Data Dependency, in Proceedings of the SPIE Defense, 

Security, and Sensing Conference 8734, Baltimore 

Maryland, April 2013, 87340I.

39. W. B. Yan and K. Sayrafian,Theoretical Analysis 

and Modeling of Link Adaptation Schemes in 

Body Area Networks in Proceedings of the 3rd International Conference on Wireless Mobile 

Communication and Healthcare (MobiHealth 

2012), Paris, France, November 21-23, 2012.
Summary of Activities for Fiscal Year 2013 105

40. W. B. Yang and K. Sayrafian,Theoretical Analysis 

and Modeling of Link Adaptation Schemes in 

Body Area Networks, in Proceedings of the 3rd 

International Conference on Wireless Mobile 

Communication and Healthcare (MobiHealth 

2012), Paris, France, November 21-23, 2012.

41. L. Yu, Y. Lei, R. N. Kacker and D. R. Kuhn, 

ACTS: A Combinatorial Test Generation Tool, in 

Proceedings of Sixth IEEE International Conference on Software Testing, Verification and 

Validation (ICST), Luxembourg, March 2013, 

Testing Tools Track, paper 1.

42. L. Yu, M. N. Borazjany, Y. Lei, R. N. Kacker and 

D. R. Kuhn, An Efficient Algorithm for Constraint 

Handling in Combinatorial Test Generation, in 

Proceedings of Sixth IEEE International Conference on Software Testing, Verification and 

Validation (ICST), Luxembourg, March 2013, Research and Industry Track, paper 3.

43. L. Yu, Y. Lei, R. N. Kacker, D. R. Kuhn, R. D. 

Sriram and K. G. Brady, A General Conformance 

Testing Framework for IEEE 11073 PHD’s Communication Model, in Proceedings of 6th 

International Conference on Pervasive Technologies Related to Assistive Environments (PETRA 

2013), Athens, Greece, May 2013, ACM 978-1-

4503-1300-1/13/05.

44. L. Zappaterra, H. A. Choi, K. Sayrafian and J. I. 

H. Iinatti, On the Delay and Data Rate Performance of Throughput-Efficient Multi-Channel 

Access Algorithms in Cognitive Radio Networks,

in Proceedings of the 8th International Conference 

on Cognitive Radio Oriented Wireless Networks

(CROWNCON 2013), Washington, DC, July 8-10, 

2013.

Technical Magazine Articles

1. I. Beichl, Hail and Farewell, Computing in Science 

& Engineering 14:6 (2012), 4.

2. J. Kepner, T. Davis, J. Demmel, A. Edelman, H. 

Elman, J. Gilbert, M. Heath. D. P. O’Leary, M. 

Overton, Y. Saad, A. Sameh, M. Stonebraker, G. 

Strang, R. van de Geijn, C. Van Loan and M. 

Wright, The Role of Linear Algebra in the Computer Science Curriculum, SIAM News 46:4 (May 

2013), 8.

Technical Reports

1. G. Alagic, S. Jeffery and S. P. Jordan, Partialindistinguishability Obfuscation Using Braids. 

arXiv:1212.6458, 2012. 

2. R. F. Boisvert (ed.), Applied and Computational 

Mathematics Division, Summary of Activities for 

Fiscal Year 2012, NISTIR 7931, April 2013.

3. A. S. Carasso, Alternative Methods of Latent Fingerprint Enhancement and Metrics for Comparing

Them, NISTIR 7910, January 2013.

4. A. S. Carasso, The Use of ‘Slow Motion’ Lévy

Stable Fractional Diffusion Smoothing in Alternative Methods of Latent Fingerprint Enhancement, 

NISTIR 7932, April 2013.

5. A. S. Carasso, Compensating Operators and Stable 

Backward in Time Marching in Nonlinear Parabolic Equations, NISTIR 7967, November 2013.

6. J. A. Warren and R. F. Boisvert (eds.), Building 

the Materials Innovation Infrastructure: Data and 

Standards, NISTIR 7898, November 2012.

7. O. Narayan, I. Saniee and V. Marbukh, Congestion 

Due to Random Walk Routing, arXiv:1309.0066, 

2013.

Accepted

1. Z. Gimbutas and S. Veerapaneni, A Fast Algorithm for Spherical Grid Rotations and its 

Application to Singular Quadrature, SIAM Journal 

on Scientific Computing.

2. W. Griffin and M. Olano, Objective Image Quality 

Assessment of Texture Compression, ACM 

SIGGRAPH Symposium on Interactive 3D 

Graphics and Games.

3. C. Hagwood, J. Bernal, M. Halter, J. Elliot and T. 

Brennan, Testing Equality of Cell Populations 

Based on Shape and Geodesic Distance, IEEE 

Transactions on Medical Imaging.

4. S. P. Jordan, K. S. M. Lee and J. Preskill, Quantum Computation of Scattering in Quantum Field 

Theories, Quantum Information and Computation.

5. J. F. Lawrence, R. N. Kacker and R. Kessel, Obtaining a Trapezoidal Distribution, 

Communications in Statistics – Theory and Methods.

6. Y.-K. Liu, Building One-Time Memories from 

Isolated Qubits, Proceedings of Innovations in 

Theoretical Computer Science (ITCS 2014).

7. H. Mahboubi, K. Moezzi, A. G. Aghdam, K. Sayrafian and V. Marbukh, Distributed Deployment 

Algorithms for Improved Coverage in a Network 

of Wireless Mobile Sensors, IEEE Transactions on 

Industrial Informatics.
106 NIST Applied and Computational Mathematics Division

8. I. Matei, A. Gueye and J. S. Baras., Flow Control 

in Time-Varying, Random Supply Chain Networks 

Journal Transportation Research Part E: Logistics 

and Transportation Review.

9. W. Mitchell and M. McClain, A Comparison of 

hp-Adaptive Strategies for Elliptic Partial Differential Equations, ACM Transactions on 

Mathematical Software.

10. F. A. Potra, Interior Point Methods for Sufficient 

Horizontal LCP in a Wide Neighborhood of the 

Central Path with Best Known Iteration Complexity SIAM Journal on Optimization.

11. R. Sekerka, S. Coriell, and G. McFadden, Morphological Stability, Handbook of Crystal Growth.

12. J. C. Wu, A. F. Martin and R. N. Kacker, Bootstrap Variability Studies in ROC Analysis on 

Large Datasets, Communications in Statistics -

Simulation and Computation.

13. D. Yeo and F. A. Potra, Sustainable Design of 

Reinforced Concrete Structures through CO2 

Emission Optimization, Special Issue on Sustainable Building Structures, Journal of Structural 

Engineering-ASCE. 

In Review

1. A. Boliong, H. S. Cohl and S. Weiss, A Function 

Selection Procedure for Determining Resonant 

Modes of Patch Antennas on Spherical Surfaces.

2. A. Anandkumar, D. P. Foster, D. Hsu, S. M. Kakade and Y.-K. Liu, A Spectral Algorithm for 

Latent Dirichlet Allocation. 

3. A. S. Carasso, Compensating Operators and Stable 

Backward in Time Marching in Nonlinear Parabolic Equations.

4. B. Cloteaux, M. D. LaMar, E. Moseman and J. 

Shook. Threshold Digraphs.

5. E. Cobanera, G. Ortiz, and E. Knill, The NonAbelian Duality Problem.

6. H. S. Cohl, Antiderivatives and Integral Representations of Associated Legendre Functions with 

Degree and Order Equal to Within a Sign.

7. H. S. Cohl and Hans Volkmer, Expansions for a 

Fundamental Solution of Laplace’s Equation on R

3 

in 5-cyclidic Harmonics.

8. D. Cotrell, A. Lott and G. McFadden, Boundary 

Slip Effects on the Stability of Spiral Poiseuille 

Flow.

9. C. F. Ferraris, N. Martys, and W. L. George, Development of Standard Reference Materials for 

Cement-Based Materials Cement and Concrete 

Composites.

10. A. Gueye, A. Lazska, J. C. Walrand and V. Anantharan. A Polyhedral-Based Analysis of Nash 

Equilibria of Quasi-Zero-Sum Games and its Applications to Communication Network Security. 

11. S. P. Jordan, Strong Equivalence of Reversible 

Circuits is coNP-complete.

12. N. Kaslovsky and F. G. Meyer, Non-asymptotic 

Analysis of Tangent Space Perturbation.

13. Y.-S. Kim, O. Slattery, P. S. Kuo and X. Tang, 

Two-photon Interference with Continuous-wave 

Multi-mode Coherent Light.

14. A. Lazska and A. Gueye, Network Topology Vulnerability/Cost Tradeoff: Model, Application, and 

Computational Complexity.

15. A. Luna, G. McFadden, M. Aladjem and K. Kohn, 

Predicted Role of NAD Utilization in the Control 

of Circadian Rhythms During DNA Damage Response.

16. I. Sahin and A. J. Kearsley, Using Quadratic Functions over Lines in an Evolutionary Optimization 

Algorithm.

17. B. Saunders, Q. Wang and B. Antonishek, Adaptive Composite B-Spline Grid Generation for 

Interactive 3D Visualizations.

18. M. J. Stevens, S. Glancy, S. W. Nam and R. P. 

Mirin, Third-order Antibunching from an Imperfect Single-photon Source.

19. A. Streib, N. Streib, I. Beichl and F. Sullivan, 

Stratified Sampling for the Ising Model - A Graph 

Theoretic Approach.

20. A. Streib, N. Streib, I. Beichl and F. Sullivan, A 

Binomial Approximation Method for the Ising 

Model.

21. A. Streib and N. Streib, Cycle Basis Markov 

Chains for the Ising Model.

22. F. Sullivan and I. Beichl, Permanents, alphaPermanents and Sinkhorn Balancing.

Invention Disclosures

1. A. Carasso, Enhancement and Denoising of Latent 

Fingerprints, May 2013.
Summary of Activities for Fiscal Year 2013 107

Presentations

Invited Talks

1. R. F. Boisvert, “Society Publishing and the Fair 

Access Model,” Dagstuhl Perspectives Workshop 

on the Publication Culture in Computing Research, 

Schloss Dagstuhl, Liebnitz-Zentrum fuer Informatik, Wadern, Germany, November 7, 2012. 

2. R. F. Boisvert, “Reproducibility at ACM,” Panel 

on Journal Policies and Experiences, Workshop on 

Reproducibility in Computational and Experimental Mathematics, Institute for Computational 

and Experimental Mathematics (ICERM), Brown 

University, Providence, RI, December 11, 2012.

3. R. F. Boisvert, “A Survey of Data Intensive Problems at NIST,” International Workshop on Data 

Intensive Scientific Discovery, Shanghai, China, 

August 2, 2013.

4. A. S. Carasso, “Unexpected Success and Surprising Failure in Backward in Time Continuation in 

Linear and Nonlinear Parabolic Equations and 

Their Applications,” International Conference on 

Computational Analysis of Inverse Problems and 

Partial Differential Equations, University of Central Florida, Orlando, FL, May 9-11 2013.

5. H. S. Cohl, “Generalizations of Generating Functions for Hypergeometric Orthogonal 

Polynomials,” The Norbert Wiener Center Seminar, The Norbert Weiner Center for Harmonic 

Analysis, University of Maryland, College Park, 

MD, October 16, 2012.

6. H. S. Cohl, “Expansions for the Iterated Poisson 

Equation on d-dimensional Euclidean Space,” Department of Mathematical Sciences Colloquium, 

George Mason University, Fairfax, VA, December 

7, 2012.

7. H. S. Cohl, “Generalizations of Generating Functions for Hypergeometric Orthogonal 

Polynomials,” Department of Mathematics, Tulane 

University, New Orleans, LA, February 21, 2013.

8. H. S. Cohl, “Fourier and Legendre Expansions for 

Green's Functions of Elliptic PDEs,” Army Research Laboratory, Adelphi, MD, March 13, 2013.

9. H. S. Cohl, “Fourier and Gegenbauer Expansions 

of a Fundamental Solution of Laplace's Equation 

Riemannian Spaces of Constant Curvature,” 

Clifford Analysis Seminar, Department of Mathematical Analysis, Ghent University, Ghent, 

Belgium, April 4, 2013.

10. G. Doğan, “Variational Algorithms for Fast and 

Robust Shape Reconstruction in Imaging,” Fields 

Institute, University of Toronto, Canada, March 

25, 2013.

11. G. Doğan, “Gradient Flows for General Curvaturedependent Surface Energies and Shape Optimization and Applications in Imaging,” Summer 

Graduate Program on Flow, Geometric Motion, 

Deformation, and Mass Transport in Physiological 

Processes, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, 

MN, July15, 2013.

12. J. T. Fong, “Quantitative NDE and Stochastic 

Modeling of Fatigue of Aging Structures,” Department of Mechanical Engineering, Yokohama 

National University, Yokohama, Japan, Oct. 15, 

2012.

13. J. T. Fong, “Quantitative Nondestructive Evaluation (QT-NDE): Key to Innovative Manufacturing 

and Aging Equipment Management,” School of 

Mechanical and Power Engineering, East China 

University of Science and Technology, Shanghai, 

China, Oct. 19, 2012.

14. J. T. Fong, “Quantitative Nondestructive Evaluation (QT-NDE): Key to Innovative Manufacturing 

and Aging Equipment Management,” China 

Standards Committee on Boilers and Pressure 

Vessels, Beijing, China, Oct. 22, 2012.

15. J. T. Fong, “Quantitative Nondestructive Evaluation (QT-NDE): Key to Innovative Manufacturing 

and Aging Equipment Management,” School of 

Mechanical Engineering, Beijing Institute of 

Technology, Beijing, China, Oct. 23, 2012.

16. J. T. Fong, “Quantitative Nondestructive Evaluation (QT-NDE): Key to Innovative Manufacturing 

and Aging Equipment Management,” School of 

Materials Science and Engineering, Dalian University of Technology, Dalian, China, Oct. 25, 

2012.

17. J. T. Fong, “Quantitative Nondestructive Evaluation (QT-NDE): Key to Innovative Manufacturing 

and Aging Equipment Management,” School of 

Mechanical Engineering, China University of Petroleum, Qingdao, China, Oct. 29, 2012.

18. J. T. Fong, “A Stochastic and Local Theory of 

Fatigue for Aging Pressure Vessels and Piping,”

International Symposium on Structural Integrity 

(ISSI2012), Shandong University, Jinan, China, 

Nov. 1, 2013.

19. J. T. Fong, “A Bayesian Stochastic Approach to 

Multi-Scale Modeling, Electromagnetics Division 
108 NIST Applied and Computational Mathematics Division

Seminar Series,” NIST, Boulder, CO., Feb. 26, 

2013.

20. J. T. Fong, “Structural Health Monitoring of Complex Structures with Advanced NDE, Multi-Scale 

Modeling, and Modern Statistics,” Department of 

Mechanical and Industrial Engineering, University 

of Illinois-Chicago Circle, Chicago, IL, Apr. 18, 

2013.

21. J. T. Fong, “On the Finite Element Method-based 

Solutions of Electro-magnetics Problems using 

ABAQUS, COMSOL, and MATLAB,” Electromagnetics Division Seminar Series, NIST, 

Boulder, CO., Apr. 30, 2013.

22. J. T. Fong, “Quantitative NDE and Bayesian Fatigue Modeling: Key to Improving Reliability of 

Aging Structures and Components,” International

Conference on Computational and Experimental 

Engineering and Science (ICCES’13), Bellevue, 

WA, May 24, 2013.

23. J. T. Fong, “Real-Time Health Monitoring of 

Structures and Components with Advanced NDE, 

Multi-Scale Modeling, and Modern Statistics,” International Conference on Computational and 

Experimental Engineering and Science 

(ICCES’13), Bellevue, WA, May 27, 2013.

24. J. T. Fong, “A Design of Experiments Approach to 

Uncertainty Assessment of NDE Field Work,” 40th

Review Meeting on Quantitative Nondestructive 

Evaluation, Baltimore, MD, July 24, 2013.

25. J. T. Fong, “Application of FEM- COMSOL Version 4.3b MEMS Module to the Simulation of an 

Electromagnetics-biased Resonator,” Applied

Chemicals and Materials Division, NIST, Boulder, 

CO, August 8, 2013. 

26. S. Glancy, “Linear Density Matrix Estimation 

from Homodyne Measurements: Uncertainty 

Comparison,” Southwest Quantum Information 

Technology Network Workshop, Santa Barbara, 

CA, February 21, 2013.

27. A. Gueye, “Science-Based Metrics for Network 

Topology Resilience against Attacks,” Mathematical Sciences Colloquium, College of Sciences, 

George Mason University Fairfax, VA, October 

18, 2013.

28. A. Gueye, “A Game Theoretic Framework for 

Evaluating Resilience of Networks Against Attacks,” Electrical and Computer Engineering 

Department, University of Maryland, College 

Park, MD, February 7, 2013.

29. A. Gueye, “Game Theoretic Framework for Evaluating Resilience of Networks,” University of 

Southern California, Los Angeles, CA, January 14, 

2013.

30. A. Gueye, “Game Theoretic Framework for Evaluating Resilience of Networks,” NetEcon Meeting, 

University of California, Berkeley, CA, January 

15, 2013.

31. A. Gueye, “Blocking Games: A Game Theoretic 

Framework for Analyzing Adversarial Relationship,” TRUST Seminar Series, University of 

California, Berkeley, CA, January 24, 2013.

32. A. Gueye, “Game Theoretic Framework for Evaluating Resilience of Networks,” NCD Seminar 

Series, University of California, Berkeley, CA, 

January 18, 2013.

33. S. Jordan, “Quantum Algorithms for Quantum 

Field Theories,” Quantum Information Processing 

(QIP2013), Beijing, China, January 14, 2013.

34. S. Jordan, “Quantum Algorithms for Quantum 

Field Theories,” Physics Colloquium, University 

of Pennsylvania, Philadelphia, PA, December 5, 

2012.

35. S. Jordan, “Super-polynomial Quantum Speedups 

Tutorial,” Post-quantum Cryptography Workshop, 

Lorentz Center, Leiden, Netherlands, November 5, 

2012.

36. S. Jordan, “Partial-indistinguishability Obfuscation 

using Braids,” PIQuDos Seminar, Perimeter Institute, Waterloo, Canada, April 18, 2013.

37. S. Jordan, “Partial-indistinguishability Obfuscation 

using Braids” Institute for Quantum Information 

and Matter Seminar, Caltech, Pasadena, CA, January 8, 2013.

38. S. Jordan, “Partial-indistinguishability Obfuscation 

using Braids,” Hughes Research Laboratory, Malibu, CA, January 17, 2013.

39. D. N. Kaslovsky, “Tangent Plane Recovery and 

the Noise Curvature Trade Off for Local Data Parameterization,” Applied Mathematics and 

Statistics Colloquium, Colorado School of Mines, 

CO, November 16, 2012.

40. A. J. Kearsley, “Simulation and Control of Systems Governed by PDE,” Sampoerna University, 

Jakarta, Indonesia, August 20, 2013.

41. A. J. Kearsley, “Time Delay Estimation by Minimizing Differences between Linear-Phase Shifted 

DFTs,” University of Indonesia, August 21, 2013.

42. P. S. Kuo, J. S. Pelc, O. Slattery, Y.-S. Kim and 

X. Tang, “Entangled Photon Generation in a 

Phase-modulated, Quasi-phase Matched Crystal,”
Summary of Activities for Fiscal Year 2013 109

SPIE Optics and Photonics 2013, San Diego, CA, 

August 25-29, 2013. 

43. P. S. Kuo, J. Bravo-Abad, and G. S. Solomon, 

“Demonstration of Second-harmonic Generation 

by 4-bar-quasi-phasematching in a GaAs Microdisk Cavity,” OSA Nonlinear Optics Conference, 

Kohala Coast, HI, July 21-26, 2013.

44. P. S. Kuo, “Optical Frequency Conversion and its 

Applications for Quantum Information,” Army 

Research Laboratory, Adelphi, MD, January 25, 

2013.

45. Y.-K. Liu, “Building One-Time Memories from 

Isolated Qubits,” Institute for Quantum Information and Matter Seminar, Caltech, Pasadena, 

CA, April 30, 2013.

46. D. P. O’Leary, “Tracking Objects Using Wavelets 

and Shearlets,” February Fourier Talks, University 

of Maryland, College Park, MD, February 2013.

47. D. P. O’Leary, “Image Restoration and Uncertainty Quantification,” 25th Biennial Numerical 

Analysis Conference Glasgow, Scotland, June 

2013. (Plenary Talk)

48. D. P. O’Leary, “Eckart-Young Meets Bayes: Optimal Regularized Low-Rank Inverse 

Approximation,” International Linear Algebra Society 2013 Meeting, Providence, RI, June 2013. 

(Plenary Talk)

49. N. S. Martys and W. L. George, “Computer Simulation of Suspensions: Application to Cementbased Materials,” Exxon Mobil Research, Clinton, 

NJ, September 10, 2013.

50. G. McFadden, “Bubble Motion and Size Variation 

during Thermal Migration with Phase Change,”

Materials Science and Technology 2013 

(MS&T’13), Montreal, Canada, October 28, 2013.

51. F. A. Potra, “Interior Point Methods for Sufficient 

LCP in a Wide Neighborhood of the Central Path,”

XXVI EURO-INFORMS 26th European Conference on Operations Research, Rome, Italy, July 1-

4, 2013.

52. S. Ressler, “Declarative 3D Graphics for the Web, 

Integrating X3DOM, jQuery, WebGL and 

HTML5,” Gettysburg College, Gettysburg, PA,

Oct. 10, 2013 (ACM Distinguished Speaker).

53. B. Saunders, “Mesh Generation for Interactive 3D 

Graphs in the NIST Digital Library of Mathematical Functions,” 19th Conference for African 

American Researchers in the Mathematical Sciences (CAARMS 19), San Diego, CA, July 25, 

2013.

54. K. Sayrafian, “Using Virtual Reality to Study RF 

Propagation, Interference & Kinetic Energy Harvesting in Body Area Networks,” 8th International 

Conference on Body Area Networks (BodyNets 

2013), September 30–October 2, 2013, Boston, 

MA (Keynote).

55. K. Sayrafian, “A Virtual Reality Platform to Study 

RF Propagation in Body Area Networks,” IEEE 

International Conference on Cognitive Infocommunications, December 2012.

56. K. Sayrafian, “Body Area Networks: Standardization Activities and Technology Challenges,” 

University of Surrey, Guildford, UK, October 10, 

2012.

57. K. Sayrafian, “Health and Medical CPS,” NSF 

CPS PI Meeting, October 5, 2012 (Invited Panelist).

58. J. Shook, “Threshold Digraphs,” University of 

Colorado at Denver, Denver, CO, October 5, 2012.

59. J. Shook, “Math at NIST,” University of Colorado 

at Denver, Denver, CO, October 8, 2012.

60. J. Shook, “Threshold Digraphs,” Atlanta Lecture 

Series in Combinatorics and Graph Theory VIII,

Georgia State University, Atlanta, GA, February 

11, 2013.

61. J. Shook, “Threshold Digraphs,” American Mathematical Society Southeastern Spring Sectional, 

University of Mississippi, University, MS, March 

1, 2013.

62. J. Shook, “Math at NIST,” University of Mississippi Mathematics Seminar, University, MS, 

March 4, 2013.

63. A. Streib and N. Streib, “A Stratified Sampling 

Approach to the Ising Model,” Workshop on Deep 

Computation in Statistical Physics, Santa Fe Institute, Santa Fe, NM, August 8, 2013.

64. A. Streib, “Mixing times of Self-organizing Lists 

and Biased Permutations,” IDA Center for Computing Sciences, Bowie, MD, January 30, 2013.

65. N. Streib, “Approximating the Partition Function 

of the Ising Model,” IDA Center for Computing 

Sciences, Bowie MD, January 28, 2013. 

66. N. Streib, “An Application of Graph Theory in 

Theoretical Physics,” Discrete Mathematics Seminar, Virginia Commonwealth University, 

Richmond, VA, December 2013.
110 NIST Applied and Computational Mathematics Division

Conference Presentations

1. P. Bhakta, S. Miracle, D. Randall and A. P. Streib, 

“Mixing Times of Markov Chains for SelfOrganizing Lists and Biased Permutations,” 

SIAM Symposium on Discrete Algorithms 

(SODA), New Orleans, LA, January 6, 2013.

2. G. W. Bryant, N. Malkova, and J. Sims, “Electricfield Control of Exciton Fine Structure: Atomic 

Scale Manipulation of Exchange Splitting,” American Physical Society March Meeting, Baltimore, 

MD, March 2013. 

3. G. W. Bryant and J. S. Sims, “Magnetoexcitons in 

Quantum Dots: Atomistic Theory of G-Factors, 

Diamagnetic Shifts and Spin Mixing,” International Conference on Optics of Excitons in Confined 

Systems, Rome, Italy, September 9-13, 2013. 

4. B. Cloteaux, “Limits in Modeling Power Grid Topology,” IEEE Network Science Workshop, West 

Point, NY, May 1, 2013.

5. H. S. Cohl, “Hypergeometric Orthogonal Polynomial Expansions,” 12th International Symposium 

on Orthogonal Polynomials, Special Functions and 

Applications, Sousse, Tunisia, March 28, 2013.

6. J. Conroy, S. T. Davis, J. Kubina, Y.-K. Liu, D. P. 

O’Leary and J. D Schlesinger, “Multilingual 

Summarization: Dimensionality Reduction and a 

Step Towards Optimal Term Coverage,” Workshop on Multilingual Multi-document 

Summarization (MultiLing 2013), Sofia, Bulgaria, 

August 2013.

7. G. Doğan, “Shape Reconstruction from Direct and 

Indirect Measurements,” Joint Mathematics Meetings, San Diego, CA, January 11, 2013.

8. G. Doğan, “Shape Reconstruction in Computed 

Tomography,” Conference on Computational 

Analysis of Inverse Problems and Partial Differential Equations, University of Central Florida, 

Orlando, FL, May 9, 2013.

9. G. Doğan, “An Algorithm for Shape Detection in 

Computed Tomography,” SIAM Conference on 

Computational Science and Engineering, Boston, 

MA, February 29, 2013.

10. G. Doğan, “Shape Reconstruction in Inverse Problems,” DelMar Annual Workshop on 

Computational Mathematics, University of Maryland, College Park, MD, May 4, 2013.

11. M. J. Donahue, “Structure and Periodicity of 

Cross-tie Walls in Thin Magnetic Strips,” 12th 

Joint MMM/Intermag Conference, Chicago, Illinois, January 16, 2013. 

12. C. F. Ferraris, N. Martys and W. L. George, “Development of Standard Reference Materials for 

Cement-Based Materials,” Fifth North American 

Conference on the Design and Use of SelfConsolidating Concrete (SCC2013), Chicago, IL, 

May 12-15, 2013.

13. A. Gueye, “Network Topology Robustness under 

Adversarial Environment and Budget Constraints,” 

4th Conference on Decision and Game Theory for 

Security, Dallas, TX, November 11-12, 2013.

14. A. Gueye, “A Game Theoretic Approach to Communication Security,” MAA Session: Research in 

Applied Mathematics III, Joint Mathematics Meetings, San Diego, CA, January 9-12, 2013.

15. A. Gueye, “Cost/Benefit Analysis of Network 

Vulnerability Reduction: Element Hardening vs. 

Adding Redundancy,” W-PIN+NetEcon 2013: The 

Joint Workshop on Pricing and Incentives in Networks and Systems, Pittsburgh, PA , June 21, 

2013.

16. J. Hagedorn, K. Sayrafian, J. Terrill, “A Dynamic 

Human Body Computational Phantom for RF 

Propagation Study,” 4th International Workshop 

on Computational Phantoms, Zurich, Switzerland, 

May 2013, 21-23. 

17. A. Harvey, E. Simiu, F. A. Potra, K. Quinlan and 

N. Chokshi, “Design-basis Hurricane Winds and 

Missiles for Nuclear Power Plants,” 22nd International Conference on Structural Mechanics in 

Reactor Technology (SMiRT-22), San Francisco, 

CA, August 18-23, 2013.

18. F. Hunt, “Characterizing Important Nodes in a 

Network as Effective Spreaders,” SIAM Workshop on Network Science, San Diego, CA, July 8, 

2013.

19. A. J. Kearsley and W. E. Wallace “Numerical Optimization of Instrument Settings in Reference 

Material Certification',” SIAM Conference on 

Computational Science and Engineering, Boston, 

MA, March 1, 2013.

20. A. J. Kearsley, “Hierarchical Control of Mass 

Spectrometer Instrument Performance,” 3rd IEEE 

International Conference on Instrumentation Control and Automation (ICA), Ungasan, Indonesia, 

August 29, 2013.

21. A. J. Kearsley, “Stochastic Regression Modeling 

of Noisy Spectra,” 9th Harsh-Environment Mass 

Spectrometry Workshop,” St. Petersburg, FL, September 15, 2013.

22. E. Knill and A. Meier, “Randomized Benchmarking,” IARPA Multi-qubit Coherent Operations 

(MQCO) Verification and Validation of Multi-
Summary of Activities for Fiscal Year 2013 111

Qubit Systems Technical Exchange Workshop, 

San Diego, CA, January 2013.

23. P. S. Kuo, J. S. Pelc, O. Slattery, Y.-S. Kim, M. 

M. Fejer, and X. Tang, “Efficient, Low-noise, Single-Photon Frequency Conversion,” Conference 

on Lasers and Electro-Optics (CLEO), San Jose, 

CA, June 9-14, 2013. 

24. Y.-K. Liu, “Building One-time Memories from 

Isolated Qubits,” 3rd International Conference on 

Quantum Cryptography (QCrypt 2013), Waterloo, 

Canada, August 6, 2013.

25. Y.-K. Liu, “Evaluating the Security of Postquantum Cryptosystems,” European Telecommunications Standards Institute (ETSI) Workshop on 

Quantum-Safe Cryptography, Sophia-Antipolis, 

France, September 27, 2013.

26. D. Lozier and A. Cuyt, “Toward an On-Demand 

Data Service for Special Functions,” Minisymposium on Special Functions: Applications and 

Numerical Aspects, SIAM Annual Meeting, San 

Diego, CA, July 11, 2013.

27. B. R. Miller and D. I. Ginev, “LaTeXML 2013 - A 

Year of LaTeXML,” Conference on Intelligent 

Computer Mathematics, Bath, UK, July 8-12, 

2013.

28. B. R. Miller, “Three Years of DLMF: Web, Math 

and Search,” Conference on Intelligent Computer 

Mathematics, Bath, UK, July 8-12, 2013.

29. A. Mink and A. Nakassis, “Practical Strategies for 

QKD Key Production,” SPIE Defense Security 

and Sensing, Baltimore, MD, April 5-9, 2013. 

30. A. Mink and J. Bienfang, “QKD on a Board Limited by Detector Rates in a Free-Space 

Environment,” International Conference on Quantum, Nano and Micro Technologies, Barcelona, 

Spain, August 25-31, 2013.

31. W. Mitchell, “Performance of hp-Adaptive Strategies for Elliptic Partial Differential Equations,” 4

th

International Congress on Computational Engineering and Sciences (FEMTEC), Las Vegas, NV, 

May 21, 2013.

32. D. G. Porter, “Scaling Tcl Data Structures,” 20th 

Annual Tcl/Tk Conference, New Orleans, LA, 

September 26, 2013.

33. R. Pozo, Efficient Q-matrix Computation for the 

Visualization of Complex Networks,” Complex 

Networks 2013, 8th International Conference on 

Signal Image Technology and Internet Based Systems, Sorrento, Italy, November 27, 2012.

34. R. Pozo, “A Network Measure for the Analysis of 

Large-scale Graphs,” SIAM Workshop on Network Science, San Diego, CA, July 8, 2013.

35. R. Pozo, “Detecting Network Randomization: 

How Real Networks Differ from Random Graphs 

with the Same Joint-degree Distribution,” NetSci, 

International School and Conference on Network 

Science, Copenhagen, Denmark, June 6, 2013.

36. S. Ressler, “Web3D 2013: Scaling Up: Integrating 

X3DOM with Whole Body Laser Scan Data,” 18th 

International Conference on 3D Web Technology

(Web3D’13), San Sebastian, Spain, June 20 - 22, 

2013. 

37. S. Ressler and K. Leber, “Web Based 3D Body 

Laser Scans,” 4th International Conference and 

Exhibition on 3D Body Scanning Technologies,”

Long Beach CA, Nov. 19-20, 2013.

38. K. Sayrafian, “A Dynamic Human Body Computational Phantom for RF Propagation Study,”

Workshop on Computational Phantoms for Radiation Protection, Imaging, and Radiotherapy, 

Zurich, Switzerland, May 20-22, 2013.

39. K. Sayrafian, “Theoretical Analysis and Modeling 

of Link Adaptation Schemes in Body Area Networks,” 3rd International Conference on Wireless 

Mobile Communication and Healthcare (MobiHealth 2012), Paris, France, November 21-23, 

2012.

40. K. Sayrafian, “Inter-BAN Interference Evaluation 

and Mitigation: A Preliminary Study,” Cooperative Radio Communications for Green Smart 

Environments Meeting (COST IC1004), Ghent, 

Belgium, September 25-27, 2013.

41. B. Saunders, “Using Adaptive Composite B-Spline 

Grid Generation to Enhance 3D Web Visualizations,” SIAM Conference on Geometric and 

Physical Modeling,” Denver, Colorado, November 

14, 2013. 

42. B. Saunders, B. Miller, M. McClain and D. Lozier, 

“DLMF Live! Tables: NIST Digital Library of 

Mathematical Functions Tables Project,” Mathematical Association of America (MAA) MD-DCVA Section Meeting, Salisbury University, Salisbury, MD, April 13, 2013.

43. B. Saunders, “Balancing Research Interests with 

Project Goals at the National Institute of Standards 

and Technology,” MAA Session on Mathematics 

Experiences in Business, Industry, and Government, Joint Mathematics Meetings, San Diego, 

California, January 12, 2013. 

44. B. Saunders, B. Antonishek and Q. Wang, “Adaptive Composite B-Spline Grid Generation for
112 NIST Applied and Computational Mathematics Division

Interactive 3D Visualizations,” 8th International 

Conference on Mathematical Methods for Curves 

and Surfaces (MASCOT/ISGG 2012), Las Palmas 

de Gran Canaria, Spain, October 25, 2012. 

45. K. Sayrafian-Pour, J. Hagedorn, W. Yang and J. 

Terrill, “A Virtual Reality Platform to Study RF 

Propagation in Body Area Networks,” 3rd IEEE 

International Conference on Cognitive Infocommunications (CogInfoCom 2012), Kosice, 

Slovakia, December 2-5, 2012.

46. J. Shook, “Threshold Digraphs,” Joint Mathematics Meetings, San Diego, CA, San Diego, 

California, January 12, 2013.

47. O. Slattery, P. Kuo, X. Tang, I. Aharonovich and 

S. Castelletto, “Towards Interference between

Single Photons from Independent Diamond Defect 

and SPDC Sources,” SPIE Optics and Photonics, 

San Diego, CA, August 25-29, 2013.

48. A. Streib, “Clustering in Interfering Models of 

Binary Mixtures,” Joint Mathematics Meetings, 

San Diego CA, January 12, 2013.

49. N. Streib, “Dimension-Preserving Contractions 

and a Finite List of 3-Irreducible Posets,” 

Joint Mathematics Meetings, San Diego CA, January 12, 2013.

Web Services

1. Adaptive Mesh Refinement Benchmark Problems30: a collection of benchmark partial 

differential equations for testing and comparing 

adaptive mesh refinement algorithms.

2. Digital Library of Mathematical Functions31: a 

repository of information on the special functions 

of applied mathematics.

3. Guide to Available Mathematical Functions32: a 

virtual repository of mathematical software components. (dormant)

4. Matrix Market33: a repository of matrices for testing of algorithms and software for numerical linear 

algebra. (dormant)

5. muMAG34: a collection of micromagnetic reference problems and submitted solutions.

6. SciMark35: a benchmark for scientific computing 

in Java. (dormant)

 

30 http://math.nist.gov/amr-benchmark

31 http://dlmf.nist.gov/

32 http://gams.nist.gov/

33 http://math.nist.gov/matrixmarket/

34 http://www.ctcms.nist.gov/mumag/mumag.org.html

Software Released

1. ACTS36: Combinatorial Test Suite Generation with 

Support of Constraints. Version 2.9 – Y. Lei, D.

R. Kuhn and R. Kacker

2. LaTeXML37: LaTeX to XML converter. Version 

0.8.0 – B. Miller

3. OOF238: Finite element modeling of material microstructures. Version 2.1.8 – S. Langer

4. PHAML39: Parallel Hierarchical Adaptive MultiLevel finite element program for the solution of 

elliptic partial differential equations. Versions

1.12.0, 1.12.1 and 1.13.0 – W. Mitchell.

5. Tcl/Tk40: Extensible scripting language and GUI 

toolkit. Versions 8.4.20, 8.5.13, 8.5.14, 8.5.15, 

8.6.0, 8.6.1 – D. Porter

6. Itcl: C++ inspired Object Oriented commands for 

Tcl. Version 4.0.0 – D. G. Porter.

7. Thread: Thread management commands for Tcl.

Version 2.7.0 – D. G. Porter.

8. TDBC. Database connection commands for Tcl.

Version 1.0.0 – D. G. Porter.

Conferences, Minisymposia, 

Lecture Series, Courses

MCSD Seminar Series

B. Cloteaux served as Chair of the ACMD Seminar 

Series. There were 23 talks presented during this period.

1. W. Morris (George Mason University), “Clique 

Number and Chromatic Number of Graphs Defined by Convex Geometries,” October 18, 2012. 

2. J. Ray (Sandia National Laboratories, Livermore), 

“Generating Conditional Realizations of Graphs 

and Fields Using Markov Chain Monte Carlo,”

November 5, 2012.

3. K. Hickmann (Tulane University), “Inverse Problems for Material Characterization Using 

Thermoacoustic Imaging,” November 16, 2012. 

 

35 http://math.nist.gov/scimark/

36http://csrc.nist.gov/groups/SNS/acts/documents/comparisonreport.html#acts

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

38 http://www.ctcms.nist.gov/oof/

39 http://math.nist.gov/phaml/

40 http://sourceforge.net/projects/tcl/files/Tcl/8.6.1/
Summary of Activities for Fiscal Year 2013 113

4. Z. Gimbutas (New York University), “Robust 

High Order Integral Equation Solvers for Electromagnetic Scattering in Complex Geometries,” 

November 29, 2012.

5. A. Carasso (ACMD), “Hazardous Continuation 

Backward in Time in Nonlinear Parabolic Equations, and an Experiment in Deblurring 

Nonlinearly Blurred Imagery,” December 4, 2012.

6. A. Streib (ACMD), “Mixing Times of SelfOrganizing Lists and Biased Permutations,” December 12, 2012.

7. N. Streib (ACMD), “Dimension and Height for 

Posets with Planar Cover Graphs,” January 22, 

2013.

8. E. Moseman (ACMD), “The Edge of Graphicality,” February 5, 2013.

9. A. Draganescu (University of Maryland Baltimore 

County), “Multigrid Preconditioners for Linear 

Systems Arising in PDE Constrained Optimization,” March 5, 2013. 

10. D. Cranston (Virginia Commonwealth University), 

“The Game of Revolutionaries and Spies on a 

Graph,” March 12, 2013.

11. Y. Wan (University of North Texas), “Decisionmaking in Large-scale Dynamical Networks: 

Modeling, Evaluation, Estimation and Control,” 

April 4, 2013.

12. A. Gueye (ACMD), “A Game Theoretic Framework for Evaluating Resilience of Networks 

against Attacks,” April 16, 2013.

13. J. Chen (University of Maryland Baltimore County), “A Visualization Language,” May 14, 2013.

14. G. Chen (Georgia State University), “Reed-Frost 

Transition on Dense Graphs,” May 22, 2013.

15. S. Colbert-Kelly (ACMD), “Analysis of a Ginzburg-Landau Type Energy Model for Smectic-C* 

Liquid Crystal with Defects,” May 28, 2013. 

16. Y. Zhao (George Mason University), “On Consistency of Community Detection in Networks,”

June 2, 2013. 

17. S. Wang (University of Houston), “Advanced Materials, Manufacturing and Design Integration for 

Large Offshore Wind Turbine Blades,” June 12, 

2013. 

18. T. Kolda (Sandia National Laboratories, Livermore), “An Adaptive Power Method for the 

Generalized Tensor Eigenproblem,” June 26, 

2013.

19. S. Sarkar (Indian Statistical Institute), “Cryptanalysis of RSA Variants and Implicit Factorization,”

August 20, 2013.

20. M. Mascagni (Florida State University), “Monte 

Carlo Methods and Partial Differential Equations: 

Algorithms and Implications for HighPerformance Computing,” August 27, 2013.

21. L. Getoor (University of Maryland), “Entity-based 

Data Science,” September 5, 2013.

22. M. Heroux (Sandia National Laboratories), 

“Building the Next Generation of Parallel and Resilient Applications and Libraries,” September 16, 

2013.

23. J. Torres-Jimenez (CINVESTAV, Mexico), “A 

Post-Processing Algorithm Applied to Reduce the 

Size of the Covering Arrays from the NIST Repository,” September 19, 2013.

Courses/Shortcourses Taught

1. J. T. Fong, “Finite Element Method-based Model 

Simulation of Piezoelectric and Electromagnetic 

Phenomena,” Applied Chemical and Materials Division, NIST, Boulder, CO, Feb. 25, 2013.

2. J. T. Fong, “An Introduction to Finite Element 

Method-based Model Simulation of Piezoelectric 

and Electromagnetic Phenomena,” Department of 

Civil and Environmental Engineering, University 

of South Carolina, May 17, 2013.

3. J. T. Fong, “Uncertainty Quantification for Improving Engineering Reliability,” Composites 

Design Workshop, Department of Aeronautics and 

Astronautics, Stanford University, July 18, 2013.

4. J. T. Fong, “Introduction to FEM-COMSOL, and 

its SM, AC/DC, and MEMS Modules,” Electromagnetics Division, NIST, Boulder, CO., August 

5-7, 2013.

5. F. Hunt, “Stochastic Processes,” Graduate Course,

Howard University, academic year 2012-2013.

Conference Organization

1. T. J. Burns, Mentor, Mathematical Modeling in 

Industry XVII – a Workshop for Graduate Students, Institute for Mathematics and Its

Applications, Minneapolis, MN, August 7-16, 

2013.

2. H. S. Cohl, Member, Scientific Organizing Committee, 13th International Symposium on 

Orthogonal Polynomials, Special Functions, and 

Applications (OPSFA-13), SIAM Special Interest 
114 NIST Applied and Computational Mathematics Division

Group on Orthogonal Polynomials and Special 

Functions, Gaithersburg, MD, 2015.

3. G. Doğan, Co-organizer, Minisymposium on Advances in Computer Algorithms for Imaging 

Science, SIAM Conference on Computational Science and Engineering, Boston, MA, February 25 –

March 1, 2013.

4. M. Donahue, Co-organizer Micromagnetics I Session, MMM/Intermag, Chicago, IL, January 2013.

5. W. Griffin, Publicity Chair, ACM SIGGRAPH 

Symposium on Interactive 3D Graphics and 

Games, Lake Buena Vista, FL, 2013. 

6. Wesley Griffin, Publicity Chair, ACM 

SIGGRAPH Symposium on Interactive 3D 

Graphics and Games, San Francisco, CA, 2014. 

7. R. N. Kacker, Co-organizer and Member, Program 

Committee, Second International Workshop on 

Combinatorial Testing (IWCT 2013), Luxembourg, March 2013.

8. R. N. Kacker, Co-organizer, First Asian Workshop 

on Combinatorial Testing for Complex Computer 

Systems (AWCTCCS 2013), National University 

of Singapore, July 2013.

9. A. Kearsley, Member, International Organizing 

Committee, 3rd IEEE International Conference on 

Instrumentation Control and Automation, Ungasan, Indonesia, 2013.

10. P. Kuo, Member, Program Committee, CLEO S&I 

4: Nonlinear Optical Technologies, Conference on 

Lasers and Electro-Optics (CLEO), San Jose, CA,

June 9-14, 2013.

11. D. Lozier, Co-Chair, 13th International Symposium 

on Orthogonal Polynomials, Special Functions, 

and Applications (OPSFA-13), SIAM Special Interest Group on Orthogonal Polynomials and 

Special Functions, Gaithersburg, MD, 2015.

12. V. Marbukh, Co-organizer, Bell Labs-NIST Workshop on Large-Scale Networks, Alcatel-Lucent 

Bell Labs, Murray Hill, NJ, October 25, 2013.

13. B. R. Miller, Member, Program Committee, Conferences on Intelligent Computer Mathematics, 

Coimbra, Portugal, July 7-11, 2014.

14. W. Mitchell, Member, Scientific Committee, International Conference of Numerical Analysis and 

Applied Mathematics (ICNAAM), Rhodes, 

Greece, September 21-27, 2013.

15. Y. Parker and J. Terrill, Co-organizers, NIST 

booth, SC12, the 2012 International Conference 

for High Performance Computing, Networking, 

Storage and Analysis, Salt Lake City, Utah, November 13-19, 2012. 

16. Y. Parker and J. Terrill, Co-organizers, NIST 

booth, SC13, the 2013 International Conference 

for High Performance Computing, Networking, 

Storage and Analysis, Denver, CO, November 17-

21, 2013.

17. F. A. Potra, Stream Organizer, Nonlinear Optimization, XXVI EURO-INFORMS 26th European 

Conference on Operations Research, Rome, Italy,

July 1-4, 2013.

18. S. Ressler, Tutorial Chair, Web3D’13: 18th International Conference on 3D Web Technology, San 

Sebastian, Spain, June 20-22, 2013. 

19. S. Ressler, Host and Co-organizer, Web3D Tech 

Talk Session, 40th International Conference on 

Computer Graphics and Interactive Techniques, 

Anaheim CA, July 21-25, 2013.

20. K. Sayrafian, Member, Technical Program Committee, 7th International Symposium on Medical 

Information and Communication Technology 

(ISMICT 2013), Tokyo, Japan, March 6-8, 2013.

21. K. Sayrafian, Member, Technical Program Committee, 2013 IEEE International Conference on 

Internet of Things (iThings 2013), Beijing, China, 

August 20-23, 2013.

22. K. Sayrafian, Member, Technical Program Committee, 8th International Symposium on Medical 

Information and Communication Technology 

(ISMICT 2014), Florence, Italy, April 2-4, 2014.

23. K. Sayrafian, Member, Technical Program Committee, Symposium on Sensing, Propagation, and 

Wireless Networks for Healthcare Applications,

IEEE International Conference on Intelligent Sensors, Sensor Networks and Information Processing 

(ISSNIP), Singapore, April 21-24, 2014.

24. K. Sayrafian, Member, Technical Program Committee, Seventh International Conference on 

Sensor Technologies and Applications 

(SENSORCOMM 2013), Barcelona, Spain, August 25 - 31, 2013.

25. X. Tang, Member, Program Committee, SPIE 

Conference 8875: Quantum Communications and 

Quantum Imaging XI, SPIE Optics and Photonics, 

Prague, Czech Republic, 2013.
Summary of Activities for Fiscal Year 2013 115

Other Professional Activities 

Internal

1. I. Beichl, ITL Director, Summer Undergraduate 

Research Fellowship (SURF) Program.

2. R. Boisvert, NIST Scientific Computing Steering 

Group.

3. R. Boisvert, ITL Diversity Committee.

4. S. Glancy, NIST Boulder SURF Committee.

5. S. Glancy, ITL Diversity Committee.

6. W. Mitchell, ITL Awards Committee.

7. S. Ressler, NIST Lobby Display Advisory Council.

External 

Editorial

1. I. Beichl, Editor-in-Chief, Computing in Science & 

Engineering.

2. R. Boisvert, Associate Editor, ACM Transactions 

on Mathematical Software. 

3. R. Boisvert, Editor, Numerical Analysis, Mathematical Software and Computational Engineering, 

Finance and Science areas, Computing Research 

Repository (CoRR) preprint service.41

4. A. Dienstfrey, Associate Editor, International 

Journal of Uncertainty Quantification.

5. Z. Gimbutas, Member, Editorial Board, Advances 

in Computational Mathematics.

6. A. Kearsley, Member, Editorial Board, ISRN 

Journal on Applied Mathematics.

7. D. Lozier, Associate Editor, Journal of Numerical 

Analysis, Industrial and Applied Mathematics.

8. W. Mitchell, Associate Editor, Journal of Numerical Analysis, Industrial and Applied Mathematics.

9. D. P. O’Leary, Editor-in-Chief, SIAM Journal on 

Matrix Analysis and Applications.

10. D. P. O’Leary, Member, Editorial Board, Education Section, SIAM Review.

11. D. P. O’Leary, Member, Editorial Board, SIAM 

Books.

 

41 http://www.arXiv.org/

12. D. P. O’Leary, Department Editor, Your Homework Assignment, Computing in Science & 

Engineering.

13. D. P. O'Leary, Member, Editorial Board, Computing in Science & Engineering.

14. F. Potra, Regional Editor for the Americas, Optimization Methods and Software.

15. F. Potra, Associate Editor, Journal of Optimization 

Theory and Applications.

16. F. Potra, Associate Editor, Numerical Functional 

Analysis and Optimization.

17. F. Potra, Associate Editor, Optimization and Engineering.

18. R. Pozo, Associate Editor, ACM Transactions on 

Mathematical Software. 

19. B. Saunders, Webmaster, SIAM Activity Group on 

Orthogonal Polynomials and Special Functions.

20. B. Saunders, OP-SF Talk listserv Moderator,

SIAM Activity Group on Orthogonal Polynomials 

and Special Functions.

21. K. Sayrafian, Associate Editor, International 

Journal on Wireless Information Networks.

Boards and Committees

1. I. Beichl, Member, Magazine Operations Committee, IEEE Computer Society.

2. R. Bohn, Member, Cloud Computing Scoping 

Subcommittee, President’s National Security Telecommunications Advisory Committee (NSTAC).

3. R. Bohn. Co-chair, Faster Administration of Science and Technology Education and Research 

(FASTER) Community of Practice, Networking 

and Information Technology R&D (NITRD) Program.

4. R. Boisvert, Member, International Federation for 

Information Processing’s (IFIP) Working Group 

2.5 (Numerical Software).

5. R. Boisvert, Co-chair, Publication Board, Association for Computing Machinery (ACM).

6. R. Boisvert, Member, Program Review Committee, Center for Computing Sciences, Institute for 

Defense Analysis.

7. R. Boisvert, Member, External Review Committee, Computer Science Department, George 

Washington University.

8. R. Boisvert, Member, Subcommittee on the Materials Genome Initiative, Committee on 
116 NIST Applied and Computational Mathematics Division

Technology, National Science and Technology 

Council.

9. A. Dienstfrey, Member, International Federation 

for Information Processing’s (IFIP) Working 

Group 2.5 (Numerical Software).

10. W. George, Member, User Advisory Council, Argonne Leadership Computing Facility.

11. E. Knill, Member, Technical Advisory Panel, 

Quantum Computer Science Program, IARPA.

12. D. Lozier, Member, Steering Committee, Painlevé 

Project.

13. D. P. O’Leary, Member, Oversight Committee, 

Gene Golub SIAM Summer Schools.

14. D. P. O’Leary, Member, Advisory Committee, 

SIAM Linear Algebra Activity Group International Summer School on Numerical Linear Algebra.

15. V. Marbukh, Member, Network Complexity Research Group, Internet Research Task Force 

(IRTF).

16. G. B. McFadden, Member, Selection Committee, 

SIAM Kleinman Prize.

17. B. Miller, Member, Math Working Group, World 

Wide Web Consortium.

18. D. Porter, Release Manager, Tcl Core Team.

19. S. Ressler, Member, Declarative 3D for the Web 

Architecture Community Group42.

20. S. Ressler, Member, Web3D Consortium.

21. B. Saunders, Member, MAA Committee on Business, Industry and Government Mathematics.

22. B. Saunders, Member, Advisory Group for NSF 

CoSMIC Scholars Program, Towson University. 

23. B. Saunders, Member, National Selection Committee Review Panel, 2013 Presidential Awards for 

Excellence in Mathematics and Science Teaching 

(PAEMST), National Science Foundation.

24. K. Sayrafian, Member, IEEE 802.15 Working

Group on Wireless Personal Area Networks.

25. K. Sayrafian, Member, COST-IC1004, Action on

Cooperative Radio Communications for Green 

Smart Environments, Body Area Networking

Group.

26. K. Sayrafian, Member, External Advisory Committee, Quantum Medical Device Interoperability

Project (NIH funded), Medical Device “Plug-andPlay” Interoperability Program (MD PnP), Massachusetts General Hospital.

 

42 http://www.w3.org/community/declarative3d/

27. K. Sayrafian, Member, Wireless Medical Technologies Working Group, National Institute for 

Biomedical Imaging and Bioengineering 

(NIBIB/NIH).

28. J. Terrill, Member, High End Computing Research 

and Development and Infrastructure Interagency 

Working Groups, Networking and Information 

Technology R&D (NITRD) Program.

Thesis Direction

1. B. K. Alpert, Member, Ph.D. Thesis Committee,

Ryan Lewis, Applied Mathematics, University of 

Colorado, Boulder. Title: Nonlinear Approximations in Filter Design and Wave Propagation. 

Completed April 9, 2013.

2. Z. Gimbutas, Member, Ph.D. Thesis Committee, 

Sija Hao, Applied Mathematics, University of 

Colorado, Boulder. Title: Numerical Methods for 

Solving Linear Elliptic PDEs: Direct Solvers and 

High Order Accurate Discretization. Completed 

2013.

3. E. Knill, Ph.D. Thesis Adviser, Adam Meier, 

Physics, University of Colorado, Boulder. Title: 

Randomized Benchmarking of Clifford Operators. 

Completed April 19, 2013.

4. E. Knill, Ph.D. Thesis Adviser, Michael Mullan, 

Physics, University of Colorado, Boulder. Title: 

Quantum Algorithms for Atomic Clocks. Completed 

May 17, 2013.

5. E. Knill, Ph.D. Thesis Adviser, Yanbao Zhang, 

Physics, University of Colorado, Boulder. Title: 

Analysis of Tests of Local Realism. Completed 

August 20, 2013.

6. G.B. McFadden, Member, Ph.D. Thesis Committee, Augustin Luna, Biology, Boston University.

Title: Formalization of Molecular Interaction 

Maps in Systems Biology; Application to Simulations of the Relationship between DNA Damage 

Response and Circadian Rhythms. Completed July 

23, 2013.

7. B. Miller, Member, Ph.D. Thesis Committee, 

Deyan Ginev, Computer Science, Jacobs University Bremen. Title: Designing Definition Discovery; 

Read, Recognize, Reflect, Repeat. In process.

8. B. Miller, Member, Ph.D. Thesis Committee, Qun 

Zhang, Computer Science, George Washington 

University. Title: Semantics-Sensitive MathSimilarity Search. In process.

9. K. Sayrafian, Member, Ph.D. Thesis Committee,

Ruijun Fu, Ye, Electrical and Computer Engineering, Worcester Polytechnic Institute. Title: 
Summary of Activities for Fiscal Year 2013 117

Empirical RF Propagation Modeling of Human 

Body Motions for Activity Classification. Completed November 28, 2012.

10. K. Sayrafian, Member, Ph.D. Thesis Committee,

Yunxing Ye, Electrical and Computer Engineering, Worcester Polytechnic Institute. Title: 

Comparative Performance Evaluation of RSS and 

TOA based Localization for Video Capsule Endoscopy inside the GI Tract. Completed May 24, 

2013.

Grants Awarded

ACMD awards a small amount of funding through the 

NIST Measurement Science Grants Program for projects that make direct contributions to its research 

programs. Often such grants support direct cooperation 

between an external awardee and ACMD. This year the 

following new cooperative agreements were initiated.

1. Society for Industrial and Applied Mathematics 

(SIAM): 13th International Symposium on Orthogonal Polynomials, Special Functions and 

Applications, $29,998 (1 year). PI: Dr. James 

Crowley.

2. Theiss Research: Advanced Computational Tools 

for Shape Measurement and Analysis, $402,830 (3 

years). PI: Dr. Gunay Doğan.

3. University of Maryland Baltimore County: Interactive Measurement and Visualization for 

Heterogeneous Data Exploration in Immersive 

Virtual Environments, $438,613 (5 years). PI: 

Prof. Jian Chen.

4. University of Maryland: A Science-Based Approach to Security of Complex Systems, $485,859

(3 years). PIs: Prof. Richard La, Dr. Assane 

Gueye.

5. Washington University (St. Louis): Four-Wave 

Mixing in On-Chip High-Q Whispering Gallery 

Mode Resonators for Information Technology,

$194,510 (3 years). PI: Prof. Lan Yang.

External Contacts

ACMD staff members make contact with a wide variety of organizations in the course of their work. 

Examples of these follow.

Industrial Labs

Alcatel Lucent Bell Laboratories

ActiveState

ADVR, Inc.

Cadence

CD-adapco

Feeling Structures (Brazil)

GE Healthcare

Gener8

Gulfstream Aerospace Corporation

IBM Research

KnowledgeVis, Inc.

Lepton Technology

Lockheed Martin

Mentor Graphics

Microsoft

MusixMatch

Robert Bosch GmbH (Germany)

Setterholm Consultant

Government/Non-profit Organizations

Argonne National Laboratory

Air Force Office of Scientific Research

Army Research Laboratory

Association for Computing Machinery 

Center for Integration of Medicine and Innovative 

Technology ‒ CIMIT

Centro Nacional de Metrologia (Mexico)

China Special Equipment Inspection and Research Institute (Beijing, China)

Electric Power Research Institute ‒ EPRI

European Telecommunications Standards Institute

Food and Drug Administration ‒ FDA

IDA Center for Computing Sciences

Indian Statistical Institute (India)

Institute of Physics and Chemistry of Materials (Strasbourg, France)

Intelligence Advanced Research Projects Agency ‒ 

IARPA

Kentucky Science and Engineering Foundation

Lawrence Livermore National Laboratory 

Leibniz Center for Informatics (Germany)

L’Istituto Nazionale di Ricerca Metrologica (Italy)

Los Alamos National Laboratory

Massachusetts General Hospital

National Security Agency ‒ NSA

NASA Goddard Space Flight Center

NASA Ind. Verification and Validation Facility

National Center for Atmospheric Research

National Cancer Institute

National Institutes of Health ‒ NIH

National Institute of Biomedical Imaging and Bioengineering ‒ NIBIB

National Institute of Information and Communications 

Technology ‒ NICT

National Oceanographic and Atmospheric Administration ‒ NOAA

National Physical Laboratory (UK)

National Polytechnic Institute (Mexico)

National Renewable Energy Laboratory

National Science Foundation ‒ NSF

Nuclear Regulatory Commission
118 NIST Applied and Computational Mathematics Division

Oak Ridge National Laboratory

Pacific Northwest National Laboratory

Quantum Chemistry Research Institute (Kyoto, Japan)

Sandia National Laboratories

SINTEF (Norway)

Society for Industrial and Applied Mathematics ‒ 

SIAM

Southwest Research Institute

Theiss Research

US Air Force Eglin Air Force Base

US Department of Defense

US Department of Energy

Web3D Consortium 

WEAR (World Engineering Anthropometry Resource) 

World Wide Web Consortium 

Universities

Adam Mickiewicz University (Poland)

Bandung Institute of Technology (Indonesia)

Beijing Institute of Technology (China)

Boston University

California Institute of Technology

Carnegie Mellon University

China University of Petroleum (China)

City University of Hong Kong (China)

Concordia University (Canada)

Dalian University of Technology (China)

East China University of Science and Technology 

(China)

Ecole Polytechnique de Montreal (Canada)

Federal University of Rio Grande do Norte (Brazil)

Federal University of Ceará (Brazil)

Friedrich-Alexander Universitat (Germany)

George Mason University

George Washington University

Georgetown University

Ghent University (Belgium)

Humboldt University of Berlin (Germany)

Imperial College (London)

Indiana University

Iowa State University

Jacobs University Bremen (Germany)

Johns Hopkins University Applied Physics Lab

Institut Supérieur d’Informatique de Modélisation et de 

leurs Applications ‒ ISIMA (France)

National University of Singapore (Singapore)

Nanjing University of Technology (China)

Nanyang University (Singapore)

New York University

Ningbo University (China)

Northwestern University

Oklahoma State University

Oregon State University

Oslo University (Norway)

Rice University

Royal Institute of Technology (Sweden)

Shandong University (China)

Shanghai University (China)

Shippensburg University

Stanford University

Technical University of Denmark (Denmark)

Technion Israel Institute of Technology (Israel)

The College of William and Mary

Towson University

Tsinghua University (China)

Tulane University

University of Antwerp (Belgium)

University of Belgrade (Serbia)

University of Bergamo (Italy)

University of British Columbia (Canada)

University of California at Berkeley

University of California at Irvine

University of California San Diego

University of Campinas (Brazil)

University of Cantabria (Spain)

University of Central Florida

University of Colorado

University of Glasgow

University of Hong Kong (China)

University of Illinois at Urbana-Champaign

University of Kaiserslautern (Germany)

University of Maryland College Park

University of Maryland Baltimore County

University of Melbourne (Australia)

University of Miami

University of Michigan

University of Minnesota

University of Minnesota-Duluth

University of Montana

University of Montreal (Canada)

University of Nottingham (UK)

University of Oulu (Finland)

University of South Carolina

University of Technology Sydney (Australia)

University of Texas at Arlington

University of Texas at Austin

University of Texas El Paso

University of Texas Pan American

University of Tokyo (Japan)

University of Vienna (Austria)

University of Western Ontario (Canada)

University of Zagreb (Croatia)

Virginia Polytechnic Institute and State University

Washington University

Worcester Polytechnic Institute

Yale University

Yokohama National University (Japan)
Summary of Activities for Fiscal Year 2013 119

Part V: Appendix

 Part V

Appendix
120 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2013 121

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 special appointments. The following list reflects all 

appointments held during any portion of the reporting period (October 2012 – December 2013). For students and interns, see Table 2, page 11. (*) Denotes staff at NIST Boulder.

Division Staff

Ronald Boisvert, Chief, Ph.D. (Computer Science), Purdue University, 1979

Catherine Graham, 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

*Andrew Dienstfrey, Ph.D. (Mathematics), New York University, 1998

Jeffrey Fong, Ph. D. (Applied Mechanics and Mathematics), Stanford University, 1966

*Zydrunas Gimbutas, Ph.D. (Applied Mathematics), Yale University, 1999

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

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

Sean Colbert-Kelly, Ph.D. (Mathematics), Purdue University, 2012

Michael Cromer, Ph.D. (Applied Mathematics), University of Delaware, 2011

NIST-ARRA Postdoctoral Fellows

Asha Nurse, Ph.D. (Mechanical Engineering), Brown University, 2011

Ismet Sahin, Ph.D. (Electrical and Computer Engineering), University of Pittsburgh, 2006

 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

Michael Mascagni, Ph.D. / Florida State University

Florian Potra, Ph.D. / University of Maryland Baltimore County

Guest Researchers (Name, Degree / Home Institution)

Mirit Aladjem, Ph.D. / National Institutes of Health

James Benson, Ph.D. / Northern Illinois University

David Cotrell, Ph.D. / CD-Adapco

*John Gary, Ph.D. / NIST (retired)

David Gilsinn, Ph.D. / NIST (retired)

*Daniel Kaslovsky, Ph.D. / University of Colorado

Yu (Jeff) Lei, Ph.D. / University of Texas at Arlington
122 NIST Applied and Computational Mathematics Division

P. Aaron Lott, Ph.D. / Lawrence Livermore National Laboratory

Itzel Dominquez Mendoza / Centro Nacional de Metrología, Mexico

Bruce Murray, Ph.D. / SUNY Binghamton

Santanu Sarkar, Ph.D. / Indian Statistical Institute

Christoph Witzgall, Ph.D., NIST Scientist Emeritus

Mathematical Software Group

Michael Donahue, Leader Ph.D. (Mathematics), Ohio State University, 1991

Javier Bernal, Ph.D. (Mathematics), Catholic University, 1980

Stephen Langer, Ph.D. (Physics), Cornell University, 1989

Daniel Lozier, Ph.D. (Applied Mathematics), University of Maryland, 1979 

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

Howard Cohl, Ph.D. (Mathematics), University of Auckland, 2010

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

Contractors (Name, Degree / Home Institution)

Qiming Wang / Dakota Consulting

Guest Researchers (Name, Degree / Home Institution)

Gunay Dogan, Ph.D. / Theiss Research

Adri Olde Daalhuis, Ph.D. / University of Edinburgh

Tamara Kolda, Ph.D. / Sandia Laboratories, Livermore

Computing and Communications Theory Group

Ronald Boisvert, Acting Leader

 Isabel Beichl, Project Leader, 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

Stephen Jordan, Ph.D. (Physics), Massachusetts Institute of Technology, 2008

 *Emanuel Knill, NIST Fellow, Ph.D. (Mathematics), University of Colorado at Boulder, 1991

Paulina Kuo, Ph.D. (Physics), Stanford University, 2008

 Yi-Kai Liu, Ph.D. (Computer Science), University of California, San Diego, 2007

 Vladimir Marbukh, Ph.D. (Mathematics) Leningrad Polytechnic University, 1986

Oliver Slattery, M.S. (Electrical Engineering), Johns Hopkins University, 2008

Kamran Sayrafian-Pour, Ph.D. (Electrical and Computer Engineering), University of Maryland, 1999

Xiao Tang, Project Leader, Ph.D (Physics), Chinese Academy of Sciences, 1985

NRC Postdoctoral Associates

Yvonne Kemper, Ph.D. (Mathematics), University of California at Davis, 2013

Elizabeth Moseman, Ph.D. (Mathematics), Dartmouth College, 2007

James Shook, Ph.D. (Mathematics), University of Mississippi, 2010
Summary of Activities for Fiscal Year 2013 123

Amanda Streib, Ph.D. (Mathematics), Georgia Institute of Technology, 2012

Noah Streib, Ph.D. (Mathematics), Georgia Institute of Technology, 2012

NIST-ARRA Postdoctoral Fellows

Assane Gueye, Ph.D. (Computer Science), University of California, Berkeley, 2011

Contractors (Name, Degree / Home Institution)

Alan Mink, Ph.D. / Wagner Consulting

Faculty Appointees (Name, Degree / Home Institution)

James Lawrence, Ph.D. / George Mason University

Guest Researchers (Name, Degree / Home Institution)

*Bryan Eastin, PhD. / Northrup Grumman

Yong-Su Kim, Ph.D. / Pohang University of Science and Technology

Richard La, Ph.D. / University of Maryland

Francis Sullivan, Ph.D. / IDA Center for Computing Sciences

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

Wesley Griffin, M.S. (Computer Science), University of Maryland Baltimore County, 2010

John Hagedorn, M.S. (Mathematics), Rutgers University, 1980

*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 (Name, Degree / Home Institution)

Marc Olano, Ph.D. / University of Maryland Baltimore County
124 NIST Applied and Computational Mathematics Division

Glossary of Acronyms

2D two-dimensional

3D three-dimensional

ACM Association for Computing Machinery

ACMD NIST/ITL Applied and Computational Mathematics Division

ACTS Advanced Combinatorial Testing System

AIP American Institute of Physics

AMS American Mathematical Society

ARRA American Recovery and Reinvestment Act

arXiv preprint archive housed at Cornell University (http://arxiv.org/)

ASCE American Society of Civil Engineers

ASTM ASTM International, formerly known as the American Society for Testing and Materials

BAN body area network

BMP Bateman Manuscript Project

Caltech California Institute of Technology

CCS IDA Center for Computing Sciences

CHiMaD Center for Hierarchical Materials Design

CI configuration interaction

CNRS Centre National de la Recherche Scientifique (France)

CNST NIST Center for Nanoscale Science and Technology

CODATA Committee on Data for Science and Technology

CPA cryoprotective agent

CPU central processing unit

CT combinatorial testing

CT computed tomography

CY calendar year

DARPA DOD Defense Advanced Research Projects Agency

DFT discrete Fourier transform

DLMF Digital Library of Mathematical Functions

DMI Dzyaloshinskii-Moriya interaction

DNA deoxyribonucleic acid

DOD U.S. Department of Defense

DOE U.S. Department of Energy

DOM Document Object Model

DPD dissipative particle dynamics

DRMF digital repository of mathematical functions

EC error correction

ECG electrocardiogram

EL NIST Engineering Laboratory

ESPCI École Supérieure de Physique et Chimie Industrielles de la Ville de Paris (France)

ETSI European Telecommunications Standards Institute

FASTER Faster Administration of Science and Technology Education and Research

FDA Food and Drug Administration

FEM finite element method

FFT fast Fourier transform

FPGA field-programmable gate array

FY fiscal year

F90gl Fortran 90 interface to OpenGL graphics standard

GAC Geodesic Active Contour

GAMS Guide to Available Mathematical Software

GPU graphics processing units

GUI graphical user interface

HTML hypertext markup language

HVAC heating, ventilation and air conditioning

HVACSIM+ simulation testbed for HVAC systems
Summary of Activities for Fiscal Year 2013 125

Hy-CI Hylleraas-Configuration Interaction technique

IARPA Intelligence Advanced Research Projects Agency

IDA Institute for Defense Analysis

IEEE Institute of Electronics and Electrical Engineers

IFIP International Federation for Information Processing

IMA Institute for Mathematics and Its Applications

IMS Innovations in Measurement Science

INCITE Innovative and Novel Computational Impact on Theory and Experiment (DOE Program)

IP Internet Protocol

IPSEC secure IP

IRTF Internet Research Task Force

ISGG International Society for Grid Generation

ISIMA Institut Supérieur d’Informatique, de Modélisation et de leurs Applications (France)

ISO International Organization for Standardization

IT information technology

ITL NIST Information Technology Laboratory

JILA joint NIST-University of Colorado physics research institute

JAMA Java Matrix package (software)

KLS Koekoek, Lesky and Swarttouw

LaTeX a math-oriented text processing system

LaTeXML LaTeX to MathML translator

LDPC low density parity check

LR local realism

MAA Mathematical Association of America

MALDI/TOF matrix-assisted laser desorption/ionization time-of-flight 

MathML Mathematical Markup Language (W3C standard)

MEMS micro-electro-mechanical system

MGI Materials Genome Initiative

MIT Massachusetts Institute of Technology

MKM mathematical knowledge management

MML NIST Material Measurement Laboratory

MPI Message Passing Interface

MRAM magneto-resistive random access memory

MRI magnetic resonance imaging

MSN mobile sensor network

muMAG Micromagnetic Activity Group

NASA National Aeronautics and Space Administration

NBS National Bureau of Standards

NCAR National Center for Atmospheric Research

NDE non-destructive evaluation

Ngraph Network Graph (software)

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

NMR nuclear magnetic resonance

NPSC National Physical Science Consortium

NRC National Research Council

NSF National Science Foundation

NYU New York University

OECD Organization for Economic Cooperation and Development

OOF Object-Oriented Finite Elements (software)

OOMMF Object-Oriented Micromagnetic Modeling Framework (software)

PDE partial differential equation

PHAML Parallel Hierarchical Adaptive Multi Level (software)

PIV personal identity verification
126 NIST Applied and Computational Mathematics Division

PML NIST Physical Measurement Laboratory

PREP Professional Research Experience Program

QDPD quarternion-based dissipative particle dynamics

QIS quantum information science

QKD quantum key distribution

R&D research and development

RF radio frequency

SBIR Small Business Innovative Research

SCO NIST Standards Coordination Office

SDE stochastic differential equation

SFI Santa Fe Institute

SHIP NIST Summer High School Internship Program

SIAM Society for Industrial and Applied Mathematics

SIGGRAPH ACM Special Interest Group on Graphics

SPIE International Society for Optical Engineering

SRM standard reference material

SUNY State University of New York

SURF Student Undergraduate Research Fellowship

SVG scalable vector graphics

TES transition edge sensor

TLS transport-layer security

TNT Template Numerical Toolkit (software)

TV total variation

UK United Kingdom

UMBC University of Maryland Baltimore County

UQ uncertainty quantification

VRML virtual reality modeling language

W3C World Wide Web Consortium

WebGL Web-based Graphics Library

X3D Extensible 3D

X3DOM an open-source framework for integrating X3D and HTML5

XML Extensible Markup Language