NISTIR 7931

http://dx.doi.org/10.6028/NIST.IR.7931

Applied and Computational

Mathematics Division

Summary of Activities for Fiscal Year 2012

 

NISTIR 7931

Applied and Computational

Mathematics Division

Summary of Activities for Fiscal Year 2012

Ronald F. Boisvert, Editor

Applied and Computational Mathematics Division

Information Technology Laboratory

http://dx.doi.org/10.6028/NIST.IR.7931

April 2013

U.S. Department of Commerce 

Rebecca Blank, Acting Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director

Summary of Activities for Fiscal Year 2012 iii

Abstract

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

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

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

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

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

Division staff members have participated. The reporting period covered by this document is October 2011

through December 2012.

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: Snapshot from a simulation of a four-blade vane rheometer with a suspension of 

hard spheres. Each sphere is colored-coded by the rheometer octant in which it was located at the start of 

the simulation. The blades are rotating clockwise and have made approximately two full rotations at the 

time of this snapshot. For details, see page 28.

Acknowledgements: Thanks to Timothy Burns, Daniel Samarov, and Ginger White for their very careful 

reading of the manuscript.

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. 
iv NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2012 v

Contents

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

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

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

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

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

Administrative News............................................................................................................................................ 9

Recognition........................................................................................................................................................ 13

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

Quantum Algorithms for Quantum Field Theories .......................................................................................... 17

Micromagnetic Investigation of Periodic Cross-Tie/Vortex Wall Geometry.................................................. 19

Continuation Backward in Time in 2D Nonlinear Parabolic Equations, and an Experiment in Deblurring 

Nonlinearly Blurred Imagery.............................................................................................................................. 22

Metrics for Manipulation and Enhancement of Forensic Images ................................................................... 25

Rheology of Dense Suspensions........................................................................................................................... 28

Visualization and Modeling of RF Propagation in Body Area Networks ....................................................... 32

A Stochastic Theory of Fatigue for Aging Structures....................................................................................... 34

PART III: PROJECT SUMMARIES ............................................................................................................................... 37

Mathematics of Metrology .................................................................................................................................. 39

Continuation Backward in Time in 2D Nonlinear Parabolic Equations........................................................... 39

Micromagnetic Investigation of Periodic Cross-Tie/Vortex Wall Geometry..................................................... 39

Metrics for Manipulation and Enhancement of Forensic Images ..................................................................... 39

A Stochastic Theory of Fatigue for Aging Structures........................................................................................ 39

Molecular Movies: Imaging Femtosecond Motion during Electrochemical Transitions.................................. 39

Virtual Measurements in Quantum Chemistry .................................................................................................. 41

Bubble Motion and Size Variation during Thermal Migration with Phase Change.......................................... 41

On the Stability of Rotating Drops .................................................................................................................... 42

Moving Grain Boundary Groove Under Stress................................................................................................. 43

Measurement and Modeling of Plastic Flow Stress for High-Speed Machining Simulations........................... 44

Selecting an Appropriate Statistical Distribution for a Class of Engineering Material Property Data............ 45

A Bayesian Nondestructive Evaluation Approach to Estimating Remaining Life of Aging Structures ............. 46

Simulation of Bioregulatory Networks Involved in Cell Cycle Control............................................................. 47

Mathematical Optimization of Procedures for Cryoprotectant Equilibration .................................................. 48

Hurricane-Borne Missile Speeds....................................................................................................................... 48

Multi-Hazard Engineering Design .................................................................................................................... 49

Alternative Methods of Latent Fingerprint Enhancement and Metrics for Comparison ................................... 50
vi NIST Applied and Computational Mathematics Division

Shape Analysis...................................................................................................................................................52

A Standard Candle for Extragalactic Metrology ...............................................................................................52

Unfolding Optical Spectrum Measurements......................................................................................................53

High Performance Computing and Visualization..............................................................................................56

Rheology of Dense Suspensions.........................................................................................................................56

Visualization and Modeling of RF Propagation in Body Area Networks ..........................................................56

Modeling and Visualization of Cement Paste Hydration and Microstructure Development.............................56

Nano-structures, Nano-optics, and How to Control Exciton Fine Structure with Electric Fields.....................57

High Precision Calculations of Fundamental Properties of Few-Electron Atomic Systems.............................58

Determination of Computational Features to Quantitatively Characterize Stem Cell Colony Quality .............59

An Automated Method for Locating Phantom Nodules in Phantom CT Studies................................................59

Declarative 3D Graphics...................................................................................................................................61

Information Visualization for Cloud Computing ...............................................................................................62

Interactive Visualization and Analysis Tools for the National Vulnerability Database ....................................63

WebGL Enhancements for DLMF Visualization................................................................................................63

Scientific Software................................................................................................................................................64

OOF: Finite Element Analysis of Material Microstructures .............................................................................64

Micromagnetic Modeling...................................................................................................................................65

Parallel Adaptive Refinement and Multigrid Finite Element Methods..............................................................66

Digital Library of Mathematical Functions .......................................................................................................68

Digital Library of Mathematical Functions.......................................................................................................68

Mathematical Knowledge Management.............................................................................................................69

Visualization of Complex Function Data...........................................................................................................69

DLMF Standard Reference Tables on Demand .................................................................................................71

Special Function Expansions and Definite Integrals Associated with Fundamental Solutions of Linear Partial 

Differential Equations........................................................................................................................................72

Quantum Information..........................................................................................................................................75

Quantum Algorithms for Quantum Field Theories............................................................................................75

Quantum Computing Theory..............................................................................................................................75

Quantum Computing Benchmarks .....................................................................................................................76

Quantum State Estimation Theory and Applications.........................................................................................77

Quantum State Tomography using Compressed Sensing...................................................................................77

Cryptography Beyond Quantum Key Distribution.............................................................................................78

Post-Quantum Cryptography.............................................................................................................................78

Quantum and Classical Circuit Obfuscation with Braids..................................................................................79

Generating Random Bits from Entangled Quantum States................................................................................79

Quantum Communications.................................................................................................................................80

Low Density Parity Codes for Quantum Key Distribution.................................................................................81

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

A Game-theoretic Approach to the Security of Complex Systems......................................................................82

An Algebraic Formulation for the Analysis and Visualization of Network Graphs...........................................83
Summary of Activities for Fiscal Year 2012 vii

Threshold Digraphs........................................................................................................................................... 84

Random Generation of Digraphs ...................................................................................................................... 85

Topological Models of Power Grids ................................................................................................................. 86

Geometry of Networks....................................................................................................................................... 87

Broadcast and Spread of Information in Complex Networks............................................................................ 88

Security Risk Analysis of Enterprise Networks Using Attack Graphs............................................................... 89

Distributed Motion Control in Mobile Sensor Networks................................................................................... 90

Combinatorial Testing....................................................................................................................................... 91

Approximating the Ising Partition Function...................................................................................................... 92

Spectral Algorithms for Document Topic Modeling.......................................................................................... 93

PART IV: ACTIVITY DATA .................................................................................................................................... 95

Publications .......................................................................................................................................................... 97

Appeared ........................................................................................................................................................... 97

Refereed Journals....................................................................................................................................... 97

Journal of Research of NIST ..................................................................................................................... 99

Books............................................................................................................................................................ 99

Book Chapters ............................................................................................................................................ 99

Conference Proceedings............................................................................................................................. 99

Technical Magazine Articles.................................................................................................................... 102

Technical Reports..................................................................................................................................... 102

Accepted .......................................................................................................................................................... 102

In Review ........................................................................................................................................................ 103

Presentations ...................................................................................................................................................... 104

Invited Talks ................................................................................................................................................... 104

Conference Presentations............................................................................................................................... 108

Web Services....................................................................................................................................................... 110

Software Released .............................................................................................................................................. 110

Conferences, Minisymposia, Lecture Series, Courses..................................................................................... 111

MCSD Seminar Series.................................................................................................................................... 111

Conference Committees.................................................................................................................................. 112

Other ............................................................................................................................................................... 113

Other Professional Activities............................................................................................................................. 113

Internal ........................................................................................................................................................... 113

External .......................................................................................................................................................... 113

Grants Awarded................................................................................................................................................. 114

External Contacts............................................................................................................................................... 115

PART V: APPENDIX .................................................................................................................................................. 117

Staff ..................................................................................................................................................................... 118

Glossary of Acronyms........................................................................................................................................ 121
viii NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2012 1

Part I: Overview

 Part I

Overview
2 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2012 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, Acting 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 Bechl 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 seven thematic areas; these are described in the sidebar. Six of these are represented by project descriptions in Section III of this document. The seventh, 

Virtual Measurements, is a cross-cutting program whose work is found under the Mathematics of Metrology, High Performance Computing and Visualization, and Scientific Software project descriptions. 

Projects that contribute to this crosscut note this fact in their descriptions in Section III.
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 the resulting data into useful information. The goal of this work is 

to develop fundamental mathematical methods and analytical tools necessary for NIST to continue as a worldclass metrology institute, and to apply them to critical 

measurement science applications. 

High Performance Computing and Visualization.

Computational capability is advancing rapidly. This means 

that modeling and simulation can be done with greatly 

increased fidelity (e.g., higher resolution, more complex 

physics). However, developing large-scale parallel applications remains highly challenging, requiring expertise that 

application scientists rarely have. In addition, the hardware landscape is changing rapidly, so new algorithmic 

techniques must constantly be developed. We are developing and applying facilities and expertise of this type for 

application to NIST problems. Large scale computations 

and laboratory experiments invariably produce large volumes of scientific data, which cannot be readily 

comprehended without some form of visual analysis. We 

are developing the infrastructure necessary for advanced 

visualization of scientific data, including the use of 3D 

immersive environments and applying this to NIST problems. One of our goals is to develop the 3D immersive 

environment into a true interactive measurement laboratory.

Virtual Measurements. A virtual measurement is a quantitative result and its associated uncertainty, obtained by a 

computer simulation or computer-assisted measurements. We seek to develop metrology constructs, 

standard references, uncertainty characterization, and 

traceability into scientific computation and computerassisted measurements to enable predictive computing 

with quantified reliability.

Scientific Software. Modern science and engineering in 

general, and modern measurement science in particular, 

require a wide variety of software tools for scientific 

discovery, exploration, and analysis. As scientific inquiry 

becomes deeper and more specialized, so must the supporting software tools. The goal of this work is to 

develop critical software tools that support measurement 

science at NIST, as well as computational science and 

engineering at large.

Digital Library of Mathematical Functions. The special 

functions of applied mathematics are fundamental tools 

enabling modeling and analysis in all areas of science and 

engineering. To make effective use of such functions, 

practitioners must have ready access to a reliable source 

of information on their properties. The goal of this work 

is the development and dissemination of definitive reference data on the special functions of applied mathematics. 

The centerpiece of this effort is the DLMF, a freely available interactive and richly linked online resource.

Quantum Information. An emerging discipline at the 

intersection of physics and computer science, quantum 

information science (QIS) is likely to revolutionize science 

and technology in the same way that lasers, electronics, 

and computers did in the 20th century. By encoding information into quantum states of matter, one can, in 

theory, exploit the seemingly strange and counterintuitive behavior of quantum systems to enable phenomenal increases in information storage and processing 

capability, as well as communication channels with extremely high levels of security. Although many of the 

necessary physical manipulations of quantum states have 

been demonstrated experimentally, scaling these up to 

enable fully capable quantum computers remains a grand 

challenge. We 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 electrical power distribution. In spite of 

our increasing reliance on such systems, our ability to 

build far outpaces our ability to secure. Protocols controlling the behavior of individual nodes lead to 

unexpected macroscopic behavior. Local power anomalies propagate in unexpected ways leading to large-scale 

outages. Computer system vulnerabilities are exploited in 

viral attacks resulting in widespread loss of data and system availability. The long term stability of our critical 

infrastructure is simply unknown. Measurement science 

has long provided a basis for the understanding and control of physical systems. Similar types of deep 

understanding and insight are lacking for complex information systems. We seek to develop the mathematical 

foundations needed for a true measurement science for 

complex networked information systems.
Summary of Activities for Fiscal Year 2012 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).

Digital Library of Mathematical Functions

The NIST Handbook of Mathematical Functions, published by Cambridge University Press in 

May 2010, has passed the 400 citation mark on Google Scholar1. The Handbook provides a succinct reference on the properties of the special functions of applied mathematics, which are a staple of 

mathematical modeling in many fields. Recent citations have come from published work on light scattering, instabilities in rocks, cosmology, elementary quantum systems, quantum field theory, general 

relativity, statistical mechanics, nanophotonics and search algorithms. The NIST Digital Library of Mathematical Functions2

(DLMF), a parallel free online resource, has satisfied nearly 5 million full page 

requests resulting from more than 615,000 user sessions over the same 32 month period. The main goal of 

the DLMF project, conceived nearly 15 years ago and carried out by ITL and PML, was to develop a 21st

century successor to the legendary Handbook of Mathematical Functions, a classic 1964 NBS publication edited by Milton Abramowitz and Irene Stegun (A&S). The most cited publication in NIST history, 

A&S still holds the lead in citations, with more than 60,000 recorded on Google Scholar, albeit with nearly a 50-year head start over DLMF. Together, A&S and DLMF present vibrant faces of NIST to the 

technical community, one of great heritage, the other looking forward. [See page 68.]

Quantum Information

Stephen Jordan of ACMD, working with colleagues at Caltech and the University of Pittsburgh, 

has developed the first quantum algorithm for efficiently simulating a quantum field theory. The paper 

describing this work was published as a feature article in Science on June 1, 2012. The significance of the 

achievement was explained in an associated Perspectives article by Hauke, Tagliacozzo and Lewenstein3. 

Quantum field theories are used to describe systems in which the effects of quantum mechanics and special relativity are both important. The Standard Model of particle physics, which aims to explain all 

physical phenomena excluding gravity, is a quantum field theory. Calculating quantitative predictions 

from a quantum field theory is extremely difficult. In particular, no efficient algorithm is known for classical computers to simulate the dynamics of quantum field theories involving strongly-interacting 

particles. Jordan and colleagues devised a quantum algorithm to simulate the simplest nontrivial quantum 

field theory, massive phi-fourth (φ4) theory. Their algorithm calculates scattering probabilities in relativistic particle collisions similar to those that occur in particle accelerators like the Large Hadron Collider. 

The algorithm scales in time polynomially in the number of particles, their energy, and the desired precision, and works even when the coupling between particles is strong. By studying whether quantum 

computers can efficiently simulate the Standard Model, Jordan and colleagues also hope to shed light on

the question of the fundamental computational power of the universe, by either confirming or refuting the 

oft-repeated claim that the universe is equivalent in computational power to a quantum computer. [See 

page 17.]

NIST has developed a robust experimental program in quantum-based masurements4. A fundamental problem in this area is how to fully characterize a quantum state created in a laboratory. 

 

1

http://scholar.google.com/

2

http://dlmf.nist.gov/

3

P. Hauke, L. Tagliacozzo and M. Lewenstein, Speeding Up Quantum Field Theories, Science 336 (June 1, 2012), 1122-1123.

4

http://www.nist.gov/public_affairs/factsheet/quantum_meas_2010.cfm
6 NIST Applied and Computational Mathematics Division

Unfortunately, no single measurement can completely characterize a quantum state. Furthermore, any 

single measurement is, in fact, destructive. Thus, 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. We are working to develop improved mathematical techniques for doing this. Two 

major efforts have been undertaken. Scott Glancy and Manny Knill are working to ameliorate well-known 

biases in traditional methods of quantum state estimation, applying the resulting techniques to the characterization of quantum states produced in PML. Yi-Kai Liu is exploiting methods of compressed sensing to

significantly reduce the experimental and computational burden on state estimation through greatly improved sampling techniques. [See page 77.]

Tests performed by Paulina Kuo, Oliver Slattery, and Xiao Tang of ACMD show that a prototype 

device developed with collaborators at Stanford University can significantly speed up quantum information transfer through fiber-optic cables5

. Conventional fiber-optic systems, in use for decades, transmit 

data as a series of light pulses. Such pulse streams can be intercepted by third parties undetectably. But 

individual photons themselves can carry data, encoded in their quantum states. Because any attempt to 

intercept that data alters the quantum state, eavesdroppers can always be detected. This property is the 

basis for the security of quantum key distribution systems. While information scientists have found a way 

to encode photon quantum states successfully, practical systems need the photons to be at wavelengths 

compatible with both existing optical-fiber networks and single-photon sensitive (and economically viable) silicon detectors. Unfortunately, these wavelengths are different. One potential solution is to change 

the photons’ wavelength from the infrared—desirable for fiber networks—to the visible spectrum, so that 

a silicon detector can “see” them. A method of doing so is to mix the information-carrying photons with a 

second photon beam. The information-carrying photons absorb this second beam’s additional energy and 

get kicked up from the infrared region of the spectrum to the wavelength of visible red light, which silicon sensors can detect. However, silicon single-photon detectors cannot operate very fast, which puts 

limitations on data rates and ultimately, their usefulness for quantum information transmission systems.

The heart of the newly developed device is a new crystal that goes beyond converting the wavelength of 

the photons. Designed and fabricated by Stanford’s Jason Pelc, the crystal is capable of splitting the beam 

of infrared, information-carrying photons into two distinct beams of slightly different color, and directing 

the different-colored photons to different outputs. Controlling the flow to either output allows the team to 

use two “slow” detectors in place of one, thereby doubling the overall system speed. ACMD tests showed 

that this innovation allows twice as much data to be sent in a single beam. Since the photons conceivably 

can be split not just into two, but several different beams, this provides a promising solution to the detector problem. [See page 80.]

Scientific Software

This year ACMD’s software system, PHAML6, for parallel solution of elliptic partial differential 

equations (PDEs) based on adaptive grid refinement and multigrid methods, was used as a platform for a 

major survey of methods for hp adaptive grid refinement. Adaptive methods, which automatically make 

localized adjustments to the method to optimize use of computational resources, are essential for successfully attacking the most challenging modeling problems based on PDEs. h-based methods adapt by 

refining in space (i.e., reducing size of triangles in the computational grid), while p-based methods adapt

by increasing the polynomial order of approximation on fixed-size grid elements. hp methods combine 

the two. Many heuristics have been proposed for implementing such a refinement strategy. 13 separate 

strategies were evaluated on a battery of 12 test problems. Not only do the results provide useful data on 

the comparative performance of the methods, but they also provide insight on practical tradeoffs between 

efficiency and performance. The work was carried out by William Mitchell and Marjorie McClain. [See 

page 66.]

 

5 This description is adapted from an article in NIST TechBeat.

6

PHAML stands for Parallel Hierarchical Adaptive Multi-Level; see http://math.nist.gov/phaml/
Summary of Activities for Fiscal Year 2012 7

High Performance Computing and Visualization

A team of researchers from ACMD and EL were awarded 22 million hours of computer time in

2012 from the Department of Energy to support the study of the flow properties of large-particle suspensions such as concrete7

. The award is for the second year of a three year, peer reviewed, proposal to 

DOE's Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program8. 

High fidelity flow simulations with many thousands of particles, with a wide range of sizes and shapes in 

a non-Newtonian fluid matrix, are enabling the determination of fundamental rheological parameters such 

as stress and strain rate in non-analytical rheometers and mixing geometries, properties that cannot now 

be measured accurately in industrial settings. NIST standard reference materials for suspension rheology 

are also being designed using the results of these simulations. Not only is this work solving a critical outstanding problem in the cement and concrete industry, but it is expected to have an enormous influence on 

the wide array of industries that use vane rheometers and mixers such as food processing, water treatment, 

coatings, and pharmaceuticals. The research team includes William George, Marc Olano, and Judith Terrill of ACMD, Nicos Martys and Edward Garboczi of the NIST Engineering Laboratory, and Pascal 

Hebraud of CNRS/ESPCI (France). Simulations are being run in the Leadership Computing Facility of 

Argonne National Laboratory on “Intrepid,” an IBM Blue Gene/P system with 164,000 cores, 80 terabytes of RAM, and a peak performance of 557 teraflops. [See page 28.]

ACMD staff members are also contributing to the improvement of medical imaging technology. 

The Quantitative Imaging (QI-Bench) group is a NIST-sponsored organization developing “open-source 

informatics tooling used to characterize the performance of quantitative medical imaging as needed to 

advance the field”

9

. QI-Bench maintains a publicly available FDA database consisting of more than 1,000

CT scans of artificial lungs embedded with “phantom” tumors intended for facilitating the assessment of 

lung cancer nodule size estimation methodologies and tools. The use of these scans would be greatly facilitated by the availability of phantom nodule location data (“ground truth”). This data is currently 

unavailable, and generating it through laborious inspections of trained radiologists is prohibitively time 

consuming and expensive. Adele Peskin of ACMD has written and tested an initial version of software to 

perform automatic lung cancer nodule location. For data sets with thin slice distances (0.4 mm vs. 1.25 

mm), her algorithm accurately locates over 93% of the nodules as identified by subject matter experts, 

with a false positive rate of 3.5%. Preliminary results were presented this year at a peer-reviewed conference. The software is currently being enhanced to extend this NIST-developed analysis to the 1,187 sets 

of CT scans of FDA phantoms on the QI-bench website. [See page 59.]

Foundations of Measurement Science for Information Systems

On June 8, 2012 ACMD hosted a Workshop on Large-scale Complex Networks aimed at highlighting and discussing current research on: (a) large-scale geometry of complex networks, including 

hyperbolicity and its possible impact on network performance, reliability, robustness, and security; (b) 

processes on complex networks, including percolation and diffusion; and (c) interplay between processes 

on networks and network evolution. Some 30 people participated, including researchers from institutions 

such as the Army Research Lab, Bell Labs, Stanford University, Stony Brook University, the University 

of Illinois, the University of Maryland, and the University of Southern California. This was the second of 

a series of workshops on this topic co-sponsored by Bell Labs and NIST. Vladimir Marbukh and Assane 

Gueye organized the event.

This year we also established a new external partnership that will allow us to engage the complex 

systems research community on topics of interest to ACMD. Using grant funding from NIST, the Santa 

Fe Institute (SFI) will organize a series of small working groups, larger workshops, and collaborative visits to and from SFI in the areas of network science, biologically inspired computation, and computer 

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

From Graphs to Rich Data will be held in Santa Fe in May 2013. That workshop will consider how net-

 

7

http://www.alcf.anl.gov/articles/us-department-energy-awards-alcf-resources-researchers-addressing-global-science-issues

8

http://www.science.energy.gov/news/in-focus/2011/11-15-11-2/

9

http://www.qi-bench.org/
8 NIST Applied and Computational Mathematics Division

work data beyond simple connectivity can be captured and used to obtain new understanding of complex 

interconnected systems. The second, entitled Deep Computation in Statistical Physics, to be held in the 

summer of 2013, will consider how novel algorithms and methods of statistical physics can contribute to 

the understanding of complex systems more broadly.

Mathematics of Metrology

Fingerprint evidence collected at crime scenes is rarely pristine. The images are incomplete, suffer 

from pressure gradations, are partially obscured by underlying surface patterns and colors, etc. Due to the 

low signal quality of the fingerprint such images are often not suitable for input into fingerprint identification software to search for matches. Because of this, forensic scientists currently use a variety of image 

processing tools to improve the quality of these images. To date, such latent fingerprint image enhancement has been treated as a preprocessing step for subsequent identity matching analysis. As dramatic and 

essential as these transformations are, no research exists to characterize this step of the evidentiary analysis chain. Lack of such characterizations can result in detrimental consequences for reproducibility, 

traceability, and quantification of accuracy. This year Andrew Dienstfrey and Alfred Carasso of ACMD, 

in collaboration with a larger NIST team, have undertaken a first investigation of this step of the forensic 

analysis workflow. [See page 39.]

Finally, this year we also established a formal partnership with the Institute for Mathematics and Its 

Applications (IMA) at the University of Minnesota for work associated with the Materials Genome Initiative. The IMA project will study molecular dynamics (MD) modeling as used to predict the material 

properties of resins. Resins are a critical component of composite materials such as those used in the development of the Boeing 787 Dreamliner. Of particular interest is the development of techniques and 

tools to quantify the uncertainty in the results of such MD simulations. The work will be a collaboration 

between the IMA, Boeing, and NIST. To facilitate the collaboration, the IMA will identify an industrial 

postdoctoral fellow who will spend time at each institution.

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 51 articles appearing in peer-reviewed journals, 37 papers in conference 

proceedings, and 7 magazine articles. Sixteen additional papers have been accepted for publication, while 

22 others are undergoing review. Division staff members gave 93 invited technical talks and presented 48

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) 2012, the division web 

server satisfied more than 4.4 million requests for pages from more than 370,000 distinct hosts. In total, 

there have been more than 326 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 148 such papers which 

were published in CY 2012 alone (more than 1,440 such papers have been identified since 2001). 

Members of the Division are also active in professional circles. Staff members hold a total of 15 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, and 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 18 organizing/steering/program 

committees. 

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

and is a member of the ACM Council, the association’s board of directors. In addition, staff members 
Summary of Activities for Fiscal Year 2012 9

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 completed 10 

years of service as Chair of the International Federation for Information Processing (IFIP) Working 

Group 2.5 on Numerical Software, Donald Porter is a member of the Tcl Core Team, 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, 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 Co-Chair 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.

Administrative News

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

Arrivals

Kamran Sayrafian joined ACMD after four years of service as the ITL Program Manager for Pervasive 

Information Technology. Kamran holds Ph.D., M.S. and B.S. degrees in Electrical and Computer Engineering from University of Maryland, Villanova University and Sharif University of Technology, 

respectively. He has been at NIST since 2004. Prior to joining NIST, he was the cofounder of Zagros 

Networks, Inc., a fabless semiconductor company based in Rockville, MD where he served as President 

and senior member of the architecture team. Kamran is the co-inventor of four U.S. patents. He is a senior 

member of IEEE and an adjunct faculty of the University of Maryland. While an ITL Program Manager, 

Kamran started up and participated in several research efforts in collaboration with ACMD, including 

studies of RF propagation in body area networks and in the optimal deployment of mobile sensors.

An expert in computer graphics, Wesley Griffin joined ACMD’s permanent staff in the fall of 2012 as 

part of the High Performance Computing and Visualization Group. Wesley received a B.S. degree from 

the University of Maryland, and an M.S. from UMBC, both in Computer Science. He is presently a Ph.D. 

candidate at UMBC, working under the direction of ACMD faculty appointee Marc Olano on variable bit 

rate texture compression, real-time decompression, and objective color image quality assessment. 

Amanda Streib and Noah Streib began two-year appointments in ACMD as NIST NRC Postdoctoral 

Associates in July 2012. Amanda received a B.S. in mathematics from Furman University in 2006 and a 

Ph.D. from Georgia Tech’s program in Algorithms, Combinatorics and Optimization in May 2012. Her 

thesis studied mixing rates of Markov chains with applications in computer science and statistical physics. 

She was a National Physical Sciences Consortium Fellow at Georgia Tech. Noah also graduated with a 

Ph.D. from the same program at Georgia Tech. He received a B.A. in mathematics from Oberlin College 

in 2006. At Georgia Tech he studied the combinatorics of finite partially ordered sets, completing a thesis 

Table 1. Downloads of Selected Division Software Packages During CY 2012

Package Description Downloads

JAMA Linear algebra in Java 27,426

OOMMF Modeling of nano-magnetic phenomena 5,000

TNT Linear algebra using C++ templates 3,890

OOF Modeling materials with complex microstructure 1,217

f90gl Fortran 90 interface to OpenGL graphics 1,162

spblas Sparse basic linear algebra components 1,131

Ngraph Basic graph algorithms; web crawler 812

PHAML Parallel adaptive solution of partial differential equations 518
10 NIST Applied and Computational Mathematics Division

on planar and Hamiltonian cover graphs. At NIST Amanda and Noah are working with Isabel Beichl on 

approximations of the partition function for the Ising model of statistical physics.

Recipient of an NSF Postdoctoral Fellowship for Transformative Computational Science using CyberInfrastructure, Daniel Kaslovsky joined ACMD in Boulder in the fall of 2012 as a guest researcher. 

Daniel received a B.A. in computer science from Colgate University in 2003 and a Ph.D. in Applied 

Mathematics from the University of Colorado in Boulder in May 2012. At NIST he will be working with 

Brad Alpert on the development of computational algorithms based on random sampling for efficient processing of compressible data. 

Catherine Graham joined ACMD as Division Secretary in February 2012. A NIST staff member since 

2000, Cathy had previous assignments in the NIST Manufacturing Engineering Laboratory and the NIST 

Baldridge Performance Excellence Program.

Paulina Kuo of the Joint Quantum Institute (a cooperative venture of NIST and the University of Maryland) joined ACMD in October 2011 as a Guest Researcher. Paulina 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 an NRC Postdoctoral Associate in PML. An expert in nonlinear optics,

Paulina will be contributing to the Division's experimental efforts in quantum communications.

Ismet Sahin began a term in ACMD as an ARRA Senior Fellow in October 2011. Sahin has a PhD in 

Electrical and Computer Engineering from the University of Pittsburgh (2006). He was most recently a

Guest Researcher in the NIST National Center for Neutron Research. Ismet will be working with Anthony 

Kearsley on optimization methods applied to waveform time delay estimation algorithms that are used in 

seismology, radar, sonar, and biomedical science.

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

and Technology (POSTECH) in South Korea. An expert in quantum optics, Yong-Su is contributing to 

ITL’s quantum communications project, especially in experimental techniques for the conversion of flying qubits to stationary qubits.

Itzel Dominquez Mendoza of the Centro Nacional de Metrología (CENAM), NIST’s sister institution 

from Mexico began an appointment as a guest researcher in ACMD in September 2012. Participating in 

the ITL project on combinatorial software testing, she is working on the inclusion of constraints in the 

team’s coverage measurement tool.

Santanu Sarkar, a recent Ph.D. in Mathematics from the Indian Statistical Institute joined ACMD as a 

guest researcher in late 2012. An expert on cryptanalysis, Santanu is working with the cryptography 

group from ITL’s Computer Security Division on number-theoretic tools for improving performance 

and/or functionality of cryptographic applications.

Departures

Daniel Lozier retired from NIST in February 2012 after 47 years of Federal service. Dan’s government 

career began in 1963 at the Army R&D Lab at Ft. Belvoir. He joined the National Bureau of Standards in 

1969 after completing a Ph.D. in applied mathematics from the University of Maryland. An expert in the computation of special functions, Dan held many 

leadership positions during his long tenure at NIST including Chair of the SIAM 

Activity Group on Orthogonal Polynomials and Special Functions, President of the 

NIST Chapter of Sigma Xi, Associate Editor of the Mathematics of Computation, 

and Leader of the NIST Mathematical Software Group. Dan’s most significant 

contribution was as project lead for the NIST Digital Library of Mathematical 

Functions (DLMF), for which he earned a Department of Commerce Gold Medal 

in 2011. In the spring of 2012 Dan returned to NIST to continue his contributions 

to the DLMF project on a part-time basis.

Figure 1. Daniel Lozier.
Summary of Activities for Fiscal Year 2012 11

Table 2. Student Interns in ACMD

Name Institution Level Program Mentor Project Title

Styvens 

Belloge

ISIMA 

(France) G

Guest 

Researcher J. Terrill Visualization and analysis of the National Vulnerability Database

Hamza 

Attak

ISIMA 

(France) G

Guest 

Researcher J. Terrill Visualization algorithms

Gregory 

Rami

ISIMA 

(France) G

Guest 

Researcher J. Terrill Impact of fire on building structures

Martina 

Barbi

University 

of Bologna G

Guest 

Researcher K. Sayrafian RF propagation in body-area networks

Deyan 

Ginev

Jacobs 

University 

(Germany)

G

Guest 

Researcher B. Miller Semantics of mathematical documents

Adam 

Meier

University 

of Colorado G PREP E. Knill Quantum computer simulation

Michael

Mullan

University 

of Colorado G PREP E. Knill Quantum computing theory

Yanbao 

Zhang

University 

of Colorado G PREP E. Knill Tests of local realism

Catherine 

Baker

De Pauw 

University U SURF B. Cloteaux Graph toughness conjecture

Brian 

Clanton

Rochester 

Instiute of 

Technology

U SURF S. Ressler Declarative 3D and web based 

graphics

Jeffrey 

Jacobs

University 

of Maryland U SURF A. Mink LDPC error correction on GPUs

Andrew 

Keller

De Pauw 

University U SURF J. Terrill Visualization in cybersecurity

Connor 

MacKenzie

Westminster 

College U SURF H. Cohl Associated Legendre function representations

Divya 

Mouli

Carnegie 

Mellon U SURF J. Terrill Gesture in an immersive visualization environment

Johnathan 

Orthwein Columbia U SURF G. McFadden Spectral analysis for the detection of gases

Katelyn 

Weber

Montana 

State U SURF S. Glancy Quantum state estimation

Jason 

Wu Berkeley U SURF F. Hunt Stochastic models of gene regulatory networks

Joel Muskin-PierretWashington 

University U STEP J. Terrill Visualization

Michael 

Ekstrom

Montgomery 

Blair HS HS SHIP J. Terrill Visualization for cybersecurity

Jonathan 

Ibers

Poolesville 

HS HS SHIP J. Terrill Visualization for cybersecurity

Legend G: Graduate student

U: Undergraduate student

HS: High school student

PREP: NIST Professional Research Experience Program (Boulder)

SHIP: Summer High-school Internship Program

STEP: Student Employment Program

SURF: NIST Summer Undergraduate Student Fellowship Program

 
12 NIST Applied and Computational Mathematics Division

Robin Bickel, ACMD’s Division Secretary, retired from 

NIST in February 2012 after 36 years of Federal service. 

Robin began her assignment as Division Secretary in 1989. 

An exemplary secretary, Robin received the ITL Outstanding Support Award on two occasions. 

John Kelso, a member of ACMD’s High Performance 

Computing and Communication Group for nine years, left 

the Federal service in September 2012. John was a key 

member of the team developing the software infrastructure 

for HPCV’s immersive visualization facility. He resides in 

Blacksburg, VA. 

Agnes (Abbie) O’Gallagher of ACMD-Boulder retired in 

November 2012 after 27 years of service. During her career

at NIST Abbie 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.

Peter Ketcham resigned from NIST in October 2011 after 

service as a mathematician at NIST for 14 years. During the late 1990s Ketcham worked with David Feder of the NIST Physics Lab and others to develop visualizations of models of the newly discovered Bose 

Einstein condensate. These striking images made their way to the covers of Physics Today, Optics and 

Photonics News, Parity, and the lead illustration in a Scientific American article. In 2000 Ketcham was a 

joint recipient of the NIST Bronze Medal.

Lijun Ma, an ITL guest researcher for seven years, left NIST in October 2011 to take a position as a research assistant professor in the Biomedical Engineering Department at Washington University in St. 

Louis. An expert in quantum optics, Ma was a significant contributor to ITL’s experimental efforts in 

quantum communications. An incredibly productive researcher, Ma co-authored 52 papers in journals and 

conference proceedings during his six years at NIST. Ma received his PhD in Physics from Tsinghua 

University in China in 2001. He recently became a permanent resident of the US.

Students

During FY 2012 ACMD was able to support the work of 20 student interns, including nine in the 

Student Undergraduate Research Fellowship (SURF) program, three graduate students in Boulder’s Professional Research Experience Program (PREP), and two high school volunteers. We also hosted three

graduate students from French universities; this was facilitated by a Memorandum of Understanding 

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

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

This year ACMD issued a grant to the National Physical Sciences Consortium (NPSC) to support 

the graduate research of three students. The NPSC is a partnership between government agencies and laboratories, industry, and higher education, whose goal is to increase the number of American citizens with 

graduate degrees in the physical sciences and related engineering fields, emphasizing recruitment of a 

diverse applicant pool10. As part of their studies, NPSC students spend at least one summer in residence at 

NIST. The students selected for NIST support beginning in the fall of 2012 are: 

 Earl Bellinger, Indiana University: High performance computing (J. Terrill, mentor)

 Bryan Gard, Louisiana State University, Quantum information (M. Knill, mentor)

 Franz Sauer, University of California at Davis, Scientific visualization (J. Terrill, mentor)

 

10 http://www.npsc.org/

Figure 2. Robin Bickel and husband Keith. Robin retired in February 2012 after serving as Division 

Secretary for 23 years.
Summary of Activities for Fiscal Year 2012 13

Recognition

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

Geoffrey McFadden of ACMD was named a Fellow 

of the Society for Industrial and Applied Mathematics (SIAM) at the society’s annual meeting on July 10, 

2012 in Minneapolis. McFadden was cited for advances 

in mathematics applied to fluid dynamics, solidification, 

and the interaction of the two, using sharp and diffuse 

interface theories. SIAM inaugurated its Fellows Program in 2008 to recognize members who have made 

outstanding contributions to industrial and applied 

mathematics.

Geoffrey McFadden was also selected to receive the 2012 Washington Academy of Sciences (WAS) Award for merit and distinction in Mathematics and 

Computer Science. McFadden is one of 10 awardees representing multiple fields in 

the sciences and engineering who was recognized at the WAS annual meeting and 

awards banquet held on May 10 in Arlington, VA. Previous winners of the WAS 

award in mathematics and computer science include James Yorke, Eitan Tadmor, 

and Victor Basili of the University of Maryland, and Stuart Katzke of ITL. An applied mathematician, McFadden’s contributions have been in mathematical 

modeling in fluid dynamics, solidification, and pattern formation, with application 

to materials science and other fields. 

On September 28, 2012 Ronald Boisvert of ACMD received an Outstanding 

Alumni distinction from the Purdue University College of Science. Purdue’s Computer Science Department, which celebrates its 50th anniversary this year, 

developed the nomination. Boisvert received a Ph.D. in computer science from 

Purdue in 1979.

Figure 3. Ronald Boisvert was named an 

Outstanding Alumni by 

the Computer Science 

Department at Purdue.

Figure 4. Geoffrey McFadden and spouse, Roberta, at the 

Washington Academy of Sciences Awards Ceremony.
14 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2012 15

Part II: Features

 

 Part II

Features
16 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2012 17

Quantum Algorithms for Quantum Field Theories 

Quantum field theories are needed to describe systems 

in which the effects of quantum mechanics and special 

relativity are both important. The Standard Model of 

particle physics, which aims to explain all physical 

phenomena excluding gravity, is a quantum field theory. Calculating quantitative predictions from a 

quantum field theory can be extremely difficult. In particular, no efficient algorithm is known for classical 

computers to simulate the dynamics of quantum field 

theories involving strongly-interacting particles. In this 

project, we are developing methods by which quantum 

computers could efficiently simulate the dynamics of 

quantum field theories, even when the interactions between particles are strong. If quantum computers are 

successfully built, our methods could be of practical

use in predicting the outcomes of experiments at particle accelerators. Furthermore, by studying whether 

quantum computers can efficiently simulate the Standard Model, we hope to address the fundamental 

computational power of the universe by either confirming or refuting the oft-repeated claim that the universe 

is equivalent in computational power to a quantum 

computer.

Stephen Jordan

Ever since Richard Feynman’s original proposal for 

quantum computers, one of the primary applications 

envisioned has been efficient simulation of other quantum systems. In fact, it has been conjectured that 

quantum computers are universal simulators, which can 

simulate all physical systems using computational resources that scale polynomially with the system’s 

number of degrees of freedom. Quantum field theories 

have posed a challenge in that the set of degrees of 

freedom is formally infinite. In this project, we are 

working to show that quantum computers, if built,

could nevertheless efficiently simulate quantum field 

theories at bounded energy scales.

So far, we have devised a quantum algorithm to 

simulate the simplest nontrivial quantum field theory 

we could find, namely massive phi-fourth (φ4) theory 

[1]. Our algorithm calculates scattering probabilities in 

relativistic particle collisions similar to those that occur 

in particle accelerators such as the Large Hadron Collider. Our algorithm runs in time scaling polynomially 

in the number of particles, their energy, and the desired 

precision, and works even when the coupling between 

particles is strong. In contrast, known polynomial-time

classical algorithms break down when computing dynamical quantities such as scattering amplitudes in 

situations involving strong coupling or requiring high 

precision.

Although we believe the algorithm of [1] represents a major first step in simulating quantum field 

theories, much work remains to be done. In particular, 

matter consists of two main classes of particles called 

bosons and fermions. φ

4 theory involves only bosons. 

Currently, we are working to generalize our algorithm 

to treat quantum field theories involving fermions [2]. 

In future work we will attempt to extend our algorithm 

to handle massless particles and gauge symmetries. If 

successful, this will result in a quantum algorithm capable of efficiently simulating the Standard Model of 

particle physics, which encompasses all known physical processes not involving gravity.

In the theory of computational complexity, it has 

proven fruitful to categorize computational problems 

into those that can be solved using a number of computational steps that scales polynomially with the input 

size, and those that require a larger-than-polynomial 

(typically exponential) amount of computation. Being 

coarse-grained, this distinction is highly independent of 

the details of the model of computation used to define 

the notion of computational steps. In fact, prior to the 

discovery of quantum computation, it was widely believed that the polynomial vs. superpolynomial 

categorization was completely robust; no realistic form 

of computation was believed to be more powerful than 

standard Turing machines. This assertion can be formalized as the complexity-theoretic Church-Turing 

thesis: anything that can be computed in polynomial 

Figure 5. Richard Feynman proposed the idea of a universal 

quantum simulator in 1982. He postulated that while a classical 

Turing machine would require exponential resources to simulate 

quantum phenomena, a simulator based itself on quantum principles would not.

Photo: http://en.wikipedia.org/wiki/File:Richard_Feynman_Nobel.jpg
18 NIST Applied and Computational Mathematics Division

time can be computed in polynomial time on a Turing 

machine.

The philosophical status of the complexitytheoretic Church-Turing thesis has long been a source 

of discomfort. Being unwilling to call it either a theorem or a definition, mathematicians deferred the issue

of identifying the status of the claim by calling it a 

“thesis”. In the 1980s, David Deutsch put forth the 

interpretation that the complexity-theoretic ChurchTuring thesis only becomes meaningful when interpreted as a claim about physics: “Anything that can be 

computed in polynomial-time by physical means can 

be computed in polynomial-time by a Turing machine.” Furthermore, building on previous observations 

by Feynman, Deutsch conjectured that this claim is 

false, due to quantum-mechanical processes that seem 

to be exponentially hard to simulate using standard 

classical Turing machines.

The point of view espoused by Feynman and 

Deutsch gained much support from Peter Shor’s spectacular 1994 discovery of a polynomial-time quantum 

algorithm for factoring n-digit integers, a problem 

widely believed to require superpolynomial time to 

solve classically. The complexity-theoretic ChurchTuring thesis was soon superseded by the quantum 

Church-Turing hypothesis: “Anything that can be 

computed in polynomial-time by physical means can 

be computed in polynomial time by a quantum Turing 

machine.” Paralleling the history of classical computation, many theoretical models of quantum computation 

were proposed, such as quantum generalizations of 

logic circuits, and quantum analogues of simulated 

annealing, and all of these were proven to be simulatable with polynomial overhead by quantum Turing

machines. Furthermore, polynomial-time quantum algorithms were eventually developed to simulate 

various quantum phenomena in nature, such as chemical reactions, and the dynamics of spin systems. All of

these simulation results gave additional support to the 

validity of the quantum Church-Turing thesis, and the 

notion that the universe is equivalent to a large quantum computer began to permeate the popular press [3].

Although potentially very valuable if quantum 

computers are successfully built, the polynomial-time 

quantum algorithms for simulating chemical reactions 

and spin dynamics do not provide fully convincing

evidence for the validity of the quantum Church-Turing

thesis. Fundamentally, all of these quantum algorithms 

for simulating were designed to simulate many-body 

systems, and have runtime scaling polynomially in the 

number of degrees of freedom being simulated. In

principle, a field has infinitely many degrees of freedom, as it is specified by its value at every point in 

space. In contrast, a system of n particles has only 3n

degrees of freedom: the three spatial coordinates of 

each particle. Direct application of existing algorithms 

is not possible and one is faced with an open question: 

can quantum computers in polynomial time simulate 

the dynamics of quantum field theories such as the 

standard model?

The obvious response to the infinite degrees of 

freedom in a field is to discretize. This is invariably 

done in simulating classical fields, for instance by finite-element methods. What we have learned in the

course of our research so far is that discretizing space 

on a lattice yields an efficient method for simulating 

quantum field theories on quantum computers and the 

discretization errors converge to zero as the lattice 

spacing is taken to zero, just as one would hope. However, the means by which this convergence is achieved 

has some uniquely quantum-mechanical quirks. Specifically, the parameters of the physical model, such as 

the particle mass and coupling strength, must be adjusted as functions of the lattice spacing in order to 

achieve convergence to a continuum limit. This infamous aspect of quantum field theory is known as 

renormalization, and its conceptual and quantitative 

elucidation was only achieved in the 1970s and 1980s, 

led by Kenneth Wilson.

The main technical aspects of our algorithm for 

simulating φ

4 theory are the efficient preparation of 

physically realistic initial states, and the renormalization-based analysis of discretization errors. Both of 

these aspects are highly dependent on the underlying

physics. Thus, extension of our results to more general 

quantum field theories, such as the Standard Model 

remains nontrivial. Our suspicion is that quantum computers can in polynomial time simulate the entire 

Standard Model. Proving this remains a guiding goal 

for our future work. On the other hand, if this turns out 

to be false, we can instead look forward to quantum 

field computers, at least as a theoretical construct, that 

are exponentially more powerful than standard quantum computers.

References

[1] S. Jordan, K. S. M. Lee, and J. Preskill, Quantum Algorithms for Quantum Field Theories, Science 336 (2012) 

1130-1133.

[2] S. Jordan, K. S. M. Lee, and J. Preskill, Quantum Algorithms for Fermionic Quantum Field Theories, in 

preparation.

[3] S. Lloyd, Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos, Vintage Press, 

2007.

Participants

Stephen Jordan (ACMD), Keith Lee (University of 

Pittsburgh), John Preskill (Caltech)
Summary of Activities for Fiscal Year 2012 19

Micromagnetic Investigation of Periodic Cross-Tie/Vortex Wall 

Geometry

A careful examination of magnetization structure in

thin film elements has been conducted via a systematic 

series of micromagnetic simulations. Depending on the 

element dimensions, a particular structure known as a 

cross-tie wall can occur in these elements. The physical processes supporting cross-tie wall formation are 

revealed and a phase diagram that predicts the existence or not of cross-tie walls is produced. These results 

are of interest because they differ from analytic results 

in the infinitely thin film limit. The results are of practical interest because the performance of devices such 

as computer hard drive read heads and nascent magnetic memory technology such as MRAM are 

dependent on fine details of magnetization structure in 

thin film elements.

Michael J. Donahue

Magnetic materials are generally classified into two 

categories, “hard” materials that hold a remnant magnetization and resist change to the magnetization, and 

“soft” materials with magnetization that is easily 

changed by an applied magnetic field. The former are 

used, for example, in permanent magnets and computer 

hard drive platters, while the latter are in transformers, 

magnetic field sensors, computer hard drive read heads, 

and in new classes of magnetic memory devices such 

as MRAM.

As a result of energy minimization, the magnetization in magnetic materials tends to form domains of 

more or less uniformly magnetized regions separated 

by narrow transition regions called domain walls, as

shown in Figure 6. The number and type of domains 

and domain walls can influence the behavior and response speeds of magnetic devices.

In thin magnetic films of the type primarily deployed in present day devices, the archetypal domain 

walls are Néel walls, where the magnetization in the 

wall rotates in the plane of the film, and Bloch walls,

where the magnetization rotation is about the axis normal to the plane of the wall. Néel walls occur in very 

thin films, Bloch walls are found in thicker samples, 

and numerous transitional structures [1-3] are obtained 

at intermediate thicknesses. One of the more interesting transitional structures is the cross-tie/vortex (or 

simply cross-tie) wall which alternates cross-ties and 

vortices between counter-rotating segments of Néel

walls. The configuration in Figure 6a shows one crosstie with an “X”-shaped magnetization pattern in the

center of the strip, and vortices on either side with circular magnetization patterns with counterclockwise 

flow about each vortex core. The connecting region 

between the cross-tie and each vortex has the form of a 

180o Néel wall. Cross-tie/vortex walls are observed 

experimentally [4-6], in micromagnetic simulations [6-

9], and in theory [10,11]. In finite samples, this wall 

type appears in low remanence closed-flux Landau 

patterns; if the structure is long enough, then multiple 

cross-tie/vortex pairs may appear (Figure 6b).

In the following, energy densities are reported 

relative to the material magnetostatic energy density Kd

= μ0 Ms

2

/2, and lengths relative to the magnetostaticexchange length lex = (A/Kd)

1/2. (Ms

is the saturation 

magnetization in A/m2,and A is the material exchange 

coefficient in J/m). This makes the results applicable 

to any soft magnetic film. For the NiFe material in

Figure 6, Kd = 400 kJ/m and lex = 5 nm. All results in 

this report are based on simulations using the OOMMF 

micromagnetic program [12].

To understand how cross-tie/vortex structures 

lower the energy density as compared to a Néel wall, 

examine the checkerboard pattern formed by the magnetic charges in Figure 6 or the close-up shown in 

Figure 6. Two remanent equilibrium states for identical 2645 nm 

× 530 nm × 32 nm NiFe film rectangles. Grayscale indicates 

magnetic charge, ‒ ∙ M. Each of these configurations is energetically stable, however configuration (b) has lower energy.

Figure 7. Detail of equilibrium configuration for strip with width 

Y=200 lex, thickness Z=2 lex, and X-period length 317 lex (which is 

the natural period length for this Y and Z): (a) Magnetization 

pattern, (b) stray-field energy density. In (a) the grayscale indicates magnetic charge; in (b) the grayscale runs from white (low 

energy density) to black (high energy density).
20 NIST Applied and Computational Mathematics Division

Figure 7a. Looking first at the section of the Néel portion of the wall between the left hand vortex and the 

cross-tie, and moving from bottom to top across the 

wall, the magnetization rotates counterclockwise. This 

configuration produces negative magnetic charge on 

the lower half of the strip (dark region) and positive 

charges on the upper half (light region). This sets up a 

stray field running from the positive charges to the 

negative charges, counter to the magnetization in the 

center of the wall, making the wall center a region of 

high stray field energy density. However, in the checkerboard pattern, stray field between charge blocks runs 

not only up and down across the Néel sections of the 

wall, but also left and right horizontally parallel to the 

wall. The orientation of the magnetization about each 

vortex core is such that it aligns with the stray field 

from the nearby charge blocks, so that the regions 

above and below each vortex are regions of low stray 

field energy density. This effect is displayed directly in 

Figure 7b, where the light-colored low energy density 

regions above and below the vortex core are clearly 

visible. Conversely, the areas around the cross-tie are 

dark-colored high energy density regions. More detailed analysis of these simulations confirms that at 

these thicknesses the vortex/cross-tie wall is energetically favorable relative to a Néel wall because of the 

magnetostatic energy savings around the vortex. This 

result stands in contrast to analytic studies in the infinitely thin film limit [10, 11], which find the cross-tie 

to be energetically favored and the vortex to be disfavored.

Vortices and cross-ties pin easily on material defects, affecting wall movement and magnetization 

evolution. Also the cross-tie/vortex wall structure is 

periodic, and the energy density in the wall is affected 

by the period length. Therefore it is useful for design 

purposes, as well as being a matter of theoretical interest, to understand the mechanisms behind the 

formation of cross-tie walls and to be able to predict 

the occurrence and cross-tie/vortex period length in this 

type of wall. In order to study this structure free from 

effects of edge domains in finite-length samples, a systematic series of simulations was performed with 

periodic boundary conditions along the direction of the 

wall. (This requires some care because the field from 

each periodic image affects the magnetization in all the 

other periodic images [13].) In this study the strip 

width and thickness is fixed, a period length is selected 

and then the magnetization is relaxed until a (local) 

energy minimum is reached. The energy density for 

this equilibrium is recorded, and the process is repeated 

for a different period length.

In Figure 8, each point marks the energy density 

at equilibrium resulting from a simulation with width Y

= 200 lex at the indicated thickness Z and period length 

X. There is one cross-tie/vortex pair in each period, so 

as the period length X grows large the wall becomes 

essentially two Néel segments interrupted by a cross-tie 

and vortex at either end. This is evident in the behavior of the curves for large X, as for each thickness Z the 

curve asymptotically converges to the energy density 

of the associated Néel wall. For small period lengths 

(X < 100 lex) the energy density grows sharply as the 

exchange energy resists compression of the complex 

cross-tie/vortex structure.

In the thicker films there is a unique minimum 

on each curve, which corresponds to a “natural” period 

length—this is the period length that minimizes the 

energy for a cross-tie/vortex wall at the given film 

thickness and strip width. Note though that each point 

in Figure 8 is a stable equilibrium configuration under 

the fixed period assumption. So if the period length is 

constrained by geometry or other means such as pinning defects, then period lengths other than the natural 

length are possible, as seen in Figure 6.

For thinner films (Z under about 1 lex for Y = 200 

lex), the energy density curves are monotonically decreasing. This means that in a thin, infinite strip, if the 

cross-tie and vortex are not pinned by some means,

they will spread out indefinitely leaving behind a plain 

Néel wall. This is consistent with the experimental 

result that cross-tie/vortex walls are not observed in 

ultra-thin films. One can obtain a good estimate of the 

critical thickness below which pure Néel walls are favored by finding the natural period length for each 

thickness and fitting a curve through the data. This 

curve has a pole at the critical thickness. The 

pole/critical thickness is a function of the strip width; 

the data from simulation series at various strip widths 

is collected on the log-log plot in Figure 9. Across this 

range of values the data are fit quite well by the relaFigure 8. Average total energy density as a function of period 

length X for simulations with width Y = 200 lex for various thicknesses Z (measured in lex). Symbols represent simulation results, 

lines are a guide to the eye. Each of the curves with Z ≥ 2 lex

exhibits a minimum value between 125 lex and 320 lex. The curves 

for Z ≤ 1 lex are monotonically decreasing with X across the displayed range.
Summary of Activities for Fiscal Year 2012 21

tion Zcrit ≈ 30/Y

2/3. This graph represents a phase diagram for walls in thin film strips—strips with

thickness/width combinations below this line will prefer Néel walls, while thickness/width combinations 

above this line will favor cross-tie/vortex walls. Additional details and results are available in [14].

References

[1] R. Kirchner and W. Döring, Thin Films: Domain Walls 

and Related Topics, Journal of Applied Physics 39

(1968), 855–856.

[2] D. V. Berkov, K. Ramstöck, and A. Hubert, Solving 

Micromagnetic Problems. Towards an Optimal Numerical Method, Physicus Status Solidi (a) 137 (1993), 207–

225.

[3] K. Ramstöck, W. Hartung, and A. Hubert, The Phase 

Diagram of Domain Walls in Narrow Magnetic Strips, 

Physicus Status Solidi (a) 155 (1996), 505–518.

[4] R. Ploessl, J. N. Chapman, A. M. Thompson, J. Zweck, 

and H. Hoffmann, Investigation of the Micromagnetic 

Structure of Cross-tie Walls in Permalloy, Journal of 

Applied Physics 73 (1993), 2447–2452.

[5] A. Hubert and R. Schäfer, Magnetic Domains. Springer, 

1998.

[6] S. Huo, G. Pan, D. J. Mapps, W. W. Clegg, G. Heydon, 

W. M. Rainforth, H. A. Davies, J. E. L. Bishop, J. W. 

Tucker, and M. R. J. Gibbs, Magnetic Force Microscopy 

and Micromagnetic Study of Cross-tie Wall Structures 

in Co91Nb6Zr3 Amorphous Thin Films, Journal of Applied Physics 87 (2000), 1096–1102.

[7] M. Redjdal, A. Kakay, M. F. Ruane, and F. B. Humphrey, Cross-tie Walls in Thin Permalloy Films, IEEE 

Transactions on Magnetics 38 (2002), 2471–2473.

[8] W. Rave and A. Hubert, Magnetic Ground State of a 

Thin-Film Element, IEEE Transactions on Magnetics 36

(2000), 3886–3899,

[9] R. Hertel, Thickness Dependence of Magnetization 

Structures in Thin Permalloy Rectangles, Zeitshrift für 

Metallkunde 93 (2002), 957–962.

[10] F. Alouges, T. Rivière, and S. Serfaty, Néel and Crosstie Wall Energies for Planar Micromagnetic Configurations, ESAIM: Control, Optimization and Calculus of 

Variations 8 (2002), 31–68.

[11] A. DeSimone, H. Knüpfer, F. Otto, 2-d Stability of the 

Néel Wall, Calculus of Variations and Partial Differential Equations 27 (2006), 233–253.

[12] M. J. Donahue and D. G. Porter, OOMMF Object Oriented Micromagnetic Framework, National Institute of 

Standards and Technology, Gaithersburg, MD. 

http://math.nist.gov/oommf.

[13] K. M. Lebecki, M. J. Donahue, and M. W. Gutowski, 

Periodic Boundary Conditions for Demagnetization Interactions in Micromagnetic Simulations, Journal of 

Physics D ‒ Applied Physics 41 (2008), 175005. 

[14] M. J. Donahue, Micromagnetic Investigation of Periodic 

Cross-Tie/Vortex Wall Geometry, Advances in Condensed Matter Physics (2012), 908692 (8 pages).

Figure 9. Critical strip thickness for which the pure Néel wall has 

lower energy density than a cross-tie/vortex wall of any period, as 

a function of strip width Y. Data points represent results from 

simulations; the line is the fit curve 30/Y2/3.
22 NIST Applied and Computational Mathematics Division

Continuation Backward in Time in 2D Nonlinear Parabolic 

Equations, and an Experiment in Deblurring Nonlinearly 

Blurred Imagery

Identifying sources of ground water pollution by solving the advection dispersion equation (ADE) backward 

in time, the so-called hydrologic inversion problem, is 

of major interest in environmental engineering [1]. In 

an entirely different direction, ACMD has pioneered 

the use of time-reversed fractional and logarithmic 

diffusion equations in blind image deblurring in such 

areas as MRI and PET brain scans, nanoscale scanning electron and Helium ion micrographs, and 

Hubble space telescope imagery [2]. Here, the recorded blurred image is viewed as the solution at time t = 1 

in an appropriate linear parabolic equation, and the 

desired ideal image is the corresponding initial value 

at time t = 0. These and other successful inverse reconstructions have generated a great deal of current 

mathematical interest in backward in time continuation 

in parabolic equations. Not surprisingly, very little is 

known either analytically or computationally in the 

significantly more challenging area of backward continuation in nonlinear multidimensional parabolic 

equations. We discuss instructive examples illustrating 

the unexpected influence of certain types of nonlinearities. Visually and statistically indistinguishable blurred 

images are presented, with vastly different deblurring 

results. These examples indicate that how an image is 

nonlinearly blurred is critical, in addition to the 

amount of blur. The equations studied represent nonlinear generalizations of Brownian motion, and the 

blurred images may be interpreted as visually expressing the results of novel stochastic processes.

Alfred S. Carasso

It is instructive to study 2D second order parabolic 

equations such as the following,

 

( , ,0) ( , )

(1) (cos ) (0, )

( ) ( , , )

2

w x y g x y

c ww d w w T

w r w q x y t w

x y

t



  

    

on the unit square Ω, with homogeneous Neumann 

conditions on the boundary of Ω. Here γ, c, d are appropriately chosen positive constants, q(x, y, t) is a 

positive non-isotropic diffusivity, and the positive nonlinear function r(w) is exponential in w. By varying the 

constants in r(w) and in the nonlinearities in the wx and 

wyterms, a variety of interesting examples can be created. Numerous other types of nonlinearities can also 

be considered. Such nonlinear equations may occur in 

diverse scientific and engineering contexts.

Useful computational exploration of ill-posed 

backward continuation in Eq. (1) requires intelligent 

choices for the initial values g(x, y), which must be 

sufficiently complex and rich in high frequency components in order to adequately probe behavior. As 

shown in Figure 10, images can provide unusually interesting candidates g(x, y). Irrespective of the ultimate 

intended application of Eq. (1), an efficient exploration

strategy can be based on creating fictitious blurred image data by using sharp images for g(x, y), and 

selecting the corresponding solution at time T > 0 as 

the given continuation data. Successful backward continuation from t = T to t = 0 would recover the sharp 

image. An important advantage is that visual recognition can provide useful and immediate evaluation of 

the degree of success or failure in that continuation. 

This can then be translated into the intended application of Eq. (1), unrelated to imaging.

Hazardous backward continuation. For any initial 

value g(x, y), Eq. (1) has a unique solution w(x, y, T) at 

time T > 0. The function w(x, y, T) belongs to a very 

restricted class of smooth functions and is seldom 

known exactly. Rather, only approximate values f(x, y) 

are typically known. A major challenge is to obtain a

useful approximation to the true initial value g(x, y), by 

backward continuation from t = T using the noisy data 

f(x, y). Indeed, if ||w(., T ) − f ||2 ≤ δ with small δ > 0,

and we constrain the continuations to satisfy a prescribed L

2

bound M at t = 0, the difference between any 

two possible continuations wi(x, y, t), i = 1, 2, obeys the

following stability inequality

Figure 10. Images provide unusually interesting non negative 

initial values g(x, y) that can be used to generate approximate 

values f(x, y), for the exact solution w(x, y, T) at time T in Eq. (1).
Summary of Activities for Fiscal Year 2012 23

(2) (., ) (., ) 2 , 0 .

1 ( ) ( )

1 2 2

w t w t M t T

t t     



In the best case scenario, that of a linear autonomous 

selfadjoint parabolic equation, we have μ(t) = t/T in Eq. 

(2), implying a systematic loss of reconstruction accuracy as t ↓ 0. Nevertheless, as shown in [2], useful 

reconstruction may still be possible. However, in nonlinear equations deviating strongly from the 

autonomous selfadjoint case, μ(t) may exhibit rapid 

exponential decay as t ↓ 0. The resulting loss of accuracy may then be so severe that useful reconstruction is 

not possible, despite the use of regularizing smoothness 

and non-negativity constraints. Examples of smooth, 

non-negative, physically plausible, yet false backward 

reconstructions are given in [3].

Van Cittert iterative procedure. Recently, a useful 

approach to such non-linear continuation problems as 

Eq. (1) has been discovered in ACMD. It is based on

adapting an iterative procedure originating in the field 

of spectroscopy in the 1930’s. This is the Van Cittert 

iteration [4], which was designed for solving 1D linear 

convolution integral equations Sg = f, with explicitly

known kernels having positive Fourier transforms. 

With suitable fixed λ such that 0 < λ < 1, and h

1

(x) = λ

f(x), Van Cittert’s method solves Sg = f using the iteration

(3) ( ) ( )  ( )  ( ), 1

1

   



h x h x f x S h x m

m m m 

There is no explicitly known linear convolution operator S in the case of Eq. (1). Instead, we can construct a 

discrete nonlinear solution operator Λ, which maps the

initial value g(x, y) into w(x, y, T). We restrict attention 

to 256 × 256 pixel 8-bit images. Imposing a 256 × 256 

mesh on the unit square, we use centered space differencing in Eq. (1), together with explicit time 

differencing, while lagging all non-linearities at the 

previous time step. With T = NΔt, the discrete solution 

operator Λ is defined on 256 × 256 images w

0

, by 

Λ[w

0

] = w

N

. Thus, Λ applied to a given image uses that 

image as data w

0

at t = 0 in the difference scheme, and 

marches that image N time steps forward in time, to 

produce a blurred image w

N

at T = NΔt, in accordance 

with Eq. (1).

Given the sharp 256 × 256 image g(x, y) as initial 

value in Eq. (1), applying the discrete solution operator 

Λ to g(x, y) produces a blurred image f(x, y), which is a

noisy approximation to the unknown, highly elusive, 

smooth, exact solution w(x, y, T ). Backward continuation from t = T in Eq. (1) using the given data f(x, y), 

requires solving the 2D nonlinear equation Λg = f, in 

analogy with the simpler 1D linear equation Sg = f in 

Eq. (3). Accordingly, with suitable fixed λ such that 0 < 

λ< 1, and h

1

(x, y) = λ f(x, y), Van Cittert nonlinear 

deblurring is defined by

(4) ( , ) ( , )  ( , )  ( , ), 1

1

   

 h x y h x y f x y h x y mm m m 

Nonlinear deblurring experiment. It is remarkable 

that Eq. (4) can be used successfully in backward continuation in a wide class of 2D nonlinear parabolic

equations similar to Eq. (1). However, as indicated by 

Eq. (2), stability difficulties should be anticipated in 

parabolic equations deviating too strongly from the 

Figure 11. Nonlinear parabolic blurring of sharp USS Eisenhower image, by using it as the initial value g(x,y) in Eq. (1) with two different 

sets of constants c, d. Blurred images (H) and (I) are visually and statistically indistinguishable, with the same PSNR values, and almost identical L1

, L2, and TV norm values.

Table 3. Behavior using Eq. (1) in nonlinear blurring in Figure 

11.

Image 

f(x,y)

Parameters 

c / d || f ||1

|| f ||2 || f ||1 PSNR

G Not blurred 139 153 4760 

H 2.5 / 0.3 134 147 1720 20

I 2.5 / 1.5 134 148 1770 20
24 NIST Applied and Computational Mathematics Division

linear, autonomous, selfadjoint canonical model. Additional difficulties may arise from the Van Cittert 

iteration, originally intended for linear convolution 

equations Sg = f, where the kernel in S has a positive 

Fourier transform.

The following nonlinear deblurring experiment illustrates the strengths and limitations of the above 

methodology. In Figure 11, a sharp image of the aircraft carrier USS Eisenhower is blurred, using Eq. (1) 

with two different sets of values for the constants c and 

d. Because d is larger in image (I) than it is in image 

(H), the nonlinearity is stronger in image (I). However, 

as shown in Table 3, images (I) and (H) have almost

the same values for their L

1

, L

2

, and k || ∇f ||1 norms. In 

addition, images (I) and (H) have identical PSNR values, an image quality metric that 

measures the degradation away 

from the original sharp image 

(G). Thus, images (I) and (H) are 

visually and statistically indistinguishable in Figure 11.

In Figure 12, the nonlinearly 

blurred image (H) is successfully 

deblurred after 100 iterations. 

This is a highly encouraging result, as there are very few pubpublished examples of successful 

nonlinear multi-dimensional 

backward parabolic continuations. Many other such examples, 

involving a variety of nonlinearities, are equally feasible.

The unsuccessful deblurring 

of image (I) suggests that if the 

nonlinearities are too strong in 

the parabolic equation, the resulting backward stability may be 

too weak to permit useful reconstruction. In addition, the Van 

Cittert iteration may become illbehaved, even if the blurred image is virtually indistinguishable

from an image that can be usefully deblurred.

References

[1] C. Bagtzoglou and J. Atmadja, Marching-jury Backward 

Beam Equation and Quasireversibility Methods for Hydrologic 

Inversion: Application to Contaminant Plume Spatial Distribution Recovery, Water Resources Research 39 (2003), 1038–1052. 

[2] A. S. Carasso, Bochner Subordination, Logarithmic 

Diffusion Equations, and Blind Deconvolution of Hubble Space Telescope Imagery and Other Scientific Data, 

SIAM Journal of Imaging Sciences 3 (2010), 954–980.

[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 (2012), DOI: 

10.1002/mma.2582.

[4] P. H. Van Cittert, Zum Einfluss der Spaltbreite auf die 

Intensittsverteilung in Spektrallinien II, Z. Physik 69

(1931), 298-308.

Figure 12. Nonlinearly blurred image (H) was successfully deblurred after 100 interations. 

Visually indistinguishable image (I), blurred with stronger nonlinearities, could not be usefully 

deblurred. Evidently, how an image was blurred, and not just the amount of blur, is critical in 

nonlinearly blurred imagery. 
Summary of Activities for Fiscal Year 2012 25

Metrics for Manipulation and Enhancement of Forensic Images

Fingerprint evidence is routinely used to convict offenders of crimes, but such evidence is rarely pristine. 

Factors that influence the quality of latent fingerprint 

evidence collected from a crime scene include: incomplete prints, pressure gradations, variability in 

underlying surface and materials, including colors. 

Due to the low signal quality of the fingerprint in relation to other systematic image features (color, pattern, 

text etc.), these images are not suitable for input into 

fingerprint identification software to search for matches. In response to this problem the forensics community 

currently uses a variety of image processing tools to 

improve the quality of these images. To date, latent 

image enhancement has been treated as a preprocessing step for subsequent identity matching analysis. 

As dramatic and essential as these transformations are, 

no research exists to characterize this step of the evidentiary analysis chain. Detrimental consequences for 

reproducibility, traceability, and quantification of accuracy follow [2]. This project represents a first 

investigation of this step of the forensic analysis workflow.

Andrew Dienstfrey

In FY 2012 we initiated a new project to research and 

develop metrics to characterize image processing performed in the course of forensic analysis of latent 

fingerprint images. Previously this critical step in the 

evidentiary workflow has been insufficiently characterized, and its reproducibility has not been studied. This 

project will facilitate the creation of reproducible and 

quantitative analysis to promote a scientific basis for 

latent fingerprint enhancement. We expect that this 

project will provide a foundation for comparable studies in other forensic image analysis workflows.

To establish a controlled testbed, two expert forensic analysis companies—Schwarz Forensic Enterprises 

and ForayTechnologies—created a database of surrogate latent fingerprints and their associated 

enhancements. The images shown in Figure 13 are two 

examples from this new database. The original latent 

fingerprints are shown on the left, and the associated 

enhancements are shown to the right, Figure 13 (a), (c) 

and (b), (d) respectively. Visually, the result of the enhancement process is striking. While fingerprints can 

barely be seen in the original images, the combination 

of the removal of systematic background features and 

color processing reveals enhanced images that undeniably contain fingerprints. Schwarz and Foray initially 

provided 39 before-after pairs and associated metadata 

(see below). A second round consisting of more than

60 additional enhancement pairs has been provided and 

uploaded to NIST servers and will be analyzed in follow-up work.

Our first goal was to understand the scope of image transformations most often used to enhance latent 

prints. Forensic guidelines require that enhanced images be accompanied by metadata indicating all 

processing applied to an evidentiary article. Adobe

Photoshop is the image enhancement software of 

choice in the forensic sciences as practiced today. 

Within Photoshop this metadata requirement is met by 

activating a logging utility that records the sequence of 

Photoshop commands executed by the analysts. All

enhancements in the new NIST latent fingerprint archive are accompanied by such text files. This 

compendium provides valuable data for analysis of the 

nature of the enhancement processing. For example, a 

parser was written to extract command usage from the 

log files. A preliminary result on the frequency of 

command usage is shown in Figure 14. The space of 

image processing possibilities is quite large. Using a 

ranking-by-frequency approach this analysis represents 

the first systematic investigation of the relative importance of enhancement procedures of which we are

aware.

In addition, this collection of log files enables us to 

begin addressing the question of enhancement reproducibility. In current forensic practice the metadata 

files are required as a mechanism for reproducibility of 

the enhancement process should it be questioned in an

evidentiary proceeding. However, a comparative study 

of the Photoshop command structure and the details 

Figure 13. Sample latent prints in the NIST database and their 

Photoshop enhancements.
26 NIST Applied and Computational Mathematics Division

provided in the metadata logs reveals a substantial inadequacy in this regard. For example, in a preliminary 

analysis of 40 latent enhancements we find that combination of either burn and dodge commands is used 

over 120 times; indicative of frequent and repeated 

utilization. However, while in practice these commands 

require user-specified parameters in the form of bounding boxes and “strength’” (i.e., of the lightening or 

darkening associated with the dodge or burn respectively), in the case of burn and dodge, the log files 

simply record the command name with no parameter

information. It follows that pixel-by-pixel reproducibility is not possible using this record-keeping utility in 

the Photoshop enhancement workflow. This example,

along with others, provides a basis for future research 

on details and implementation of reproducibility requirements in the forensic image enhancement 

workflow.

Finally we investigated possibilities for metrical 

analysis of the enhancements as well as alternative 

image enhancements performed independently of Photoshop. In Figure 15 we show an example of an 

enhancement performed using Matlab in comparison

with the result achieved with Photoshop. Visually the 

resulting enhancements appear comparable. Consideration of such alternative enhancements may better 

inform the subsequent matching and identification procedure as they provide an idea of the range of images 

that may be reasonably obtained. In addition, using 

scientific packages such as Matlab, IDL, and PV-Wave 

provides additional benefits as they generally include a 

broader set of processing commands, yet do so in a 

more rigorous and reproducible manner.

Concerning the metrical analysis, among the many 

image metrics we are investigating we draw attention 

here to the discrete L

1

and L

2

image norms, as well as 

the discrete L

1

and L

2

image gradient norms. For an 

image f(x,y) of size Nx by Nythese are defined by

p

N N

x y

p

x y

p

x y

f x y

N N

f

1/

,

, 1

( , )

1



















 

p

N N

x y

p

y

x

x y

p

x y

f x y

f x y

N N

f

1/

1, 1

, 1

2 / 2

2

( ( , )) )

1 (( ( , ))

















 





  

 



f (x, y) N f (x 1, y) f (x, y) x

x

  

f (x, y) N f (x, y 1) f (x, y) y

y

  

Figure 14. Frequency of command usage obtained by parsing 39 metadata files
Summary of Activities for Fiscal Year 2012 27

Note that the gradient L

1

norm is a discrete version of 

the total variation (TV) norm frequently used in image 

analysis. Table 4 shows these norms applied to the four 

images in Figure 15. While the Photoshop and Matlab 

performed enhancements appear visually comparable, 

the L

2

image and gradient norms report different values 

for these two images. We also observe that the L

1

versions of these norms appear to be less discerning of this

difference. We have performed similar analysis on several additional enhancements and find this pattern to be 

consistent. Specifically, the gradient L

2

norms routinely 

return different values, distinguishing diverse analysis 

workflows.

The above work has been documented in a NIST 

report [1]. In FY 2013 we expect to further investigate 

the metrical analysis using additional fingerprintspecific image metrics including the spectral image 

verification and validation described in [3]. 

This work was sponsored by a 2012 NIST Forensic 

Measurement Challenges grant. 

References

[1] A. Carasso, Alternative Methods of Latent Fingerprint 

Enhancement and Metrics for Comparing Them, 

NISTIR 7910, National Institute of Standards and Technology, Gaithersburg, MD, January 2013.

[2] Expert Working Group on Human Factors in Latent 

Print Analysis, Latent Print Examination and Human 

Factors: Improving the Practice through a Systems Approach, NISTIR 7842, National Institute of Standards 

and Technology, Gaithersburg, MD, February 2012.

[3] J. M. Libert, J. Grantham, and S. Orandi. A 1D Spectral 

Image Validation/Verification Metric for Fingerprints,

NISTIR 7599, National Institute of Standards and Technology, Gaithersburg, MD, 2009.

Participants

Andrew Dienstfrey, Alfred Carasso (ACMD); Mary 

Theofanos (NIST SCO), Peter Bajcsy (ITL SSD), Haiying Guan (ITL IAD), David Witzke (Foray 

Technologies), Matt Schwarz (Schwarz Forensic Enterprises)

Figure 15. Sample enhancements performed independently of Adobe

Photoshop.

Table 4. Result of measuring alternative enhancement workflows with different norms.

Image ||f||1 ||f||2 ||f||1 ||f||2

Original Laten 16 18 2600 3900

Forensic Photoshop 61 75 25000 36000

Matlab Contrast Adj. 60 80 25000 40000

Matlab Histogram Eq. 112 138 42000 60000
28 NIST Applied and Computational Mathematics Division

Rheology of Dense Suspensions

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 (Quaternion-based Dissipative Particle Dynamics), which is 

capable of performing large-scale simulations of dense 

suspensions. 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

at Argonne National Laboratory. Our goal in this project is to advance understanding of the flow properties 

of a specific material, fresh concrete, a dense suspension composed of cement, water, sand, and rocks.

Our current focus is on enabling the use of vane 

rheometers for measuring the flow properties of fresh 

concrete, something not currently possible. While different concrete flow measurements can be found to 

correlate, they usually do not agree well. A vane geometry combined with a strongly random suspension 

will result in complex local stress and strain/strain rate 

fields. Current vanes are not optimized for precise 

measurement (or mixers for best mixing practice).

These simulations will enable us to map out

stress/strain fields in 3D, and bring insight into the 

vane design process. In addition to the advancement of 

our understanding of the flow of dense suspensions, we 

are also using this simulator in the design process for 

new standard reference materials (SRMs) which will be 

used for calibrating mortar and concrete rheometers.

William George

Concrete is the most widely used building material in 

the world, representing a 100 billion dollar industry in 

the US that is crucial for our nation’s physical infrastructure. There is now a strong interest in making 

concrete a more sustainable material by finding new 

ways to recycle it, and by changing its ingredients in 

order to reduce the amount of greenhouse gas from its 

production. (The manufacture of concrete’s key ingredient, cement, is responsible for about 8% to 10% of 

global CO2 production.) As new mixture designs of 

concrete are developed to meet these needs, it is important to measure and control rheological (i.e., flow) 

properties to satisfy performance specifications. Failure 

to control the flow of concrete on a job site can lead to 

significant cost overruns and months of delay by having to correct previous errors.

Often fluids are characterized by the properties 

yield stress and viscosity, both of which can vary as a 

function of shear rate. Yield stress is the force applied 

per unit area to initiate the flow. Viscosity is the applied 

force per unit area needed to maintain a shear rate. 

Shear rate is the velocity gradient perpendicular to the 

flow direction. An image showing the local stress in a 

vane rheometer is shown in Figure 16. 

Figure 16. Top: Snapshot from a simulation of a four-blade vane 

rheometer with a suspension of hard spheres. Each sphere is colored-coded by the rheometer octant in which it was located at the 

start of the simulation. The blades are rotating clockwise and have 

made approximately two full rotations at the time of this snapshot.

Bottom: Vane rheometer simulation displayed with a volume visualization of the magnitude of the local stress within the system.

Only four of the eight octants are shown here in order to see details around the vanes. Here stress is color-coded from yellow 

(low stress), to green (high stress), with stresses below a set 

threshold show in light purple.
Summary of Activities for Fiscal Year 2012 29

Many factors control viscosity and yield stress. 

For example, in building materials such as concrete, 

viscosity and yield stress depend on the ratio of water 

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

their shape and size distribution. There can be great 

variation in each material depending on its history and 

where it was obtained. For example, rocks from quarries are usually angular because they are crushed when 

processed, whereas rocks obtained from river beds are 

typically rounded due to erosion. Additionally, it turns 

out that the more similar the size of the rocks in a concrete suspension, the harder it is to get that concrete to 

flow. In this case, the concrete may actually jam when 

poured through a narrow opening, thus causing delays 

in construction. Clearly, to optimize the flow properties 

of concrete and other suspensions, one needs to understand the relationship between flow and properties of 

the fluid’s constituents.

Quaternion-based Dissipative Particle Dynamics. 

Modeling and predicting the flow of suspensions such 

as concrete represents a great scientific challenge, since 

these are complex disordered systems with a variety of 

components that can interact in many different ways. 

Indeed, accounting for the size and shape variation of 

the solid components of the suspension (cement particles, sand, or rocks) poses many computational 

challenges. A representative system may entail keeping 

track of up to 100,000 solids of varying shape and size. 

Further, many of the forces between particles depend 

on the local surface curvature of the aggregate at points 

close to neighboring aggregates, which requires keeping track of the location, orientation and shortest 

distance between neighboring solids. Clearly, modeling such systems necessitates large scale simulations at 

a fundamental level to accurately predict its properties. 

We have adopted and developed some novel approaches, originally based on cellular automata methods that

can successfully take into account many of the features 

of a suspension. Our code, QDPD, has been validated 

by both theory and experiments on idealized systems 

and has been extended to account for random shaped 

objects with different interparticle interactions.

QDPD [1], which stands for Quaternion-based 

Dissipative Particle Dynamics (DPD), uses modified 

versions 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, in order to simulate dense suspensions such as cement paste, mortar, and concrete. In 

addition to the forces computed using the DPD and 

SPH techniques, other forces are computed in these 

systems to better account for the interaction between 

the suspended particles, that is, the sand and gravel. 

These additional forces include lubrication forces that 

help keep these suspended particles separated, and van 

der Waals forces that introduce an attractive interparticle force. Brownian forces are also present in QDPD 

to maintain system temperature.

High Performance Computing. Starting with the 

original serial version of this simulator we have enhanced QDPD to utilize the power of large parallel 

machines regularly using 8000+ processors, and, for 

large production runs, using 32,000 processors or 

more. The performance of QDPD running a typical 

simulation on an IBM Blue Gene/P is shown in Figure 

17 in terms of speedup [8]. QDPD remains under constant development to improve its capabilities as well as 

to improve its parallel performance. For example, we 

have recently begun basic algorithm changes to enable 

the efficient execution of our simulations on at least 

170,000 processors of Mira, the latest DOE machine at 

the Argonne Leadership Computing Facility (ALCF). 

This includes changes in inter-processor communications as well as the addition of multi-threading.

During the 2012 calendar year we have had access 

to the IBM Blue Gene/P supercomputer Intrepid, having been awarded 22 million CPU-hours of compute 

time on this machine from the DOE INCITE program 

(Innovative and Novel Computational Impact on Theory and Experiment). This access has enabled us to 

perform several very large simulations of a 4-blade 

vane rheometer. We have been awarded a third year of 

compute time, for 2013, at ALCF through our latest 

peer-reviewed INCITE proposal. For 2013 we will 

have a total of 30 million CPU-hours of compute time 

at the ALCF, including 10 million CPU-hours of time 

on Mira, the new IBM Blue Gene/Q at Argonne. Mira, 

which consists of 786,432 processors, and is ranked 

Figure 17. Performance of QDPD on Intrepid, an IBM Blue 

Gene/P, on a system of approximately 105inclusions (rocks) and 

108 DPD particles.
30 NIST Applied and Computational Mathematics Division

number 4 on the November 2012 Top 500 Supercomputers list11

.

Visualization. A major part of this project involves the 

development and use of specialized visualization software to investigate in detail the results of our 

simulations. This includes both the display of the systems under study as well as techniques to probe and 

measure aspects of the system we are viewing. For 

performance reasons we rely heavily on the programmable capabilities of GPUs (Graphics Processing 

Units). For example, within the images in each of the 

figures, each suspended sphere is rendered within the 

GPU as a point sprite, i.e., a 2D textured image at a 

single 3D point, which requires only location and size 

information for display, rather than using a polygonal 

representation of these spheres. We also use volume 

visualization techniques to display various properties 

within the system, such as in Figure 16 (bottom) which 

shows the local stress value throughout the system. As 

shown in Figure 18 and Figure 19, we can interactively 

probe a system to reveal values of properties at specific 

locations or areas in the system. All of our visualizations can also be used within our 3D immersive 

visualization system for full immersion into the simulated systems. This system consists of 3 large displays 

(each approximately 2.5m by 2.5m), arranged as two 

walls and a floor forming the corner of a cube.

Results. Over the last few years our simulations have 

provided fundamental insights into the mechanisms 

that control the onset of flow in suspensions that can be 

linked to macroscopic properties such as yield stress 

and viscosity [4, 7]. Our studies have also enabled us to 

discover that, given the rheological properties of a nonNewtonian fluid matrix in a dense suspension, such as 

 

11 http:// www.top500.org/

a mortar or concrete, we can predict key rheological 

properties. For example, we have simulated the flow of 

dense suspensions consisting of 1 mm diameter glass 

beads suspended in a matrix fluid of known properties, 

NIST SRM 2492 [5], for volume fractions ranging 

from 10% to 49% glass beads. These simulations have 

been performed for a large range of shear rates. From 

our studies, we have discovered that, given the rheological properties of a non-Newtonian fluid matrix, we 

can predict the rheological properties of suspensions 

composed of hard spheres in this fluid [6]. We are currently writing a paper detailing this discovery. Such 

suspensions are currently being evaluated as a new 

candidate SRM for mortars. As a consequence of this 

discovery, one only needs to measure the fluid properties of the matrix fluid, which is generally far easier to 

do than measuring the suspension. Hence, fewer experiments are needed to obtain the rheological properties 

of the suspension, saving cost and time for industry. 

Currently these results apply only to hard sphere suspensions. However, we plan to test this scaling 

approach on suspensions composed of more complex 

shaped inclusions.

Finally, while the main thrust of our research focuses on predicting the rheological properties of 

cement based materials such as concrete, an improved 

general understanding of rheological properties derived 

from this research should have a broad impact. Suspensions are utilized in a wide variety of technological 

processes and, as our study is largely parametric in 

nature, results will be transferable to other suspensions 

of interest such as nanoparticle systems. Understanding 

mechanisms for the dispersion or agglomeration of 

such systems remains a challenge in many industries,

ranging from pharmaceuticals to coatings.

References

[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 Dynamics, Europhysics Letters

19 (1992), 155-160.

[3] J. J. Monaghan, Smoothed Particle Hydrodynamics. 

Reports on Progress in Physics 68 (2005), 1703–1759.

[4] 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), 20 (7 pages).

[5] C. F. Ferraris, P. Stutzman, J. Winpigler, and W. F. 

Guthrie, Certification of SRM 2492: Bingham Paste 

Mixture for Rheological Measurements, NIST Special 

Publication SP 260-174 Rev. 2012, U.S. Government 

Printing Office: Washington, DC (2012).

[6] D. Lootens, N. Martys, and P. Hebraud, Universal 

Figure 18. Interactively positioning a line probe in a system. Each 

endpoint is indicated with a 3D cursor consisting of three orthogonal pairs of small cones surrounding the chosen point. The 

endpoints of this line probe can be positioned anywhere within the 

simulation box shown in this image. The hard spheres and volume 

visualization of the stress have been turned off for this image in 

order to highlight the probe.
Summary of Activities for Fiscal Year 2012 31

Behaviour of Non-Newtonian Suspensions, XVIth

International Conference on Rheology, Lisbon, Portugal, 

05-Aug-2012.

[7] P. Hebraud, D. Lootens, and N. Martys, Stress 

Organization in an Attractive Concentrated Colloidal 

Suspension under Flow,, XVIth International 

Conference on Rheology, Lisbon, Portugal, 05-Aug2012.

[8] W. George, N. Martys, C. Ferraris, S. Satterfield, M.

Olano, and J. Terrill, Computational Based Study of 

Suspension Flow in Vane Rheometers, Workshop on 

High-Performance Computing for Industry, Rensselaer 

Polytechnic Institute, Troy, New York, October 26-38 

(2011).

Participants

William George, Steven Satterfield, Marc Olano, Judith Terrill (ACMD); Nicos Martys, Edward Garboczi

(NIST EL); Pascal Hebraud (CNRS/ESPCI, France).

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

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

Figure 19. This is the identical display as in Figure 18 except that now we have turned on the volume visualization of the stress data as well as 

some of the hard spheres. The stress along the probe line is shown in the sub-window labeled Stress Profile. This plot is dynamically generated 

and updates each frame as the simulation is animated.
32 NIST Applied and Computational Mathematics Division

Visualization and Modeling of RF Propagation in Body Area 

Networks 

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), temperature, respiration, and heart rate. While 

BAN is poised to be a promising technology with novel 

uses in pervasive healthcare, there are still numerous 

technical, commercial and regulatory challenges, including usability, interoperability, energy source, 

miniaturization, security, and privacy. One of the prerequisites for the safe and effective design of such 

systems is an understanding of RF propagation around 

and inside the body. We have developed a visualization 

platform for the study of human body RF propagation 

and are applying it in support of IEEE standardization 

efforts.

Kamran Sayrafian

With recent advances in microelectronics, the technology to build very small and extremely low power 

wearable and implantable devices is clearly within our 

reach. However, commercial success of this technology 

depends on the widespread adoption of a global standard for its communication protocol (i.e., air interface). 

Knowledge of RF propagation is a critical step in this 

process, enabling RF engineers to optimize their physical layer design to achieve better communication 

performance. Such information is typically gathered by 

conducting physical experiments and processing the 

measured data to obtain propagation channel characteristics. Obtaining data sufficient to study this for various 

scenarios is difficult for wearable BAN sensors. 

Moreover, obtaining any data through physical experimentation is extremely challenging to impossible for 

implantable devices.

In view of the above, a 3D modeling and visualization platform that is capable of emulating physical 

experiments can be extremely beneficial in understanding the radio waves propagation behavior in body area 

networks. Although validation with physical experiment is ultimately needed to investigate the reliability 

of the results, such a platform can be used to determine 

the best (i.e., optimized) test scenarios for more limited 

physical experiments. 

For this reason, we have set up a unique 3D immersive visualization environment that allows virtual 

experiments to be performed in order to study various 

RF propagation scenarios among implantable or wearable body sensors. Inhomogeneity and complexity of 

the propagation medium, along with possible propagation paths from any direction, necessitate a 3D 

environment to better capture, visualize, and understand 

RF propagation. The complexity of the environment

surrounding a medical implant also implies that an appropriately designed immersive platform would be very 

helpful in better understanding the radio frequency 

channel characteristics inside the human body. Lack of 

a sufficiently detailed human body model and realistic 

wearable/implantable antenna models are usually 

among the shortcomings of previous simulation studies 

in this area. The present work overcomes these limitations. 

Our 3D immersive platform, as shown in Figure 

20, includes several components: a visual display consisting of three large screens, stereoscopic glasses that 

are motion-tracked, and a hand-held input device that is 

also motion-tracked. The three large projection screens 

are arranged edge-to-edge in a corner configuration; 

these are used as a single 3D stereo display. The 3D 

scene is updated for the position of the stereo glasses 

given by the motion tracker. This enables system to 

present a virtual 3D world within which the user can 

move and interact with the virtual objects; this is the 

essence of the immersive experience. A hand-held 

three button motion-tracked wand with a joystick is the 

principal interaction device. 

Figure 20. Our 3D-immersive platform for the study of RF propagation in body-area networks.
Summary of Activities for Fiscal Year 2012 33

In this environment, a researcher can place a custom designed antenna at the desired location of the 

human body, set the operating frequency of the node, 

and study the RF propagation at any location inside or 

around the body. The platform user can observe the 

data representations at his desired scale and position. 

The user can physically move through data, and change 

visual orientation. The user can also control the elements of the virtual world using a variety of interactive 

measurement and analysis techniques. All of these capabilities are especially useful for the 3D study of RF 

propagation to/from implanted or wearable body devices. In addition, a more convenient and natural 

interaction between experts with different backgrounds 

is possible using this system. For example, a surgeon 

can point to the exact location of an implant using the 

interactive tools, and then an antenna designer can design the antenna to fit the chosen location, given the 

physical and biological constraints. An RF engineer, in 

turn, would be able to observe the propagation performance for the target communication link, or compute 

other measures, such as specific absorption rate (SAR),

given the transmitted power.

Some of our results that are related to the statistical modeling of path-loss for implant communication 

have been adopted by the IEEE 802.15.6 International 

standard on body area networks [1]. In [2], we have 

explained how our simulation platform can be used to 

better understand the discrepancies between various 

sets of physical measurements related to body surface 

propagation. The impact of an aortic valve on this type 

of propagation has also been determined using our platform [3]. Evaluating the efficiency of custom made 

antennas and studying the creeping wave propagation 

on the body surface can be easily done in our system as 

well [4]. In addition to qualitative and quantitative data 

observation and statistical processing, studying RF 

propagation for specific medical applications such as 

cochlear implants, brain neural interface and retina 

implants is also possible using such platforms.

We are currently studying 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. To accomplish this, we have developed 

computational methods for deforming the 3D body 

model (including the internal body organs) into various 

poses. The most difficult problem that we had to solve 

in the body deformation was to ensure that the deformed internal structures do not intersect one another,

thereby rendering the model invalid for our simulations. We plan to use these methods to create a 

sequence of poses to describe a motion such as walking. Figure 21 shows three poses from a sequence that 

describes a walking motion. The posed body models 

are then used as the basis for a series of simulations. 

Through collaborative efforts with other research institutes, we plan to 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.

References

[1] K. Sayrafian-Pour, W. Yang, J. Hagedorn, J. Terrill, K. 

Y. Yazdandoost, A Statistical Path Loss Model for Medical Implant Communication Channels, in Proceedings 

of the IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, 2009.

[2] W. Yang, K. Sayrafian-Pour, J. Hagedorn, J. Terrill, K. 

Y. Yazdandoost, Simulation Study of Body Surface RF 

Propagation for UWB Wearable Medical Sensors, in 

Proceedings of the 2nd International Symposium on Applied Sciences in Biomedical and Communication TechTechnologies, November 2009.

[3] W. Yang, K. Sayrafian, J. Hagedorn, J. Terrill, K. 

Yazdandoost, A. Taparugssanagorn, M. Hämäläinen, J. 

Iinatti, Impact of an Aortic Valve Implant on Body Surface UWB Propagation: A Preliminary Study, in ProProceedings of the 5th International Symposium on 

Medical Information and Communication Technology

(ISMICT), March 2011.

[4] K. Sayrafian, J. Hagedorn, W. Yang, J. Terrill, A Virtual 

Reality Platform to Study RF Propagation in Body Area 

Networks, in Proceedings of the 3

rd IEEE International 

Conference on Cognitive Info-communications, December 2012.

Participants

John Hagedorn, Kamran Sayrafian, Judith Terrill

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

Figure 21. Several body poses from a walking sequence.
34 NIST Applied and Computational Mathematics Division

A Stochastic Theory of Fatigue for Aging Structures 

Engineering components and structures are designed 

to function without premature failures due to aging. 

Traditionally, for new structures, their useful lives have 

been estimated from mathematical models of fatigue 

which are deterministic. Those models contain parameters that are determined from experiments using 

specimens of the structure when new. It is well-known 

that as structures age, their properties change, and 

hence the models based on the original materials are 

no longer applicable. In other words, it is not correct 

to simulate the performance of the aging structures 

when their current properties are not known. To address this gap-in-modeling problem, we develop a 

stochastic theory of fatigue, using in-situ nondestructive evaluation (NDE) measurements of detectable crack lengths and crack growth rates in an aging

component or structure as a basis for estimating the 

mean and standard deviation of its remaining life.

Jeffrey Fong

It has been almost fifty years since Paris [1] proposed a 

simple model to describe the crack growth behavior of 

a large number of engineering materials by a relationship between cyclic crack growth rate, da/dN and stress 

intensity range K,

m

(1) da / dN  C (K)

where a is the crack length, N is the number of cycles, and C and m are two material constants that are 

estimated from a log-log plot of test data (after Paris, et 

al. [2]). The model has since been widely accepted 

(see, e.g., Kanninen and Popelar [3], Dowling [4]). In 

particular, it has been adopted in the ASME Boiler and

Pressure Vessel Code for fatigue design of new and 

nondestructive evaluation (NDE) of aging pressure 

vessels and piping (see, e.g., Bamford [5]). 

It turns out that the constant C is a pseudo material 

property parameter, because it is sensitive not only to 

the cyclic stress ratio R (= smin / smax), as shown by 

Dennis [6] for a constant amplitude cyclic stress test 

with the stress range S defined by (smax - smin), but also 

to three additional empirical material parameters as 

proposed by Walker [7] and documented by Dowling 

[4, p. 506, Table 11.2]. In spite of these complications

in modeling fatigue crack growth, engineers have devised a formula for estimating the useful life (in 

cycles), Nif , of a new component or structure by integrating Eq. (1):

( ) (1 / 2)

(2)

1 / 2 1 / 2

C F S m

a a

N

m

m

i

m

f

if  





 



where the third constant, F, is a geometric factor that is 

introduced to account for a reduction in the estimated 

life, Nif , when the crack tip is located too close to a 

boundary. It is important to note that neither the initial 

nor final crack lengths (ai and af ) are measurable by 

NDE methods. As shown in Figure 22 (after Dowling 

[4, p. 49]), what is measurable by an NDE team is ad, 

the minimum crack size that can be “reliably” detected, 

where ad > ai.

Another interesting material property parameter, 

known as the critical crack length, ac , is also indirectly measurable, because it is the length that causes a 

specimen or full-scale structure to fail, and can be estimated from a formula (see Dowling [4, p. 521, Eq. 

11.33]) based on the theory of brittle fracture. If a material is ductile, the final crack length, af

, is always 

greater than ac. In other words, af > ac > ad > ai.

For most metals and alloys, Eq. (2) can be simplified by dropping the term involving the quantity af

using the following argument. Assuming we are working with a component made of AISI 4340 steel with 

crack growth data given in Figure 22. For R = 0.7,

Dowling [4, p.507] estimated that, for Eq. (2), the constant C = 2.49 × 10-9

, and m = 3.46. From a plot in 

Dowling [4, p. 301, Fig. 8.12], and assuming that the 

crack tip is far from a boundary, we estimate that the 

geometric constant F in Eq. (2) is approximately equal 

to 1.0. Let the maximum stress, smax, be equal to 300 

MPa. With R = 0.7, the minimum stress, smin, is equal 

Figure 22. Effect of R-ratio on crack growth rates for an alloy 

steel. For R < 0, the compressive portion of the load cycle is here 

included in calculating ΔK. (After Dowling [4, p.494] with data 

from Dennis [6]).
Summary of Activities for Fiscal Year 2012 35

to 0.7 × 300 = 210 MPa. The stress range, S, is, 

therefore, equal to 300 – 210 = 90 MPa. Let us assume, based on best estimates from the literature (see 

Kitagawa and Suzuki [10], and also Nisitani and Takao 

[11]), that the initial crack length, ai, is of the order of 

0.1 mm. Let us also assume that the final crack length, 

af, equals 50 mm. Substituting all of the above values 

of C, m, F, S , ai, and af, into Eq. (2), we obtain Nif 

= 193 cycles. If we drop the term involving af, we 

obtain Nif = 197 cycles, a difference of about 2%.

Motivated by the large scatter of fatigue test data 

at microstructural, specimen, and full-scale structural 

levels, we have applied the classical theory of error 

propagation (see Ku [12]) to the simplified Eq. (2) and 

developed a stochastic single-crack-growth theory of 

fatigue [9], as illustrated in Figure 23 and the following 

equations. (Note that ‘ = (

1-m/2

– 1) / (1 – m/2), in 

which  = af/ ai. )

i m

i

if Q

a

N

,

(3) 















  2

,

,

2 2

,

2

2 Var( ) Var( )

(4) Var( ) ( )

i m

i m

i

i

i m

i

if Q

Q

a

a

Q

a

N 

where 

a ai

i m

dN

da Q















, 

References

[1] P. C. Paris, The Fracture Mechanics Approach to 

Fatigue, in Proceedings on the Symposium on Fatigue –

An Interdisciplinary Approach (J. J. Burke, et al., eds.), 

10th Sagamore Army Materials Research Conference, 

Syracuse University Press (1964), 107-127. 

[2] P. C. Paris, et al., Extensive Studies of Low Fatigue 

Crack Growth Rates in A533 and A508 Steels, in Stress 

Analysis and Growth of Cracks, Proceedings of 1971 

National Symposium on Fracture Mechanics, Part 1, 

ASTM STP 513, ASTM (1972), 141-176.

[3] M. F. Kanninen, and C. H. Popelar, Advanced Fracture 

Mechanics, Oxford University Press (1985).

[4] N. E. Dowling, Mechanical Behavior of Materials, 2

nd

Edition, Prentice-Hall (1999).

[5] W. H. Bamford, Chapter 31. Fatigue Crack Growth, 

Fatigue, and Stress Corrosion Crack Growth: Section XI 

Evaluation, in Companion Guide to the ASME Boiler & 

Pressure Vessel Code, Vol. 2, (K. R. Rao, ed.), 3rd edition, ASME Press (2009), 535-567.

[6] K. R. Dennis, Fatigue Crack Growth of Gun Tube Steel 

under Spectrum Loading, MS Thesis, Virginia 

Polytechnic Institute and State University (1986).

[7] K. Walker, The Effect of Stress Ratio during Crack 

Propagation and Fatigue for 2024-T3 and 7075-T6 

Aluminum, in Proceedings of the Symposium on Effects 

of Environment and Complex Loading History on 

Fatigue Life, ASTM STP 462, ASTM International, 

West Conshohocken, PA (1970), 1-14.

[8] J. T. Fong, P. V. Marcal, O. F. Hedden, Y. J. Chao, and 

P. S. Lam, A Web-based Uncertainty Plug-In (WUPI) 

for Fatigue Life Prediction Based on NDE Data and 

Fracture Mechanics Analysis, in Proceedings of the

ASME Pressure Vessels & Piping Conference, July 26-

30, 2009, Prague, ASME, New York, NY (2009), Paper 

PVP2009-77827.

[9] J. T. Fong, N. A. Heckert, and J. J. Filliben, A Stochastic and Local Theory of Fatigue for Aging Pressure 

Vessels & Piping, in From Failure to Better Design, 

Manufacture and Construction, (S. T. Tu, Z. D. Wang, 

and G. C. Sih, eds.), Proceedings of the 3

rd International 

Symposium on Structural Integrity, Oct. 31 – Nov. 4, 

2012, Shandong University, Jinan, China, East China 

University of Science and Technology Press, Shanghai, 

China (2012), 19-31.

[10] H. Kitagawa, and I. Suzuki, in Reliability Approach in 

Structural Engineering, (A. M. Freudenthal, et al., eds.), 

Maruzen, Tokyo, Japan (1975), 217-233.

[11] H. Nisitani, and K. Takao, Significance of initiation, 

Propagation ad Crack Closure of Micro-cracks in High 

Cycle Fatigue of Ductile Metals, Engineering Fracture 

Mechanics 15 (3-4) (1981), 445-456.

[12] H. H. Ku, Notes on the Use of Propagation of Error 

Formulas, Journal of Research of the National Bureau 

of Standards – C. Engineering and Instrumentation, 

70C (4) (1966), 263-273.

Participants

Jeffrey T. Fong (ACMD); N. Alan Heckert, James J. 

Filliben (ITL SED), Richard A. Fields, Stephen W. 

Freiman (NIST MML); Pedro V. Marcal (MPACT 

Corp., Oak Park, CA); Y. J. (Bill) Chao (University of

South Carolina); Poh-San Lam (DOE Savannah River 

National Laboratory); Owen F. Hedden (ASME Codes 

& Standards)

Figure 23. An application of the stochastic single-crack-growth 

theory (after Fong, et al. [8, 9]).
36 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2012 37

Part III: Project Summaries

 Part III

Project Summaries
38 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2012 39

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. 

Continuation Backward in Time in 

2D Nonlinear Parabolic Equations

Alfred Carasso

See feature article, page 22

Micromagnetic Investigation of 

Periodic Cross-Tie/Vortex Wall 

Geometry

Michael Donahue

See feature article page 19.

Metrics for Manipulation and 

Enhancement of Forensic Images

Andrew Dienstfrey

Alfred Carasso

Mary Theofanos (NIST SCO)

Peter Bajcsy (ITL SSD)

Haiying Guan (ITL IAD)

David Witzke (Foray Technologies)

Matt Schwarz (Schwarz Forensic Enterprises)

See feature article, page 25.

A Stochastic Theory of Fatigue for 

Aging Structures 

Jeffrey T. Fong

N. Alan Heckert (ITL SED)

James J. Filliben (ITL SED)

Richard A. Fields (NIST MML)

Stephen W. Freiman (NIST MML)

Pedro V. Marcal (MPACT Corp.)

Y. J. (Bill) Chao (University of South Carolina)

Poh-San Lam (Savannah River National Laboratory)

Owen F. Hedden (ASME Codes & Standards)

See feature article, page 34.

[Contributes to Virtual Measurements crosscut.]

Molecular Movies: Imaging 

Femtosecond Motion during 

Electrochemical Transitions

Bradley Alpert

Joel Ullom et al. (NIST PML)

Chris Cromer et al. (NIST PML)

Ralph Jimenez et al. (NIST PML/JILA)

Henry Kapteyn et al. (University of Colorado/JILA)

Vital to the development of next-generation nanomaterials, including photovoltaics and industrial 

catalysts, is an understanding gained through measurement of electron release, transport, and transfer in

engineered nanostructures. This project, supported for 

the last two years by a NIST Innovations in Measurement Science award, proposes a revolutionary, tabletop x-ray imaging system to capture the motion of electrons, atoms, and molecules on femtosecond time 

scales and with picometer spatial resolution.

The combination of table-top x-ray lasers, a dramatic recent breakthrough developed at JILA, with 

transition-edge sensor (TES) microcalorimeter spectroscopy, intensively developed and refined in 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,
40 NIST Applied and Computational Mathematics Division

 Improving efficiency in elimination of lowfrequency background noise, and

 Extending multiplexing and reducing cross talk in 

extracting the signals from below 1 degree Kelvin 

to room temperatures.

Wiener filtering, long used among astronomers for 

estimating amplitudes of pulses of known shape contaminated with noise of known 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 proposed method for computing filters in 

the time domain, rather than the frequency domain, allowing for orthogonality to prior pulse 

tails, was evaluated on gamma-ray data. In addition to an initial successful test at low rate pulses 

[1], a subsequent experiment demonstrated its better preservation of excellent energy resolution at 

high pulse rates than that possible under the standard method [2].

2. A filtering method recently proposed by other researchers, which is intended for inline processing 

and trades some resolution for simplicity and ability to handle high pulse rates, was analyzed [3].

3. An efficient procedure was developed for noise 

whitening, in which a photon detector’s observed 

noise power spectrum is approximated by a rational function and a time-domain infinite impulse 

response filter is constructed. This procedure is 

expected to enable a nonlinear least squares procedure for processing piled-up pulses to be 

performed efficiently.

Attention is currently focused on recovering photon energies when the corresponding pulses are so 

closely spaced that the detector response is significantly nonlinear. In addition, the new experimental

apparatus is now close to fully functional and we expect further sources of uncertainty will arise and need 

characterization.

[1] B. Alpert, J. Fowler, D. Bennett, R. Doriese, J. Ullom, 

A. Hoover, N. Hoteling, and M. Rabin, Improved High 

Rate Pulse Processing Algorithms for Microcalorimeters, 14th International Workshop on Low Temperature 

Detectors, August 2, 2011.

[2] 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, Filters for High Rate Pulse Processing, in 

review.

[3] B. K. Alpert, W. B. Doriese, J. W. Fowler, J. N. Ullom,

Predicted Energy Resolution of a Running-Sum Algorithm for Microcalorimeters, Journal of Low 

Temperature Physics 167:5-6 (2012), 582-587.

[4] 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, L. R. 

Vale, Optimization of the TES-Bias Circuit for Multiplexed Microcalorimeter Array, Journal of Low 

Temperature Physics 167:5-6 (2012), 595-601.

[5] 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, J. N. Ullom, A High Resolution Gamma-ray Spectrometer based on Superconducting Microcalorimeters,

Review of Scientific Instruments 83:9 (2012), 093113.

Figure 24. 97 keV line histogram. Photon-count histograms near 

the 97.431 keV gamma-ray emission line of 153Gd for an average 

pulse rate of 13.15 Hz are shown for three processing filters. The 

standard “Wiener” filter constructed by means of the discrete 

Fourier transform (DFT) on the average pulse and the power 

spectral density is in the top subplot. In the middle subplot is 

shown the result of a filter constructed from the average pulse and

noise autocorrelation with the new time-domain procedure that

would coincide with the standard procedure if the DFT were a true 

Fourier transform but which in fact obviates artifacts from the 

DFT's artificial periodicity. The bottom subplot shows the result 

of the new procedure when the filter is constrained to be orthogonal to a decaying exponential tail (τ = 6 ms), reducing sensitivity 

to prior pulses. (For all three plots, the filters are orthogonal to

constants, to eliminate baseline sensitivity.) Color denotes the

pulse arrival time lag since the previous pulse, averaged over the

histogram bin, and illustrates that filtering errors, concentrated in

heavily piled-up pulses, are nearly eliminated by the filter orthogonal to exponentials.
Summary of Activities for Fiscal Year 2012 41

Virtual Measurements in Quantum

Chemistry

Raghu Kacker

Karl Irikura (NIST MML)

Russell Johnson III (NIST MML)

Ruth Jacobsen (NIST MML)

By a virtual measurement we mean a prediction along 

with its associated uncertainty for the value of a measurand determined from a computational model as an 

alternative to a physical measurement. Computational 

models are improving and are being increasingly used 

in science and engineering. An important application is 

quantum chemistry, where carefully determined uncertainties associated with computationally determined 

values have not been reported. As the technology improves, the need and importance of reliable 

uncertainties is being recognized. This project is focused on developing and applying methods for 

quantifying the uncertainty associated with a virtual 

measurement in quantum chemistry. The benefits accrue to research and development of chemical 

processes, materials development, and drug discovery.

Predictions from computational quantum chemistry models seldom agree with the corresponding highquality physical measurements. The differences are 

not random but systematic. Therefore, a common practice is to apply an empirical scaling factor to 

computational predictions to bring them closer to the 

true quantity values. The empirical scaling factor carries uncertainty. We have developed a methodology to 

quantify the uncertainty associated with a scaling factor. This approach is based on the Guide to the 

Expression of Uncertainty in Measurement, which is an 

international standard. The uncertainties for scaling 

factors lead to the corresponding uncertainties for virtual predictions.

We had reported in the Journal of Physical Chemistry (2005) scaling factors and uncertainties for 

vibrational harmonic frequencies. We had reported in 

the Journal of Chemical Theory and Computation

(2010) scaling factors and uncertainties for vibrational 

anharmonic frequencies. Anharmonic frequencies are 

calculated from higher order models and require considerably more computational effort. Therefore 

anharmonic calculations are significantly more expensive than harmonic calculations. In 2011 and 2012 we 

determined that without empirical scaling, anharmonic 

frequencies are clearly more accurate than harmonic 

frequencies, as expected. However, the scaled frequencies for both harmonic and anharmonic calculations are 

all of comparable accuracy. The much greater cost of 

anharmonic calculations does not provide a benefit for 

the electronic structure methods. Our paper entitled 

“Anharmonic vibrational frequency calculations are not 

worthwhile for small basis sets” has been accepted for 

publication in the Journal of Chemical Theory and 

Computation [1]. We continue to address uncertainties 

with the outputs of computational quantum chemistry 

models.

[1] R. L. Jacobsen, R. D. Johnson III, K. K. Irikura and R. 

Kacker, Anharmonic Vibrational Frequency Calculations are not Worthwhile for Small Basis Sets, Journal 

of Chemical Theory and Computation, to appear.

[Contributes to Virtual Measurements crosscut.]

Bubble Motion and Size Variation 

during Thermal Migration with 

Phase Change

Asha Nurse

Geoffrey McFadden

Sam Coriell (NIST MML)

If a temperature gradient is applied to a fluid containing liquid drops or gas bubbles, the drops can migrate 

to the direction of higher temperature, even overcoming the buoyancy forces on the drops. This migration is 

due to the Marangoni forces that arise due to stresses 

associated with the temperature variation of the surface 

energy at the fluid-fluid interface. Generally the surface energy tends to decrease with temperature, and the 

resulting tangential flow along the interface is from the 

hotter end of the bubble to the cooler end, moving the 

bubble into the region of higher temperatures. Marangoni effects arise in many material processing 

techniques and can have a significant effect on the 

quality of the resulting material. 

Steve Hardy, a NIST material scientist, conducted 

a series of experiments on the motion of an air bubble 

in silicone oil under carefully controlled thermal conditions [1]. He measured the vertical position and 

diameter of the air bubble for a specific temperature 

gradient and observed oscillations of both the bubble 

position and the radius when the system is heated from 

below. Hardy attributed the oscillations to the diffusion 

of air into or out of the bubble from the surrounding 

silicone oil as the bubble moves into regions of higher 

or lower temperature. At the turning points of the motion where the velocity vanishes, Hardy used the 

theoretical analysis for the thermal migration of an 

immiscible bubble developed by Young, Goldstein, 

and Block [2], who obtained an expression for the velocity of a migrating bubble as a function of the 

temperature gradient, gravitational acceleration, and 

material properties of the system. In this way Hardy 

was able to measure the variation of the surface energy 

with temperature. The model of Young et al. is not able 

to predict the oscillations in position and radius of the 

bubble that Hardy observed, however.
42 NIST Applied and Computational Mathematics Division

Generally motivated by Hardy’s observations, we 

extend [3] the analysis of Young et al. by considering a 

drop that is the vapor phase of the surrounding unbounded liquid and vice versa. The drop radius and 

position are both allowed to vary in time as flow normal to the interface occurs due to phase change. We 

assume the flow is governed by the incompressible 

Stokes equations and is coupled to a quasi-static thermal field. The flow equations are solved with 

associated boundary conditions that include the release 

of latent heat upon a change of phase at the surface, 

and also permit flow through the surface of the bubble, 

in contrast to the case of the thermal migration of an 

immiscible drop. 

For a spherical drop, an explicit solution gives a 

pair of coupled ordinary differential equations that 

govern the rate of change of the drop radius and position. Our expression for the drop velocity contains 

terms proportional to the temperature gradient and the 

gravitational acceleration, just as in the analogous expression obtained by Young et al. However, our 

expression contains a number of additional materials 

parameters, resulting in a more complicated dependence on the drop radius. The steady state solutions of 

these equations generally describe a balance between 

buoyancy and thermal effects and is illustrated using 

material properties corresponding to a water-steam 

system in Figure 25. For smaller drops, the results are 

similar to those for the immiscible case treated by 

Young et al [2], while for larger drops, the Marangoni 

effect can be overwhelmed by the effects of latent heat 

release.

We have analyzed the linear stability of the steadystate solutions of the governing equations and found 

conditions that lead to solutions that oscillate in position and radius as were observed experimentally by 

Hardy. We note that a drop or bubble with an immiscible interface cannot undergo purely radial oscillations 

if the flow is incompressible, since there is no local 

mass flux through the interface. Analogous to Hardy’s 

diffusion problem, the cycle of oscillation here is that a 

downward displacement into a region of higher temperature produces an increase in bubble radius due to 

evaporation; the larger bubble then rises due to increased buoyancy. Overshooting its original position, it 

then rises to regions of colder temperature, where it 

shrinks due to condensation and falls due to reduced 

buoyancy to repeat the cycle. We have also performed 

a weakly-nonlinear analysis of the oscillatory modes, 

and compared the result with a numerical solution of 

the nonlinear equations. Future work will extend this 

single-component model to include the effects of gaseous diffusion, which should allow more accurate 

comparisons with the experimental results of Hardy.

[1] S. C. Hardy. The Motion of Bubbles in a Vertical Temperature Gradient, Journal of Colloid and Interface 

Science 69 (1979), 157–162.

[2] N. G. Young, J. S. Goldstein, and M. J. Block, The Motion of Bubbles in a Vertical Temperature Gradient,

Journal of Fluid Mechanics 6 (1959), 350–356.

[3] A. K. Nurse, G. B. McFadden, and S. R. Coriell, Bubble 

Motion and Size Variation during Thermal Migration 

with Phase Change, in review.

On the Stability of Rotating Drops

Asha Nurse

Geoffrey McFadden

Sam Coriell (NIST MML)

Analyses of the dynamics of a rotating liquid drop held 

together by surface tension were initiated by Plateau 

(1863). Generally, an effectively weightless liquid drop 

is immersed in an immiscible liquid and then spun at a 

controllable rate. Assuming rigid body motion and taking into account solely axisymmetric drop 

configurations, the drops evolve from spherical configurations at zero rotation rate through a family of 

axisymmetric shapes that progressively flatten at the 

poles while developing an equatorial bulge. At large 

enough rotation rates, Plateau observed transient toroidal configurations that tended to break up into smaller 

drops.

Recently, there has been interest in the stability of 

toroidal shapes. Experiments on neonatal fibroblast 

Figure 25. The steady state radius, R, versus temperature gradient, 

G, for a stationary bubble of steam in water heated from below at 

373.15 K. The solid curve is our exact solution; open circles show 

results obtained by “turning off” the Marangoni effects, and the 

dashed curve shows the immiscible bubble results of Young et al.
Summary of Activities for Fiscal Year 2012 43

cells that have self-assembled into a toroidal cluster 

about the base of a conical pillar, have shown that the 

toroidal cluster will actively do work to climb the pillar 

to become a sphere or will remain at the base of the 

pillar and break up to form smaller clusters [1]. Subsequent theoretical work on this self-assembled system 

points to the minimization of the surface energy as a 

key factor in the configurational driving force for the 

motion of the cluster [2]. As for the thinner toroidal 

clusters that do not climb the conical pillar, the development of localized deformations along its 

circumference is viewed to as a result of the unstable 

growth of surface fluctuations. These works have revived interest in the stability of a rotating drop held 

together by surface tension, which we consider here. 

Theoretical analysis of the spherical liquid drop 

and its resulting axisymmetric shapes has been done by 

Brown and Scriven [3], who performed finite element 

computations of the deformed shapes, and by Chandrasekhar [4], who included fluid flow inside the drop and 

used a method of moments. We employ a Lagrangian 

energy functional that represents the difference between a drop’s potential energy, due to capillary forces, 

and the kinetic energy of rotation, subject to a volume 

constraint. The stationary points of the energy functional are used to determine the equilibrium shapes of 

spheroidal and toroidal drops. We obtain numerical 

solutions for these shapes in terms of an angle arc 

length formulation. 

For a drop undergoing rigid body rotation with a 

fluid of a different density, the application of an external torque may be necessary to maintain a given 

rotation rate. This is referred to as a driven drop. Alternatively, if there is no applied external torque, the drop 

rotates with constant angular momentum and is termed 

an isolated drop. The energy functional for the drop is a 

function of the drop’s shape and angular momentum. 

The stability of either case can be described in terms of 

the second variation of their energy functionals. For 

axisymmetric perturbations stability results for driven 

and isolated drops differ, as shown in Figure 26, with 

the isolated drop being more stable than the driven 

drop. Here λ is an eigenvalue determining the linear 

stability of the rotating drop, with negative values of λ 

corresponding to instabilities that are saddle points in 

the energy profile. In our work we have derived expressions for the second variation of the energy of both 

isolated and driven drops, and obtained numerical results for the stability of rotating spheroidal and toroidal 

configurations. In particular we find that toroidal drops 

with large major radii are subject to a wide class of 

non-axisymmetric perturbations, as suggested by Plateau’s original experiments. Future work will include 

the modeling of the interaction of a toroidal drop with 

an underlying substrate, which may allow more accurate simulations of the observed instabilities in the 

fibroblast cellular clusters.

[1] J. Youssef, A. K. Nurse, L. B. Freund and J. R. Morgan, Quantification of the forces driving self-assembly 

of three-dimensional microtissues, Proceedings of the 

National Academy of Science 108 (2011) 6993–6998.

[2] A.K. Nurse, L. B. Freund and J. Youssef, A Model of 

Force Generation in a Three Dimensional Toroidal Cluster of Cells, Journal of Applied Mechanics 79 (2012) 

1013.

[3] R.A. Brown and L.E. Scriven, The shape and stability of 

rotating liquid drops, Proceedings of the Royal Society 

of London A 371 (1980), 331–357.

[4] S. Chandrasekhar, The stability of a rotating liquid drop, 

Proceedings of the Royal Society of London A 286

(1965), 1–26.

Moving Grain Boundary Groove 

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. An example in a tin system is 

shown in Figure 27. The formation of such “hillocks”

is commonly observed in thin films under compression, 

and has been conjectured to lead to the formation of 

crystalline “whiskers” that can bridge gaps between 

electronic components and lead to electrical failure. 

Figure 26. Linear stability of rotating spheroidal drops. The least 

stable values of λ for axisymmetric disturbances (n = 0) are shown 

for driven and isolated drops as a function of the normalized angular 

momentum L*.
44 NIST Applied and Computational Mathematics Division

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 the present work we have extended 

that work by improving the description of the grain 

boundary junction where the interfaces intersect, and 

by extending 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. The model contains 

dimensionless parameters that represent the ratios of 

surface energies, m, the flux of atoms up the grain 

boundary due to stress, j, kinetic effects due to differences in chemical potentials at the groove, c, and the 

groove velocity, a. An example is shown in Figure 28, 

where the variation in the shape of the solid-vapor interface is shown for a given groove velocity, a, with no 

applied stress or kinetic effects, as the surface energy 

changes. A linear theory can be used when the slopes 

are small (small m), and the figure shows a comparison 

of those results with a nonlinear theory that is valid for 

finite slopes (larger m). The groove is moving to the 

right, and the elevation of surface height to the right of 

the groove represents the formation of a hillock in this 

model.

Future work may include the effects of perturbations perpendicular to the groove, which are observed 

as corrugated structures along the grains, and simulations of the dynamical behavior of the groove in response to variations in stress.

[1] W. W. Mullins, The Effect of Thermal Grooving on 

Grain Boundary Motion, Acta Metallurgica 6 (1958), 

414-427.

[2] F. Y. Genin, W. W. Mullins and P. Wynblatt, The Effect 

of Stress on Grain Boundary Grooving, Acta Metallurgica 41 (1993), 3541-3547.

Measurement and Modeling of 

Plastic Flow Stress for High-Speed 

Machining Simulations

Timothy Burns

Steven Mates (NIST MML)

Richard Rhorer (NIST EL)

Eric Whitenton (NIST EL)

Debasis Basak (Orbital Sciences Corporation)

A high-speed metal machining operation provides an 

interesting and industrially important setting for the 

study of plastic flow under extreme conditions. In the 

thin region where cutting takes place, it is not uncommon, in alloys of interest in manufacturing, to have 

shear strains on the order of 200%, shear strain rates on 

the order of 104s

-1

, and heating so rapid that the local 

workpiece temperature increases from ambient to a 

significant fraction of the melting temperature in a time 

on the order of a tenth of a second or less. In order to 

obtain useful predictive computer simulations of the 

cutting conditions during a high-speed metal machining operation, such as the cutting forces and the 

temperature along the interface between the tool and 

the work material, a constitutive response model for the 

flow stress in the work material, and a model for the 

friction between the workpiece and the cutting surface 

of the tool, must be specified. Despite years of research 

on this subject, the current state of the art is unsatisfactory. For example, in a study that used data from 

cutting experiments performed at NIST in 2007 [1], it 

was found that the force predictions made using a state 

of the art finite-element software package that was developed specifically for machining simulations, were 

off by about 20%.

In work performed this year [2], an analysis was 

made using some experimental measurements of the 

temperature along the tool-chip interface (segment A-B 

in Figure 30) during some high-speed machining tests 

[3], together with an empirically determined tool-chip 

interface friction model, to make an estimate of the 

flow stress in the workpiece material that provided the 

best peak temperature prediction for four different sets 

of cutting tests that had been performed at NIST. This 

stress estimate was then compared with two different 

Figure 27. Scanning electron micrograph view of a cross section of a 

tin electrodeposit containing hillocks. There is evidence of grain 

boundary motion in the deposit under each hillock.

Figure 28. Groove shapes for a = 2, with j = c = 0. The dotted lines 

show the linear (small slope) solution, and the solid curves are the 

numerical (finite slope) solution.
Summary of Activities for Fiscal Year 2012 45

constitutive models for the flow stress for the same 

material, which had been determined, respectively, 

using data that were measured in two different sets of 

experiments. The first set of experiments was performed on a Kolsky bar in a Dutch laboratory. In these 

tests, which were performed specifically for application 

to the study of high-speed machining, the sample material was pre-heated using a small oven, prior to loading 

the sample in compression [4]. In the second set of 

tests, which were performed on the NIST pulse-heated 

Kolsky bar, the sample material was pre-heated much 

more rapidly prior to loading in compression, and it 

was found that the material exhibited a significantly 

stiffer constitutive response, i.e., a higher shear stress 

at the same strain, strain rate, and temperature [5]. The 

results of this study are summarized in Figure 29. The 

stiffer response of the pulse-heated data is evident. 

However, it is clear that neither constitutive model for 

the flow stress that was determined using Kolsky bar 

experimental data set does an overall good job of 

matching the stress that was estimated independently. 

In work in progress, this method of estimating the 

stress using an interface friction model together with 

in-situ temperature measurements during high-speed 

cutting tests, is being extended using a more sophisticated model for the friction between the tool and the 

work material.

[1] R. Ivester, E. Whitenton, J. Heigel, T. Marusich and C. 

Arthur, Measuring Chip Segmentation by High-speed 

Microvideography, and Comparison to Finite-element 

Modeling Simulations, in Proceedings of the 10th CIRP 

International Workshop on Modeling of Machining Operations, Calabria, Italy, August 27-28, 2007.

[2] T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. Whitenton

and D. Basak, Transient Convection-diffusion Modelling of Peak Temperature in Orthogonal Cutting, in 

Proceedings of the 23rd International Congress of Theoretical and Applied Mechanics (ICTAM2012), Beijing, 

China, August 19-24, 2012.

[3] M. A. Davies, H. Yoon, T. L. Schmitz, T. J. Burns and 

M. D. Kennedy, Calibrated Thermal Microscopy of the 

Tool-chip Interface in Machining, Machining Science & 

Technology 7 (2003), 166-190.

[4] S. P. F. C. Jaspers and J. H. Dautzenberg, 2002, Material 

Behaviour in Conditions Similar to Metal Cutting: Flow 

Stress in the Primary Shear Zone, Journal of Materials 

Processing Technology 122 (2002), 322-330.

[5] T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. Whitenton

and D. Basak, Modelling the Peak Cutting Temperature 

during High-speed Machining of AISI 1045 Steel, Engineering Transactions 60:2 (2012), 118-124.

Selecting an Appropriate Statistical 

Distribution for a Class of 

Engineering Material Property Data

Jeffrey T. Fong

N. Alan Heckert (ITL SED)

James J. Filliben (ITL SED)

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 

uniaxial ultimate strength 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 

at the origin.

Figure 30. False color thermal image of high-speed, steady-state 

orthogonal machining of AISI 1045 steel; taken from [3].

Figure 29. Comparison of estimated shear flow stress during four 

different high-speed cutting tests (black) with shear stress predicted from constitutive models based on “slow”-heated (blue) and 

NIST pulse-heated Kolsky bar data (green).
46 NIST Applied and Computational Mathematics Division

In this work, we take a brute-force and somewhat 

exhaustive approach by developing a screening 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 [2]. 

2. Probability Plot Correlation Coefficient [3]. 

The four goodness-of-fit criteria are: 

a. Kolmogorov-Smirnov [4]. 

b. Anderson-Darling [5, 6]. 

c. Akaike-Burnham-Anderson [7, 8]. 

d. Probability Plot Correlation Coefficient [3].

Using public-domain statistical analysis software 

named DATAPLOT [9], we develop a generic screening tool, and demonstrate its feasibility by applying to 

three sets of data, one for a glassy material and two for

steels [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, reapproved 2008, West Conshohocken, PA, 19428-2959.

[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 System12, National Institute of 

Standards and Technology, Gaithersburg, MD 20899, 

2002.

[10] J. T. Fong, N. A. 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.

A Bayesian Nondestructive 

Evaluation Approach to Estimating 

Remaining Life of Aging Structures

Jeffrey T. Fong

N. Alan Heckert (ITL SED)

James J. Filliben (ITL SED)

William F. Guthrie (ITL SED)

The formulation of a stochastic multi-crack-growth 

(MCG) –based theory of fatigue for aging structures 

[1] paved the way for us to use the powerful Bayesian 

statistical method for non-destructive evaluation (NDE)

data analysis. This method allows us to use prior 

knowledge of the likely distributions of the crack 

length and crack-growth-rate data to iterate for the best 

estimation and to validate the model to make sure it 

provides a reasonable description of the variation in the 

observed data. 

With the Bayesian analysis software WinBUGS 

[2] as a simulation platform, we used a Bayesian statistical model fit with a Markov-Chain-Monte-Carlo

(MCMC) algorithm [3-7] to implement the four governing equations as reported in [1]. Since most of the 

NDE data on inspection of commercial pressure vessels 

and piping are proprietary, we used a set of synthetic 

data of the crack growth of five cracks as input to an 

example of the MCG-based theory.

[1] J. T. Fong, N. A. Heckert, and J. J. Filliben, A Stochastic and Local Theory of Fatigue for Aging Pressure 

Vessels & Piping, in From Failure to Better Design, 

Manufacture and Construction, (S. T. Tu, Z. D. Wang, 

and G. C. Sih, eds.), Proceedings of the 3

rd International 

Symposium on Structural Integrity, Oct. 31 – Nov. 4, 

2012, Shandong University, Jinan, China, East China 

University of Science and Technology Press, Shanghai, 

China, 2012, 19-31.

[2] D. J. Lunn, A. Thomas, N. Best, and D. Spiegelhalter, 

WinBUGS – A Bayesian Modeling Framework: Concepts, Structure, and Extensibility, Statistics and 

Computing 10 (2000), 325-337.

[3] A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin, 

Bayesian Data Analysis, Chapman & Hall, London 

1995.

 

12 http://www.itl.nist.gov/div898/software/dataplot.html
Summary of Activities for Fiscal Year 2012 47

[4] D. Berry, Statistics: A Bayesian Perspective, Wadsworth 

Publishing Co., Belmont, CA, 1996.

[5] P. M. Lee, Bayesian Statistics: An Introduction, 2

nd

edition, Arnold Publishing, London, 1997.

[6] O. Haggstrom, Finite Markov Chains and Algorithmic 

Applications, Cambridge University Press, 2002.

[7] G. Casella, and E. I. George, Explaining the Gibbs Sampler, American Statistician 46 (1992), 167-174.

Simulation of Bioregulatory 

Networks Involved in Cell Cycle 

Control

Geoffrey B. McFadden

Mirit Aladjem (National Institutes of Health) 

S. Kim (National Institutes of Health) 

Kurt Kohn (National Institutes of Health) 

A. Luna (NIH and Boston University)

G. McFadden is a co-advisor to Sohyoung Kim, an 

NIH post-doctoral fellow, and Augustin Luna, a graduate student from Boston University, who are both doing 

research at the National Institutes of Health (NIH); 

their co-advisors are NIH researchers M. Aladjem and 

K. Kohn. The team is developing models of bioregulatory networks that are involved in cell cycle control. 

The models consist of systems of nonlinear ordinary 

differential equations that typically exhibit switching 

behavior, limit cycles, and other types of bifurcations. 

Proper cell growth depends on a network of interacting 

molecules that monitors cellular metabolism and environmental signals. This network ensures that cells halt 

their growth in response to unfavorable conditions such 

as the absence of sufficient nutrients or the presence of 

potentially damaging agents. When cells escape these 

controls, the results are developmental abnormalities, 

genomic instability, and cancer.

Current work by Sohyoung Kim focuses on a protein known as p53, a tumor suppressor that causes cell 

cycle arrest or programmed cell death in response to 

stress signals such as DNA damage. Regulating the 

appropriate levels of p53 is essential for cell survival. 

Recent modeling work [1] has suggested experimental 

investigations of the role played by another regulatory 

protein, Mdmx, in the cell cycle that are currently being performed by Dr. Kim at the Laboratory for 

Molecular Pharmacology at the NIH National Cancer 

Institute. She has developed a specialized cell line that 

is designed to allow the measurement of p53 levels in a 

single cell by tagging individual species in the cell with 

green florescent proteins whose luminous intensity 

varies with concentration (see Figure 31). In this way 

the model predictions of the role of Mdmx can be tested experimentally [2]. Future work will include the 

development of refined models to better account for the 

newest experimental results.

Recent work by Augustin Luna includes the development of models for the role played by a protein, 

SIRT1, in regulating cellular response to DNA damage. 

This work is modeling the effects of SIRT1 on the 

mammalian circadian clock cycle. It is known that the 

Figure 31. Images of a single cell exhibiting cyclic response to DNA 

damage (introduction of ‘NCS’ agent). The measured intensity at a 

foci (red highlighted circle) is a measure of the local p53 concentration.

Figure 32. Numerical simulation of the dynamics of a model for the 

interaction between the DNA damage response and the circadian 

cycle in cells. The concentration of the model’s species are shown as 

a function of time (hours).
48 NIST Applied and Computational Mathematics Division

time of day that cancer treatments are administered 

affects drug efficacy, and circadian rhythms are also 

known to affect DNA damage response. SIRT1 is 

known to play a role in the DNA damage sensor that 

triggers the cellular response to genotoxic stress. In this 

work existing models for the circadian clock are being 

modified to include the specific effects of SIRT1 on the 

interaction between the DNA damage response and the 

circadian cycle in cells; a numerical example is shown 

in Figure 32.

A poster describing this work was presented at a 

recent international conference on systems biology [3]. 

This work is currently being written up as part of Dr. 

Luna’s Ph.D. thesis, which will be defended in 2013. 

[1] S. Kim, M. I. Aladjem, G. B. McFadden, and K. W.

Kohn, Predicted Functions of MdmX in Fine-tuning the 

Response of p53 to DNA Damage, PLoS Computational 

Biology 6 (2010), e1000665 (18 pages).

[2] S. Kim, M. I. Aladjem, G. B. McFadden, and K. W. 

Kohn, Testing in silico Predictions of p53 Dynamics by 

Direct Measurements of Transcription Kinetics, NIH 

Research Festival, Bethesda, MD, October 9-12, 2012.

[3] A. Luna, G. McFadden, M. Aladjem, and K. Kohn, A 

Computational Mammalian Circadian Clock Model with 

Connections to the DNA Damage Response, 20th Annual 

International Conference on Intelligent Systems for Molecular Biology, Long Beach, CA, July 15-17, 2012.n

Mathematical Optimization of 

Procedures for Cryoprotectant 

Equilibration

Anthony Kearsley

Daniel Anderson (George Mason University)

James Benson (Northern Illinois University)

Adam Higgins (Oregon State University)

Cryopreservation procedures permit cells to be stored 

indefinitely using extremely cold temperatures to suspend all metabolic activities and therefore preserve the 

cell and cell 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 -196 C. Cryoprotectants must be removed later during the thawing 

process and slowly the water balance in the cell can be 

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) 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 cells but research is ongoing to optimize the cryobiology of cells. 

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 (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 representative 

cell type with high clinical relevance. The resulting 

toxicity-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 procedure identified is a first step in 

deriving procedures that significantly reduce damage 

due to toxicity. 

[1] J. D. Benson, A. J. Kearsley, A. Z. Higgins, 

Mathematical Optimization Procedures for 

Cryoprotectant Equilibration using a Toxicity Cost 

Function, Cryobiology 64 (3) (2012), 144-151. 

Hurricane-Borne Missile Speeds

Florian A. Potra

Emil Simiu (NIST EL)

Brad Harvey (Nuclear Regulatory Commission) 

Kevin Quinlan (Nuclear Regulatory Commission)

The safety of nuclear power plants is a matter of paramount national concern. The U.S. Nuclear Regulatory 

Commission (NRC) contracted NIST to perform a 

study of hurricane-borne missiles (i.e., debris), and 

their possible impacts on nuclear power plants. The 

study resulted in a comprehensive technical report [2] 

intended to provide the technical basis for a new regulatory guide [3] that would provide licensees and 
Summary of Activities for Fiscal Year 2012 49

applicants with guidance that the staff of the NRC considers acceptable for use in selecting the design-basis 

hurricane-borne missile speeds for the design of nuclear power plants. The design must prevent undue risk to 

the health and safety of the public in accordance with 

General Design Criterion 2, “Design Bases for Protection Against Natural Phenomena,” and General Design 

Criterion 4, “Environmental and Dynamic Effects Design Bases,” of Appendix A, “General Design Criteria 

for Nuclear Power Plants,” to Title 10, Part 50, of the 

Code of Federal Regulations, “Domestic Licensing of 

Production and Utilization Facilities.” 

The report documents the approach to and results 

of calculations of hurricane-borne missile speeds that 

may be considered in the design of nuclear power 

plants. The missile spectrum, the assumptions on which 

the analyses are based -- which are similar to assumptions used for the development of Revision 1 to 

Regulatory Guide 1.76, “Design-Basis Tornado and 

Tornado Missiles for Nuclear Power Plants,”— and the 

range of wind speeds being considered, were based on 

consultations between the authors and NRC staff. In 

addition, calculated missile speeds based on assumptions on the initial missile height above ground that 

differ from the assumption used in Revision 1 to Regulatory Guide 1.76 are included in Appendixes. The 

staff initiated this study because Revision 1 to Regulatory Guide 1.76 was based on the new Enhanced Fujita 

scale, in which tornado design-basis wind speeds are 

lower than in the earlier Fujita scale. The design-basis 

tornado wind speeds presented in Regulatory Guide 

1.76 correspond to an exceedance probability of 10-7

per year. This report covers missile speeds that, under 

several hypotheses, could occur in hurricanes with 10-7

per year probability of exceedance wind speeds. Software for estimating speeds and trajectories for different 

types of hurricane-borne missiles is available13. 

A joint paper with NRC colleagues [1] discusses 

the findings of the report, and concludes that the study 

of extreme wind gusts during hurricanes showed that 

wind speeds from the design-basis tornado remain 

bounding except for locations along the United States 

Gulf Coast and the southern Atlantic Coast. The study 

of missile speeds during hurricanes also concluded that 

airborne missiles fly faster in a hurricane wind field as 

compared to a tornado wind field of the same strength. 

Consequently, applicants for new power plants with 

sites along the Gulf and Atlantic coasts where the design-basis tornado may not bound the design-basis 

hurricane are expected to show that their applicable 

structures can withstand, independently, the total design-basis tornado load and the total design-basis 

hurricane load as extreme environmental conditions. 

Additional comments are given in [4].

 

13 http://www.itl.nist.gov/div898/winds/mathematica/nrc.htm

[1] B. Harvey, E. Simiu, F. A. Potra, and K. Quinlan, Design-Basis Hurricane Winds and Missiles for Nuclear 

Power Plants, in Transactions of the 22nd International 

Conference on Structural Mechanics in Reactor Technology, SMiRT-22, San Francisco, California, August 

18-23, 2013, in review.

[2] E. Simiu and F. A. Potra, Technical Basis for Regulatory Guidance on Design-Basis Hurricane-Borne Missile 

Speeds for Nuclear Power Plants (NUREG/CR-7004), 

Office of Nuclear Regulatory Research, U.S. Nuclear 

Regulatory Commission, Washington, DC 20555-0001, 

November 2011, (110 pages).

[3] U.S. Nuclear Regulatory Commission (NRC), DesignBasis Hurricane and Hurricane Missiles for Nuclear 

Power Plants, Regulatory Guide 1.221, 2011.

[4] D.H. Yeo, F. T. Lombardo, D. K. Banerjee, E. J. Letvin, 

E. Simiu, M. L. Levitan and F. A. Potra, NIST Advances in Computer-aided and Computational Methods in 

Wind Engineering, in Proceedings of the ATC-SEI Advances in Hurricane Engineering Conference, Miami, 

FL, 2012 (12 pages).

Multi-Hazard Engineering Design 

Florian A. Potra 

Chiara Crosti (NIST EL) 

Dat Duthinh (NIST EL) 

Jay Harris (NIST EL) 

Long T. Phan (NIST EL)

Emil Simiu (NIST EL)

There is a growing interest in the development of procedures for the design of structures exposed to multiple 

hazards, including strong winds. The goal is to achieve 

safer and more economical or “greener” designs than 

would be the case if the demands on structures were 

calculated independently for each individual hazard 

and an envelope of those demands were used for member sizing. A broad, multidisciplinary foundation for 

multi-hazard design should include structural analysis, 

optimization, and probabilistic structural reliability 

components. A paper presented at the 13th International Conference on Wind Engineering [1] discusses this 

interdisciplinary approach to engineering in a multihazard context and presents new procedures and results

obtained by NIST researchers. Additional details are 

provided in [2]. 

The development of the current American Society 

of Civil Engineers (ASCE) 7 Standard provisions on 

structural design for regions with strong wind and 

seismic hazards is based on the belief that such provisions should be determined strictly by the fact that the 

probability of simultaneous occurrence of such hazards 

is negligible. Figure 33 represents schematically a water tower located on the coast in South Carolina, a state 

with both strong wind and hurricane hazards. A complete description of the structure can be found in [1]. 
50 NIST Applied and Computational Mathematics Division

The calculations show that the legs of the water tower 

reach similar limit states under combined gravity and 

wind loading, and under combined gravity and earthquake loading. This means that, during its life, the legs 

would experience the limit states being considered with 

a probability that is approximately twice as large as the 

probability inherent in the ASCE 7-05 Standard.

A design that improves the performance of a structure under one hazard is called synergistic if it also 

improves the performance of the structure under a second hazard. For example, Hayes et al. [2] found that 

strengthening of a structure for seismic loads can also 

improve performance under blast loads as well as behavior with respect to progressive collapse. 

Optimization under multiple hazards imposes multiple sets of constraints, all of which are applied 

simultaneously to the nonlinear programming problem 

(NLP) associated with the design. Among the applications of the optimization procedure is the reduction of 

the carbon footprint inherent in the energy embodied in 

structures via the minimization of an objective cost 

function that may include the cost of carbon emissions. 

A case study presented in [1] and [3] considers the 

structure of Figure 34, representing one in a long row 

of columns free at the top and fixed at the base that 

support a pipe filled with water. The water is heated by 

ground-level, computer-controlled rotating mirrors that 

focus reflected solar rays onto the pipe. The resulting 

heat is used for power generation. The multi-hazard 

optimal design problem for this case study consists of 

determining the design variables in such way that the 

structure is guaranteed to sustain both wind and seismic loads and its cost is minimized. This problem was 

formulated as an NLP and solved by an interior point 

method. 

[1] C. Crosti, D. Duthinh, J. Harris, L. T. Phan, F. A. Potra 

and E. Simiu, Wind engineering in a multi-hazard context: probabilistic, synergy, and optimization issues, in 

Proceedings of the 13th International Conference on 

Wind Engineering, IAWE, Amsterdam, The Netherlands, 2011 (8 pages).

[2] J. R. Hayes, S. C. Woodson, R. G. Pekelnicky, C. D. 

Poland, W. G. Corley and M. Sozen, Can Strengthening 

for Earthquake Improve Blast and Progressive Collapse 

Resistance?, Journal of Structural Engineering 131

(2005), 1157-1177.

[3] E. Simiu, F. A. Potra and D. Duthinh, Methodological 

and Probabilistic Issues in Multi-hazard Engineering 

Design, in Applications of Statistics and Probability in 

Civil Engineering (M. Faber, J. Koehler and K. Nishijima, eds.), CRC Press, Leiden, 2011, 836-839.

Alternative Methods of Latent 

Fingerprint Enhancement and 

Metrics for Comparison

Alfred S. Carasso

This work is a contribution to the FY 2012 research 

project Metrics for Manipulation and Enhancement of 

Forensic Images sponsored by the NIST Deputy Director for Laboratory Programs. That project is primarily 

focused on the processes used for digital image enhancement of poor quality latent fingerprints left 

unintentionally at a crime scene. To facilitate this 

study, law enforcement forensic experts provided NIST 

with a database of fingerprint image pairs, before and 

after enhancement. Such enhancements result exclusively from Adobe Photoshop image processing, which 

is the methodology preferred by law enforcement professionals.

In recent years, skepticism has occasionally been 

expressed about the reliability of such digital enhancements of latent fingerprints [1, 2]. Of major concern is

the possibility that the particular combination of Photoshop steps used in the enhancement process may 

inadvertently eliminate vital fine scale information, 

information that might exclude a suspect. Accordingly, 

Figure 33. Schematic of water tower structure.

Figure 34. Vertical view and cross section of column.

Wind or seismic 

horizontal force

G

2bt

2bb

h

H

c

s s

w

Cross section s-s

2b

2a

Pe or Pwcos θ

θ

w w

Vertical view w-w

q(a,b,θ)

(L)

Fig. 1. Vertical view and cross section of column
Summary of Activities for Fiscal Year 2012 51

a recently issued NIST Internal Report [7] explores 

alternative approaches to latent fingerprint enhancement that are independent of Photoshop. Consideration 

of such alternative enhancements, alongside the traditional Photoshop result, may better inform the 

subsequent, crucial, matching and identification procedure.

The proposed alternative methods yield reproducible results, and are based on the use of simple 

commands from such widely used scientific image 

analysis software packages as MATLAB [3], IDL [4], 

and PV-WAVE [5]. The uses and purposes of these 

commands are documented and illustrated in the accompanying user’s manuals. In addition, [6] provides a 

thorough discussion of the theoretical ideas underlying 

the various enhancement techniques available in the 

above packages. Note that implementations vary 

among different packages, and the same enhancement 

technique can produce slightly different images in different packages. Such enhancement methods are 

designed to bring into better visual range potentially 

significant structures that are present in the original 

image, but not easily discernible.

Software routines that can be used with the above 

packages are included in [7]. These routines can perform contrast adjustment, Sobel filtering, unsharp 

masking, and histogram equalization. The results of 

applying various these various enhancement methods 

to the same latent print, can be objectively compared 

using discrete L

1

and L

2

image norms, as well as L

1

and 

L

2

image gradient norms. 

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

Finger at the Innocent, Chicago Tribune, January 3, 

2005.

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

[3] Image Processing Toolbox User’s Guide, The MathWorks, Inc. Natick, MA 01760, 2012.

[4] ITTVIS Interactive Data Language (IDL), 

http://www.exelisvis.com/IDL.aspx.

[5] PV-Wave 7.5 Image Processing Toolkit User’s Guide, 

Visual Numerics, Inc. Houston, TX 77042.

[6] W. K. Pratt, Digital Image Processing, WileyFigure 35. Enhancements of latent fingerprint. Original print, accompanying forensic Photoshop enhancement, and two alternative 

MATLAB enhancements. Significant enhancement of background 

features is apparent in histogram equalized image. This is reflected 

in the image gradient norms in Table 5.

Figure 36. Reverse images in the latent print enhancements shown in 

Figure 35.

Table 5. Image metrics in enhancements of latent print (A).

Image ||f||1 ||f||2 ||f||1 ||f||2

Original Latent Print (A) 16 18 2600 3900

Forensic Photoshop (A) 61 75 25000 36000

Matlab Contrast Adj. (A) 60 80 25000 40000

Matlab Histogram Eq. (A) 112 138 42000 60000
52 NIST Applied and Computational Mathematics Division

Interscience, New York, 2012.

[7] A. S. Carasso, Alternate Methods of Latent Fingerprint 

Enhancement and Metrics for Comparing Them, 

NISTIR 7910, January 2013.

Shape Analysis

Javier Bernal

Charles Hagwood (ITL SED)

John Elliott (NIST MML)

Michael Halter (NIST MML)

Many cell-based biomedical studies rely on the analysis of cell populations in the form of image data. 

Among the features that can be extracted from image 

data, cell shape is one that uniquely identifies a cell 

population. Accordingly, cell shape is an attribute on 

which statistical inference can be based regarding the 

effect of treating a disease in a particular way. The statistical tests used this way then provide the ability to

identify homogeneous cell populations, and to differentiate between treated and untreated cells.

Shape governs a cell’s motility, division, taxonomy, and oftentimes shape changes are a precursor to 

disease. Shape is generated by the outline of an object. 

Besides being required to be closed, smooth and simple, shapes are required to possess additional attributes 

such as scale, translational, rotational and reparametrization invariance. A theoretical foundation 

has been developed for shape space, in which the space 

is treated as a Riemannian manifold, so that calculus

and other analysis can be performed. In particular the 

geodesic distance and path between elements of the 

space can be computed. This distance is used as a dissimilarity measure in the statistical tests (see Figure 

37).

This year, we continued our work in cell biology, 

using mathematical and statistical techniques as mentioned above to characterize and analyze cell 

populations. What makes this work different from traditional applications in applied mathematics is that our 

data are not points in Euclidean space, but closed contours of cells treated as points in a space with a 

Riemannian structure, i.e., shape space. The data come 

embedded in fluorescent images. In previous work, we 

analyzed algorithms for segmenting cell images, from 

which the cell contours are obtained. We found the kmeans algorithm with (k=4), under a variety of imaging 

conditions, to be the best algorithm of four algorithms 

considered: k-means, Canny, Otsu thresholding and 

watershed. We used the cumulative distribution function of misclassification errors to compare algorithms, 

a new method we have introduced to the field. This 

work was published in 2012 in the IEEE Transactions 

on Medical Imaging [1]. Next, test procedures to compare cell populations based on cell shape were found. 

Shape provides a unique contour descriptor up to the 

invariants mentioned above. With the geodesic distance 

between shapes as a dissimilarity measure between 

cells, three nonparametric statistical tests for equality 

of populations were adapted to geodesic distance. This 

work was submitted to IEEE Transactions on Medical 

Imaging [2] and is under review.

[1] C. Hagwood, J. Bernal, M. Halter, J. Elliott, Evaluation 

of Segmentation Algorithms on Cell Populations using 

CDF Curves, IEEE Transactions on Medical Imaging 31

(2012), 380-390.

[2] C. Hagwood, J. Bernal, M. Halter, J. Elliott, T. Brennan, 

Testing Equality of Cell Populations based on Shape and 

Geodesic Distances, in review.

A Standard Candle for Extragalactic 

Metrology

Bert W. Rust

Katherine M. Mullen (UCLA)

To use Type Ia supernovae as standard candles in extragalactic metrology, we have developed a provisional 

calibration of the luminosities of six well-observed 

light curves in nearby galaxies whose distances are 

well known. Accurate metrology of the light curves 

was enabled by fitting them with our recently developed model,

( ) ( )  ( ) 2.146 ( ),

1 2 1 1 2 2 L t CW t C k N t  k N t

where

( ) ( ; , , ) 1 2 3 W t W t

is a three parameter Weibull probability density function used to represent the pulse shape for the nuclear 

fusion reactions that deposit 56Ni in the supernova, 

N1(t) and N2(t) are the subsequent pulses in the nuclear 

decay chain

Figure 37. Geodesic path between two contours.
Summary of Activities for Fiscal Year 2012 53

Ni Co Fe 56 56 56 1 2

k k

  ,

and .

111.42

1

,

8.764

1

4

2

4

1

 

k  k 

The fitting parameters C1 and C2 are the constants 

which convert the relative abundances represented by 

the pulses into observed luminosities. The four nonlinear fitting parameters are: (1) α1, the time that 56Ni 

deposition begins, (2) α2, a shape parameter, (3) α3, a 

scale parameter, and (4) α4 (0 < α4 ≤ 1), an acceleration

factor specifying the shortening of the half-lives of the

two nuclear decays because of the extreme temperatures and densities inside the supernova. Strong 

evidence for such an acceleration effect was given 

many years ago by Rust, Leventhal and McCall [1], 

and recently confirmed by our work at NIST. The 

ODEs for the relative abundances can be written

, ( ) 0,

, ( ) 0,

( ) , ( ) 0,

2 2 3 1

3

1 1 2 2 2 1

2

1 1 1 1

1

 

  

  







k N N

dt

dN

k N k N N

dt

dN

W t k N N

dt

dN

Using the nonlinear fitting program VARPRO14, we 

were able to get extremely good fits of the above model to the six light curves in the study. One of them is 

given in Figure 38. The other five fits were of similar 

quality, with all of them explaining more that 99% of 

the variance in the measured data (R2 > 0.99).

Since all six of the supernovae were in galaxies 

whose distances D (in Mpc), were already known, it 

was easy to convert the maximum apparent magnitudes 

Bmax to maximum absolute magnitudes MBmax via the 

formula

MBmax = Bmax − 5 log10 D − 25.

The luminosity calibration is possible because this 

measure of the absolute luminosity is very strongly 

correlated with the decay acceleration parameter α4. 

This correlation is illustrated in Figure 39. To estimate 

the distance to a faraway supernova: (1) measure its 

light curve, (2) fit the above model to estimate α4 and 

Bmax, (3) estimate MBmax from the correlation line in 

Figure 39, and (4) estimate D from the preceding formula.

[1] B.W. Rust, M. Leventhal and S.L. McCall, Evidence for 

a Radioactive Decay Hypothesis for Supernova Luminosity, Nature 262 (1976) pp. 118-120.

Unfolding Optical Spectrum 

Measurements

Bert W. Rust

Stephen W. Brown (NIST PML)

The integral equations which must be inverted to correct optical spectrum measurements for scattered light

in a certain spectrometer can be written

198.9388 873.9835,

( ) ( , ) ( ) ( ), *

859.920

220.0000

 

  

i

i i L L d L i

y K x



      

where y(λi) the observed spectrum, K(λi,λL) is the instrument response function, shown in Figure 40, ε(λi) 

are random measurement errors, and x

*

( λL) is the unknown corrected spectrum. The black curve in Figure 

 

14 http://www.netlib.org/opt/varpro

Figure 38. The light curve of SN1998aq. The time is measured in 

days since Ni deposition began. The discrete data points are observed apparent B magnitudes and the smooth curve is the model fit. 

The vertical magenta line indicates the maximum brightness Bmax.

Figure 39. The correlation between MBmax and the decay acceleration parameter α4.
54 NIST Applied and Computational Mathematics Division

41 is a mathematically computed test spectrum x

*

(λL)

comprised by a linear combination of two Lorentzians,

and the blue curve is the instrument’s response y

*

(λ)

that would be obtained if no random measurement errors were present. When the integral equations are 

discretized (with a 1024 × 1024 matrix K), the result is 

a linear regression problem

,~ (0, ), * 2y  Kx   N S

where S

2

is the positive definite covariance matrix for 

the measurement errors. If there were no measurement 

errors, it would be easy to compute the corrected spectrum by

* 1 *

x y



 K .

The results of that calculation are shown in Figure 42.

The outcome would have been much different if any 

random measuring errors had been added to y

*

. Even 

with rounding errors so small that they changed y

*

only 

in the 5th or 6th digit, the resulting estimate of x

*

would have oscillated wildly between positive and 

negative values. One way often used to stabilize such 

problems is to impose a non-negativity constraint on 

them, i.e., to replace the least squares problem,

min ,

2

SSR y x

x

  K

with

min .

2

0

SSR y x

x

  K



The Matlab Optimization Toolbox contains two commands, fmincon and lsqnonneg which purport to solve 

the latter problem, but as seen in Figure 43, our initial 

experiments show that they both fail when used to estimate x

*

. Since these routines cannot provide good 

estimates when there are no measurement errors in the 

observed y(λ), they should not be trusted in real problems when the observations do contain measurement 

errors.

Figure 41. The instrument response y*to a mathematical test 

spectrum x*in the absence of measurement errors. The difference 

between the two curves is the scattered light produced by the 

spectrometer.

Figure 42. The true spectrum x

*

and the estimated spectrum K

-

1

y

*

. The two vectors agree to around 5 significant digits, so they 

are graphically identical.

Figure 40. Instrument response matrix for the spectrometer, 

plotted on a log scale to show the small perturbations responsible 

for producing the scattered light.
Summary of Activities for Fiscal Year 2012 55

 

Figure 43. Two Matlab estimates of x*. Most of the elements in 

the vector estimate xlsqnonneg are exact zeros, and most of them on 

the estimate xfmincon are numbers of order 10-16.
56 NIST Applied and Computational Mathematics Division

High Performance Computing and Visualization

Computational capability is advancing rapidly. This means that modeling and simulation can be done with 

greatly increased fidelity (e.g. higher resolution, more complex physics). However, developing large-scale 

parallel applications remains highly challenging, requiring expertise that application scientists rarely have

In addition, the hardware landscape is changing rapidly, 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.

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 feature article, page 28.

Visualization and Modeling of RF 

Propagation in Body Area Networks 

John Hagedorn

Kamran Sayrafian

Judith Terrill

See feature article, page 32.

Modeling and Visualization of 

Cement Paste Hydration and 

Microstructure Development

William George

Steven Satterfield

Judith Terrill

Joel Muskin-Pierret

Jean-Loup Traore

Jeffrey Bullard (NIST EL)

Edward Garboczi (NIST EL)

Paul E. Stutzman (NIST EL)

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

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

When cement powder is mixed with water, the 

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. Computational modeling of the 

hydration of cement is challenging because it involves 

a large number of coupled nonlinear rate equations that 

must be solved in a highly irregular three-dimensional 

spatial 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 

Figure 44. Plot of time variation of: b) portlandite for C3S and 

C3S  ̃+ gypsum systems. The vertical dotted lines represent the 

approximate beginning of acceleration for the systems with and 

without gypsum. Microstructure shown at 0 h, 3 h, and 7 h for the 

C3S + 2.5 % gypsum system, with light blue = C3S, yellow = 

gypsum, dark blue = portlandite, and gray = C–S–H.
Summary of Activities for Fiscal Year 2012 57

validation and to understand the results. 

This year we extended the computational model 

and ran a number of validation studies, including the 

creation and coalescence of void space in the simulation. We also analyzed the Message Passing Interface 

(MPI) calls in HydratiCA to aid in removing inefficiencies. Finally, we successfully implemented and 

tested checkpointing. 

We have used HydatiCA to investigate the kinetic 

effect of sulfate incorporation and the possible implications for the determination of the “optimum sulfate.”

We ran computer simulations for two kinds of systems: 

C–S–H+ gypsum + portlandite, and C3S with gypsum 

varying between 0 % and 7.5 % by mass of solids. The 

simulations indicated that, for the mechanisms that 

were assumed, sulfate ions should cause a shortening 

of the initial period of slow reaction as well as an overall increase in the hydration rate when C-S-H is able to 

incorporate sulfate ions. Some published experimental 

data indicate a lengthening of the slow reaction period 

when sulfates are present, so these assumed mechanisms may need to be re-evaluated.

In the coming year we will study the rate controlling mechanism for early age cement hydration. The 

results of these simulations will provide new insights 

into hydration mechanisms, will help resolve some 

long-standing controversies in the literature, and will 

pave the way toward better measurement science that 

will lead to improved standard test methods for early 

age concrete properties, as called for in a recent 

roadmap for hydration kinetics research published 

jointly by NIST and the Federal Highway Administration.

[1] L. Valentini, J. W. Bullard, G. Artioli, J.-L. Traore, S.

G. Satterfield, J. E. Terrill, and M. Magistri, Role of 

Sulfate Incorporation into C–S–H during Cement Hydration: Results from Numerical Modeling of the 

System C3S + Gypsum, in preparation.

[2] J. W. Bullard, D. P. Bentz, E. J. Garboczi, S .G. Satterfield, P. E. Stutzman, L. Valenti, and G. Artioli, 

“Simulating Solution Chemistry and Phase Evolution in 

Early-age Cement Pastes”, invited presentation at the 

ACI Spring 2012 Convention, Dallas, TX, March 18-22, 

2012.

[3] L. Valentini, G. Artioli, J. W. Bullard, and S. G. Satterfield, “Modeling the Effect of Calcium Sulfate on C3S 

Hydration: Implications for the Origin of the Optimum 

Sulfate”, Advances in Cement-Based Materials: Characterization, Processing, Modeling and Sensing, Austin, 

Texas, June 10-12, 2012.

[4] J. J. Biernacki, J. W. Bullard, D. Constantiner, M. 

Juenger, J. H. Cheung, W. Hansen, R. D. Hooton, A.

Luttge, and J. Thomas, Paving the Way for a More Sustainable Concrete Infrastructure: A Vision for 

Developing a Comprehensive Description of Cement 

Hydration Kinetics, NIST SP 1138, November 2012.

Nano-structures, Nano-optics, and 

How to Control Exciton Fine 

Structure with Electric Fields

James S. Sims

John Kelso

Garnett W. Bryant (NIST PML)

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

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

Research and development of nanotechnology, with 

applications ranging from smart materials to quantum 

computation to biolabs on a chip, has the highest national priority. Semiconductor nanoparticles, also 

known as nanocrystals and quantum dots, are one of 

the most intensely studied nanotechnology paradigms. 

Nanoparticles are typically 1 nm to 10 nm in size, 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 

engineer properties completely different from the bulk 

and from small clusters. As a result of enhanced quantum confinement effects, nanoparticles act as artificial, 

man-made atoms with discrete electronic spectra that 

can be exploited as light sources for novel enhanced 

lasers, discrete components in nanoelectronics, qubits 

for quantum information processing, and enhanced 

ultrastable fluorescent labels for biosensors to detect, 

for example, cancers, malaria or other pathogens, and 

to do cell biology.

We are working with the NIST Physical Measurement Laboratory to develop computationally 

efficient large scale simulations of such nanostructures, 

and also 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 cases 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 and analysis tools necessary for a systematic, 

comprehensive study.

This year the work was focused on modulating and 

controlling the optical properties of self-assembled 

quantum dots using electric fields, culminating in a 

paper submitted to the Physical Review Letters [1]. 

Calculations were carried out on NIST’s 4,404-

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. We 

are now doing new runs (and new research) incorporat-
58 NIST Applied and Computational Mathematics Division

ing the effect of magnetic fields to what has already 

been investigated without including the effect of magnetic fields. This year we have completed testing the 

changes to the nanotech code for these imaginary parameters, and it is giving reasonable looking results. 

We have also redone some results from last year on 

bigger dots than we have been able to do before, and 

we are getting much better looking results than before. 

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 the work will be focused on 

modulating and controlling the optical properties of 

self-assembled quantum dots via external magnetic 

fields using this new feature of our nanostructure 

codes.

[1] G. W. Bryant, N. Malkova, and J. Sims, Electric-field 

Control of Exciton Fine Structure: Atomic Scale Manipulation of Exchange Splitting, in review.

High Precision Calculations of 

Fundamental Properties of FewElectron Atomic Systems

James Sims

Stanley Hagstrom (Indiana University)

M. B. Ruiz (University of Erlangen)

NIST has long been involved in supplying critically 

evaluated data on atomic and molecular properties such 

as the atomic properties of the elements contained in 

the Periodic Table and the vibrational and electronic 

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

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

property more accurately than even the most accurate 

experiments. It is our goal to be able to 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 

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 mathematical cusp

behavior of many-body wave functions in regions of 

close electron proximity, the so-called electron cusp 

region of the exact electronic wave function [1-3].

This flaw leads to incomplete accounting of instantaneous, short-range correlation among electrons. We are 

undertaking the theoretical development of our hybrid 

Hylleraas-CI wave function method to solve the electron cusp problem and bring sub-chemical accuracy to 

atomic systems with more than two electrons. Our HyCI method has been employed over the past two 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 four excited states of the 

lithium atom to two orders of magnitude greater than 

has been done before [4].

At the four electron level, in calculations published 

in the Physical Review A: Atomic, Molecular, and Optical Physics [5], we have demonstrated the ability of 

Hy-CI calculations to achieve 0.1 μh 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 microh accuracy to somewhere close to the nanohartre 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 election integral techniques. We will be employing the 

results of these improvements to our methodology in a 

much bigger beryllium calculation which will determine whether really accurate calculations on atoms 

with more than four electrons are feasible.

[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, Hylleraas-configurationinteraction study of the 2 2

S ground state of neutral lithium and the first five excited 2

S states, Physical Review A

80 (2009), 052507.

[5] J. S. Sims and S. A. Hagstrom, Hylleraas Configuration 

Interaction Study of the Singlet 1S Ground State of Beryllium, Physical Review A 83 (2011), 032518.

[Contributes to Virtual Measurements crosscut.]
Summary of Activities for Fiscal Year 2012 59

Determination of Computational

Features to Quantitatively

Characterize Stem Cell Colony

Quality

Adele Peskin

Ya-Shian Li-Baboud (ITL SSD)

Peter Bajcsy (ITL SSD)

Michael Halter (NIST MML)

Anne Plant (NIST MML)

Working with biologists in MML and at the Lieber 

Institute, we have identified qualitative attributes of 

images of stem cell colonies that can help to automate 

the process of identifying colonies of healthy, undifferentiated cells. Our current reference data includes 182 

image colonies that have been manually ranked on a 

scale of 1-5, with 1 representing colonies of differentiated cells, and 5 representing colonies of healthy 

undifferentiated cells. However, the rankings are subjective and often inconsistent from one person’s 

assessment to another. So we are faced with two simultaneous questions: how to quantify image features in 

order to classify the colonies, and how to establish 

these classifications given that our reference data is 

sometimes inconsistent. Figure 45 shows a range of 

colonies from undifferentiated to differentiated.

We are working with a variety of image features, 

several of which are constructed specifically for this 

investigation, including a measure of contrast within a 

colony, which biologically represents how well individual cell edges are defined within the colony, and a 

measure of homogeneity, which represents the fraction 

of cells within the colony that are in the same biological state. Both of these measures are calculated from 

local standard deviations of pixel intensity, within 

small neighborhoods of each pixel, the size of which 

are representative of the size of individual cells within 

the colony. Other features include circularity of the 

colony, which indicates consistent growth within the 

colony, size of the colony, and smoothness of colony 

edges. A new method for colony segmentation was 

constructed, which was challenging due to the ambiguous edges of the colonies, in part due to another strain 

of cells that are grown along with the stem cells. Different approaches are currently being taken to classify 

the colonies given quantitative colony features, including decision trees based on sets of observer data where 

there is agreement [1].

[1] H., Witten, E. Frank, and M. A. Hall, Data Mining, 

Third Edition, Elsevier, Amsterdam, 2011.

An Automated Method for Locating 

Phantom Nodules in Phantom CT 

Studies

Adele Peskin

Alden Dima (ITL SSD)

Ganesh Saiprasad (ITL SSD)

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

The Cancer Imaging Archive (TCIA) has a publicly 

available FDA database consisting of just over thousand CT scans intended to facilitate the assessment of 

lung nodule size estimation methodologies, the development of image analysis software, as well as a wide 

range of different analyses. The use of these scans 

would be greatly enhanced by the availability of phantom nodule location data that could be input into 

methods that require them. We have developed a new 

image processing method to locate the phantom nodules in these CT scans in order to avoid the need for 

laborious manual location prior to their use. We present 

a method for extracting the phantom nodules from the 

CT data, which involves phantom lung wall removal 

and separation of the phantom nodules from surrounding phantom blood vessels.

Nodules in the lung are classified according to 

their measured growth in CT scans taken over a period 

of time. Many prognostic techniques for cancerous 

Figure 45. Examples of three types of stem cell colony images: healthy and undifferentiated cells, less healthy cells, and differentiated cells.
60 NIST Applied and Computational Mathematics Division

nodules depend on accurate volumetric measurement 

techniques. Fully automated volumetric techniques 

must be able to handle the complex task of separating 

nodules from the blood vessels and structures around 

them, and often attached to them. Many different techniques have been developed, both fully and semiautomated, and comparative studies have been done 

and are still underway [1,2]. The Radiological Society 

of North America’s QIBA (Quantitative Imaging Biomarkers Alliance) Volumetric CT Study 3A is in the 

process of testing the variation and performance of 

algorithms for computing nodule volumes in CT lung 

nodule data sets15. The study is being currently being 

performed on phantom lung nodule data. The phantom 

data, generated at the FDA, is available via the TCIA 

for lung nodule size estimation assessment and image 

analysis software development16. However, the locations of the phantom nodules in these sets are not 

 

15 http://qibawiki.rsna.org/index.php?title=Main_Page

16 https://wiki.cancerimagingarchive.net/display/Public/Phantom 

+FDA

known well enough to be used as inputs to 

methods which require them. Figure 46

shows a picture of the FDA lung phantom 

used to create the CT lung nodule data and 

the assortment of nodules.

The extraction of nodule locations in the 

lung data takes place in a series of three

main steps: definition of the lung wall in the 

CT data, removal of the lung wall, and finally separation of the nodules from 

surrounding blood vessels. Locating the lung 

wall in the CT data takes advantage of the 

large intensity difference between the lung 

wall and the air inside the lungs. By locating 

sections of the higher intensity pixels that 

span the height of the lung, we extract sections of lung wall and locate nodules that are 

attached to the lung wall, which are then 

removed. Figure 47 shows an iso-surface of 

an entire CT lung data set at an iso-value of 

‒100 Hounsfield units (HU), a small section 

of an iso-surface at ‒100 HU containing a 

nodule attached to the lung wall, and a sample of a lung wall extraction. After lung wall 

removal, higher intensity pixels are clustered, and nodules are separated from blood 

vessels according to the sizes and geometries 

of remaining pixel clusters.

Some results are shown in Figure 48, 

for a data set containing nodules with two 

different densities, in the 0 HU and ‒600 

HU ranges. We tested our nodule extraction 

methods against 40 sets of data for which 

manually selected reference data was available. For the thin-sliced data sets, where the 

slice thickness is approximately equal to the 

pixel-pixel distance within a slice, our algorithm correctly located 96.4% of the nodules in all of the sets, 

with a false positive selection in only 2.55% of the 

data. We are currently processing 1200 sets of FDA CT 

lung data for a variety of data mining projects.

[1] A. C. Jirapatnakul, A. P. Reeves, T. V. Apanasovich, A. 

M. Biancadi, D. F. Yankelevitz, and C. I. Henschke, 

Pulmonary Nodule Classification: Size Distribution Issues, in Proceedings of the International Symposium on 

Biomedical Imaging, 2007, 1248-1251.

[2] Kostis, W.J., Reeves, A.P., Yankelevitz, D.F., Henschke, C.I. Three-Dimensional Segmentation and GrowthRate Estimation of Small Pulmonary Nodules in Helical 

CT Images, IEEE Transactions on Medical Imaging

22:10 (2003).

[3] A. P. Peskin, A. Dima, and G. Saiprasad, Anthropomorphic Thoracic Phantom CT Studies, in Proceedings 

of the International Conference on Image Processing, 

Computer Vision, and Pattern Recognition, Las Vegas, 

July 16-19, 2012.

Figure 46. FDA lung phantom and nodules.
Summary of Activities for Fiscal Year 2012 61

Declarative 3D Graphics 

Sandy Ressler

Manipulating and presenting 3D computer graphics as 

native elements of web pages is a once elusive goal 

that is now becoming a reality. Working with the 

Web3D Consortium and the Declarative 3D for Web 

Architecture Community Group of the World Wide 

Web Consortium (W3C), we have produced a number 

of demonstrations and an extensive tutorial illustrating 

the power and practicality of declarative markup for 

3D. 

Declarative, as opposed to imperative, markup describes the geometric objects of interest which are then 

interpreted by the web browser and rendered to the 

screen. Graphical objects such as “spheres”, “cones”, 

and so on, are treated in exactly the same way that 

“paragraphs”, “headings” and other page elements are 

treated. These graphical objects appear in the web 

page’s Document Object Model (DOM) just like regular page elements. This allows 3D application 

developers to use the rich infrastructure of web applications, including many widely used JavaScript 

frameworks, directly for their applications. The current 

implementation of declarative 3D that we use is called 

X3DOM, developed primarily by Franhoffer and the 

Web3D Consortium.

We have produced a collection of demonstrations 

that embed declarative 3D graphics into HTML-based 

slide shows. These demonstrations are available at a 

NIST website17 and were demonstrated at the W3C 

 

17 http://math.nist.gov/~SRessler/dec3Dslides.html

Figure 49. Declarative 3D Graphics embedded in an HTML 

slide show.

 

Figure 47. Iso-surface at -100 HU of an entire data set; close-up of nodule attached to wall; lung wall from a CT data set consisting of 119 

slices, each 2.5 mm.

 

Figure 48. Isosurface at -100 Hounsfield units of a CT data set and the corresponding lung wall in grey and nodules in red (0 HU nodules) 

and blue (-600 HU nodules).
62 NIST Applied and Computational Mathematics Division

Technical Plenary Advisory Committee (TPAC) 2012 

in Lyon France [1]. We also produced an extensive 

tutorial presented at the Web3D Conference in August 

of 2012 [3]. The tutorial ties together the use of 

X3DOM with jQuery and HTML5, and demonstrates 

many of the technical possibilities of declarative 

markup. These include the ability to dynamically generate user interface components that smoothly integrate 

with 3D graphics; the ability to associate semantics 

with graphical elements; and the ability to associate 

web based events with graphical models.

Finally we used the application of human anthropometry as a test-bed to demonstrate the use of 

declarative markup for a specific application [2].

[1] S. Ressler, Slides, Filters and Mobile Oh My! (Demonstrations of HTML and Declarative 3D Integration), 1st 

International Workshop on Declarative 3D for the Web 

Architecture, April 17, 2012, Lyon, France.

[2] S. Ressler, Web-based Declarative 3D Graphics for 

Anthropometry Visualization and Education, The

Graphical Web 2012, September 13, 2012, Zurich, Switzerland.

[3] S. Ressler, Not Your Mother’s Web3D: Integrating 

X3DOM, jQuery and HTML5, Web3D 2012, August 4, 

2012, Los Angeles, CA. 

Information Visualization for Cloud 

Computing 

Sandy Ressler

Kevin Mills (ITL ANTD)

As part of the Measurement Science for Complex Information Systems project we produced a series of 

visualizations with the explicit goal of producing results quickly so as to be meaningful to the researchers 

during their period of inquiry and to influence the direction of the research. The visualization approach was 

to take the data from the researchers (K. Mills) and 

process it via a set of R scripts which generated the 

individual frames of the animation. Initially a set of 2D 

animations was produced for each of the 12 experiments. In addition a set of 3D animations, also using R,

was produced.

An interactive VRML-based visualization was 

produced, with which the user can interact in real time 

(for individual time frames); see Figure 50. The user 

can spin the data object in real time, and more informatively, when the cursor is placed over the sphere, the 

fitness value appears as a popup. The color also corresponds to fitness.

Finally, an interactive web site using a new information visualization library called d3.js was used to 

implement a set of parallel coordinates to visualize the 

quantities of all the variables; see Figure 51. As you 

watch the animation18 (taking place in real-time in the 

web browser) move through successive generations,

you can observe the increase in fitness. 

We plan on continuing to work with the research 

team of the Measurement Science project19, which is 

now focused on characterizing resource utilization for 

cloud computing.

 

18 http://math.nist.gov/~SRessler/d3/partest/partestB.html

19 http://www.nist.gov/itl/antd/emergent_behavior.cfm

Figure 50. Genetic Algorithm visualization results illustrating 

convergence to high fitnesss.

Figure 51. Parallel coordinate display of genetic algorithm variables.
Summary of Activities for Fiscal Year 2012 63

Interactive Visualization and 

Analysis Tools for the National 

Vulnerability Database

Judith Terrill

Styvens Belloge

Sandy Ressler

Michael Ekstrom

Johathan Ibers

Harold Booth (ITL CSD)

The National Vulnerability Database (NVD) is the U.S. 

government repository of standards based vulnerability 

management data. It includes security checklists, security related software flaws, misconfigurations, product 

names, and impact metrics. This data enables automation of vulnerability management, security 

measurement, and compliance. Updated daily, it is 

available on the web as XML data. We are currently 

developing visualization and analysis tools to facilitate 

use of and insight into the NVD.

This year we created a schema for the XML data 

and created a tool to import the data into an SQLite

database. The database is updated nightly after the new 

vulnerabilities are added to the website. We created a 

front end visualization and analysis tool, NVDsql, to 

facilitate study of the database. We developed a series 

of interactive web based visualizations using the Data 

Driven Documents (D3) tool. We gave a variety of D3 

demos at the NIST booth at the 8th Annual IT Security 

Automation Conference, October 3-5, 2012, Baltimore 

MD. See Figure 52 for an example. In the coming year,

we will be expanding our D3 tool set with the goal of 

incorporating these into the NVD web site when it undergoes its planned upgrade. 

WebGL Enhancements for DLMF 

Visualization

Sandy Ressler

Brian Clanton (University of Rochester)

Marc Olano 

WebGL is a relatively new technology that enables 

web browsers to display OpenGL type 3D graphics 

natively on web pages. This allows users to create sophisticated graphics that take advantage of hardware 

GPU chips to produce high performance graphics displayed right in the web page. Using the new HTML5 

“canvas” element one can place these graphics in the 

page, and most importantly, these graphics are portable 

and interoperable on most computing and web browser 

platforms. The NIST Digital Library of Mathematical 

Functions (DLMF) currently uses older visualization 

technology to display graphics. Interoperability is problematic, and maintenance is highly labor intensive. In 

addition to interoperability issues, we wanted to 

demonstrate more advanced capabilities and some of 

the visual potential of applying WebGL to the future 

visualization needs of the DLMF.

We have created a DLMF Model Viewer20 that 

displays the surfaces in a variety of different shadings; 

see Figure 53. The viewer has the ability to place a 

clipping plane at an arbitrary angle, an ability that had 

never been explored in the DLMF project. 

With the successful conclusion of this demonstration, the next steps are to determine if this capability 

can be added to the production version of the DLMF. 

In addition, we anticipate improving the usability and 

visualizations of the model viewer as precursors to the 

production DLMF web site.

 

20 http://math.nist.gov/~SRessler/webgl/brianCMesh/index.html

Figure 52. A dynamic visualization of the cases of cross site 

scripting with score above 43. The circle radii are based on the 

score of each case, with the smallest being 50 and the largest 

being 93. There is additional color coding for the year (user selected attribute). A user can select an individual case and see 

details on it. The red circle is currently selected and the information on this case is shown on the right.

Figure 53. The DLMF Model Viewer.
64 NIST Applied and Computational Mathematics Division

Scientific Software

Modern science and engineering in general, and modern measurement science in particular, require a wide 

variety of software tools for scientific discovery, exploration, and analysis. As scientific inquiry becomes 

deeper and more specialized, so must the supporting software tools. The goal of this work is to develop critical software tools that support measurement science at NIST, as well as computational science and 

engineering at large.

OOF: Finite Element Analysis of 

Material Microstructures

Stephen A. Langer

Andrew C.E. Reid (NIST MML)

Günay Doğan (Theiss Research)

http://www.ctcms.nist.gov/oof/

The OOF Project, a collaboration between ACMD and 

MML, is developing software tools for analyzing real 

material microstructure. The microstructure of a material is the (usually) complex ensemble of

polycrystalline grains, second phases, cracks, pores, 

and other features occurring on length scales large 

compared to atomic sizes. The goal of OOF is to use 

data from a micrograph of a real or simulated material 

to compute the macroscopic behavior of the material

via finite element analysis. OOF is intended to be a 

general tool, applicable to a wide variety of microstructures in a wide variety of physical situations.

The currently available version of OOF is OOF2, 

which solves two dimensional time-dependent problems. Two versions were released this year, 2.1.6 and 

2.1.7. These versions fixed bugs and improved 

OOF2’s handling of electron backscatter diffraction 

data, which allows users to load experimentally measured crystalline orientation data directly into the 

program. OOF2 can now also generate pole figures, 

which are a way of viewing the orientation data, allowing users to check that the data was read correctly. (A 

number of parameters affect interpretation of the data, 

and OOF2’s assumptions may not always match the 

assumptions of the software that produced the data.)

One major area of development this year was 

OOF3D, which solves three dimensional problems

starting from three dimensional micrographs. A large 

fraction of the work on OOF3D involved writing and 

rewriting its graphics code. OOF3D’s graphics uses the 

vtk library21, which is very powerful and often maddeningly difficult to use. Shortcomings in the graphics 

interface were brought to light by development of the 

test suite, and new visualization methods were required 

to determine if mesh modification routines were operating correctly.

 

21 http://www.vtk.org/

A second area of development this year has been 

image segmentation, although this work has not yet 

been integrated into a released version of OOF2. Image segmentation is the task of identifying distinct

regions and structures in given images. It is critical to 

the analysis of material micrographs. The OOF approach to image segmentation is energy minimization, 

trying to match curves to region boundaries in images 

using special segmentation energies. In the last fiscal 

year, several computational procedures were developed 

and implemented, enabling the efficient and robust 

deployment of two very effective segmentation energies, the piecewise-constant Mumford-Shah model and

the Geodesic Active Contour (GAC) model. The two 

models are useful for segmenting images with flat regions and images with distinct boundaries, 

respectively. The implementation of the GAC model

contains procedures to compute high-quality edge indicator functions, reliable image derivatives and

interpolation, and uses special components for the corresponding Newton’s method for faster computation. 

The piecewise-constant model employs sophisticated

meshing and integration routines that quickly compute 

statistics of arbitrary image regions. Key ingredients to 

this model are adaptive mesh refinement and statistical 

error estimators used to determine the right amount of 

work to obtain the result, taking into account the inherent limitations on the available information due to 

finite image resolution. Significant effort was invested 

into improving the numerical infrastructure as well. 

Extensive tests and profiling led to many improved 

components and achieved significant speed-ups, ranging between 3X-100X.

The OOF team also worked on adding new features to OOF2. They completed the infrastructure for 

surface properties, and implemented a demonstration 

surface property with a prescribed flux on one side of 

the surface. This likely completes the prerequisites for 

OOF to support discontinuous surface effects such as 

those present in electrochemical problems. Also during this year, they made substantial progress on 

understanding the fundamentals of crystal plasticity,

having worked through some simple example problems 

in other codes. These results form the beginnings of a 

validation suite, to ensure that the OOF implementation 

of crystal plasticity is correct.
Summary of Activities for Fiscal Year 2012 65

The OOF2 team has worked with developers on 

the nanoHUB site22 to update the version of OOF2 that 

is installed there. 244 people used OOF2 on nanoHUB 

this FY (October 2011 – September 2012).

OOF2 was downloaded from its home page 1,217 

times between August 2011 and July 2012. 82,761 

manual pages were read online during that period.

[1] Valerie R. Coffman, Andrew C. E. Reid, Stephen A. 

Langer, and Gunay Dogan, OOF3D: An Image-based 

Finite Element Solver for Materials Science, Mathematics and Computers in Simulation 82 (2012), 2951.

 

22 http://www.nanohub.org/

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, magnetic nonvolatile memory (MRAM), 

and magnetic logic devices are dependent on an understanding of magnetization processes in magnetic

materials at the nanometer level. Micromagnetics, a 

mathematical model used to simulate magnetic behavior, is needed to interpret measurements at this scale.

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 

Figure 54. Segmentation and meshing of a micrograph: The top row shows the original input micrograph (left, courtesy of Dale Newbury, 

MML), its segmentation by thresholding (middle), a widely used method for image segmentation, and its segmentation with our implementation 

of the Chan-Vese model (right), which produces coherent regions unlike thresholding (which results in many unwanted speckles). The bottom 

row shows the meshes corresponding to the two phases of the micrograph. The meshes are of high quality and suitable for finite element simulations, and, they do not require any adjustment by the user. The meshes contain many fewer degrees of freedom compared to the original pixel 

grid, 10,131 and 11,006 elements respectively, whereas the input image has 819,200 pixels. Reduction of megapixel images to meshes of a few 

tens of thousands of high quality elements is typical in our experiments.
66 NIST Applied and Computational Mathematics Division

code for doing computational micromagnetics, the Object-Oriented Micromagnetic Modeling Framework 

(OOMMF). OOMMF serves as an open, welldocumented environment in which algorithms can be 

evaluated on benchmark problems. OOMMF has a 

modular structure that allows independent developers 

to contribute extensions that add to the basic functionality of OOMMF. OOMMF also provides a fully 

functional micromagnetic modeling system, handling 

both two and three-dimensional problems, with sophisticated extensible input and output mechanisms. In 

fiscal year 2012 alone, the software was downloaded 

more than 5,000 times, and use of OOMMF was 

acknowledged in 186 peer-reviewed journal articles. 

OOMMF has become an invaluable tool in the magnetics research community.

Key new developments in OOMMF over the last 

year include:

1. Continued development on measurement, analysis, 

and improvement of the performance of multithreaded computations. Efforts included enabling 

more code modules to use the SSE instruction set 

where available, development of a multi-level 

thread launch and join control system, and techniques for striping data arrays across memory nodes 

of non-uniform memory access (NUMA) architectures. 

2. Improvements to numeric accuracy when computing magnetostatic fields, particularly for

computational cells with large aspect ratios, and 

when computing the angle between spins in adjacent cells, which is important in error and step-size 

control.

3. A uniaxial anisotropy energy that can vary with 

simulated time, or calculation stage.

4. Support for adding Zhang damping to the computed 

magneto dynamics.

5. A snapshot release delivering the latest developments to the micromagnetic community.

Ongoing work includes extension of periodic boundary 

condition support to two dimensions, and collaboration 

with the University of California, San Diego, on porting some OOMMF calculations to massively parallel 

graphical processing units (GPUs) with the support of 

the Materials Genome Initiative.

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. The 

latest standard problem is an extension of a proposal 

[1] aimed at validation of simulations of spin momentum transfer in the “current parallel to plane” geometry. 

A solver that computes spin momentum transfer is 

based on one of two competing equations. The extensions to the proposed standard problem serve to

illustrate where the two competing equations diverge in 

their predictions. Ongoing work includes development 

of OOMMF input files and post-processing scripts capable of computing the interpolated vortex position 

demanded by the terms of the problem.

In addition to the continuing development of 

OOMMF, the project also does collaborative research 

using OOMMF. The project played an instrumental 

role in the 2007 Innovation in Measurement Science 

project (with CNST, MML and PML), Magnetic 

Nanostructures for Post-CMOS Electronics. This work 

involved development of methods for modeling polycrystalline materials with magnetically thick grain 

boundaries. Recent work has used OOMMF to investigate the scaling of input fields of an s-shaped nanoscale 

magnetic logic device with device size [2]. In all,

ACMD micromagnetic project produced two journal 

papers, three invited talks, and one conference presentation this past year.

[1] M. Najafi, et al., Proposal for a standard problem for

micromagnetic simulations including spin-transfer 

torque, Journal of Applied Physics 105 (2009) 113914-

113921.

[2] G. S. Abo, Y.-K. Hong, B.-C. Choi, M. J. Donahue, S.

Bae, J. Jalli, J. Park, J. Lee, M.-H. Park, and S.-H. Gee, 

Micromagnetic Computer Simulated Scaling Effect of 

S-shaped Permalloy Nano-element on Operating Fields 

for AND or OR Logic, IEEE Transactions on Magnetics

48 (2012), 1851-1855.

[3] M. J. Donahue, Micromagnetic Investigation of Periodic 

Cross-tie/Vortex Wall Geometry, Advances in Condensed Matter Physics (May 2012) 908692, 8 pages.

[Contributes to Virtual Measurements crosscut.]

Parallel Adaptive Refinement and 

Multigrid Finite Element Methods

William F. Mitchell

Marjorie A. McClain

Eite Tiesinga (NIST PML)

Paul Julienne (NIST PML)

Thomas Hanna (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. Adaptive 

refinement reduces the number of grid points by concentrating the grid in the areas where the action is, and 
Summary of Activities for Fiscal Year 2012 67

multigrid methods solve the resulting linear systems in 

an optimal number of operations. Recent research has 

focused on hp-adaptive methods where adaptivity is in 

both the grid size and the polynomial order of approximation, resulting in exponential rates of convergence. 

W. Mitchell has been developing a code, PHAML, to 

apply these methods on parallel computers. The expertise and software developed in this project are useful 

for many NIST laboratory programs, including material

design, semiconductor device simulation, and the quantum physics of matter.

This year we completed a study of the performance of 13 proposed hp-adaptive strategies in terms 

of accuracy vs. degrees of freedom. 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 [1,2,3,6,8]. 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 socalled reference solution methods performed well uniformly, but are very expensive computationally. Of the 

less expensive methods, the simple smooth prediction 

and type parameter strategies performed well most of 

the time. We have subsequently put effort into improving the efficiency of the code, and are now examining 

accuracy vs. computation time.

The development and application of PHAML continue to be of prime importance. As multicore 

computers begin to dominate the market, additional 

models of parallelism need to be implemented in scientific software. During the past year we continued the 

addition of OpenMP directives to PHAML to implement a shared memory model [7]. Not only is this 

appropriate for a multicore computer, but it can be 

combined with the previously implemented MPI message passing model to form a hybrid MPI/OpenMP 

model that uses shared memory parallelism on the multicore nodes of a cluster and message passing between 

the nodes.

PHAML was originally developed to solve elliptic 

partial differential equations in two spatial dimensions. 

We are now extending it to 3D, in support of collaborations with PML. This year we implemented the basic

functionality, but still lack many features including 

high order elements and parallel execution.

There are two major collaborative efforts with 

PML that apply PHAML to their physical models.

 In collaboration with Eite Tiesinga and Tom 

Hanna, PHAML was used to calculate the bound 

states, scattering properties and dynamics of two 

dipolar molecules held in a cylindrically symmetric trap [4,5]. We have studied in detail the twobody energy spectrum, and shown for the first 

time that the trap may be used to actively control 

the strength of the interactions. In collaboration 

with Eite Tiesinga and Paul Julienne, we are currently extending these simulations to a 3D model.

 We began a new collaboration 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. John has a code that models electron 

scattering in materials, secondary electron production, and detection. We are coupling this 

code with PHAML, which will perform the finite 

element analysis 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, complete the extension of PHAML to 3D

problems, and continue collaborations that use 

PHAML to solve NIST applications.

[1] W. F. Mitchell and M. A. McClain, A Survey of hpAdaptive Strategies for Elliptic Partial Differential 

Equations, in Recent Advances in Computational and 

Applied Mathematics (T. E. Simos, ed.), Springer, 2011, 

227-258.

[2] W. F. Mitchell and M. A. McClain, A Comparison of 

hp-Adaptive Strategies for Elliptic Partial Differential 

Equations, in review.

[3] W. F. Mitchell, A Collection of 2D Elliptic Problems for 

Testing Adaptive Algorithms, in review.

[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).

[5] T. M. Hanna, E. Tiesinga, W. F. Mitchell and P. S. Julienne, Bound states of interacting polar molecules in an 

optical lattice, 42nd Annual DAMOP Meeting, Atlanta, 

GA, June 2011.

[6] W. F. Mitchell and M. A. McClain, Comparison of hpAdaptive Finite Element Strategies, Foundations of 

Computational Mathematics, Budapest, July 2011.

[7] W. F. Mitchell, Experience with MPI and OpenMP in an 

Adaptive FEM Code, SIAM Conference on Parallel 

Processing for Scientific Computing, Savannah, GA, 

February 2012.

[8] W. F. Mitchell, Comparison of hp-Adaptive Finite Element Strategies, George Washington University, 

Washington, DC, March 2012.
68 NIST Applied and Computational Mathematics Division

Digital Library of Mathematical Functions

The special functions of applied mathematics are fundamental tools enabling modeling and analysis in all 

areas of science and engineering. To make effective use of such functions, practitioners must have ready access to a reliable source of information on their properties. The goal of this work is the development and 

dissemination of definitive reference data on the special functions of applied mathematics. The centerpiece of 

this effort is the DLMF, a freely available interactive and richly linked online resource.

Digital Library of Mathematical 

Functions

Daniel Lozier

Frank Olver

Ronald Boisvert

Marjorie McClain

Bruce Miller

Bonita Saunders

Abdou Youssef

Brian Antonishek (NIST ITL)

Charles Clark (NIST PL)

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 functions requires 

ready access to their many intricate properties. This 

need was capably satisfied for 50 years by the NBS

Handbook of Mathematical Functions [1]. 21st century 

needs, greatly enlarged since 1964, are being met by 

the NIST Digital Library of Mathematical Functions23

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 downloadable software.

The website is being updated regularly based on 

user feedback as well as continual review of the latest 

published research and tracking of emerging web technologies by the DLMF editors and staff. There have 

been five updates since public release in May 2010, 

 

23 http://dlmf.nist.gov/

two in calendar year 2012. The update on March 2 

made several improvements affecting display of math 

and graphics, augmented the software index, and updated the help files. The October 1 update corrected 11 

reported errors, four of which were math errors in formulas and the rest were relatively less important 

clarifications of math statements. It also included six

new formulas, 36 new references to recently published 

literature, and a few textual clarifications and other 

minor improvements in the bibliography and index.

This update is the first time formulas have been added 

to the original DLMF content. A complete record of 

changes since original release is available online24.

In August 2012 Dr. Adri Olde Daalhuis of the

University of Edinburgh was added as a DLMF Mathematics Editor. Dr. Olde Daalhuis is (co-)author of 

three DLMF chapters. He has made substantial contributions to the five DLMF web updates, especially the 

fifth one, and he is actively engaging with the other 

four editors in planning for a second edition of the 

printed handbook, which will bring it up to date with 

respect to the website.

We are working with Cambridge University Press 

to maximize adoption of the DLMF as a replacement 

for the old Abramowitz and Stegun handbook. Sales to 

date of the Cambridge volume have exceeded 4,000 

copies. Google Scholar currently lists about 400 citations. This number covers all academic fields, 

including physics, which in our experience is the 

source of many applications that use math functions. 

Finally, for calendar year 2012 there were more than 

256,000 visits to the DLMF web site by some 140,000 

unique visitors. Those visitors download more than 2 

million individual DLMF web pages.

[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.

 

24 http://dlmf.nist.gov/errata
Summary of Activities for Fiscal Year 2012 69

Mathematical Knowledge 

Management

Bruce Miller

Joe Corneli (Open University, UK)

Deyan Ginev (Jacobs University, Germany)

Michael Kohlhase (Jacobs University, Germany)

Heinrich Stamerjohanns (Jacobs University, Germany)

Abdou Youssef (George Washington University)

Most of ACMD’s current activity in Mathematical 

Knowledge Management (MKM) revolves around 

work-flows that use LaTeX markup as the document 

source, as was the case with the NIST Digital Library 

of Mathematical Functions (DLMF), for which we developed the LaTeXML [1] system. Newer applications 

continue to rely on the LaTeX markup familiar and 

convenient to authors in most heavily mathematical 

fields. The LaTeXML system converts that markup 

into XML and MathML for use on the web, with improved usability, reusability and accessibility.

We have reported previously on the arXMLiv project [2] based at Jacobs University. This project 

assembles a collection of workstations to convert, in 

parallel, the over half-million documents stored in 

Cornell’s preprint server. Between the large volume of

material and its sometimes haphazard markup quality,

this corpus exercises the software to the utmost. The 

result however is not only a more convenient means of 

browsing the repository, but also an extremely useful

data set for research in search, semantic analysis and 

other topics. Recent developments have improved the 

automation of RDFa (Resource Description Framework) metadata for the documents.

The development of a server-based Daemon [3] 

provided a web-service whereby other applications can 

convert LaTeX authored mathematics into usable 

forms. This opened up a number of interesting possibilities, including supporting mathematics in various 

Wikis. A particularly high profile Wiki containing 

mathematics is the Planet Math web site25. Planet Math 

is currently developing a beta version based on ideas 

from the Planetary project [4]. Here, the conversion to 

MathML should support the benefits of semantic representation of mathematics in terms of reuse, search and 

discovery of mathematical relationships.

Recent work has brought us close to realizing the 

conversion to SVG (Scalable Vector Graphics) of 

many forms of graphical markup used in LaTeX documents. While SVG may not provide the same level of 

accessibility to the truly blind as does MathML, it significantly improve the usability and scalability.

The real challenge, however, is ongoing work involving the generation of Content MathML, or 

semantic representation, of the mathematics. Always a 

 

25 http://planetmath.org/

goal, and further prodded by the Planetary project, inferring the semantics of ambiguous markup is not 

necessarily always possible, short of full human intelligence (or AI?). Nevertheless, much can be inferred or 

clarified by augmenting the documents or, at least, recording and representing the ambiguities for later 

analysis. How such inferences are best done, on the one 

hand, and how to represent ambiguities, on the other,

are continuing work [5]. Much infrastructural work 

within LaTeXML has been carried out to support such 

conversions and the interconnected parallel representations needed to make use of them.

All of these developments eventually lead back to 

DLMF. Truly reusable mathematics based on content 

MathML will allow importing to other software such as 

computer algebra or graphics systems, perhaps even 

automated validation. Capabilities such as the Planetary system could be used for mathematics-aware 

social media related to DLMF.

[1] B. Miller and A. Youssef, Technical Aspects of the Digital Library of Mathematical Functions, Annals of 

Mathematics and Artificial Intelligence 38 (2003), 121-

136. And see http://dlmf.nist.gov/.

[2] H. Stammerjohanns, M Kohlhase, D. Ginev, C. David, 

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

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

[3] D. Ginev, H. Stammerjohanns, B. Miller, and M. Kohlhase, The LaTeXML Daemon: Editable Math on the 

Collaborative Web, Lecture Notes in Computer Science 

6824 (2011), 292-294.

[4] M. Kohlhase, et al., The planetary System: Web 3.0 & 

active documents for STEM, Procedia Computer Science 4 (2011), Special issue: Proceedings of the 

International Conference on Computational Science 

(ICCS) (Mitsuhisa Sato, et al., eds.)

[5] D. Ginev, The Structure of Mathematical Expressions,

Master’s Thesis, Jacobs University, 2011.

Visualization of Complex Function

Data 

Bonita Saunders

Brian Antonishek (NIST ITL)

Qiming Wang

Bruce Miller

Sandy Ressler

Daniel Lozier

Frank Olver

Any visualization of complex function data must be 

both accurate and accessible if it is to be of use to a 

mathematical or physical scientist trying to understand 

the behavior of the function. The goal of our work is to 

create highly accurate visualizations that can be viewed 
70 NIST Applied and Computational Mathematics Division

by users on most widely used computer platforms. A 

properly constructed adaptive computational grid can 

enhance the fidelity and usability of a visualization by 

bringing out key features of the function such as zeros 

and poles while minimizing file size. We have had 

some success in developing such grids using a composite map consisting of tensor product B-splines together 

with variational techniques. Preliminary results were 

presented at the biannual meeting of the International 

Society for Grid Generation (ISGG 2012) [1].

We have attacked the accessibility problem in a 

variety of ways. We successfully created PDF files

with embedded interactive 3D graphics from the 

DLMF. Qiming Wang and Brian Antonishek worked 

with Bruce Miller to integrate this work into the DLMF 

so that the visualizations are embedded automatically 

whenever the DLMF PDF is regenerated. The resulting 

file can be viewed on any platform using an Adobe 

Acrobat Reader. 

Currently, DLMF website visualizations are rendered using two common technologies for 3D graphics 

on the web: Virtual Reality Modeling Language 

(VRML) and X3D. Although users may view the visualizations by downloading a free plugin, we have not 

found an acceptable viewer for the Linux operating 

system that easily handles all the custom features. Consequently, we have been looking at WebGL as an 

alternative. WebGL is a JavaScript API for rendering 

interactive 3D graphics inside an HTML5 web page 

without the use of a plugin. Primarily due to excellent 

work by Qiming Wang, we have made outstanding 

progress toward creating WebGL versions of the 

DLMF visualizations. Expanding on work originally 

done by Sandy Ressler, Qiming has successfully implemented in WebGL all the capabilities present in the 

DLMF visualizations, including alternative color maps, 

viewpoints, scaling and cutting plane animation. A 

sample rendering is shown in Figure 55.

WebGL visualizations are usable on Windows, 

Mac, and Linux platforms in most HTML5 compatible 

browsers with the exception of Internet Explorer (IE). 

Microsoft supports HTML5, but the company has indicated they have no intention of supporting WebGL 

because of security concerns. We are looking at a 

work-around using Chrome Frame or Flash which will 

allow a user to view a WebGL file even when attempting to access it through IE. Also, we are automating the 

transformation of the DLMF X3D files into the 

WebGL format and working with Bruce Miller to design the best way to integrate the files into the DLMF. 

For now, we expect WebGL to be another option in 

addition to the VRML and X3D formats, but in the 

future we expect to be able to drop the other formats 

when WebGL is more established.

[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.

[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, in Revised Selected Papers of the Seventh International 

Conference (MMCS 2008), Tonsberg, Norway, June 26-

July 1, 2008, Lecture Notes in Computer Science, Vol. 

5862, Springer, 2010, 385-393. 

[3] B. Saunders and Q. Wang, Tensor Product Grid Generation for Complex Surface Visualizations in a Digital 

Library of Mathematical Functions, 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, in 

CODATA Data Science Journal 6 (2007) (Supplement 

on the Proceedings of the 20th International CODATA 

Conference, Beijing, China, October 2006), S146- S154. 

[5] B. Saunders, Q. Wang, From B-Spline Mesh Generation 

to Effective Visualizations for the NIST Digital Library 

of Mathematical Functions, Curve and Surface Design: 

Avignon 2006, Sixth International Conference on 

Curves and Surfaces, Avignon, France, Nashboro Press, 

2007, 235-243. 

Figure 55. Modulus of hyperbolic umbilic canonical integral function |

(H)(x,y,0)|.
Summary of Activities for Fiscal Year 2012 71

DLMF 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)

Researchers and mathematical software designers have 

long used tables of elementary and special function 

values for numerical exploration, software validation, 

algorithm development, or graphics production, but 

previously published tables often suffered from severe 

limitations: low precision, restriction to real arguments, limited number of arguments and parameters, 

and inability to accommodate alternate function definitions. The goal of our project is to provide a state of the 

art online system where these limitations become attributes which the user has some flexibility to specify. 

The system output will be function values with an accuracy certification. 

The first phase of the project involves the integration of a front-end developed at NIST with high 

precision reference software developed by a research 

group at the University of Antwerp under the leadership of Dr. Annie Cuyt. Their software, which uses 

continued fractions as the main tool, establishes an 

error bound for the function computation. The group 

continues to add new functions to their package, but a 

substantial subset of the functions in the Digital Library of Mathematical Functions (DLMF) is currently 

covered.

On December 6-11, 2011 we hosted a workshop 

with Annie Cuyt’s group to discuss the implementation 

of a prototype for the first phase. In less than two days 

Bruce Miller (ITL) and Stefan Becuwe (Antwerp) 

merged our frontend with the C++ code of Cuyt’s 

group to produce a working prototype with a small 

number of functions. During the two week meeting a 

selected group of testers at NIST and the University of 

Antwerp were given access to the system. We made 

some initial changes based on feedback from the testers. Additional changes were made over the following 

months after emails and numerous conference calls 

with Cuyt’s group. New mathematical functions were 

added and the website interface improved. We added 

MathJax, a JavaScript display engine for mathematics, 

to make our web page math content accessible to users 

with browsers that don’t support MathML. We implemented help features, including simple function 

descriptions and links to the appropriate pages of the 

DLMF. We are currently discussing the possibility of 

providing links to extensive documentation and references for users interested in a more in depth understanding of the function validation techniques being 

used. 

Daniel Lozier and Annie Cuyt each presented invited talks on aspects of the project at the Workshop on 

Numerical Software: Design, Analysis, and Verification, Santander, Spain, July 4-6, 2012 [1] held in 

association with the yearly meeting of IFIP’s Working 

Group 2.5 on Numerical Software. Over the next few 

months additional modifications and testing will be 

conducted before the public release of the first phase. 

[1] F. Backeljauw, S. Becuwe, A. Cuyt, J. Van Deun, and 

D. Lozier, Validated Evaluation of Special Mathematical Functions, in Proceedings of Workshop on 

Numerical Software: Design, Analysis, and Verification, 

Santander, Spain, July 4-6, 2012, Science of Computer 

Programming, in review. 

[Contributes to Virtual Measurements crosscut.]

Figure 56. User interface to the Standard Reference Tables.
72 NIST Applied and Computational Mathematics Division

Special Function Expansions and 

Definite Integrals Associated with 

Fundamental Solutions of Linear 

Partial Differential Equations

Howard S. Cohl

Hans Volkmer (University of Wisconsin Milwaukee)

Ernie G. Kalnins (University of Waikato)

Gestur Ólafsson (Louisiana State University)

The concept of a function expresses the idea that one 

quantity (the input) completely determines another

quantity (the output). This project is about special functions and orthogonal polynomials. A special function is 

a function which has appeared in the mathematical 

sciences so often that it has been given a name. Our

research centers on a type of special function called a 

Green’s function or a fundamental solution (named 

after the British mathematician George Green, who 

first developed the concept in the 1830s). Green’s functions can be used to describe the influence of natural 

phenomena such as electromagnetism, gravity, heat 

and waves. For instance in electromagnetism, a 

Green’s function describes the influence of a point 

charge. The possible inputs are all of space (with the 

exception of a singular region), and the output is the 

“force” exerted from the point charge throughout 

space.

Green’s functions play an important role in the 

fundamental area of mathematics called partial differential equations, where they provide a powerful 

mechanism for obtaining their solutions. We study 

Green’s functions in spaces which are curved, and in 

particular, those spaces which locally look the same in 

every direction. These spaces are called 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. Our 

study is fundamental to the mathematical understanding of the universe, which as Einstein showed is 

curved.

We have focused on the following.

1. The determination in separable coordinate systems 

of eigenfunctions and eigenfunction expansions for 

fundamental solutions of Laplace’s equation on 

three-dimensional Euclidean space.

2. The computation of generalizations for generating

functions of hypergeometric orthogonal polynomials, generalized series expansions for higher 

transcendental functions associated with linear separable partial differential equations, and related definite integrals. 

3. The determination of eigenfunction expansions and 

addition theorems connected with fundamental solutions for linear elliptic partial differential equaequations on isotropic Riemannian manifolds.

Hypergeometric orthogonal polynomials are polynomials which are orthogonal with respect to a 

measure on an interval of the real line. We study eigenfunction expansions of integration kernels in terms of 

orthogonal polynomials (i.e., Jacobi, Gegenbauer, 

Chebyshev, Legendre and Laguerre). Some important 

kernels which can be expanded in terms of these polynomials are fundamental solutions of linear partial 

differential equations in rotationally-invariant coordinate systems and generating functions.

In collaboration with Hans Volkmer (Department of 

Mathematical Sciences, University of Wisconsin Milwaukee) we have derived eigenfunction expansions for 

a fundamental solution of Laplace’s equation on R

3

in 

parabolic and elliptic cylinder coordinates [4]. These 

expansions are given in terms of Hermite functions, 

modified parabolic cylinder functions, Mathieu functions and modified Mathieu functions. As an 

application of orthogonality and closure relations, we 

have obtained new definite integrals for products of 

associated Legendre functions with Bessel functions, 

associated Legendre functions, Ferrers functions, and 

Chebyshev polynomials of the first kind [3]. Some of 

these new definite integrals correspond to infinite series addition theorems for fundamental solutions of 

elliptic PDEs and are obtained using orthogonality relations for Ferrers functions of the first kind with integer 

degree and order, and Chebyshev polynomials of the 

first kind. We also obtain new definite integrals from 

pre-existing definite integrals by the application of the 

closure relation for the Hankel transform.

In terms of real Euclidean space, we have used expansions of a power-law fundamental solution of the 

polyharmonic equation on R

d

in terms of Chebyshev 

polynomials of the first kind and Gegenbauer polynomials to derive addition theorems in polyspherical 

coordinate systems for the resulting azimuthal Fourier 

coefficients. We have also developed polyspherical

addition theorems for a logarithmic fundamental solution of the polyharmonic equation in even-dimensional 

Euclidean space by comparing azimuthal Fourier expansions of this fundamental solution to corresponding 

Gegenbauer polynomial expansions.
Summary of Activities for Fiscal Year 2012 73

We also study special function representations for 

fundamental solutions of Laplace’s equation in terms 

of the global geodesic distance function on Riemannian 

spaces of constant curvature. In [1] we derive several 

alternative expressions for a fundamental solution of 

Laplace’s equation 

d SR

on the d-dimensional R-radius 

hypersphere

d

SR

. These expressions include definite

integral, Gauss hypergeometric function, finitesummation and Ferrers function of the second kind 

representations. In [2], we derive several alternative 

expressions for a fundamental solution of Laplace’s 

equation 

d H R

on the d-dimensional R-radius hyperboloid

d HR

(see Figure 57). These expressions include 

definite integral, Gauss hypergeometric function, finite-summation and associated Legendre function of

the second kind representations.

Concerning eigenfunction expansions and addition 

theorems for fundamental solutions of linear elliptic 

PDEs on curved isotropic Riemannian manifolds, we 

have had recent successes in Cohl & Kalnins (2012) [2] 

on 

d HR

. In [2], we compute azimuthal Fourier and 

Gegenbauer expansions for

d H R

. In particular, we 

derive azimuthal Fourier expansions in rotationallyinvariant coordinate systems and Gegenbauer polynomial expansions in polyspherical coordinate systems

which parameterize points on 

d HR

. The Gegenbauer 

polynomial expansion is given in terms of products of 

associated Legendre functions of the first and second 

kind and Gegenbauer polynomials which are the reproducing kernel for the space of polyspherical harmonics 

on a (d-1)-dimensional hypersphere embedded within 

d HR

.

On this project, we are currently collaborating with 

Gestur Ólafsson (Department of Mathematics, Louisiana State University). We have obtained for the rank 

one symmetric spaces, formulae for the global geodesic 

distance function as well as the radial coefficients

which multiply the Laplace-Beltrami operator for the 

Grassmann submanifolds embedded within these symmetric spaces. A fundamental solution of Laplace’s 

equation on the rank one symmetric spaces is radial 

and can be written as a solution to a second order ODE, 

of which eigenfunctions are known to be given in terms 

of specific Jacobi polynomials. Product addition theorems (in analogy with the addition theorem for 

Hyperspherical harmonics) which correspond to the 

harmonics on the embedded Grassmann submanifolds 

have also been computed. These are analogous to the 

polyspherical harmonics on embedded (d-1)-

dimensional hyperspheres within 

d HR

and 

d

SR

. One 

can expand the eigenfunctions of the Laplace-Beltrami

operator on a d-dimensional rank one symmetric space 

in terms of the reproducing kernel of the harmonics on

the (d-1)-dimensional embedded Grassmann manifolds 

G

d-1

. We know that

m

d

L G  Y



( )

2 1

, where

Ym

is 

the space of harmonics of degree m on G

d-1

. This is a 

finite dimensional Hilbert space where point evaluation 

is linear and continuous.

In [2], we computed azimuthal Fourier and 

Gegenbauer polynomial expansions for 

d H R

along 

with corresponding polyspherical addition theorems. 

We aim to compute azimuthal Fourier, Gegenbauer 

polynomial expansions and polyspherical addition theorems for 

d SR

on 

d

SR

. Our main goal is to understand

the global analysis, derive and introduce eigenfunction 

expansions and generate corresponding special function addition theorems for a fundamental solution of 

Laplace’s equation on the remaining rank one symmetric spaces such as complex, quaternionic and 

octonionic projective spaces as well as complex, quaternionic, and octonionic hyperbolic spaces.

[1] H. S. Cohl, Fundamental Solution of Laplace’s Equation 

in Hyperspherical Geometry, Symmetry, Integrability 

and Geometry: Methods and Applications 7 (2011), 108 

(14 pages).

[2] H. S. Cohl and E. G. Kalnins, Fourier and Gegenbauer 

Expansions for a Fundamental Solution of the Laplacian 

in the Hyperboloid Model of Hyperbolic Geometry,

Figure 57. A graphical depiction of the hyperbolid model of hyperbolic geometry 

d HR

with stereographic projection from the 

hyperbolid model to the Poincaré ball model.
74 NIST Applied and Computational Mathematics Division

Journal of Physics A: Mathematical and Theoretical 45

(2012), 145206 (33 pages).

[3] H. S. Cohl and H. Volkmer, Definite Integrals using

Orthogonality and Integral Transforms, Symmetry, Integrability and Geometry. Methods and Applications 8

(2012), 077.

[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 (2012), 

355204 (20 pages). 
Summary of Activities for Fiscal Year 2012 75

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. 

Quantum Algorithms for Quantum 

Field Theories

Stephen Jordan

Keith Lee (University of Pittsburgh)

John Preskill (Caltech)

See feature article, page 17.

Quantum Computing Theory

Scott Glancy

Emanuel Knill

Adam Meier

Mike Mullan

Yanbao Zhang

Bryan Eastin (Northrop Grumman)

Emilio Cobanera (University of Indiana)

Gerardo Ortiz (University of Indiana)

Our contributions to quantum computing and 

information theory at NIST span several application 

areas. We highlight our contributions to future 

improvements in the precision of atomic clocks, the 

analysis of experiments on the foundations of quantum 

mechanics, and the mathematics of physical dualities in 

condensed matter theory.

A promising strategy for improving the precision 

of atomic clocks is to exploit quantum correlations 

among multiple atoms to reduce measurement noise. In 

the relevant setting, an atomic clock consists of a 

classical “flywheel” that actually does the time 

keeping, and a fundamental frequency reference based 

on an atomic transition. The flywheel’s frequency is 

not fundamental and must be corrected to match the 

frequency reference. The flywheel is very stable, but 

still drifts over time. Therefore, the flywheel’s 

frequency must be continually controlled to match the 

frequency reference. Measurements of the frequency 

reference are used to correct the flywheel’s frequency. 

To make the measurements as informative as possible, 

multiple atoms can be prepared in a quantum correlated 

state and, after an evolution period, measured in a 

general quantum basis. We adapted semidefinite

programming techniques for optimizing quantum query 

algorithms to optimize the prepared state and final 

measurement for this purpose [1]. A key aspect of our 

method is to optimize a “cost function” that quantifies 

the quality of the measurement. Our original approach 

was greedy, optimizing an obvious quadratic cost 

independently of past measurements. We discovered 

that contrary to intuition, it is advantageous to make 

the cost function dependent on the past. To explore 

how much of an improvement can be obtained by 

exploiting quantum correlations, we implemented the 

first efficient simulation of an atomic clock that 

includes full Bayesian update cycles for correcting the 

flywheel frequency. Our first tests of the simulation

confirmed what Till Rosenband (NIST PML) found in 

his explorations of measurement techniques on two and 

three atomic systems.

Our work includes collaborations on experiments 

that use entangled photons for fundamental tests of 

quantum mechanics. Recently, these experiments have 

been expanded with the goal of demonstrating deviceindependent random number generation (see page 79). 

The analysis of data from these experiments requires 

quantifying the evidence against conventional, local 

realistic explanations for experimental data. The

quantification can be done by means of statistical pvalues in a way that is independent of the specifics of 

the experiment, thus enabling direct comparison of 

completely different experiments. Previously, we

developed an asymptotically optimal method for 

computing such p-values for rejecting local realism. 

While this method is practical for experiments in 

progress, future experiments involve more complicated

configurations requiring a more efficient approach. We 
76 NIST Applied and Computational Mathematics Division

have developed such an approach that is not limited by 

the complexity of the experimental configuration [2].

We continue to investigate techniques that promise 

to be useful for future fault-tolerant quantum 

computers. With B. Eastin, we completed work on a 

more efficient way of purifying so-called magic states

needed for universal fault-tolerant quantum computing

[3]. The work was particularly timely, as recent 

progress on IARPA’s Quantum Computing Program 

suggests that many fault-tolerant quantum 

computations are dominated by the work needed for 

such purifications. Several research groups have 

already found use for our approach in their work. As 

part of our work on fault-tolerant architectures, we also 

refined our simulations of stabilizer codes, which will 

be an important part of the soon-to-be completed Ph.D.

Thesis of Adam Meier.

Our work on physical dualities began with a now 

completed investigation of so-called non-Abelian 

dualities from the point of view of the framework of 

bond algebras developed by E. Cobanera and G. Ortiz

[4]. These kinds of dualities can be used as important 

tools to analyze phase diagrams of classical and 

quantum thermodynamic systems defined on lattices. 

As part of our work, we sought novel examples of

dualities that generalize those based on standard group 

theory and found a generalization to Hopf algebras in 

one dimension. Hopf algebras capture the essential 

algebraic properties of group algebras, so whenever an 

algebraic construction works for groups, one can

attempt to define it more generally for Hopf algebras. 

In this case, the construction was successful. We are 

presently considering whether there are any physically 

(rather than mathematically) motivated examples in 

this class that cannot be obtained from a conventional

group.

[1] M. Mullan, and E. Knill, Improving Quantum Clocks 

Via Semidefinite Programming, Quantum Informaton 

and Computation 12 (2012), 553-574.

[2] Y. Zhang, S. Glancy, and E. Knill, Asymptotically 

Optimal Data Analysis for Rejecting Local Realism, 

Physical Review A 84 (2011), 062118 (10 pages).

[3] A. Meier, B. Eastin, and E. Knill, Magic-State 

Distillation with the Four-Qubit Code, Quantum 

Information and Computation, to appear.

[4] E. Cobanera, G. Ortiz, and E. Knill, The Non-Abelian 

Duality Problem, in review.

Quantum Computing Benchmarks

Emanuel Knill

Adam Meier

Michael Mullan

Dietrich Leibfried (NIST PML)

Till Rosenband (NIST PML)

David Wineland (NIST PML)

Experimental efforts to demonstrate quantum devices 

suitable for quantum computations are rapidly growing 

and showing increasing success on multiple platforms. 

While the ion-trap platform is still leading the field, 

superconducting qubits are rapidly approaching parity, 

and solid-state qubits are showing increasing promise. 

One of our goals is to establish simple benchmarking 

protocols that can quantify the performance of these 

devices in a platform-independent way. Presently, our 

main benchmarking strategy involves the

implementation of randomized quantum networks and 

comparing the output to that expected for an ideal 

network. This yields an “error per gate” that can be 

reported as a device quality measure. Our latest

implementation of such a benchmark involved random 

two-qubit circuits and established an error per so-called 

Clifford operation as well as an error per phase-gate, 

one of the standard elementary two-qubit gates. This 

work appeared in Physical Review Letters [1] and 

established a method for benchmarking that can readily 

be scaled to more qubits. The technique has also been 

demonstrated in superconducting qubits by a group at 

IBM, obtaining similar results. In both cases, the

experimental challenge is to improve the errors per 

gate by at least an order of magnitude so that it 

becomes conceivable to scale up the systems in a faulttolerant way.

While presently available quantum devices are 

unable to realize the promised computational 

advantages of quantum computers, they are still useful 

for demonstrating basic principles of quantum 

algorithms and may suggest new ways of improving 

measurement precision. An example application is the 

use of quantum algorithm techniques for improving the 

precision of atomic clocks, where the frequency 

standard is based on a clock transition that can also 

serve as a qubit. The quantum information perspective 

has already been used to advantage in the so-called 

Al+-based quantum logic clock of the NIST Ion Storage 

group. Our theoretical work on quantum-algorithmbased clock optimization may be directly applicable to 

this clock. D. Leibfried recently suggested that the 

principles could be demonstrated on the more 

controllable Be+or Mg+quantum bits being developed 

for quantum information processing. This would also 

serve as a benchmark for algorithmic controllability of 

these quantum bits. We are in the process of

determining the feasibility of this suggestion.
Summary of Activities for Fiscal Year 2012 77

[1] J. P. Gaebler, A. M. Meier, T. R. Tan, R. Bowler, Y. 

Lin, D. Hanneke, J. D. Jost, J. P. Home, E. Knill, D. 

Leibfried, and D. J. Wineland, Randomized 

Benchmarking of Multiqubit Gates, Physical Review 

Letters 108 (2012), 260503 (5 pages).

Quantum State Estimation Theory 

and Applications

Scott Glancy

Emanuel Knill

Katelyn Weber (Montana State University)

Mark Girard (Freiburg Institute for Advanced Studies)

Gene Hilton (NIST PML)

Kent Irwin (NIST PML)

Konrad Lehnert (NIST PML)

Will Kindel (University of Colorado)

Hsiang S. 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 confident am I that it has 

prepared that state?”

One popular method to estimate quantum states is 

the maximum likelihood method, according to which 

the reported estimate is the state that maximizes the 

likelihood for the observed data. Finding the maximum 

likelihood state requires an iterative numerical optimization procedure. We formulated a statistically relevant 

criterion for stopping the iterations when the likelihood 

is “large enough”, depending on the proposed use of 

the estimated state [2]. We used classical statistical 

theory to describe several likelihood ratio confidence 

regions for the state estimate and gave stopping rules in

each case. This work has provided the first rigorous 

stopping criteria for maximum likelihood quantum 

state tomography, allowing researchers to calculate 

good quantum state estimates without wasting computational resources. The confidence regions we 

described can be used to give uncertainties for quantum 

state estimates.

Motivated by shortcomings in the maximum likelihood method (especially estimator bias and 

computation time) we implemented a new method for

quantum state characterization based on sampling of 

“pattern functions”. A quantum state’s expectation 

value of an observable (such as fidelity with any other 

pure state) can be expressed as the expectation value of 

a pattern function, where the pattern function is a function of experimentally measurable quantities. By 

repeating the measurement and calculating the mean 

value of the pattern function evaluated for each measurement result, one can estimate the desired

expectation value and its uncertainty. We found that 

the pattern function method avoids the bias that 

plagues maximum likelihood quantum state tomography, requires far less computational effort, and

provides rigorous uncertainty estimation. However, 

given equal data sets, the pattern functions showed 

slightly larger statistical error.

We continue our collaboration with the JILA laboratory of Konrad Lehnert through the 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 [1]. In 2012 

the laboratory prepared an entangled state of quantum 

microwaves and verified the entanglement with preliminary measurements. We are developing methods to 

calibrate the measurements and fully quantify the 

amount of entanglement.

[1] S. Glancy, W. Kindel, H. S. Ku, E. Knill, K. D. Irwin, 

G. C. Hilton, L. R. Vale, and K. W. Lehnert, Progress 

Towards Quantum Teleportation of Traveling Microwaves, Workshop-School in Quantum Computation and

Information, Fortaleza, Brazil, October 8, 2012.

[2] S. Glancy, E. Knill, and M. Girard, Gradient-based 

Stopping Rules for Maximum-likelihood Quantum-state 

Tomography, New Journal of Physics 14 (2012), 

095017.

Quantum State Tomography using 

Compressed Sensing

Yi-Kai Liu

Steven T. Flammia (University of Sydney)

David Gross (University of Freiburg)

Jens Eisert (Freie Universität Berlin)

Quantum state tomography is a family of techniques 

for estimating the state of a quantum system. Tomography provides a full characterization of the state, 

including all effects due to noise and decoherence. This 

makes it a useful tool in experiments involving quantum-enhanced metrology and quantum computation. 

However, tomography of large quantum systems is 

very resource-intensive: the required number of state 

preparations and measurements grows exponentially 

with the number of qubits.

Previously we studied methods for quantum state 

tomography based on compressed sensing, which can 

reconstruct quantum states that are approximately low-
78 NIST Applied and Computational Mathematics Division

rank, while achieving a quadratic reduction in the

number of measurement settings. We have proved tight 

error bounds, using a technique based on the restricted 

isometry property (RIP). In addition, in the special case 

of pure states, we have proved that compressed tomography has nearly optimal sample complexity (among all 

methods using two-outcome Pauli measurements).

In the past year, we have generalized our results on 

sample complexity to apply to low-rank mixed states; 

again, we find that compressed tomography is nearly 

optimal. We have also developed some useful tools: a 

more general version of our direct fidelity estimation 

technique, which can be used to certify low-rank mixed 

states; and a very simple compressed sensing technique 

for quantum process tomography.

We have run numerical simulations, which show 

that the sample complexity of compressed tomography 

is largely insensitive to the number of Pauli observables that one measures. This gives rise to a new degree 

of freedom when designing experiments: one can either 

measure a small set of observables relatively accurately, or measure a large (e.g., complete) set of 

observables relatively coarsely. Finally, our simulations demonstrate that compressed tomography is more 

accurate than standard maximum-likelihood estimation 

(MLE) in a variety of situations, given comparable 

experimental resources.

We are continuing to investigate compressed tomography of continuous-variable systems, as well as 

practical uses of compressed tomography in ion trap 

quantum information processors.

[1] S. T. Flammia, D. Gross, Y.-K. Liu and J. Eisert, Quantum Tomography via Compressed Sensing: Error 

Bounds, Sample Complexity, and Efficient Estimators, New Journal of Physics 14 (2012), 095022.

[2] M. Ohliger, V. Nesme, D. Gross, Y.-K. Liu and J. 

Eisert, Continuous-variable quantum compressed sensing, in review.

Cryptography Beyond Quantum Key 

Distribution

Yi-Kai Liu

Since Bennett and Brassard’s discovery of quantum 

key distribution in 1984, many researchers have wondered whether quantum information can be used to 

perform other cryptographic tasks with informationtheoretic security. Unfortunately, there are strong theoretical results that rule out the possibility of quantum 

bit-commitment and most other kinds of secure computation. Interestingly, however, some of these 

cryptographic tasks become possible, if one assumes 

additional restrictions on the adversary’s power; for 

instance, one may assume that the adversary can only 

perform k-local measurements, or that he has bounded 

or noisy storage.

We have been studying a model where it is possible to build isolated qubits, which can be measured 

individually, but cannot be entangled. This is motivated 

by recent experimental work with nitrogen vacancy 

centers, and possible cryptographic applications such 

as one-time memories and one-time programs.

Post-Quantum Cryptography

Stephen Jordan

Yi-Kai Liu

Lily Chen (ITL CSD)

Dustin Moody (ITL CSD)

Rene Peralta (ITL CSD)

Ray Perlner (ITL CSD)

Daniel Smith (ITL CSD)

Quantum information science creates both new challenges and new opportunities for cryptography. Peter 

Shor’s 1994 discovery of efficient quantum algorithms 

for integer factorization and discrete logarithms 

showed that currently used cryptosystems (such as 

RSA, Diffie-Hellman and elliptic curve cryptosystems) 

will not remain secure in a world with quantum computers. The search for alternative cryptosystems secure 

against quantum attack has grown into an active subfield called post-quantum cryptography. Staff members 

of the ACMD, in collaboration with the ITL Computer 

Security Division, are currently studying various aspects of post-quantum cryptography.

Currently there are three main classes of cryptosystems considered to be promising post-quantum 

candidates: lattice-based (such as NTRU), code-based 

(such as McEliece), and multivariate (such as HFE and 

its variants). Significant open questions remain about 

each of these candidates. First, straightforward implementations of lattice-based and code-based

cryptosystems suffer from large key sizes, scaling 

quadratically with the underlying security parameter. 

By incorporating additional structure into the keys, one 

can reduce their size; however, the security of these

structured keys against classical or quantum attack 

remains an area of active research. In addition, recent 

successful attacks on multivariate cryptosystems have 

raised questions about what kinds of algebraic constructions suffice to ensure the security of these 

schemes. Finally, while there are some proposals for 

post-quantum encryption schemes that achieve key and 

message sizes comparable to RSA, there continue to be 

challenges in developing post-quantum signature 

schemes that are equally efficient. Thus there has been 

some serious consideration of alternative solutions, 

such as hash-based signatures.
Summary of Activities for Fiscal Year 2012 79

In the past year we have surveyed various postquantum cryptosystems, to get an overview of the different constructions, security proofs, and cryptanalytic 

attacks. In addition, we have surveyed recent work on

quantum algorithms and experimental implementations 

of quantum computers. Overall, it appears that there 

are promising candidates for post-quantum cryptography, although many of these are still at the basic

research stage. The next step will be to perform a detailed evaluation of these candidate cryptosystems, to 

move them closer to practical use.

Quantum and Classical Circuit 

Obfuscation with Braids

Stephen Jordan

Gorjan Alagic (Caltech)

Stacey Jeffery (University of Waterloo)

A circuit obfuscator is an algorithm that translates logic 

circuits into functionally-equivalent similarly-sized 

logic circuits that are hard to understand. While ad hoc 

obfuscators exist, theoretical progress has mainly been 

limited to no-go results. In this project we propose a 

new notion of circuit obfuscation, which we call partial

indistinguishability. We then prove that, in contrast to 

previous definitions of obfuscation, partial indistinguishability obfuscation can be achieved by a 

polynomial-time algorithm. Variants of this algorithm 

can be applied to both classical and quantum circuits.

Circuit obfuscation, while an intuitively natural 

concept, is difficult to define formally. In 2007, 

Goldwasser and Rothblum made substantial progress 

by defining indistinguishability obfuscation. An indistinguishability obfuscator O is a map from circuits to 

circuits, such that if A and B are functionally equivalent 

then O(A) and O(B) are indistinguishable. Intuitively, 

such an obfuscator hides all information about the implementation of A and B (though not necessarily their 

functionality).

If O is a fixed, deterministic map then for O(A) to 

be indistinguishable from O(B), one requires 

O(A)=O(B). However, O may also be a probabilistic 

map, in which case it suffices for the probability distribution O(A) to be computationally infeasible to

distinguish from the probability distribution O(B). 

However, complexity-theoretic arguments show that a 

polynomial-time deterministic indistinguishability obfuscator for general circuits cannot exist unless P=NP. 

Even in the probabilistic case, no efficient construction 

for indistinguishability obfuscation of general circuits

is known.

In this work, we propose a weaker definition, 

which we call partial-indistinguishability obfuscation. 

Here, given equivalent circuits A and B, we demand 

O(A)=O(B) only if A can be obtained from B by some 

sequence of logic-gate identities taken from a fixed 

finite set G. If G is a complete set of gate identities 

then one recovers Goldwasser and Rothblum’s notion 

of indistinguishability obfuscation. For smaller sets of 

gate identities, this defines a weaker notion of obfuscation, but on the other hand, it may be actually 

achievable in polynomial time. Specifically, using ideas from topological quantum computation, we show 

that efficient obfuscators exist for both classical quantum circuits when G is taken to be the relations of the 

Artin generators for the braid group.

[1] G. Alagic, S. Jeffery, and S. P. Jordan. Partialindistinguishability obfuscation using braids, in preparation.

Generating Random Bits from 

Entangled Quantum States

Scott Glancy

Stephen Jordan

Manny Knill

Yi-Kai Liu

Paulina Kuo

Alan Mink

Xiao Tang

Lawrence Bassham (ITL CSD)

Michaela Iorga (ITL CSD)

Andrew Rukhin (ITL SED)

Joshua Bienfang (NIST PML)

Alan Migdall (NIST PML)

Sae Woo Nam (NIST PML)

Quantum information technology enables new cryptographic schemes whose security is based on physical, 

rather than computational, assumptions. This year, staff

members of the ACMD, as well as of other divisions of

the ITL and the PML, have teamed up to initiate a 

NIST Innovations in Measurement Science project to

develop a random number generator based on quantum 

entanglement. Such a generator could be used to generate the private keys used in standard cryptographic 

schemes. In addition, the team plans to integrate the 

quantum random number generator with the Computer 

Security Division’s random number beacon. The beacon will publish time-stamped random numbers on the 

internet, which can then be used to implement various 

secure multiparty protocols, such as privacy-preserving 

auctions and selective disclosure of personal information.

At the heart of this project is a fundamental connection between quantum nonlocality and randomness.

This is illustrated by “Bell tests,” which are experiments using entangled pairs of photons, whose results 

cannot be predicted by any classical (“local realistic”) 
80 NIST Applied and Computational Mathematics Division

model, but are in agreement with quantum mechanics.

The result of a Bell test turns out to have a surprising 

property: it is guaranteed to be random, in the sense 

that it could not have been predicted beforehand. 

Moreover, this guarantee can be made “deviceindependent,” i.e., any Bell test that passes a certain 

verification procedure, which involves its input-output

behavior but not its internal functioning, can be guaranteed to produce a random output.

Building a device-independent secure random 

number generator poses many experimental and theoretical challenges. In particular, it requires the 

construction of a “loophole-free” Bell test. Achieving 

such a test requires very high efficiency generation, 

transmission, and detection of entangled photons, 

which only recently has appeared within reach of experimental technique. In addition, there are theoretical 

challenges in parlaying such a test into a useful cryptographic resource, as one must show that the scheme is 

secure against both the subtleties of nature and the attacks of a malicious adversary.

Quantum Communications

Xiao Tang

Oliver Slattery 

Paulina Kuo

Yong-Su Kim

Barry Hershman

We conduct experimental research in quantum communications to identify the potential for and limitations 

of this technology for the IT sector, and to develop the 

requisite measurement science to support commercialization. More specifically, our research agenda includes 

single photon creation, transmission, storage, transduction and detection. Our goal is to demonstrate a 

complete quantum communications system that will 

create strategically selected single photons, transmit 

them (flying qubits) and interface them with an atomic 

quantum memory (stationary Qubit) for storage and 

processing. 

Previously, our research group developed an efficient frequency up-conversion detector for single 

photon level light at 1.31 μm by pumping them at 1.55 

μm. We then worked with Stanford University to develop an up-conversion detector targeting 1.55 μm, the 

other low-loss transmission window in silica based 

fibers. In this case, the single photons at 1.55 μm are 

pumped at 1.9 μm creating near visible single photons 

efficiently detectable using a silicon-based avalanche

photo diode (APD). The 1.55 μm system achieves a 

detection efficiency of more than 35% with low noise 

characteristics [1]. This development extended upconversion detection wavelength from near 1.3 μm to 1.55 

μm.

One of the drawbacks of silicon based avalanche 

detectors is so-called detection jitter, which limits the 

maximum detection rate of the system. To overcome 

this, our team previously demonstrated a proof-ofprinciple scheme to increase the data rate of quantum 

communication systems equipped with up-conversion 

detectors [2]. During this fiscal year, NIST and Stanford researchers developed a unique dual-channel upconversion device [3] in which signal photons at 1.3 

μm are pumped by two slightly separated wavelengths 

near 1.55 μm and converted to two photons at slightly 

separated visible wavelengths in the two channels. The 

visible photons are separated using a dispersion element and sent to two distinct silicon based APDs for 

detection. Therefore, the system data rate can be doubled with high detection efficiency. 

The team has further developed our signal photon 

sources to include narrowed single photons at 895 nm 

(compatible with atomic transitions of Cesium) and 

1310 nm (suitable for transmission over long distances). In addition, the development of a Cesium based 

quantum memory system was started during this year –

including outfitting a dedicated laboratory toward that 

development. 

The team also successfully completed an SBIR 

project to commercialize the upconversion detector 

technology developed at NIST. 

More details of the development and research progress by the team in recent years can be found in the 

newly published article in Physics Reports [4].

[1] J. S. Pelc, L. Ma, C. R. Phillips, Q. Zhang, C. Langrock, 

O. Slattery, X. Tang, and M. M. Fejer, Longwavelength-pumped upconversion single-photon detector at 1550 nm: performance and noise analysis, Optics 

Express 19:22 (2011) 21445. 

[2] L. Ma, J. C. Bienfang, O. Slattery and X. Tang, Upconversion single-photon detector using multiwavelength sampling techniques, Optics Express 19:6

(2011) 5470. 

[3] J. S. Pelc, P. S. Kuo, O. Slattery, L. Ma, X. Tang, and 

M. M. Fejer, Dual-channel, single-photon upconversion 

detector at 1.3 μm, Optics Express 20:17 (2012), 19075. 

[4] L. Ma, O. Slattery, X. Tang, Single photon frequency 

up-conversion and its applications, Physics Reports

(2012).
Summary of Activities for Fiscal Year 2012 81

Low Density Parity Codes for 

Quantum Key Distribution

Alan Mink 

Anastase Nakassis (ITL ANTD)

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 key distribution (QKD), which is a protocol 

that uses a pair of unsecured communication channels, 

one quantum and one classical, 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, which 

relies on computational complexity.

There are four stages to the QKD protocol. Stage 3 

is where Alice and Bob exchange information over the 

classical channel to correct errors between their bit 

sequences (the shared secret) without exposing the 

value of their bits. There is a large body of information 

about error correction codes, but QKD presents a 

somewhat different environment than conventional 

communication. Expected QKD error rates are higher

(1% to 11% vs. 0.1% or below), error correction information is sent separately over an error free channel, 

the amount of information that the error correction 

code leaks about the data must be kept below a given 

limit, and data retransmission is not possible. 

The original QKD error correction algorithm, Cascade, requires multiple round trip communications. 

Each trip leaks additional information, and the number 

of trips required is unknown in advance. An alternative 

error correction method, called low density parity 

check (LDPC), has become popular for QKD, because 

it only requires a single roundtrip communication, and 

therefore the amount of leaked information is known in 

advance. Also, a single trip reduces communication 

delays, a benefit as the distance between Alice and Bob 

increases.

We have investigated LDPC error correction codes 

customized for QKD. In particular, we have developed 

tighter bounds for the information leaked during QKD 

LDPC [1]. We have also developed efficient LDPC 

software and hardware implementation techniques.

We then followed up with a description of the 

LDPC forward error correction algorithm adapted for 

the QKD protocol in a form that is readily applied by 

developers [2]. A sparse matrix describing a set of 

check sums is a key component of LDPC. Our description includes sources for the LDPC matrices as well as 

lookup tables, data structures, and a pseudo code description of the complete LDPC algorithm, both of 

which are normally absent from LDPC descriptions. 

We also evaluated these matrices for their QKD correction performance, since different matrices present a 

tradeoff between correction performance and information leakage. A matrix that can correct a larger error 

rate also leaks more information, directly reducing the 

amount of secure key, possibly to zero. We also discussed the computational precision required for this 

LPDC algorithm and showed a simple heuristic technique to boost performance with less precision.

The objective of the QKD 3rd stage is to perform 

error correction such that it will optimize the amount of 

secure key in the time allotted. Thus, we are pursuing 

faster implementations, using hardware and GPUs, as 

well as devising strategies to maximize overall secure 

key production, within the time constraints available.

[1] A. Nakassis and A. Mink, LDPC Error Correction in the 

Context of Quantum Key Distribution, in Proceedings of 

the SPIE: Defense Security & Sensing, Baltimore, MD, 

April 2012.

[2] A. Mink and A. Nakassis, LDPC for QKD Reconciliation, The Computing Science and Technology 

International Journal 2:2 (2012), 2162-0687.
82 NIST Applied and Computational Mathematics Division

Foundations of Measurement Science for Information Systems

Modern information systems are astounding in their complexity. Software applications are built from thousands of interacting components. Computer networks interconnect millions of independently operating nodes. 

Large-scale networked applications provide the basis for services of national scope, such as financial transactions and electrical power distribution. In spite of our increasing reliance on such systems, our ability to 

build far outpaces our ability to secure. Protocols controlling the behavior of individual nodes lead to unexpected macroscopic behavior. Local power anomalies propagate in unexpected ways, leading to large-scale 

outages. Computer system vulnerabilities are exploited in viral attacks, resulting in widespread loss of data 

and system availability. The long term stability of our critical infrastructure is simply unknown. Measurement science has long provided a basis for the understanding and control of physical systems. Similar types 

of deep understanding and insight are lacking for complex information systems. We seek to develop the 

mathematical foundations needed for the emergence of a true measurement science for complex networked 

information systems.

A Game-theoretic Approach to the 

Security of Complex Systems

Assane Gueye

Vladimir Marbukh

Ion Matei (NIST EL)

John S. Baras (University of Maryland)

Richard La (University of Maryland)

Aron Laszka, (Budapest Univ. of Tech. and Economics)

Today, almost all critical infrastructures of national 

importance—transportation, financial, power grids,

military, intelligence systems, and health and safety 

systems—rely on information and communication 

technologies (ICT). Despite this vital dependency on 

ICT systems, our fundamental knowledge about their 

global behavior is quite primitive: today there is no 

science that offers the knowledge needed to build globally predictable systems. Moreover, recent failures of 

critical infrastructures (e.g., communication and financial networks, power grids) have exposed troubling 

deficiencies in our ability to prevent and mitigate such

catastrophic events. Metrics are needed which can be 

used for effectively assessing a system’s level of security and reliability. Unfortunately, conventional metrics 

are based on unrealistic assumptions, e.g., stand-alone

systems, steady state, lack of selfish user behavior in 

general and of malicious behavior in particular. Finally,

we still lack a good understanding of the fundamental 

limits in our ability to design large systems that are

secure and resilient. Only such understanding will enable the development of realistic and cost-effective tools 

to deal with present and future security threats.

Our research effort strives to address the aforementioned issues from a first principle/science-based 

approach. We are exploring three closely related and 

interdependent research directions: (a) characterizing 

macro-scale structures and dynamics of large-scale 

interconnected systems, (b) identifying fundamental 

metrics that are indicators of the system’s inherent level of security and reliability, and (c) using these metrics 

to develop efficient tools for cybersecurity risk management and appropriate feedback loops to mitigate 

risks. We envision enhancing conventional models and 

proposing new ones by explicitly recognizing that ICT 

infrastructures are distributed large-scale systems 

where some components (e.g., users, processes) are 

selfish and other components are malicious. We plan to 

leverage recent advances in complex systems research, 

and game-theoretic models of selfish and malicious 

behavior, as well as our growing ability to collect and 

analyze large amounts of data. We will also build upon 

classical analytical approaches such as decision theory, 

risk theory, information theory, and control theory. To 

reach this interdisciplinary goal, we envision close collaboration with NIST staff members as well as faculty 

members at the University of Maryland.

Our research in the last year has demonstrated the 

important role game theory can play in studying security problems by capturing the strategic nature of 

adversaries. In particular, by modeling some idealized 

security scenarios as games between an attacker and a 

defender, we have shown that the ability of a malicious/selfish agent to acquire and exploit system 

information may alter conventional predictive metrics 

of system behavior. The next step is to bring current 

models closer to real-life applications, validate them 

against real-life data, and propose new and improved 

models. To this end, we have recently consolidated our 

earlier work and built upon it to propose new metrics 

for quantifying network vulnerability to attacks [1]. 

Using these metrics, we have proposed and discussed a 

framework for analyzing the risk/cost tradeoff for supply-demand networks [2]. In [3] the framework was

generalized to other networks and the complexity of 

deriving the risk/cost tradeoff curve was analyzed. Finally, we have established the relationship between the 

proposed vulnerability metrics and well-known graph 

theory notions [4].
Summary of Activities for Fiscal Year 2012 83

In the next year, we plan to utilize these metrics 

for the analysis of ICT systems. These systems are 

complex interconnected networks for which the local 

(micro) interactions of agents (some selfish, others 

malicious) can lead to the emergence of global (macro), often undesirable behaviors. For such large 

systems, we envision developing tools and models that 

can help us understand the underlying process that 

leads to “phase transitions” in the system’s global behavior. This can be used to design systems so that their 

behavior can be predicted prior to building them, as 

well as during operation. For such networks of interacting agents, the notion of trust plays a central role in the 

process of local decision making. We intend to study 

how trust between the agents and the presence of both 

positive and negative externalities influence the dynamics and global behavior of such systems. 

Understanding the system’s behavior will enable the 

development of effective control methods to mitigate 

the risk of catastrophic events. 

The human factor is another aspect of the security 

process that we would like to explore. We are particularly interested in the issues of incentive and usability: 

how to develop the right mix of incentives (policies, 

laws) to promote adoption of best practices in cybersecurity, and how to develop security solutions that are 

intuitive and user-friendly enough to permit easy adoption. Finally, while our research is focused on the 

security of ICT systems, we plan to extend and apply 

the results to other critical systems such the power grid, 

water distribution, and transportation systems.

[1] A. Gueye, V. Marbukh, and J. C. Walrand, Towards a 

Quantification of Communication Network Vulnerability to Attacks: A Game Theoretic Approach, in 

Proceedings of the 3rd International ICST Conference 

on Game Theory for Networks, Vancouver, Canada, 

May 2012.

[2] A. Gueye and V. Marbukh, A Game-Theoretic Framework for Network Security Vulnerability Assessment 

and Mitigation, in Proceedings of the 3rd Conference on 

Decision and Game Theory for Security (GameSec), 

Springer-Verlag, Berlin, 2012.

[3] A. Lazska and A. Gueye, Quantifying Network Topology Robustness under Budget Constraints, in review.

[4] A. Gueye, A. Lazska, J. Walrand, and V. Anantharam, A 

Polyhedral-Based Analysis of Nash Equilibrium of Quasi-Zero-Sum Games and its Applications to 

Communication Network Security, in review.

An Algebraic Formulation for the 

Analysis and Visualization of 

Network Graphs

Roldan Pozo

Characterizing the topological structure of large graphs 

is 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 networks (unless they exhibit a special 

structure, such as a tree-like topology) is nearly impossible. In such cases the rendered image is nearly a 

solid blot of color in which is difficult to see any meaningful information. This difficulty is largely due to (1) 

the presence of high-degree nodes (hubs) which entangle many parts of the graph with itself, and (2) the 

sheer number of vertices and edges (well into the millions and billions) which are becoming common in 

network science.

An alternate approach is to visualize important 

network properties, rather than the actual network itself. Such network portraits attempt to capture 

interesting attributes of a large graph, such as degree

distribution, or its connectivity properties. In this research area, 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, highly connected amongst themselves, but often lost with the inclusion of more popular nodes.

The Q-matrix, in its fundamental formulation, is a 

connected component size distribution matrix for a 

percolation process on a network graph. As a simple 

example, consider the component size distribution of 

degree-limited subgraphs on an undirected network. Figure 59, for example, displays the non-trivial 

connected components of a subgraph of 

the math.nist.gov website containing only nodes of 

(in+out) degree 25 or less. The image reveals various 

structures, e.g., ladders, stars, and cluster patterns representing tightly coupled webpages. These form the 

nucleus of fringe communities of web pages, and by 

varying the degree parameter we can direct the size and 

granularity of groups revealed. As the degree threshold 

is increased from 1 to the maximum degree of the original graph, we can form a connected component size 

distribution, which can be encoded as a row of a 

(sparse) matrix. Thus, the Q-matrix formulation is 

Q(i,j) = number of connected components of size j in a 

subgraph where the maximum degree is equal to or less 

than i. This matrix is too large to view directly, but 

one may render its image by projecting the nonzero 

values onto the z-axis and displaying it as a three-
84 NIST Applied and Computational Mathematics Division

dimensional structure, as show in Figure 60. The Qmatrix 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 (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. This makes such a framework useful for 

network identification and classification. Indeed, the 

Q-matrix can be used to generate meaningful thumbnail images for network data collections.

Another useful feature is that a Q-matrix (and its 

plot) is unique to each network graph. That is, unlike 

general graph layout schemes used in visualizations, 

there is only one Q-matrix visualization. This is in 

contrast to conventional visualization and layout methods, in which the same graph may be rendered in 

multiple configurations. 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 [1].

[1] R. Pozo, Efficient Q-matrix Computation for the Visualization of Complex Networks, in Proceedings of the 8th 

International Conference on Signal Image Technology 

& Internet Based Systems, 2012.

Threshold Digraphs

Brian Cloteaux

Elizabeth Moseman

James Shook

M. Drew LaMar (College of William & Mary) 

A typical problem from the random modeling of 

networks is generating a graph with a given degree 

sequence. A threshold sequence is a graphical 

sequence that can only be realized by one labeled 

graph. The unique graph produced by these sequences 

is called a threshold graph (see Figure 58). These 

sequences define the boundary between graphical and 

non-graphical sequences, and understanding them is

vital for the creation of algorithms for manipulating 

and realizing degree sequences. While a great deal of 

theory has been developed for undirected threshold 

sequences [2], there are few published results for 

directed threshold sequences.

Figure 59. The non-trivial connected components of a subgraph of 

the math.nist.gov website containing only nodes of (in+out) degree 

25 or less.

Figure 60. The Q-matrix diagram of the math.nist.gov website.

Figure 58. Example of a Threshold Digraph
Summary of Activities for Fiscal Year 2012 85

In order to create better network models, we have 

developed a number of new fundamental results 

concerning threshold digraphs. This project has 

enabled us to condense many of the known results in 

this area, while also developing several new results to 

describe these sequences. This has enabled us to create

a new algorithm for the problem of creating a general 

realization of a digraph from a degree sequence. In 

addition, this work has produced an extremely short 

proof of the classical theorem for testing if a degree 

sequence if graphical, known as the Fulkerson-Chen 

inequalities. Further, we have shown an extension of 

the Fulkerson-Chen inequalities where the conditions 

necessary for them to be applied can be relaxed.

Beyond the immediate benefits of this project, 

such as the new algorithm for generating realizations, 

these results have application for creating new and 

faster algorithms in areas such as random network 

model generation (see below) and degree sequence 

manipulation. In addition, this work has led to a better 

understanding of how real-world networks contrast to 

these extremal examples of digraphs.

[1] B. Cloteaux, M. D. LaMar, E. Moseman, and J. Shook, 

Threshold Digraphs, arXiv:1212.1149, in review.

[2] N. V. R. Mahadev and U. N. Peled, Threshold Graphs 

and Related Topics, Elsevier, 1995.

Random Generation of Digraphs

Elizabeth Moseman

James Shook

Continuing our work in [2] on directed networks (digraphs), we address the problem of generating a model 

from a known degree sequence. Studying these models 

is the first step in understanding how the degree sequence constraint affects the network. A basic 

observation is that a directed network can be represented by a zero-one matrix with zero trace and the row 

and column sums representing the network degree sequence. There are algorithms in [1, 3, 4] to generate 

models in both contexts. The known algorithms either 

have very large running time [3] or do not generate the 

samples uniformly [1, 4].

We have developed an algorithm to generate directed graphs with a given degree sequence that is 

significantly faster than known algorithms. Our algorithm runs in O(mn) time where m is the number of 

ones in the matrix and n is the number of columns of 

the matrix. The method uses sequential importance 

sampling to generate models. The advantage of our 

algorithm is that we can calculate the number of ways 

to generate a given realization and the probability. Similar to [3], we measure the efficiency of our algorithm 

using the coefficient of variation ( ). The closer 

is to zero, the closer the generation of random digraphs 

is to uniform. We tested our algorithm on constant degree sequences. In Figure 61 the 

is plotted as a 

function of the number of nodes (n) after 100,000 trials. The data suggests that the algorithm gets closer to 

uniform as n increases. We are still testing our algorithm on a variety of different degree sequences.

In addition to modeling digraphs, our algorithm is 

able to estimate the number of digraphs with the specified degree sequence. A method of generating random 

models and an estimate of the number of digraphs leads 

to a better understanding of how network observables 

behave on these networks. In turn, this leads to a better 

understanding of how real-world networks differ from 

the models that we can generate.

[1] Y. Chen, P. Diaconis, S. P. Holmes, and J. S. Liu, Sequential Monte Carlo Methods for Statistical Analysis of 

Tables, Journal of the American Statistical Association 

100 (2005), 109–120.

[2] B. Cloteaux, M. D. LaMar, E. Moseman, and J. Shook, 

Threshold Digraphs, arXiv:1212.1149, in review.

[3] C. Greenhill, A Polynomial Bound on the Mixing Time 

of a Markov Chain for Sampling Regular Directed 

Graphs, Electronic Journal of Combinatorics 18 (2011), 

#P234.

[4] H. Kim, C. I. D. Genio, K. E. Bassler, and Z. Toroczkai, 

Constructing and sampling directed graphs with given 

degree sequences, New Journal of Physics 14 (2012), 

023012.

Figure 61. Coefficient of variation in 2 and 3 regular graphs.
86 NIST Applied and Computational Mathematics Division

Topological Models of Power Grids

Brian Cloteaux

Over the past two decades, it has been observed that 

many of the networks embedded in systems all around 

us have a number of common features. The importance 

of these networks, commonly called complex 

networks, lies in the number of areas in which they are 

found. They have been shown to arise naturally in 

systems of both biological and social interactions. In 

addition, there have also been claims that complex 

networks appear in many engineered systems such as 

the Internet, software components, and an area in 

which we are particularly interested, power grids. 

Being able to measure and model engineered 

systems has become an essential step towards being 

able to maintain and understand the reliability, safety, 

and in some cases the security of these systems. This is 

especially true for power grids, where there is a need 

for formal measurement programs. But this need poses 

several questions about how we should analyze power 

grid networks. In order to perform topological analysis 

on the structure of power grids, these networks are 

often treated in the literature as being complex 

networks. But this approach raises the question, “Why 

would a highly engineered system, such as a power 

grid, show characteristics of complex networks?” 

In order to understand where the effects of 

engineering choices show up in power grid networks, 

we examined three power grids under the dK-hierarchy 

of network models. The dK-series is a series of 

progressively refined sets of approximations for 

networks [3]. By progressively refined, we mean that 

these models have the property that every member of 

the dK-set of models for a given network is also a 

member of the (d-1)K-set of models. As d gets larger, 

these sets quickly reduce to the target network itself. 

In modeling a given network, its 1K-models are 

defined to be all of the graphs with the network’s 

degree sequence, while its 2K-models also have the 

network’s joint degree sequence, and finally its 3Kmodels also have the network’s local clustering 

coefficients. In order to capture many of the 

topological characteristics of a network, its random 

models often must be at least 2K-models, and 

sometimes they must even be 3K-models.

It has been observed that power grids seem to 

always have an exponential degree distribution with an 

exponent of 0.5. This distribution is independent of the 

underlying engineering principles used in its design. 

We speculate that this is a result of capacity limitations,

combined with consistent population distributions [2]. 

Thus, we are able to create 1K-models without 

consideration of underlying engineering choices.

For 2K-models, it is a very different story. We 

have shown a dramatic difference in the joint degree 

distribution of various power grids. Shown in Figure 

62 is the joint degree distribution of the Polish and the 

Western United States power grids. Comparing these 

two systems, we see a large difference between the 

number of two degree node that connect to other two 

degree nodes. This difference is directly attributable to 

differing engineering choices made between the two 

systems. Thus, for us to be able to create a 2K-model 

of either of these systems, we must account for the 

local engineering principles used in the design.

This has led us to develop a new modeling 

algorithm for creating random power grids similar to 

the one in the western U.S. By taking into account 

engineering choices in the design of our random 

models, we have been able to create more realistic 

topological models for our power grid research.

[1] B. Cloteaux. Modeling the Topology of Power Grids, in 

preparation.

[2] B. Jiang and T. Jia, Zipf’s Law for all the Natural Cities 

in the United States: a Geospatial Perspective,

International Journal of Geographical Information 

Science 25:8 (2011), 1269–1281.

[3] P. Mahadevan, D. Krioukov, K. Fall, and A. Vahdat, 

Systematic Topology Analysis and Generation Using 

Degree Correlations, SIGCOMM Computer 

Communications Review 36:4 (2006), 135–146.

Figure 62. Joint degree distributions. Top: Polish power grid. Bottom: Western US power grid.
Summary of Activities for Fiscal Year 2012 87

Geometry of Networks

Iraj Saniee (Bell Labs)

Sean Kennedy (Bell Labs)

Onuttom Narayan (Univ. of California at Santa Cruz)

Gabriel H. Tucci (Bell Labs)

Shi Li (Princeton University)

John D. Hobby (Bell Labs)

Sean Kennedy (Bell Labs)

Jaime Morgenstern (Carnegie Mellon University)

Gordon Wilfong (Bell Labs)

Lisa Zhang (Bell Labs)

Gromov hyperbolicity [4] is important not only in 

group theory, coarse geometry, and differential geometry, but also in many applied fields such as 

communication networks, cyber security and statistical 

physics. Hyperbolicity is observed in many real world 

networks, such as the Internet and data networks at the 

IP layer. The study of traffic flow and congestion in 

graphs is an important subject of research in graph theory. Furthermore, it is an extremely important topic in 

network theory and more specifically, in the study of 

communication networks. This research is concerned 

with investigation of hyperbolicity in large-scale networks, its measurement and detection on real data sets 

and its impact on flows. We also explore the algorithmic advantages of hyperbolicity to simplify 

computations on large graphs.

Hyperbolicity of Real-Life Large Networks (Kennedy, Narayan and Saniee). In our earlier work we 

proposed an experimental device which we called the 

curvature plot for detection of hyperbolicity in largescale networks. Hyperbolic networks are those in 

which geodesics (or shortest paths) between any triple 

set of points are always within a maximum distance δ ≥

0 of each other (“all triangles are δ-slim”). We had 

illustrated the utility of curvature plots for large graphs 

by applying them to graphs of communication networks at the IP layer using publicly available 

measurements. 

In this work, we explore hyperbolicity of more 

than two dozen networks, ranging over co-authorship, 

friendship and email graphs, peer-to-peer, Web and 

Internet graphs, road graphs, and other graphs from a 

few tens of thousands to several million nodes. We 

show that all but the road networks exhibit strong hyperbolicity (that is, δ is considerably smaller than the 

graph diameter) and in each case we document the statistics of both the hyperbolic constant δ and the graph 

diameter. This investigation shows that hyperbolicity is 

not a specialized property limited to a small class of 

graphs, but in many ways is universal, at least among 

large-scale graphs encountered in practice. We conclude with quantification of the algorithmic advantages 

of hyperbolic graphs for path computation for networks 

of up to several hundred million nodes. (To be released 

in 1Q 2013.)

Non-Hyperbolicity in Random Regular Graphs and 

their Traffic Characteristics (Tucci [1]). In this work 

we study congestion and hyperbolicity in random regular graphs. By congestion we mean the maximal load 

on the nodes of a network given a distribution of flows 

between its nodes. We study traffic congestion under 

geodesic routing, by which we mean that the path chosen to route the traffic between the nodes is the 

minimum length path, and tied paths receive equal 

fraction of each flow. Based on prior work, we would 

expect that for a hyperbolic network of size n, congestion would scale as Θ(n

2

) for uniform traffic. Here we 

show that for random d-regular graphs (i.e., each node 

has degree d ≥ 3) the maximum congestion scales as 

 

 )

 

), suggesting these graphs are nonhyperbolic. Further, we show formally that random dregular graphs are not δ-hyperbolic for any nonnegative δ asymptotically almost surely. We also provide a tighter lower bound on the graph slimness δ as a 

function of n (graph size) and d (degree) for d-regular 

graphs than what has been known so far. 

Lack of Hyperbolicity in Asymptotic Erdös-Renyi 

Sparse Random Graphs (Narayan, Saniee and Tucci

[2]). Random graphs are the simplest examples of networks with small diameter, in the sense that the largest 

distance between any pair of points scales like log(n) 

for a family of random graphs with n nodes. It is often 

thought that at least in the sparse regime, that is, when 

the number of edges is small, these graphs are highly 

tree-like and are probably hyperbolic. In this work, we 

prove that the giant component of the Erdös-Renyi

random graph is not Gromov δ-hyperbolic for any δ 

with probability tending to one as n gets large. As a 

corollary we provide an alternative proof that the spectral gap of the giant component of these random graphs 

approaches zero almost surely as n increases.

Traffic Congestion in Expanders, )-Hyperbolic 

Spaces and Product of Trees (Li and Tucci). In this 

work we extend the analysis of traffic congestion in 

Gromov hyperbolic graphs. These are graphs in which 

geodesics between any triple set of points are always 

within a maximum distance δ > 0 of each other (“triangles are δ-slim”). We study what happens to traffic 

congestion if we relax the slimness condition so that 

not all but a fraction of all triangles are δ-slim. More 

precisely, we say that a metric (X,d) is (p,δ)-hyperbolic 

if for at least a fraction p of the 3-tuples (u,v,w) in X 

the geodesic triangle Δ(uvw) is δ-slim. The case p=1 

corresponds to the classic Gromov δ-hyperbolic spaces. 

We show that congestion in these graphs scales as 

 

  

 

 

) where is the diameter of .

An important family of graphs is expanders. In 

graph theory, an expander is a sparse graph that has 
88 NIST Applied and Computational Mathematics Division

strong connectivity properties. Expander constructions 

have spawned research in pure and applied mathematics, with several applications to complexity theory, 

design of robust computer networks, and the theory of 

error-correcting codes. It is well known that random 

regular graphs are a large family of expanders. It was 

proved in [1] that random d-regular graphs have maximum vertex congestion scaling as 

 )

 

). 

Therefore, it is a natural question to ask if expanders 

have always low congestion under geodesic routing. In 

this work, we show that this is not the case. More precisely, we construct a family of expanders with 

maximum vertex congestion 

 

). (To be released in 

1Q 2013.)

Traffic Analysis in Random Delaunay Tessellations 

and Other Graphs (Hobby and Tucci [3]). Given a set 

of points in Euclidean space, the Delaunay construction 

gives a canonical triangulation whose vertices are these 

points. These triangulations have many nice combinatorial and geometric properties that make them 

extremely useful. Moreover, they can also be constructed in Riemannian manifolds. However, they do 

not exist for arbitrary sets of points: certain density 

requirements are needed to ensure that the triangulation 

can accurately represent both the topology and geometry of the manifold. These triangulations are 

canonically determined by the set of points and have 

many of the properties that Delaunay triangulations 

have in the Euclidean space.

In this paper, we focus on the following construction. Let M be a either the open unit disk or the whole 

Euclidean plane and let P be a Poisson point process 

with rotationally symmetric density ρ on M. Let T be

the Delaunay triangulation graph of P with respect to 

the Euclidean metric. Our interest is in understanding 

how this graph’s characteristics change as we change 

the density function ρ. In particular, we study how the 

maximum vertex congestion is affected by changes in 

the function ρ ). We also study how the density 

affects the degree distribution of the corresponding 

triangulation as well as other graph properties. Finally, 

we investigate the maximum vertex congestion in 

Erdös-Renyi random graphs, random geometric graphs 

and random d-regular graphs.

Hierarchical Clustering via Räcke Decomposition

(Kennedy, Morgenstern, Wilfong and Zhang). Räcke 

in 2002 identified an effective recursive hierarchical 

decomposition of a graph, with the property that each 

cluster of nodes at each level of the hierarchy is internally better connected than to their peers clusters (low 

cut value) and this property is repeated at each level of

the hierarchy. It turns out that the underlying algorithm 

for Räcke decomposition is NP-hard and subsequent 

polynomial time algorithms proposed for this decomposition use semi-definite programming and thus are

not scalable. In this work, we redefine the cut value 

with the aim of reducing the complexity of the clustering algorithm. In particular, we replace Räcke’s 

exhaustive search (to find a group of nodes with low 

cut value) with non-exhaustive approximations and 

heuristics. We benchmark the resulting algorithm on a 

test set of networks including synthetic networks with 

an underlying hierarchical structure. We show our 

results compare favorably to existing iterative methods 

for hierarchical decompositions. We expect our approach to lead to more scalable algorithms applicable 

to large-scale network clustering. (To be released in

1Q 2013.)

[1] G. H. Tucci, Random Regular Graphs are not Asymptotically Gromov Hyperbolic, arXiv: 1203.5069, in review.

[2] O. Narayan, I. Saniee and G. H. Tucci, Lack of Hyperbolicity in Asymptotic Erdös-Renyi Sparse Random 

Graphs, arXiv: 1009.5700v2, in review.

[3] J. D. Hobby and G. H. Tucci, Traffic Analysis in Random Delaunay Tessellations and Other Graphs, arXiv: 

1203.4863, in review.

[4] Jussi Väisälä, Gromov Hyperbolic Spaces, Expositiones 

Mathematicae 23:3 (2005), 187–231.

This work received partial support from NIST grant 

60NANB10D128.

Broadcast and Spread of 

Information in Complex Networks

Fern Y. Hunt

To understand the issues involved in the interaction 

between the local dynamics of agents in a network and 

the network topology, we began an investigation of the

conditions for optimal spread of information. The research literature on the general topic of spread in 

networks is encyclopedic and a lot of effort has been 

devoted to elucidating the relationship between network topology and mode of spread. The understanding 

gained has broad practical implications, from the design of efficient broadcasting algorithms, to effective 

strategies against malware, to better understanding of 

the genesis of cascades.

In 2003 J. Kleinberg et al. posed the problem of 

optimal spread of opinion or innovation in social networks in terms of finding the set of most “influential” 

nodes of a given cardinality, i.e. the set of initially activated nodes that generate the largest resulting cascade 

of activated nodes. Later, in 2010, Borkar et al. studied 

a related problem where the mode of spread is a simple 

random walk on the network graph. Despite its simplicity, this model has found wide application, for example 

in routing algorithms for networks where nodes have 

limited location information, and more generally in the 

development of so-called consensus algorithms, where 
Summary of Activities for Fiscal Year 2012 89

spread is due to nearest neighbor interaction. In this 

setting a target subset of the nodes (representing “consensus leaders”) is initially assigned consensus 

function values that remain fixed. Function values of 

the remaining nodes are computed iteratively by averaging fixed values from the boundary of the target set 

and those of its neighbors as dictated by the random 

walk. Following Borkar we seek to identify the target 

set of fixed cardinality D for which the time to consensus is shortest. It is convenient to minimize a related 

time, namely the average expected time it takes for a 

random walker initially situated outside the target set to 

reach the set for the first time—that is, the hitting time 

of the set averaged over all initial positions of the walk. 

Solving the resulting optimization problem exactly is 

quite challenging for large graphs and may be NP hard. 

An approximation to the optimal set constructed by a 

greedy algorithm was shown by Borkar et al. to be 

within a factor (1-1/e) of optimal. Our goal is not primarily to devise a better algorithm; rather, we seek to 

understand the interaction of hitting times and graph 

topology that are sufficient conditions for the existence 

of tractable optimal target sets.

Currently our efforts center on finding optimal target sets that are subsets of k-dominated subsets of a 

connected graph. A k-dominated subset is a subset of 

the graph such that every vertex v is either in it or is

within distance k of some element of it. Exact calculation of the optimal subsets of a large number of graphs 

shows that with few exceptions these sets are contained 

in a k-dominated subset. For example the vertex cover 

of the graph, a special case of k-domination for k=1, is 

an optimal target set for D, the cardinality of the cover. 

As a byproduct, we developed a method for finding 

optimal target sets as subsets of a maximal matching of 

the graph. To further our goal, we are initially restricting our study to trees and graphs with small treewidth,

because a polynomial time algorithm for finding optimal target sets in general graphs may not exist. 

However, such algorithms do exist for a similar problem for graphs with small treewidth. Moreover, there 

is a polynomial (in the number of vertices) time algorithm (motivated by the facility location problem in 

operations research) for computing k-dominating subsets or their approximations for this class of graphs and 

graphs of general topology, so there is the possibility 

that the results of this research can be applied to a 

broad range of realistic networks.

[1] F. Y. Hunt, Optimal Spread in Network Models of Consensus, in preparation.

Security Risk Analysis of Enterprise 

Networks Using Attack Graphs

Anoop Singhal (ITL SSD)

Xinming Ou (Kansas State University)

Rui Zhuang (Kansas State University)

Su Zhang (Kansas State University)

Pengsu Cheng (Concordia University)

Lingyu Wang (Concordia University)

Sushil Jajodia (George Mason University)

Stephen Noel (George Mason University)

http://csrc.nist.gov/groups/SNS/security-risk-analysis-enterprisenetworks/index.html

At present, computer networks constitute the core 

component of information technology infrastructures in 

areas such as power grids, financial data systems, and 

emergency communication systems. Protection of these 

networks from malicious intrusions is critical to the 

economy and security of our nation. Vulnerabilities are 

regularly discovered in software applications, which 

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 rely on 

objective metrics to guide and justify decision making. 

The objective of this research is to develop a 

standard model for measuring security 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.

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. Through this metric, we analyze trade-offs between security costs and security 

benefits. 

In FY2012, we integrated our techniques into an 

attack graph-based security tool called MULVAL, 

which we released as an open source system. We also 

published a SpringerBrief book [1] on this topic.

Aggregating Common Vulnerability Scoring System26 (CVSS) scores of individual vulnerabilities 

provides a practical approach to network security metrics. However, existing approaches to aggregating 

 

26 http://www.first.org/cvss
90 NIST Applied and Computational Mathematics Division

CVSS scores usually result in useful semantics of individual scores to be lost in the aggregated result. We 

published a new paper [2] in which we address this 

issue in two novel ways. First, instead of taking each 

base score as an input, our approach drills down to the 

underlying base metric level where dependency relationships have well defined semantics. Second, our 

approach interprets and aggregates base metrics in a 

way to preserve the corresponding semantics of individual scores. 

Moving-target defense has been hypothesized as a 

potential game changer in cyber defense, including that 

for computer networks. However there has been little 

work to study how much proactively changing a network’s configuration can increase the difficulty for 

attackers and thus improve the resilience of the system 

under attack. This year we presented a basic design 

schema for a moving-target network defense system

[3]. Based on this design schema, we conducted a simulation study to investigate the degree to which 

proactively changing a network’s parameters can decrease an adversary’s chance for success. We believe 

this is an important first step towards understanding 

why and how the concept of a moving target can be 

successfully applied to computer network defenses.

Finally, we also developed a new metric, “K Zero 

Day Safety,” for measuring security risk of a network 

against unknown vulnerabilities [4]. 

In FY2013, we plan to apply attack graphs to study 

the effectiveness of moving target defense. We also 

plan to publish our results as a NIST report and as papers in conferences and journals.

[1] X. Ou and A. Singhal, Quantitative Security Risk Assessment of Enterprise Networks, SpringerBriefs in 

Computer Science, Springer, New York, December 

2011.

[2] P. Cheng, L. Wang, S. Jajodia, and A. Singhal, Aggregating CVSS Base Scores for Semantics-Rich Network 

Security Metrics, in Proceedings of the 31st IEEE International Conference on Reliable and Distributed 

Systems, Irvine, CA, October 2012.

[3] R. Zhuag, S. Zhang, S. Deloach, X. Ou, and A. Singhal,

Simulation-based Approaches to Studying Effectiveness 

of Moving Target Network Defense, in Proceedings of 

the National Symposium on Moving Target Defense, 

Annapolis, MD, June 2012.

[4] L. Wang, A. Singhal, S. Jajodia, and S. Noel, A Network Security Metric for Measuring and Improving 

Computer Networks Resistance to Unknown Vulnerabilities, in review.

This research was performed in part with funding from 

ACMD.

Distributed Motion Control in 

Mobile Sensor Networks

V. Marbukh

K. Sayrafian

A.G. Aghdam (Concordia University)

H. Mahboubi (Concordia University)

A wireless sensor network is a set of spatially distributed sensors that monitor some physical targets (e.g. 

people) or environmental conditions, such as temperature, sound, pressure, etc. and cooperatively pass their 

data to a desired location through wireless connections 

in the network. A mobile sensor network (MSN) is a 

wireless sensor network in which each node is autonomously capable of moving or relocating to a new 

position. This mobility adds a new dimension to the 

capabilities of sensor networks and allows them to better adapt to changes in the environment where they are 

operating. 

Locations of sensors in a MSN affect both their 

ability to better 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. Lack of centralized control, variety of performance criteria and 

operational uncertainties, and possibilities of MSN 

topology change in a dynamic environment make MSN 

optimization an exceedingly challenging problem. In 

addition, there are a number of practical constraints,

such as energy consumption and obstacle avoidance,

which have to be taken into account in this regard. 

In our research, we have proposed aligning sensor 

mobility with the overall MSN performance 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 weighted against projected performance gains due to new sensor locations. Based on 

Voronoi-partitioning, we have developed sensor deployment strategies for effective coverage in wireless 

sensor networks. The relocation strategy is based on 

monitoring the distances of the sensors and the points 

inside its corresponding Voronoi polygon from the 

edges or vertices of the polygon [1]. Extensive simulations have confirmed the effectiveness of our proposed 

deployment algorithms, and their superiority to alternate techniques reported in the literature. 

We have also investigated energy-efficient techniques for tracking a target in a field while maximizing 

the life-span of the network. The major sources of energy depletion in the network are assumed to be 

sensing, communication and movement of the sensors. 
Summary of Activities for Fiscal Year 2012 91

The problem is formulated as a constrained optimization, and a procedure for solving this optimization 

problem has been outlined in [2].

For the future, we intend to investigate the problem of tracking a target in a field with obstacles using 

cooperative mobile sensors in an energy-efficient manner. It is desired to develop a strategy to relocate the 

sensors to optimal positions at any time instant such 

that the total energy consumption of the sensors is minimal. This will ensure sufficient network lifetime,

which is an essential design consideration for MSNs.

[1] H. Mahboubi, A. Momeni, A.G. Aghdam, K. SayrafianPour, and V. Marbukh, An Efficient Target Monitoring 

Scheme with Controlled Node Mobility for Sensor 

Networks, IEEE Transactions on Control Systems 

Technology 20 (6) (2012)1522-1533.

[2] H. Mahboubi, W. Masoudimansour, A. G. Aghda, K. 

Sayrafian, and V. Marbukh, Maximum Life Span Strategy for Target Tracking in Mobile Sensor Networks, in 

Proceedings of 2012 American Control Conference, 

Montreal, Canada, June 2012, 5096-5101.

Combinatorial Testing 

Raghu Kacker

Rick Kuhn

James Lawrence

Yu Lei (University of Texas at Arlington)

Itzel Mendoza (Centro Nacional de Metrologia)

Combinatorial testing (CT) is an approach to detect 

combinatorial interaction faults, which may cause a 

software-based system to fail when some particular 

values of certain parameters combine with some particular values of certain other parameters. Many critical 

system failures in recent times have been traced to interaction faults in the underlying software. CT is a 

versatile and broadly applicable methodology for ensuring trustworthy software in business, industrial, 

medical, scientific, and transport systems. 

It is often difficult or impossible to characterize all 

possible combinatorial interactions, let alone test them. 

Combinatorial testing is based on the insight 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. Investigations of actual 

faults show that most faults involved a single parameter, a smaller proportion of faults resulted from 

interactions between values of two parameters, and 

progressively fewer interaction faults involved 3, 4, 5, 

and 6 parameters. Most combinatorial testing has until 

recently been limited to pair-wise (2-way) testing, in 

which all interactions involving two parameters are 

detected. A reason is that efficient test methods and 

tools to detect higher order interaction faults have so 

far not been available. The goal of this project is to 

advance the technology from pair-wise to higher order 

(strength) testing and to demonstrate successful applications of high strength combinatorial testing. 

We have recently completed a major revision to 

the NIST/UTA software tool Advanced Combinatorial 

Testing System (ACTS) for generating high strength 

combinatorial test suites with support of constraints. 

We have distributed 1,250 copies worldwide to companies and individuals. We estimate the number of 

users of ACTS tool to be several thousand. We continue to provide consulting services upon request. 

Comparison benchmarking. We compared 

ACTS to other free research tools. We used both reallife systems collected from the literature, as well as

some synthesized systems. The comparison shows that 

ACTS performs better in most cases, especially for 

larger systems with more complex constraints.

Third-party constraints solver. We integrated 

the open-source constraints solver Choco in ACTS for 

better and wider constraints support. This is written in 

Java and is platform-independent. Previously (2010-

11), we had integrated constraints solver Z3 developed 

by Microsoft which is specific for Windows, which

made widespread use of ACTS more difficult.

Introduction to Combinatorial Testing. We have 

converted our NIST Special Publication on “Practical 

Combinatorial Testing” into a draft for a book to be 

published by Taylor and Francis Publishers, with additional invited chapters, in 2013.

Mini-symposium on combinatorial testing. We 

organized the First International Workshop on Combinatorial Testing (IWCT2012) in conjunction with the 

5th IEEE International Conference on Software Testing, Verification, and Validation (ICST2012) held in 

April 2012 in Montreal. Organizers were Itai Segall, 

Rick Kuhn, Raghu Kacker, and Yu Lei. We solicited 

papers from industry and academia and received 20 

submissions; 11 were selected by the Program Committee. We had a good balance of papers from industry 

and academia. The IWCT2012 had over 30 participants, and we had a good exchange of technical 

information. The organizers of ICST2013 have invited 

us to do another workshop in conjunction with 

ICST2013.

Modeling of the input test space. We have done a 

case study on the use of CT by using the ACTS tool 

itself as the software system under test. The study illustrates the challenges in modeling the input space [1]. 

Identification of failure-inducing combinations.

We have developed a novel iterative approach to identify failure-inducing combinations. A tool called “Ben” 

to help automate fault localization is under development. We have also investigated use of a classification 

tree approach to identify failure-inducing combinations. A research paper on this approach was presented 

at IWCT2012 [2].
92 NIST Applied and Computational Mathematics Division

Combinatorial coverage measurement. We have 

developed a prototype tool to determine combinatorial 

coverage of candidate test suites. The earlier version 

evaluated up to 4-way combinations. We have improved the tool to evaluate 5-way and 6-way 

combinations. A guest researcher from Mexico, Itzel 

Mendoza, is working with us to incorporate support of 

constraints in the NIST Combinatorial Coverage measurement tool. 

Combinatorial testing for electronic healthcare 

systems. We are investigating the benefits of combinatorial testing for conformance and interoperability 

testing of healthcare systems. In particular we are applying CT to an implementation of the ISO/IEEE 

11073 communication protocol for health informatics. 

Antidote is an open-source implementation of 

ISO/IEEE 11073. We have built a tool to input test 

sequence messages to Antidote. We plan to generate a 

set of combinatorial sequences. We will use the testing 

tool to apply these sequences, and then measure the 

effectiveness of these sequences in terms of code coverage and/or fault detection.

[1] M. Borazjany, L. Yu, Y. Lei, R. Kacker and D. R. Kuhn, 

Combinatorial Testing of ACTS: A Case Study, in Proceedings of the Fifth IEEE International Conference on 

Software Testing, Verification and Validation, First International Workshop on Combinatorial Testing (IWCT) 

Montreal Canada April 17-21, 2012, 591-600.

[2] K. Shakya, T. Xie, N. Li, Y. Lie, R. Kacker and D. R. 

Kuhn, Isolating Failure-Inducing Combinations in Combinatorial Testing uses Test Augmentation and 

Classification, in Proceedings of the Fifth IEEE International Conference on Software Testing, Verification and 

Validation, First International Workshop on Combinatorial Testing (IWCT) Montreal Canada, April 17-21, 

2012, 620-623.

Approximating the Ising Partition 

Function

Isabel Beichl

Amanda Streib

Noah Streib

Francis Sullivan (IDA Center for Computing Sciences)

The Ising model is a classical model in the statistical 

mechanics of magnetization. Historically, the Ising 

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 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.

The Ising model was one of the origins of the socalled Monte Carlo method and one of the first examples of a computational problem that is provably hard. 

Computational ideas and techniques that originated in 

studies of the Ising model continue to be relevant to 

current work in biosciences, material science, the understanding of networks, nanotechnology, and behavior 

of colloids.

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 spin configurations, which represent 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 the partition 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 seek to 

find approximation algorithms for Z that run quickly. 

Currently, physicists implement a Markov chain called 

the Metropolis algorithm [4], despite the fact that it has 

been proven to be inefficient at low temperatures! A 

provably polynomial algorithm is a Markov chain of 

Jerrum and Sinclair [2]. However, this algorithm is 

again too slow to use in practice. 

Figure 63. Lattice with spin configuration σ.
Summary of Activities for Fiscal Year 2012 93

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 [1] (which generalizes the pioneering work of 

Knuth [3]) with graph-theoretic and linear-algebraic 

tools. One of the serious issues with existing work on 

this problem is that convergence becomes slower and 

slower near a critical temperature. We have developed 

a radically new method that is temperature independent. The algorithm generates coefficients that, once 

computed, can be used for any temperature.

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

the Performance of Tree Searching Programs, SIAM 

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

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

on Computing 22:5 (1993), 1087-1116. 

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

Programs, in Selected Papers on Analysis of Algorithms, 

CSLI Publications, Stanford, CA (2000).

[4] 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.

Spectral Algorithms for Document 

Topic Modeling

Yi-Kai Liu

Anima Anandkumar (University of California, Irvine)

Dean Foster (University of Pennsylvania)

Daniel Hsu (Microsoft Research – New England)

Sham Kakade (Microsoft Research – New England)

An important task in machine learning is to take a collection of documents and classify them according to 

their underlying topics. This poses a number of difficulties. In particular, one may not know a priori what 

topics will appear in the documents, and moreover, 

each individual document can contain a mixture of 

several topics. Latent Dirichlet allocation (LDA) is a 

well-known model for this situation. Typically one 

uses expectation maximization (EM) to learn the parameters of the LDA model, and then uses this model 

to classify the documents. Unfortunately, the EM algorithm can be computationally expensive, and may not 

converge to a globally optimal solution in general.

We have developed a spectral algorithm for learning the LDA model, which works by estimating the 

third-order moments of the word distributions of the

documents, and computing an orthogonal tensor decomposition (a generalization of the singular value 

decomposition). This algorithm is guaranteed to recover the parameters of the LDA model exactly, and it can 

be implemented efficiently using linear algebra techniques. Numerical experiments suggest that our 

spectral algorithm is competitive with existing optimized implementations of the EM method. 

Interestingly, there are similarities between the tensor 

decomposition used in our algorithm, and certain classes of many-body quantum states.

[1] A. Anandkumar, D. P. Foster, D. Hsu, S. M. Kakade and 

Y.-K. Liu, A spectral algorithm for latent Dirichlet allocation, in Advances in Neural Information Processing 

Systems, Volume 25 (P. Bartlett and F.C.N. Pereira and 

C.J.C. Burges and L. Bottou and K.Q. Weinberger, 

eds.), 2012.

.
94 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2012 95

Part IV: Activity Data

 Part IV

Activity Data
96 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2012 97

Publications

Note: Names of (co-)authors with a current Division

affiliation are underlined.

Appeared 

Refereed Journals

1. G. S. Abo, Y. K. Hong, B. C. Choi, M. J. Donahue, S. Bae, J. Jalli, J. Park, J. Lee, M.-H. Park 

and S.-H. Gee, Micromagnetic Computer Simulated Scaling Effect of S-shaped Permalloy Nanoelement on Operating Fields for AND or OR logic, 

IEEE Transactions on Magnetics 48 (2012), 1851-

1855.

2. B. K. Alpert, W. Bertrand Doriese, Joseph W. 

Fowler and Joel N. Ullom, Predicted Energy Resolution of a Running-Sum Algorithm for 

Microcalorimeters, Journal of Low Temperature 

Physics 167:5-6 (2012) 582-587.

3. I. Beichl, E. Moseman and F. Sullivan, Computing 

Network Reliability Coefficients, Congressus Numerantium 207 (2011), 111-127.

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, J. N. Ullom, A 

High Resolution Gamma-ray Spectrometer Based 

on Superconducting Microcalorimeters, Review of 

Scientific Instruments 83 (2012), 093113.

5. R. J. Braun, R. Usha, G. B. McFadden, T. A. Driscoll, L. P. Cook and P. E. King-Smith, Thin Film 

Dynamics on a Prolate Spheroid with Application 

to the Cornea, Journal of Engineering Mathematics 73 (2012), 121-138. 

6. G. W. Bryant, Natalia Malkova, J. Sims, M. Zielinski, W. Jaskolski and J. Aizpurua, Controlling 

the Optics of Quantum Dots with Nanomechanical 

Strain, Physical Review B:Condensed Matter and 

Materials Physics 84 (2011), 235412.

7. J. D. Benson, A. J. Kearsley and A. Z. Higgins, 

Mathematical Optimization of Procedures for Cryoprotectant Equilibration using a Toxicity Cost 

Function, Cryobiology 64:3 (2012), 144-151.

8. T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. 

Whitenton and D. Basak, Modelling the Peak Cutting Temperature during High-speed Machining of 

AISI 1045 Steel, Engineering Transactions 60

(2012), 118-124.

9. A. S. Carasso, Reconstructing the Past from Imprecise Knowledge of the Present: Effective Nonuniqueness in Solving Parabolic Problems Backward in Time, Mathematical Methods in the 

Applied Sciences (2012), Wiley OnLine Library, 

DOI:10.1002/mma2582.

10. B. Cloteaux and L. A. Valentin, Counting the 

Leaves of Trees, Congressus Numerantium 207

(2011), 129-139.

11. V. R. Coffman, A. C. E. Reid, S. A. Langer, G.

Dogan, OOF3D: An Image-based Finite Element 

Solver for Materials Science, Mathematics and 

Computers in Simulation 82 (2012), 2951.

12. H. S. Cohl, Fundamental Solution of Laplace’s 

Equation in Hyperspherical Geometry, Symmetry, 

Integrability and Geometry: Methods and Applications 7 (2011), 108.

13. H. S. Cohl and E. G. Kalnins, Fourier and Gegenbauer Expansions for a Fundamental Solution of 

the Laplacian in the Hyperboloid Model of Hyperbolic Geometry, Journal of Physics A: 

Mathematical and Theoretical 45:14 (2012), 

145206.

14. H. S. Cohl, Table Errata: “Formulas and Theorems 

for the Special Functions of Mathematical Physics” by W. Magnus, F. Oberhettinger and R. P. 

Soni, Mathematics of Computation 81:280 (2012), 

2251.

15. H. S. Cohl and H. Volkmer, Eigenfunction Expansions for a Fundamental Solution of Laplace’s 

Equation on R3in Parabolic and Elliptic Cylinder 

Coordinates, Journal of Physics A: Mathematical 

and Theoretical 45:35 (2012), 355204 (20 pages).

16. H. S. Cohl, Erratum: “Developments in Determining the Gravitational Potential using Toroidal 

Functions, Astronomische Nachrichten 333:8 

(2012), 784-785.

17. H. S. Cohl and H. Volkmer, Definite Integrals using Orthogonality and Integral Transforms, 

Symmetry, Integrability and Geometry: Methods 

and Applications 8 (2012), 077.

18. G. Dogan and R. H. Nochetto, First Variation of 

the General Curvature Dependent Surface Energy, 

ESAIM: ESAIM: Mathematical Modelling and 

Numerical Analysis 46:1 (2012), 59-79.

19. M. J. Donahue, Micromagnetic Investigation of 

Periodic Cross-tie/vortex Wall Geometry, Advances in Condensed Matter Physics (2012), 908692 (8 

pages).

20. W. B. Doriese, B. K. Alpert, J. W. Fowler, G. C. 

Hilton, A. S. Hojem, K. D. Irwin, C. D. Reintse-
98 NIST Applied and Computational Mathematics Division

ma, D. R. Schmidt, G. M. Stiehl, D. S. Swetz, J. N. 

Ullom and L. R. Vale, Optimization of the TESbias Circuit for a Multiplexed Microcalorimeter 

Array, Journal of Low Temperature Physics

167:5-6 (2012) 595-601.

21. S. T. Flammia, D. Gross, Y.-K. Liu and J. Eisert, 

Quantum Tomography via Compressed Sensing: 

Error Bounds, Sample Complexity and Efficient 

Estimators, New Journal of Physics 14 (2012), 

095022.

22. J. P. Gaebler, A. M. Meier T. R. Tan, R. Bowler, 

Y. Lin, D. Hanneke, J. D. Jost, J. P. Home, E. 

Knill, D. Leibfried and D. J. Wineland, Randomized Benchmarking of Multiqubit Gates, Physical 

Review Letters 108 (2012), 260503 (5 pages).

23. T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A.

Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, 

R. H. Hadfield, R. S. Bennink, W. P. Grice, S.

Dorenbos, T. Zijlstra, T. Klapwijk and V. Zwiller,

Generation of Degenerate, Factorizable, Pulsed 

Squeezed Light at Telecom Wavelengths, Optics 

Express 19 (2011), 24434-24447.

24. S. Glancy, E. Knill and M. Girard, Gradient-Based 

Stopping Rules for Maximum-Likelihood Quantum-State Tomography, New Journal of Physics

14 (2012), 095017 (9 pages).

25. F. Gurtuna, C. Petra, F. A. Potra, O. Shevchenko 

and A. Vancea, Corrector-predictor Methods for 

Sufficient Linear Complementarity Problems, 

Computational Optimization and Applications 48

(3) (2011), 453-485.

26. C. Hagwood, J. Bernal, M. Halter, J. Elliott, Evaluation of Segmentation Algorithms on Cell 

Populations using CDF Curves, IEEE Transactions on Medical Imaging 31 (2012), 380-390.

27. P. D. Hale J. Jargon, C. M. Wang, B. Grossman, 

M. Claudius, J. Torres, A. Dienstfrey and D. Williams, A Statistical Study of De-embedding 

Applied to Eye Diagram Analysis, IEEE Transactions on Instrumentation and Measurement 61:2

(2012), 475-488.

28. 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), 

022703.

29. C. Holloway, E. Kuester and A. Dienstfrey, Characterizing Metafilms: The Connection Between 

Surface Susceptibilities and Effective Material 

Properties, IEEE Antennas and Wireless Propagation Letters 10 (2012), 1507-1511.

30. S. P. Jordan, K. S. M. Lee and J. Preskill, Quantum Algorithms for Quantum Field Theories, 

Science 336:6085 (2012), 1130-1133.

31. S. P. Jordan, H. Kobayashi, D. Nagaj and H.

Nishimura, Perfect Completeness in Classicalwitness Quantum Merlin-Arthur Proof Systems, 

Quantum Information and Computation 12:5/6 

(2012), 460-470.

32. R. Kessel, R. Kacker and K. D. Sommer, Uncertainty Budgeting for Range Calibration, 

Measurement 45 (2012), 1661-1669.

33. Z. Levine, A. Pintar, J. Hagedorn and C. Fenimore, Uncertainties in RECIST as a Measure of 

Volume for Lung Nodules and Liver Tumors, 

Medical Physics 39:5 (2012), 2628-37. 

34. Z. H. Levine, B. R. Galloway, A. P. Peskin, C. P. 

Heussel and J. J. Chen, Tumor Volume Measurement Errors of RECIST Studied with Ellipsoids, 

Medical Physics 38:5 (2011), 2552-2557. 

35. 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 (2012), 1522-

1533.

36. L. Ma, O. Slattery, Xiao Tang, Single Photon Frequency Up-conversion and its Applications, 

Physics Reports 521:2 (2012), 69-94.

37. N. Martys, M. Khalil, W. George, D. Looten, P. 

Hebraud, Stress Propagation in Colloidal Suspensions Under Shear, European Physical Journal E

35:3 (2012), 1–7. 

38. 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.

39. A. Mink and A. Nakassis, LDPC for QKD Reconciliation, The Computing Science and Technology 

International Journal 2:2 (2012).

40. M. Mullan and E. Knill, Improving Quantum 

Clocks via Semidefinite Programming, Quantum 

Information and Computation 12 (2012), 553-574.

41. J. S. Pelc, L. Ma, C. R. Phillips, Q. Zhang, C. 

Langrock, O. Slattery, X. Tang and M. M. Fejer, 

Long-wavelength-Pumped Upconversion Singlephoton Detector at 1550 nm: Performance and 

Noise Analysis, Optics Express 19:22 (2011), 

21445. 

42. J. S. Pelc, Paulina S. Kuo, O. Slattery, L. Ma, Xiao 

Tang and M. M. Fejer, Dual-channel, Singlephoton Upconversion Detector at 1.3 μm, Optics 
Summary of Activities for Fiscal Year 2012 99

Express 20:17 (2012), 19075.

43. F. A. Potra, Weighted Complementarity Problems 

- a New Paradigm for Computing Equilibria, SIAM 

Journal on Optimization 22:4 (2012), 1634-1654.

44. F. A. Potra and H. Engler, A Characterization of 

the Behavior of the Anderson Acceleration on 

Linear Problems, Linear Algebra and its Applications 438:3 (2013), 1002-1011.

45. K. Sayrafian, J. Hagedorn, W. Yang and J. Terrill,

A Virtual Reality Platform to Study RF Propagation in Body Area Networks, CogInfoCom 2012, 

the 3rd IEEE International Conference on Cognitive Infocommunications.

46. K. Sayrafian and K. Y. Yazdandoost, Wireless 

Technologies in Healthcare: Selected Papers from 

IEEE PIMRC 2011, International Journal on 

Wireless Information Networks 19:3 (2012), 159-

162.

47. W. Villanueva, W. J. Boettinger, G. B. McFadden

and J. A. Warren, A Diffuse-Interface Model of 

Reactive Wetting with Intermetallic Formation, 

Acta Materialia 60 (2012), 3799-3814.

48. D. F. Williams, M. T. Ghasr, B. Alpert, Z. Shen, 

A. Arsenovic, R. M. Weikle II and R. Zoughi, Legendre Fit of the Reflection Coefficient of a 

Radiating Rectangular Waveguide Aperture, IEEE 

Transactions on Antennas and Propagation 60:8 

(2012) 4009-4014.

49. W. Yang and K. Sayrafian, Interference Mitigation 

Using Adaptive Schemes in Body Area Networks,

International Journal on Wireless Information 

Networks 19:3 (2012), 193-200.

50. Y. Zhang, S. Glancy and E. Knill, Asymptotically 

Optimal Data Analysis for Rejecting Local Realism, Physical Review A 84 (2011), 062118 (10 

pages).

51. Y. Zhang, S. Glancy and E. Knill, Asymptotically 

optimal data analysis for rejecting local realism, 

Physical Review A 84 (2012), 062118 (10 pages).

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. R. Kessel, R. Kacker and K. D. Sommer, Combining Results from Multiple Evaluations of the Same 

Measurand, Journal of Research of the NIST 116

(2011), 809-820. 

Books

1. A. M. Dienstfrey and R. F. Boisvert, eds., Uncertainty Quantification in Scientific Computing, 

IFIP) Advances in Information and Communication Technology 377, Springer, Heidelberg, 2012.

Sponsored Research

2. X. Ou and A. Singhal, Quantitative Security Risk 

Assessment of Enterprise Networks, SpringerBriefs 

in Computer Science, Springer, New York, December 2011.

Book Chapters

1. T. Gründling, W. E. Wallace, C. Barner‐Kowollik, 

C. M. Guttman, A. J. Kearsley, Automated Data 

Processing and Quantification in Polymer Mass 

Spectrometry, in Mass Spectrometry in Polymer 

Chemistry (C. Barner-Kowollik, T. Gründling, J. 

Falkenhagen, S. Weidner, eds.), Wiley-VCH Verlag & Co, Weinheim, Germany, 2012.

2. R. Kacker, R. Kessel and K. D. Sommer, Only 

Non-Informative Bayesian Prior Distributions 

Agree with the GUM Type A Evaluations of Input 

Quantities, in Advanced Mathematical and Computational Tools in Metrology and Testing 9 (F.

Pavese, M. Bär, J.-R. Filtz, A. B. Forbes, L. Pendrill and H. Shirono, eds.), Series on Advances in 

Mathematics for Applied Sciences 84, World Scientific, Singapore, 2012, 216-223.

3. D. R. Kuhn, R. Kacker and Yu Lei, Combinatorial 

Testing, in Encyclopedia of Software Engineering

(Phillip Laplante ed.), Online Edition, Taylor and 

Francis, New York, June 2012, 12 pages.

Conference Proceedings

1. M. Borazjany, L. Yu, Y. Lei, R. Kacker and D. R. 

Kuhn, Combinatorial Testing of ACTS: A Case 

Study, in Proceedings of the Fifth IEEE International Conference on Software Testing, 

Verification and Validation, First International 

Workshop on Combinatorial Testing (IWCT) 

Montreal Canada April 17-21, 2012, 591-600.

2. T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. 

Whitenton and D. Basak, Transient Convectiondiffusion Modelling of Peak Temperature in Orthogonal Cutting, in Proceedings of the 23rd 

International Congress of Theoretical and Applied 

Mechanics (ICTAM2012), Beijing, China, August 

19-24, 2012.

3. C. Crosti, D. Duthinh, J. Harris, L.T. Phan, F. A. 

Potra and E. Simiu, Wind engineering in a multihazard context: probabilistic, synergy and optimi-
100 NIST Applied and Computational Mathematics Division

zation issues, in Proceedings of the 13th International Conference on Wind Engineering, IAWE, 

Amsterdam, The Netherlands, 2011 (8 pages).

4. A. Dienstfrey, Computation, Measurement, and 

Standards, in Proceedings of the NAFEMS North 

America Conference, Herndon, VA, September 

10-12, 2012.

5. J. T. Fong, Composites Failure Criteria, Uncertainty Propagation and Estimation of the A-basis and 

B-basis Design Allowables, in Proceedings of the 

2012 JEC/Europe Composites Forum, Paris, 

France, March 26-30, 2012, JEC Composites 

Magazine 71 (March 2012), 87-90. 

6. J. T. Fong, N. A. Heckert and J. J. Filliben, A Stochastic and Local Theory of Fatigue for Aging 

Pressure Vessels and Piping, in Proceedings of the 

3

rd International Symposium on Structural Integrity (ISSI), Jinan, China, October 31 – Nov. 2, 2012, 

pp. 19-31.

7. L. Ghandehari, Y. Lei, T. Xie, D. R. Kuhn and R. 

Kacker, Identifying Failure-Inducing Combinations in a Combinatorial Test Set, in Proceedings 

of the Fifth IEEE International Conference on 

Software Testing, Verification and Validation 

(ICST), Montreal Canada, April 17-21, 2012, 370-

379.

8. A. Gueye and V. Marbukh. A Game Theoretic 

Framework for Network Vulnerability Assessment 

and Mitigation, in 3

rd Conference on Conference 

on Decision and Game Theory for Security, Budapest, Hungary November 5-6, 2012.

9. A. Gueye, V. Marbukh and Jean C. Walrand. Towards a Metric for Communication Network 

Vulnerability to Attacks: A Game Theoretic Approach, in 3

rd

 International ICST Conference on 

Game Theory for Networks (GameNets), Vancouver, Canada, May 25-26, 2012.

10. D. Harris, F. Sullivan, and I. Beichl, Linear Algebra and Sequential Importance Sampling for 

Network Reliability, in Proceedings of the Winter 

Simulation Conference, Phoenix AZ, December 

11-14, 2011, 3344-3352.

11. R. Kacker, D. R. Kuhn, Y. Lei and J. Lawrence, 

Combinatorial Testing for Software Used in Metrology, in Proceedings of the 20-th IMEKO 

(International Measurement Confederation) World 

Congress, Busan, Korea, September 9-13, 2012, 

TC21-O-9, paper 724.

12. A. J. Kearsley, Optimality Conditions for a Hierarchical Control Problem Governed by a PDE, in 

Proceedings of the 2nd International Conference 

on Instrumentation Control and Automation

(ICA), , Bandung, Indonesia November 15-17, 

2011.

13. D. R. Kuhn, J. Higdon, J. Lawrence, R. Kacker

and Y. Lei, Combinatorial Methods for Event Sequence Testing, in Proceedings of the Fifth IEEE 

International Conference on Software Testing, 

Verification and Validation, First International 

Workshop on Combinatorial Testing (IWCT) 

Montreal Canada, April 17-21, 2012 pp. 601-609.

14. P. S. Kuo, J. S. Pelc, O. Slattery, L. Ma, M. M. 

Fejer and X. Tang, Dual-channel, Single-photon 

Upconversion Detector at 1300 nm, in Nonlinear 

Photonics, OSA Technical Digest, Optical Society 

of America, 2012, NM3C.6. 

15. P. S. Kuo, J. S. Pelc, O. Slattery, M. M. Fejer and

X. Tang, Dual-channel, Single-photon Upconversion Detector Near 1300 nm, in Proceedings of 

SPIE 8518 (2012), 85180U1-12.

16. P. S. Kuo, J. S. Pelc, O. Slattery, M. M. Fejer and

X. Tang, Photon Temporal Correlations Measured 

Using a Dual-Channel Upconversion Detector, in 

Frontiers in Optics Conference, OSA Technical 

Digest, Optical Society of America, 2012, 

FTh4B.1. 

17. Y.-K. Liu, Universal Low-rank Matrix Recovery 

from Pauli Measurements, in Advances in Neural 

Information Processing Systems (NIPS), 2011, 

1638-1646.

18. F. Maggioni, M. Bertocchi, E. Allevi, F. A. Potra

and S. W. Wallace, Stochastic second-order cone 

programming in mobile ad-hoc networks: sensitivity to input parameters, Stochastic Programming, 

Applications in Finance, Energy and Logistics (H. 

I. Gassmann, S. W. Wallace, W. T. Ziemba eds), 

World Scientific, 2012, 20 pages.

19. H. Mahboubi, W. Masoudimansour, A. G. Aghda,

K. Sayrafian, and V. Marbukh, Maximum Life 

Span Strategy for Target Tracking in Mobile Sensor Networks, in Proceedings of 2012 American 

Control Conference, Montreal, Canada, June 2012, 

5096-5101.

20. H. Mahboubi, W. Masoudimansour, A. G. Aghdam and K. Sayrafian, Cost-Efficient Routing with 

Controlled Node Mobility in Sensor Networks, in 

Proceedings of 2011 IEEE Multiconference on 

Systems & Control, Denver, USA, September 

2011, 1238-1243.

21. H. Mahboubi, K. Moezzi, A. G. Aghdam, K. Sayrafian and V. Marbukh, Distributed Deployment 

Algorithms for Improved Coverage in Mobile Sensor Networks, in Proceedings of 2011 IEEE 
Summary of Activities for Fiscal Year 2012 101

Multiconference on Systems & Control, Denver, 

USA, September 2011, 1244-1249.

22. H. Mahboubi, J. Habibi, A. G. Aghdam and K. 

Sayrafian, Cooperative Self-Deployment Strategies in a Mobile Sensor Network with Prioritized 

Coverage Plan, in Proceedings of 2011 IEEE 

Global Communications Conference 

(GLOBECOM), Houston, USA, December 2011.

23. V. Marbukh, Risks/benefits of Selfish Network 

Operations & Management in Dynamic Environment, 13th IEEE/IFIP Network Operations and 

Management Symposium (NOMS 2012), Maui, 

HI, 2012.

24. V. Marbukh, Towards Modeling Effect of Packetlevel TCP Dynamics on Internet Operations and 

Management, 13th IEEE/IFIP Network Operations 

and Management Symposium (NOMS 2012), 

Maui, HI, 2012.

25. Ion Matei, A. Gueye and John S. Baras. Flow Control in Time-Varying, Random Supply Chain 

Networks. in 20th International Symposium on 

Mathematical Theory of Networks and Systems 

(MTNS), Melbourne, Australia July 9-13, 2012.

26. A. Nakassis and A. Mink, LDPC error correction 

in the context of Quantum Key Distribution, in 

Proceedings of SPIE: Defense Security & Sensing

8400 (2012), 840009-1.

27. A. P. Peskin, D. J. Hoeppner, C. H. Stuelten, Segmentation and Cell Tracking of Breast Cancer 

Cells, in Proceedings of the 7th International Symposium on Visual Computing (G. Bebis et al., eds), 

Part I, Lecture Notes in Computer Science 6938

(2011), 381-391.

28. A. P. Peskin, A. Dima and G. Saiprasad, An Automated Method for Locating Phantom Nodules in 

Anthropomorphic Thoracic Phantom CT Studies, 

in Proceedings of the International Conference on 

Image Processing and Computer Vision, Las Vegas, July 16-19, 2012. 

29. S. Ressler, Slides, Filters and Mobile Oh My! 

(Demonstrations of HTML and Declarative 3D Integration), in Proceedings of the 1st International 

Workshop on Declarative 3D for the Web Architecture, Lyon, France, April 17, 2012. 

30. S. Ressler, Web-based Declarative 3D Graphics 

for Anthropometry Visualization and Education, in 

The Graphical Web, Zurich, Switzerland, September 13, 2012. 

31. K. Shakya, T. Xie, N. Li, Y. Lie, R. Kacker and D. 

R. Kuhn, Isolating Failure-Inducing Combinations 

in Combinatorial Testing uses Test Augmentation 

and Classification, in Proceedings of the Fifth 

IEEE International Conference on Software Testing, Verification and Validation, First International 

Workshop on Combinatorial Testing (IWCT) 

Montreal Canada, April 17-21, 2012, 620-623.

32. E. Simiu, F. A. Potra and D. Duthinh, Methodological and probabilistic issues in multi-hazard 

engineering design, in Applications of Statistics 

and Probability in Civil Engineering (Michael Faber, Jochen Koehler and Kazuyoshi Nishijima, 

Editors), CRC Press, ISBN: 978-0-415-66986-3, 

Leiden, The Netherlands, 2011, 836-839.

33. O. Slattery, Paulina Kuo, Yong-Su Kim, L. Ma 

and Xiao Tang, Narrowed Bandwidth SPDC Correlated Photon Source using Volume Bragg 

Grating, in Proceedings of SPIE 8518 (2012), 

85180Y1-10.

34. J. C. Wu, A. F. Martin, C. S. Greenberg and R. 

Kacker, Data Dependency on Measurement Uncertainties in Speaker Recognition Evaluation, in 

Active and Passive Signatures III, Proceedings of 

the SPIE 8382 (2012), 83820D, 12 pages.

35. W. Yang and K. Sayrafian, Radiation Pattern of an 

UWB Wearable Antenna: A Preliminary Study, in 

Proceedings of the 7th International Conference on 

Body Area Networking (BodyNets), Oslo, Norway, 

September 24-26, 2012

36. D. H. Yeo, F. T. Lombardo, D. K. Banerjee, E. J. 

Letvin, E. Simiu, M. L. Levitan and F. A. Potra, 

NIST advances in computer-aided and computational methods in wind engineering, in 

Proceedings of the ATC-SEI Advances in Hurricane Engineering Conference, Miami, FL, 2012 

(12 pages).

37. L. Yu, Yu Lei, R. Kacker, D. R. Kuhn and J. Lawrence, Efficient Algorithms for T-Way Test 

Sequence Generation, in Proceedings of the 17-th 

IEEE International Conference on Engineering of 

Complex Computer Systems (ICECCS), Paris, 

France, July 18-20 , 2012, 220-229.

Sponsored Research

1. P. Cheng, L. Wang, S. Jajodia and A. Singhal, 

Aggregating CVSS Base Scores for SemanticsRich Network Security Metrics, in Proceedings of 

the 31st IEEE International Conference on Reliable and Distributed Systems, Irvine, October 2012.

2. R. Zhuag, S. Zhang, S. Deloach, X. Ou, and A. 

Singhal, Simulation-based Approaches to Studying 

Effectiveness of Moving Target Network Defense, 

in Proceedings of the National Symposium on 

Moving Target Defense, Annapolis, MD, June 

2012.
102 NIST Applied and Computational Mathematics Division

Technical Magazine Articles

1. I. Beichl, Just Try, Computing in Science & Engineering 13:6 (2011), 4.

2. I. Beichl, Of Art and CS Education, Computing in 

Science & Engineering 14:1 (2012), 4.

3. I. Beichl, Is My Car Smarter than My Cat?, Computing in Science & Engineering 14:3 (2012), 4.

4. I. Beichl, Counting on Today’s Students, Computing in Science & Engineering 14:5 (2012), 4.

5. I. Beichl, Hail and Farewell, Computing in Science 

& Engineering 14:6 (2012), 4.

6. D. R. Kuhn. J. Higdon, J. Lawrence, R. Kacker

and Y. Lei, Efficient Methods for Interoperability 

Testing Using Event Sequences, CrossTalk : the 

Journal of Defense Software Engineering (July/August 2012), 15-18. 

7. D. P. O’Leary and B. W. Rust, Light a Single 

Candle: Studying Supernovae, Computing in Science and Engineering 14:2 (March/April 2012), 

90-96.

Technical Reports

1. R. F. Boisvert, Applied and Computational Mathematics Division, Summary of Activities for Fiscal 

Year 2011, NISTIR 7856, May 2012.

2. A. S. Carasso, Alternative Methods of Latent Fingerprint Enhancement and Metrics for Comparing 

Them, NISTIR 7910, January 2013.

3. W. F. Mitchell and M. A. McClain, A Comparison 

of hp-Adaptive Strategies for Elliptic Partial Differential Equations (long version), NISTIR 7824, 

October 2011.

4. E. Simiu and F. A. Potra, Technical Basis for Regulatory Guidance on Design-Basis HurricaneBorne Missile Speeds for Nuclear Power Plants 

(NUREG/CR-7004), Office of Nuclear Regulatory 

Research, U.S. Nuclear Regulatory Commission, 

Washington, DC 20555-0001, November 2011, 

(110 pages).

5. J. C. Wu, M. Halter, R. Kacker and J. Elliott, A 

New Measure in Cell Image Segmentation Data 

Analysis, NISTIR 7871, July 2012.

6. J. C. Wu, A. F. Martin, C. S. Greenberg and R. 

Kacker and V. Stanford, Significance Test in 

Speaker Recognition Data Analysis with Data Dependency” NISTIR 7884, October 2012.

Accepted

1. A. Anandkumar, D. P. Foster, D. Hsu, S. M. Kakade and Y.-K. Liu, Two SVDs Suffice: Spectral 

Decompositions for Probabilistic Topic Modeling 

and Latent Dirichlet Allocation, in Advances in 

Neural Information Processing Systems (NIPS), 

2012.

2. F. Backeljauw, S. Becuwe, A. Cuyt, J. Van Deun 

and D. W. Lozier, Validated Evaluation of Special 

Mathematical Functions, Science of Computer 

Programming.

3. H. S. Cohl, On a Generalization of the Generating 

Function for Gegenbauer Polynomials, Integral 

Transforms and Special Functions.

4. A. Gueye, V. Marbukh and J. C. Walrand. Towards a Metric for Communication Network 

Vulnerability to Attacks: A Game Theoretic Approach, 8th International Conference on 

Information Warfare and Security ICIW-2013 

Regis University, Denver, CO, March 25-26,

2013.

5. D. G. Harris, I. Beichl and F. Sullivan, Fast Sequential Importance Sampling to Estimate the 

Graph Reliability Polynomial, Algorithmica.

6. R. L. Jacobsen, R. D. Johnson III, K. K. Irikura 

and R. Kacker, Anharmonic Vibrational Frequency Calculations are not Worthwhile for Small 

Basis Sets, Journal of Chemical Theory and Computation

7. A. J. Kearsley, Constrained Hierarchical Control 

of a Diffusion Equation, International Journal of 

Applied Mathematics and Statistics.

8. 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.

9. H. Mahboubi, J. Habibi, A. G. Aghdam and K. 

Sayrafian, Distributed Deployment Strategies for 

Efficient Coverage in a Network of Mobile Sensors with Prioritized Sensing Field, IEEE 

Transactions on Industrial Informatics.

10. W. Masoudimansour, H. Mahboubi, A. G. Aghdam and K. Sayrafian, Maximum Lifetime 

Strategy for Target Monitoring in Mobile Sensor 

Networks in Presence of Obstacles, Proceedings of 

51st IEEE Conference on Decision and Control, 

Maui, USA, December 2012.
Summary of Activities for Fiscal Year 2012 103

11. A. Meier, B. Eastin and E. Knill, Magic-State Distillation with the Four-Qubit Code, Quantum 

Information and Computation.

12. A. K. Nurse, G. B. McFadden and S. R. Coriell, 

Bubble Motion and Size Variation during Thermal 

Migration with Phase Change, Physics of Fluids.

13. D. P. O’Leary and B. W. Rust, Variable Projection 

for Nonlinear Least Squares Problems, Computational Optimization and Applications.

14. R. Pozo, Efficient Q-matrix Computation for the 

Visualization of Complex Networks, in Proceedings of the 8th International Conference on Signal 

Image Technology & Internet Based Systems, 

2012.

15. J. C. Wu, A. F. Martin and R. Kacker, Bootstrap 

Variability Studies in ROC Analysis on Large Datasets, Communications in Statistics.

16. W. Yang and K. Sayrafian, Theoretical Analysis 

and Modeling of Link Adaptation Schemes in 

Body Area Networks, Proceedings of the 3th International Conference on Mobile Health

(MobiHealth), November 2012.

In Review

1. B. K. Alpert, R. D. Horansky, D. A. Bennett, W. 

B. Doriese, J. W. Fowler, A. Hoover, M. W. Rabin, J. N. Ullom, Filters for High Rate Pulse 

Processing. 

2. A. Bookatz, S. Jordan, Y.-K. Liu and P. Wocjan, 

Testing Quantum Expanders is Co-QMAcomplete.

3. A. S. Carasso, Hazardous Continuation Backward 

in Time in Nonlinear Parabolic Equations and an 

Experiment in Deblurring Nonlinearly Blurred Imagery.

4. J. Chalfoun, A. Dima, M. Kociolek, M. Halter, A. 

Cardone, A. Peskin, P. Bajcsy and M. Brady, 

Segmenting Time-lapse Phase Contrast Images of 

Adjacent NIH 3T3 Cells. 

5. H. S. Cohl and C. MacKenzie, Generalizations and 

Simplifications of Generating Functions for Jacobi, Gegenbauer, Chebyshev and Legendre 

Polynomials with Definite Integrals, 

arXiv:1210.0039.

6. H. S. Cohl, Fourier, Gegenbauer and Jacobi Expansions for a Power-law Fundamental Solution of 

the Polyharmonic Equation and Polyspherical Addition Theorems, arXiv:1209.6047.

7. H. S. Cohl, Fourier Expansions for Logarithmic 

Fundamental Solutions of the Polyharmonic Equation, arXiv:1202.1811.

8. H. S. Cohl and H. Volkmer, Separation of Variables in an Asymmetric Cyclidic Coordinate 

System, arXiv:1301.3559.

9. H.S. Cohl, Antiderivatives and Integral Representations of Associated Legendre Functions with 

μ=±ν, arXiv:1301.3556.

10. D. Cotrell, A. Lott and G. McFadden, Boundary 

Slip Effects on the Stability of Spiral Poiseuille 

Flow.

11. R. Chávez, K. Sayrafian, A. Khalegi, K. Takizawa, 

J. Wang, I. Balasingham and H. Li, Radio Propagation Models for IEEE 802.15.6 Standardization 

of Implant Communication in Body Area Networks.

12. E. Cobanera, G. Ortiz and E. Knill, The NonAbelian Duality Problem.

13. J. T. Fong, N.A. Heckert, J. J. Filliben and W.F. 

Guthrie, A Bayesian and Quantitative Nondestructive Evaluation (QNDE) Approach to Estimating 

Remaining Life of Pressure Vessels & Piping.

14. J. T. Fong, N.A. Heckert and J. J. Filliben, Composites Failure Criteria, Uncertainty Propagation

and Estimation of the A-basis and B-basis Design 

Allowables.

15. J. T. Fong, C. A. Cimini, Jr, J. D. D. Melo, N. A. 

Heckert and J. J. Filliben, Theoretical Failure Envelopes of Open Hole Composite Laminates with 

A- and B-basis Allowables Estimated from 

Smooth Specimen Properties.

16. S. W. Freiman and J. T. Fong, Determining Uncertainties in Failure Time Predictions for Brittle 

Materials.

17. A. Gueye, Aron Lazska, Jean C. Walrand and V.

Anantharan, A Polyhedral-Based Analysis of Nash 

Equilibria of Quasi-Zero-Sum Games and its Applications to Communication Network Security. 

18. C. Hagwood, J. Bernal, M. Halter, J. Elliott, T. 

Brennan, Testing Equality of Cell Populations 

based on Shape and Geodesic Distances.

19. W. F. Mitchell and M. A. McClain, A Comparison 

of hp-Adaptive Strategies for Elliptic Partial Differential Equations.

20. W. F. Mitchell, A Collection of 2D Elliptic Problems for Testing Adaptive Algorithms.

21. E. Moseman, I. Beichl and F. Sullivan, Two Algorithms to Approximate Multivariate Network 

Reliability.
104 NIST Applied and Computational Mathematics Division

22. M. Ohliger, V. Nesme, D. Gross, Y.-K. Liu and J. 

Eisert, Continuous-variable Quantum Compressed 

Sensing.

23. 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.

Sponsored Research

24. J. D. Hobby and G. H. Tucci, Traffic Analysis in 

Random Delaunay Tessellations and Other 

Graphs, arXiv: 1203.4863.

25. O. Narayan, I. Saniee and G. H. Tucci, Lack of 

Hyperbolicity in Asymptotic Erdos-Renyi Sparse 

Random Graphs, arXiv: 1009.5700v2.

26. G. H. Tucci, Random Regular Graphs are not Asymptotically Gromov Hyperbolic, arXiv: 

1203.5069.

27. L. Wang, A. Singhal, S. Jajodia and S. Noel, A 

Network Security Metric for Measuring and Improving Computer Networks Resistance to 

Unknown Vulnerabilities.

Presentations

Invited Talks

1. I. Beichl, “Linear Algebra and Sequential Importance Sampling for Network Reliability,”

Winter Simulation Conference, Phoenix, AZ, December 13, 2011.

2. R. F. Boisvert, “Fair Access: Society Publishing,” 

Perspectives Workshop on the Publication Culture 

in Computing Research, Liebnitz Center for 

Informatics, Schloss Dagstuhl, Germany, 

November 7, 2012.

3. R. F. Boisvert, “Reproducibility at ACM,” Panel 

Discussion on Journal Policies/Experiences, 

Workshop on Reproducibility in Computational 

and Experimental Mathematics, Institute for 

Computational and Experimental mathematics, 

Brown University, Providence, RI, December 11, 

2012.

4. T. J. Burns, “Transient Convection-diffusion 

Modelling of Peak Temperature in Orthogonal 

Cutting,” 23rd International Congress of 

Theoretical and Applied Mechanics 

(ICTAM2012), Beijing, China, August 24, 2012.

5. A. S. Carasso, “Unexplored Territory in Nonstandard Parabolic Equations and their 

Application,” Joint Numerical Analysis/Norbert 

Wiener Center Seminar, Mathematics Department, 

University of Maryland, College Park MD, 

December 6, 2011.

6. A. S. Carasso, “Non-standard Parabolic Equations 

and Image Reconstruction,” AMS-SIAM 

Minisymposium on Applied, Computational and

Discrete Mathematics at National Laboratories and 

Federal Research Agencies, Joint Mathematics 

Meetings, Boston, MA, January 4-7, 2012.

7. B. Cloteaux, “Affiliation Networks,” Old 

Dominion University Computer Science Seminar, 

Norfolk, VA, October 28, 2011.

8. H. S. Cohl, “The Fourier and Gegenbauer Analysis 

of Fundamental Solutions for the Laplace Equation 

on Riemannian Spaces of Constant Curvature,” 

Department of Mathematical Sciences, University 

of Wisconsin--Milwaukee, Milwaukee, Wisconsin, 

October 7, 2011.

9. H. S. Cohl, “Fourier, Gegenbauer and Jacobi 

Expansions related to a Fundamental Solution of 

the Polyharmonic Equation,” Department of 

Mathematical Sciences, University of Wisconsin--

Milwaukee, Milwaukee, Wisconsin, October 7, 

2011.

10. H. S. Cohl, “Addition Theorems in Separable 

Coordinate Systems for Fundamental Solutions,” 

Department of Mathematical Sciences, University 

of Wisconsin--Milwaukee, Milwaukee, Wisconsin, 

March 2, 2012.

11. H. S. Cohl, “Fourier, Gegenbauer and Jacobi 

Expansions,” Department of Mathematics and 

Statistics, American University, Washington DC, 

March 20, 2012.

12. H. S. Cohl, “The Fourier and Gegenbauer Analysis 

of Fundamental Solutions for Laplace’s Equation 

on Riemannian Spaces of Constant Curvature,” 

Department of Mathematics, Louisiana State 

University, Baton Rouge, Louisiana, August 14, 

2012.

13. H. S. Cohl, “Simplifications and Generalizations 

of Generating Functions for Hypergeometric 

Orthogonal Polynomials with Definite Integrals,” 

Department of Mathematical Sciences, University 

of Wisconsin--Milwaukee, Milwaukee, Wisconsin, 

September 28, 2012. 

14. H. S. Cohl, “Generalizations of Generating 

Functions for Hypergeometric Orthogonal 

Polynomials,” The Norbert Weiner Center for 

Harmonic Analysis, University of Maryland, 

College Park, Maryland, October 16, 2012.

15. H. S. Cohl, “Expansions for the Iterated Poisson 

Equation on d-dimensional Euclidean Space,” 

Department of Mathematical Sciences, George 
Summary of Activities for Fiscal Year 2012 105

Mason University, Fairfax, Virginia December 7, 

2012.

16. A. Dienstfrey, Panelist, American Society of 

Mechanical Engineers, 2012 Verification and 

Validation Symposium, Las Vegas, NV, May 2-4, 

2012.

17. A. Dienstfrey, “Computation, Measurement, and 

Standards,” NAFEMS North America Conference, 

Herndon, VA, September 10-12, 2012.

18. G. Dogan, “An Iterative Shape Reconstruction 

Algorithm for Inverse Problems,” 6th International 

Conference on Inverse Problems: Modeling & 

Simulation, Antalya, Turkey, May 21-26, 2012.

19. G. Dogan, “Variational Shape Optimization for 

Image Segmentation,” Fall Eastern American 

Mathematical Society Sectional Meeting,

Rochester Institute of Technology September 22-

23, 2012.

20. M. J. Donahue, “Numerical Methods in 

Micromagnetics for Fast, Accurate Computation of 

Demagnetization Kernels with Periodic 

Boundaries,” IMA/MCIM Industrial Problems 

Seminar at the University of Minnesota, 

Minneapolis, Minnesota, February 24, 2012.

21. M. J. Donahue, “Numerical Methods in 

Micromagnetics for Fast, Accurate Computation of 

Demagnetization Kernels with Periodic 

Boundaries,” International Workshop on 

Advanced Micromagnetics (IWAM) at the Center 

for Magnetic Recording Research, University of 

California, San Diego, May 21-22, 2012.

22. M. J. Donahue, “Recent Advances in 

Micromagnetics,” IEEE Magnetics Society, 

University of Colorado, Boulder, Colorado, 

August 2, 2012.

23. J. T. Fong, “Design of and Modern Statistics for 

Improving Reliability of Composite Materials,” 

International JEC/Asia Composite Materials 

Design Forum, Singapore, October 20, 2011. 

[Invited Keynote Lecture]

24. J. T. Fong, “Design of Experiments and Modern 

Statistics for Modeling and Failure Prediction of 

Full-Scale Structures,” Department of Mechanical 

Engineering, National University of Singapore, 

Singapore, October 21, 2011.

25. J. T. Fong, “Design of Experiments and Modern 

Statistics for Modeling and Failure Prediction of 

Full-Scale Structures,” Department of Mechanical 

Engineering, Nanyang University, Singapore, 

October 24, 2011.

26. J. T. Fong, “Uncertainty Estimation and Failure 

Prediction of Full-Scale Structures using a MultiScale Approach,” School of Mechanical 

Engineering, East China University of Science and 

Technology, Shanghai, China, December 9, 2011.

27. J. T. Fong, “Modern Statistics, Exploratory Data 

Analysis and Design of Experiments for 

Improving Reliability of Aging Engineering 

Structures,” Department of Mathematics, Ningpo 

University, Ningpo, China, December 12, 2011.

28. J. T. Fong, “Modern Statistics, Data Analysis and 

Design of Experiments for Improving Reliability 

of Aging Components and Structures,” 

Department of Mechanical Engineering, City 

University of Hong Kong, Hong Kong, December 

14, 2011.

29. J. T. Fong, “Risk-Informed Inspection and OnLine Monitoring of High-Consequence Aging 

Structures and Power Plants,” Department of 

Mechanical Engineering, City University of Hong 

Kong, Hong Kong, December 15, 2011.

30. J. T. Fong, “Engineering Statistics and Reliability 

Analysis of Composite Structures,” 6th Composite 

Design Workshop, Department of Aeronautics and 

Astronautics, Stanford University, Stanford, CA, 

Jan. 24, 2012.

31. J. T. Fong, “Composites Failure Criteria with 

Uncertainty Quantification for A- and B-Design 

Allowables,” JEC/Europe Composite Materials 

Design Forum, Paris, France, Mar. 27, 2012.

32. J. T. Fong, “Modern Statistics, Data Analysis and 

Design of Experiments for Improving Reliability 

of Aging Engineering Structures,” National 

Physical Laboratory, Teddington, United 

Kingdom, April 3, 2012. [Distinguished Science 

Lecture]

33. J. T. Fong, “Modern Statistics, Uncertainty 

Propagation and Design of Experiments for 

Improving Reliability of Aging Engineering 

Structures,” Center for Nondestructive Evaluation, 

Iowa State University, Ames, IA, April 23, 2012.

34. J. T. Fong, “Multi-scale Failure Simulation, 

Uncertainty Propagation Theory and NDE-based 

Health Monitoring of Aging Structures,” 

Department of Civil and Environmental 

Engineering, University of South Carolina, 

Columbia, SC, May 4, 2012

35. J. T. Fong, “On the Relative Value of Material 

Property Databases with, or, without an 

Expression of Uncertainty,” e-Ceramics 

Workshop, Department of Defense, Arlington, 

VA, June 4, 2012.

36. J. T. Fong, “Multi-scale Modeling with 
106 NIST Applied and Computational Mathematics Division

Uncertainty Quantification for Reliability of HighConsequence Aging Structures,” Materials 

Reliability Division, National Institute of 

Standards & Technology, Boulder, CO, July 20, 

2012.

37. J. T. Fong, “Engineering Statistics and Reliability 

Analysis of Composite Structures,” 7h Composite 

Design Workshop, Department of Aeronautics and 

Astronautics, Stanford University, Stanford, CA, 

Aug. 22, 2012.

38. J. T. Fong, “Fatigue Life Estimation of Aging 

Nuclear Components,” Electric Power Research 

Institute, Charlotte, NC, September 5, 2012.

39. J. T. Fong, “Quantitative Nondestructive 

Evaluation (QNDE) and Stochastic Modeling of 

Fatigue of Aging Structures,” Department of 

Mechanical Engineering, Yokohama National 

University, Yokohama, Japan, October 15, 2012.

40. J. T. Fong, “Quantitative Technology of 

Nondestructive Evaluation (QT-NDE): Key to 

Innovative Manufacturing and Aging Equipment 

Management,” School of Mechanical Engineering, 

East China University of Science and Technology, 

Shanghai, China, October 19, 2012.

41. J. T. Fong, “Quantitative Technology of 

Nondestructive Evaluation (QT-NDE): Key to 

Innovative Manufacturing and Aging Equipment 

Management,” China Special Equipment 

Inspection and Research Institute, Beijing, China, 

October 22, 2012. 

42. J. T. Fong, “Quantitative Technology of 

Nondestructive Evaluation (QT-NDE): Key to 

Innovative Manufacturing and Aging Equipment 

Management,” Department of Mechanical 

Engineering, Beijing Institute of Technology, 

Beijing, China, October 23, 2012.

43. J. T. Fong, “Quantitative Technology of 

Nondestructive Evaluation (QT-NDE): Key to 

Innovative Manufacturing and Aging Equipment 

Management,” Department of Materials Science, 

Dalian University of Technology, Dalian, China, 

October 25, 2012.

44. J. T. Fong, “Quantitative Technology of 

Nondestructive Evaluation (QT-NDE): Key to 

Innovative Manufacturing and Aging Equipment 

Management,” Department of Mechanical 

Engineering, China University of Petroleum, 

Qingdao, China, October 29, 2012.

45. J. T. Fong, “A Stochastic and Local Theory of 

Fatigue for Aging Pressure Vessels and Piping,”

3

rd International Symposium on Structural 

Integrity (ISSI), October 31 – Nov. 4, 2012, 

Shandong University, Jinan, China, November 1, 

2012. [Keynote Lecture]

46. W. L. George, N. S. Martys and J. E. Terrill, 

“Computational Rheology for Cement and 

Concrete,” Workshop on High-Performance 

Computing for Industry, Rensselaer Polytechnic 

Institute, October 26-28, 2011. 

47. W. L. George, N. S. Martys, S. G. Satterfield, J. E. 

Terrill, “Modeling the Flow of Cement and 

Concrete in a Rheometer,” Argonne Leadership 

Computing Facility Seminar Series, Argonne 

National Laboratory, May 21, 2012. 

48. W. L. George, N. S. Martys, S. G. Satterfield, M.

Olano and J. E. Terrill, “Advancing the Materials 

Science of Concrete with Supercomputers,” 

Argonne National Laboratory Exhibit, SC 

Conference, Seattle WA, November 2011. 

49. S. Glancy, “Progress Towards Quantum 

Teleportation of Traveling Microwaves,” 

Workshop-School in Quantum Computation and 

Information, Fortaleza, Brazil, October 11, 2012.

50. A. Gueye, “On the Value of Communication 

Network (Security),” Institute for Systems 

Research, University of Maryland, November 4, 

2011.

51. A, Gueye, “On the Value of Communication 

Network Security,” MURI workshops (MLMR,

ADCN, MAASCOM), University of California, 

Berkeley, October 27, 2011.

52. S. Jordan, “Quantum Algorithms for Simulating 

Quantum Field Theories,” NASA Future 

Technologies Conference, Mountain View, CA, 

January 21, 2012.

53. S. Jordan, “Quantum Algorithms for Simulating 

Quantum Field Theories,” C. N. Yang Institute 

Seminar, SUNY Sony Brook, NY, March 8, 2012.

54. S. Jordan, “Quantum Algorithms for Simulating 

Quantum Field Theories,” Capital Area Theory 

Seminar, University of Maryland, College Park, 

MD, April 6, 2012.

55. R. Kacker, “Introduction to Combinatorial 

Testing,” Department of Mathematics and 

Statistics, University of Maryland Baltimore 

County, December 2, 2011.

56. R. Kacker, “Combinatorial Testing for Software,”

Infosys Education and Research (E&R) Unit 

Winter School on Software Validation, 

Verification and Reliability, Bangalore, India, 

December 16, 2011. 

57. R. Kacker, “Combinatorial Testing for Software,”

Philips Research, Bangalore, India, Dec. 19, 2011.
Summary of Activities for Fiscal Year 2012 107

58. R. Kacker, “Combinatorial Testing for Software,”

IBM-India, Bangalore India, December 19, 2011

59. R. Kacker, “Evolution of Combinatorial Testing 

for Software from Design of Experiments,”

International Conference on Quality and 

Reliability Engineering (ICQRE-2011), Indian 

Statistical Institute, Bangalore India, December 20, 

2011.

60. R. Kacker, “Uncertainty Requirements in the 

Contract SOW for GOES-R and Implementation 

of VIM3 and GUM,” CALCON 2012 Technical 

Conference Utah State University, August 27, 

2012.

61. A. J. Kearsley, “Stochastic Derivative 

Approximations in Calibrating Mass 

Spectrometers,” Universitas Bakrie, Indonesia, 

September 13, 2012.

62. A. J. Kearsley, “Optimal Finite Difference 

Calculations for Maximizing Signal to Noise,” 

Jakarta State University, September 21, 2012.

63. A. J. Kearsley, “Optimality Conditions for a 

Hierarchical Control Problem Governed by a 

PDE,” 2nd International IEEE Conference on 

Instrumentation Control and Automation (ICA), 

Bandung, Indonesia, November 15-17, 2011.

64. A. J. Kearsley, “Survey of Mathematics 

Applications at NIST,” Putera Sampoerna School 

of Education, Jakarta, Indonesia, September 19, 

2012.

65. A. J. Kearsley, “Optimal Library Searching 

through Multidimensional Scaling,” University of 

Calgary, June 19, 2012.

66. A. J. Kearsley, “Instrument Tuning using a 

Stochastic Gradient Approximation,” University of 

Calgary, June 24, 2012.

67. Y.-K. Liu, “Quantum Algorithms for Testing 

Graph Expansion and Bipartiteness,” Computer 

Science Department, University of Maryland, 

March 9, 2012.

68. Y.-K. Liu, “Universal Low-rank Matrix Recovery 

from Pauli Measurements,” Perimeter Institute, 

Waterloo, Canada, April 4, 2012.

69. Y.-K. Liu, “Universal Low-rank Matrix Recovery 

from Pauli Measurements,” Microsoft Research 

New England, Boston, April 10, 2012.

70. Y.-K. Liu, “Matrix Completion,” Computer 

Science Department, George Washington 

University, April 19, 2012.

71. Y.-K. Liu, “Universal Low-rank Matrix Recovery 

from Pauli Measurements,” Institute for Defense 

Analysis Center for Computing Sciences, Bowie, 

MD, July 27, 2012.

72. Y.-K. Liu, “Some Uses of Quantum Information in 

Machine Learning and Cryptography,” JQI 

Quantum Information Science Workshop, College 

Park, MD, September 28, 2012.

73. D. W. Lozier, “DLMF Tables: A New Source of 

Data for Mathematical Software Developers,” 

Workshop on Numerical Software: Design, 

Analysis and Verification, University of Cantabria, 

Santander, Spain, July 4-6, 2012.

74. V. Marbukh, “Some Personal Observations on 

System Complexity,” Network Complexity 

Research Group (NCRG) Meeting, Internet 

Research Task Force (IRTF), Paris, France, 2012. 

75. N. Martys and W. George, “Computational 

Modeling of Suspensions: Application to Cement 

Based Materials,” Monte Verita Conference on 

Microstructure, Setting and Aging of Cement: 

From Soft Matter Physics to Sustainable Materials, 

Monte Verita, Ascona, Switzerland, August 12-16, 

2012. 

76. G. B. McFadden, “Richard Tapia’s Influence as an 

Undergraduate Teacher and Mentor,” A 

Celebration of Richard Tapia Receiving the 

National Medal of Science, Rice University, 

March 3, 2012.

77. G. B. McFadden, “Bubble Motion and Size 

Variation during Thermal Migration with Phase 

Change,” Department of Mathematical Sciences, 

University of Delaware, April 24, 2012.

78. W. F. Mitchell, “Comparison of hp-Adaptive 

Finite Element Strategies.” George Washington 

University, Washington, DC, March 22, 2012.

79. D. P. O’Leary, “Image Restoration from a 

Machine Learning Perspective,” 2012 Cray 

Distinguished Speaker, Computer Science 

Department, University of Minnesota, April, 2012.

80. A. Peskin, A. Dima and G. Saiprasad, “An 

Automated Method for Locating Phantom Nodules 

in Anthropomorphic Thoracic Phantom CT 

Studies,” American Statistical Association Spring 

Meeting, Colorado-Wyoming Chapter, April 20, 

2012, 

81. Sandy Ressler, “3D Computer Graphics on the 

World Wide Web,” Stockton Computer Society, 

Galloway NJ, March 29, 2012. [ACM 

Distinguished Lecture]

82. B. Saunders, “Interactive 3D Visualizations of 

Complex Function Data in the NIST Digital 

Library of Mathematical Functions,” SIAM Math 
108 NIST Applied and Computational Mathematics Division

Awareness Conference, Old Dominion University, 

Norfolk, VA, March 24, 2012.

83. B. Saunders, “Constructing Interactive 3D 

Visualizations for the NIST Digital Library of 

Mathematical Functions,” SIAM Minisymposium 

on Applied, Computational and Discrete 

Mathematics at National Laboratories and Federal 

Research Agencies, AMS-MAA-SIAM Joint 

Mathematics Meetings, Boston, MA, January 5, 

2012.

84. B. Saunders, Panelist, Conversation on NonAcademic Employment, Joint Mathematics 

Meetings, Boston, MA, January 5, 2012.

85. K. Sayrafian, “Body Area Networks: 

Standardization Activities and Technology 

Challenges,” Centre for Communication Systems 

Research, University of Surrey, Guildford, UK, 

October 11, 2012.

86. K. Sayrafian, “RF Propagation in Body Area 

Networks,” Workshop on Medical Communication 

Systems (ACM MedCOMM), Helsinki, Finland, 

August 13, 2012

87. K. Sayrafian, “Personalized Health: An ICT 

Perspective,” COST Strategic Conference on 

Personalised Medicine (PEMED), Larnaca, 

Cyprus, June 18-22, 2012.

88. K. Sayrafian, “Opportunities and Challenges in 

Body Area Networks,” Department of Electrical & 

Computer Engineering, Worcester Polytechnic 

Institute, Worcester, MA, February 23, 2012.

89. K. Sayrafian, Panelist, Health and Medical CPS 

Panel, National Science Foundation Cyber 

Physical Systems PI Meeting & Conference, 

October 4, 2012.

90. K. Sayrafian, “The Role of Standardization in 

Healthcare,” mHealth Summit, National Harbor, 

MD, December 5, 2011.

91. N. Streib, “An Application of Graph Theory in 

Theoretical Physics,” University, Discrete 

Mathematics Seminar, Virginia Commonwealth 

Richmond, VA, December 4, 2012.

92. Xiao Tang, “Single Photon Frequency Conversion 

and its Applications in Quantum Information 

Research,” Department of Electrical Engineering, 

Washington University, St. Louis, April 13, 2012.

93. Xiao Tang, “Dual Channel Upconversion Device 

for NIR Single-photon Detection,” The 21th 

International Laser Physics Workshop 

(LPHYS’12), University of Calgary, Calgary, 

Canada, July 23 - 27, 2012.

Conference Presentations

1. P. Bajcsy, J. Chalfoun, A. Cardone, A. Peskin, M. 

Halter, K. Bhadriraju, J. J. Filliben, J. T. Elliott, 

M. Kociolek, M. C. Brady and A. L. Plant, 

“Computational Science for Biological 

Metrology,” Poster, 5th Advances in Stem Cell 

Discovery and Development Conference, San 

Diego, October 19-21, 2011. 

2. J. W. Bullard, D. P. Bentz, E. J. Garboczi, S.G. 

Satterfield, P.E. Stutzman, L. Valenti and G. 

Artioli, “Simulating Solution Chemistry and Phase 

Evolution in Early-age Cement Pastes,” American 

Concrete Institute Spring 2012 Convention, March 

18-22, Dallas, Texas.

3. T. J. Burns, “NIST and the MGI,” IMA Special 

Workshop: Mathematics and the Materials Genome Initiative, University of Minnesota, 

Minneapolis, MN, September 13, 2012.

4. B. Cloteaux, “Extracting Hierarchies with Overlapping Structure from Network Data”, Winter 

Simulation Conference, Phoenix, AZ, December 

13, 2011.

5. B. Cloteaux, “Extracting Affiliations from Networks”, NIST-Bell Labs Workshop on LargeScale Complex Networks, Gaithersburg, MD, June 

8, 2012.

6. H. S. Cohl, “Super Expansions and Definite Integrals for Jacobi, Gegenbauer, Legendre and 

Chebyshev Polynomials,” International Symposium on Orthogonal Polynomials and Special 

Functions -- A Complex Analytic Perspective, Copenhagen, Denmark, June 14, 2012.

7. A. Dienstfrey, “A Metrology Infrastructure for 

Scientific Computing,” National Radio Science 

Meeting, University of Colorado, Boulder, CO, 

Jan 4-7, 2012.

8. G. Dogan, “Fast Iterative Algorithm for Shape 

Reconstruction in Image Processing,” Copper 

Mountain Conference on Iterative Methods, Copper Mountain, CO, March 25-30, 2012.

9. G. Dogan, “An Algorithm for Shape Detection in 

Inverse Problems,” SIAM Conference on Imaging 

Sciences, Philadelphia, PA, May 20-22, 2012.

10. G. Dogan, “Energy-based Segmentation Methods 

for Micrograph Analysis,” International Conference on 3D Materials Science, Seven Springs, PA, 

July 8-12, 2012.

11. G. Dogan, “Variational Algorithms for Fast and 

Robust Shape Reconstruction in Imaging,” European Congress on Computational Methods in 
Summary of Activities for Fiscal Year 2012 109

Applied Sciences and Engineering, Vienna, Austria, September 10-14, 2012.

12. M. J. Donahue, “Fast, Accurate Computation of 

the Demagnetization Tensor for Periodic Boundaries,” Intermag 2012, Vancouver, Canada, May 8, 

2012.

13. B. Eastin, “Simulating Concordant Computations,”

Quantum Discord Workshop, Singapore, January 

10, 2012.

14. J. T. Fong, “Uncertainty Estimation of Time-toFailure of a Full-Scale Structure on Fire using a 

Stochastic and Multi-Scale Approach,” 48th Annual Meeting of Society of Engineering Science, 

October 12-14, Northwestern University, Evanston, IL, October 13, 2011.

15. J. T. Fong, “A Bayesian Approach to Estimating 

the Uncertainty of Fatigue Life of Pressure Vessels 

and Piping,” 39th Review of Progress in QNDE 

Meeting, July 15-20, 2012, Denver, CO, July 18, 

2012.

16. J. T. Fong, “QNDE: Key to Developing CuttingEdge Tools for Manufacturing and Product Longevity,” 39th Review of Progress in QNDE 

Meeting, July 15-20, 2012, Denver, CO, July 19, 

2012.

17. A. Gueye, “A Game Theoretic Framework for 

Network Vulnerability Assessment and Mitigation,” GameSec2012, Budapest, Hungary, 

November 6, 2012.

18. A. Gueye, “Toward a Metric for Communication 

Network Vulnerability to Attacks: A Game Theoretic Approach,” GameNets2012, Vancouver, BC, 

Canada, May 25, 2012.

19. A. Kearsley, “On Calculating Distances Between 

Chemical Spectra,” 8th International Conference 

on Information, Communications & Signal Processing (ICICS), Singapore, December 15, 2011.

20. A. Kearsley, “Calibrating Chemical Spectrometers,” American Society for Mass Spectrometry, 

Vancouver, Canada, June 21, 2012.

21. A. Kearsley, “Wassterstein Metric and Multidimensional Scaling for Compound Searching,”

University of Calgary, July 20, 2012.

22. P. S. Kuo, J. S. Pelc, O. Slattery, M. M. Fejer and

X. Tang, “Photon Temporal Correlations Measured Using a Dual-Channel Upconversion 

Detector,” Frontiers in Optics Conference, Rochester, NY, October 14, 2012.

23. S. Jordan, “Super-polynomial Quantum 

Speedups,” Workshop on Post-Quantum Cryptography and Quantum Algorithms, Lorentz Center, 

Leiden, Netherlands. November 5, 2012.

24. Y.-K. Liu, “Universal Low-rank Matrix Recovery 

from Pauli Measurements,” Workshop on Quantum Information: Codes, Geometry and Random 

Structures, Centre de Recherches Mathématiques, 

Montreal, Canada, October 24, 2011.

25. Y.-K. Liu, “Sub-tomography and Fidelity Estimation,” Workshop on Quantum Tomography, Centre 

for Quantum Technologies, Singapore, November

30, 2011.

26. Y.-K. Liu, “Universal Low-rank Matrix Recovery 

from Pauli Measurements,” Neural Information 

Processing Systems (NIPS) Conference, Granada, 

Spain, December 14, 2011.

27. Y.-K. Liu, “How to Interpret a Large Density Matrix,” Workshop on Quantum Computation, 

Verification and Validation (QCVV), Bethesda, 

MD, May 1, 2012.

28. H. Mahboubi, W. Masoudimansour, A, Aghdam, 

K. Sayrafian, V. Marbukh, “Maximum Life Span 

Strategy for Target Tracking in Mobile Sensor 

Networks,” IEEE American Control Conference 

(ACC), June 27-29, 2012.

29. V. Marbukh, “Towards Modeling Effect of 

Agents’ Bounded Rationality on Performance of 

Selfish Resource Allocation,” the Latsis Symposium on Econophysics, ETH-Zurich, Switzerland, 

2012. 

30. V. Marbukh, “Risks/benefits of Selfish Network 

Operations & Management in Dynamic Environment,” 13th IEEE/IFIP Network Operations and 

Management Symposium (NOMS 2012), Maui, 

HI, 2012.

31. V. Marbukh, “Towards Modeling Effect of Packetlevel TCP Dynamics on Internet Operations and 

Management,” 13th IEEE/IFIP Network Operations and Management Symposium (NOMS 2012), 

Maui, HI, 2012.

32. N. S. Martys, C. F. Ferraris, W. L. George, S. G. 

Satterfield and M. T. Olano, “Computational 

Based Study of Suspension Flow in a Vane Rheometer,” 83rd Annual Meeting of the Society of 

Rheology, Cleveland, Ohio, October 9-13, 2011. 

33. W. F. Mitchell, “Experience With MPI and 

OpenMP in an Adaptive FEM Code,” SIAM Conference on Parallel Processing for Scientific 

Computing, Savannah, GA, February 15, 2012.

34. A. P. Peskin, A. Dima, G. Saiprasad, “An Automated Method for Locating Phantom Nodules in 

Anthropomorphic Thoracic Phantom CT Studies,”
110 NIST Applied and Computational Mathematics Division

International Conference on Image Processing and 

Computer Vision,, Las Vegas, NV, July 16-19, 

2012. 

35. R. Pozo, “Efficient Q-matrix Computation for the 

Visualization of Complex Networks,” Workshop 

on Complex networks and Their Applications, The 

8

th International Conference on Signal Image 

Technology & Internet Based Systems, Naples, Italy, November 25-29, 2012.

36. S. Ressler, “Not Your Mother’s Web3D: Integrating X3DOM, jQuery and HTML5,” Web3D 2012, 

Los Angeles, CA, August 4, 2012. 

37. S. Ressler, “Web-based Declarative 3D Graphics 

for Anthropometry Visualization and Education,” 

The Graphical Web 2012, Zurich, Switzerland, 

September 13, 2012. 

38. B. Saunders, B. Antonishek and Q. Wang, “Adaptive Composite B-Spline Grid Generation for 

Interactive 3D Visualizations,” Eighth International Conference on Mathematical Methods for 

Curves and Surfaces MASCOT/ISGG 2012 

(IMACS Workshop and International Society for 

Grid Generation Conference), Las Palmas de Gran 

Canaria, Spain, October 24, 2012. 

39. B. Saunders, “Adaptive Composite B-Spline Mesh 

Generation for the Visualization of Complex Function Surfaces,” Eighth International Conference on 

Mathematical Methods for Curves and Surfaces, 

Oslo, Norway, June 29, 2012. 

40. B. Saunders, “Adaptive Grid Generation Using the 

Composition of Tensor Product B-Splines,” SIAM 

Conference on Geometric and Physical Modeling, 

Orlando, Florida, October 27, 2011.

41. J. Shook, “Affiliation Networks,” Mathematics 

Department, University of Mississippi, Oxford, 

MS, October 6, 2011. 

42. J. Shook, “Greater than 1-tough k-trees without a 

2-factor,” International Conference on Cycles in 

Graphs, Nashville, TN, June 1, 2012.

43. V. Taroudaki and D. P. O’Leary, “Reconstruction

of Images: Computation of Confidence Intervals,”

SIAM Conference on Imaging Science, Philadelphia, May 2012.

44. V. Taroudaki and D. P. O’Leary, “Confidence 

Intervals of an Image Reconstruction,” Modern 

Mathematical Methods in Science and Technology 

(M3ST) Conference, Kalamata, Greece, August 

2012.

45. J. Terrill and S. Belloge, “Visualization and Analysis of the National Vulnerability Database,” NIST 

Booth Demo, 8th Annual IT Security Automation 

Conference, Baltimore MD, October 3-5, 2012.

46. L. Valentini, G. Artioli, J.W. Bullard, S.G. Satterfield, “Modeling the Effect of Calcium Sulfate on 

C3S Hydration: Implications for the Origin of the 

Optimum Sulfate,” 3rd Advances in CementBased Materials: Characterization, Processing, 

Modeling and Sensing, Austin, Texas, June 10-12, 

2012. 

47. W. Yang, K. Sayrafian, “Radiation Pattern of an 

UWB Wearable Antenna: A Preliminary Study,”

7

th International Conference on body Area Networks (BodyNets), September 24-26, 2012.

48. W. Yang, K. Sayrafian, “Interference Mitigation 

for Body Area Networks,” 22nd Annual IEEE International Symposium on Personal, Indoor and 

Mobile Radio Communications (PIMRC), September 11-14, 2011.

Web Services

1. Digital Library of Mathematical Functions27: a 

repository of information on the special functions 

of applied mathematics.

2. Guide to Available Mathematical Functions28: a 

virtual repository of mathematical software components.

3. Matrix Market29: a repository of matrices for testing of algorithms and software for numerical linear 

algebra.

4. SciMark30: a benchmark for scientific computing 

in Java.

Software Released31

1. ACPT: Access Control Policy Test – V. Hu, D. R. 

Kuhn and R. Kacker

2. ACTS: Combinatorial Test Suite Generation with 

Support of Constraints. Version 2.7 – Y. Lei, D. R. 

Kuhn and R. Kacker

3. Combinatorial Coverage Measurement. Version 

1.0 – D. R. Kuhn and R. Kacker

 

27 http://dlmf.nist.gov/

28 http://gams.nist.gov/

29 http://math.nist.gov/matrixmarket/

30 http://math.nist.gov/scimark/

31 In cases where multiple versions have been released during the 

year we only list the last.
Summary of Activities for Fiscal Year 2012 111

4. C-PUT: Tool for Prioritization of User-Session 

Based Test Suites – R. Bryce, S. Sampath, D. R. 

Kuhn and R. Kacker

5. Graphicality Testing Routines. Released to NetworkX – B. Cloteaux

6. NGraph++ Toolkit: Network Graph Toolkit for 

the analysis and simulation of large scale networks, Version 4.5 – R. Pozo

7. OOMMF: Object Oriented Micromagnetic 

Framework. Version 1.2a5 – D. Porter and M. Donahue

8. PHAML: Parallel Hierarchical Adaptive MultiLevel finite element program for the solution of 

elliptic partial differential equations, Versions

1.10.0, 1.11.0 – W. Mitchell.

9. Tcl/Tk. Versions 8.5.11, 8.5.12, 8.6b3 – D. Porter

10. trofs: Read-only virtual filesystem support for Tcl. 

Version 0.4.6 – D. Porter

11. varpro.m32: Variable projection Matlab software 

for least squares problems – D. P. O’Leary and B. 

W. Rust

Conferences, Minisymposia, 

Lecture Series, Courses

MCSD Seminar Series

B. Cloteaux served as Chair of the ACMD Seminar 

Series. There were 29 talks presented during this period.

1. J. Shook (ACMD), “On Finding A Minimum 

Toughness Condition for a k-tree to be Hamiltonian,” November 29, 2011.

2. C. Hogg (Ceramics Division, NIST), “What do 

Noisy Datapoints Tell Us About the True Signal?”

January 17, 2012.

3. A. Carasso (ACMD), “Some New Results in Inverse Reconstruction,” January 31, 2012.

4. S. Jordan (ACMD), “Quantum Algorithms for 

Quantum Field Theories,” February 21, 2012.

5. B. Roy (Indian Statistical Institute), “Application 

of PBIBD in Cryptology and Security,” March 6, 

2012.

6. W. Mitchell (ACMD), “Comparison of hpAdaptive Finite Element Strategies,” March 13, 

2012.

 

32 http://www.cs.umd.edu/~oleary/software/varpro.m

7. R. Goldin (George Mason University), “Exploration of a Random Dot Product Graph Model for 

Neuronal Connectivity,” March 20, 2012.

8. E. Moseman (ACMD), “Network Reliability: Approximation Algorithms,” March 30, 2012.

9. T. Taylor (National Cancer Institute), “Finding and 

Quantifying Protein Monomeric Structural Pseudo-Symmetry,” April 24, 2012.

10. R. Song (University of Illinois), "Subordinate 

Brownian Motions and Their Applications,” May 

2, 2012.

11. Y. Hu (AT&T Labs), “Visualizing Data with 

Graphs and Maps,” May 7, 2012.

12. Y. Liu (ACMD), “Universal Low-Rank Matrix 

Recovery from Pauli Measurements,” May 15, 

2012.

13. S. Casey (American University), “Signal Adaptive 

Frame Theory,” May 22, 2012.

14. M. Kohlhase (Jacobs University), “The Planetary 

System: Active Documents and a Web3.0 for 

Math,” May 30, 2012.

15. D. LaMar (The College of William and Mary), 

“Split Digraphs and Their Applications,” June 19, 

2012.

16. J. Walrand (University of California at Berkeley), 

“A Benes Packet Network,” June 22, 2012.

17. Z. Di (George Mason University), “Applications 

and Recent Developments of Multilevel Optimization Framework (MG/OPT),” July 24, 2012.

18. T. Massard (CEA, France), “Numerical Experiments and Data Mining in Huge Experimental 

Databases at Selected Nuclear Energy and Alternative Energy Research Centers in France,” July 26, 

2012.

19. K. Petersen (New York University), “Finding Minimal Energy Paths for Droplets on 

Superhydrophobic Surfaces: A Phase Field Approach,” July 30, 2012.

20. R. La (University of Maryland), “Secondary Spectrum Trading Market - Auction-based Approach to 

Spectrum Allocation and Profit Sharing,” August 

14, 2012.

21. C. Dunne (University of Maryland), “Measuring 

and Improving the Readability of Network Visualizations,” August 28, 2012.

22. D. O’Leary (University of Maryland), “Image Restoration Using Machine Learning,” September 11, 

2012.
112 NIST Applied and Computational Mathematics Division

23. J. De Loera (University of California at Irvine), 

“Integrals of Polynomials over Convex Polytopes: 

Combinatorics and Algorithms,” September 19, 

2012.

24. Walter Morris (George Mason University), 

“Clique Number and Chromatic Number of 

Graphs Defined by Convex Geometries,” October 

18, 2012.

25. Jaideep Ray (Sandia National Laboratories, Livermore), “Generating Conditional Realizations of 

Graphs and Fields Using Markov Chain Monte 

Carlo,” November 5, 2012.

26. Kyle Hickmann (Tulane University), “Inverse 

Problems for Material Characterization Using 

Thermoacoustic Imaging,” November 16, 2012.

27. Zydrunas Gimbutas (Courant Institute, New York 

University), “Robust High Order Integral Equation 

Solvers for Electromagnetic Scattering in Complex 

Geometries,” November 29, 2012.

28. Alfred Carasso (ACMD), “Hazardous Continuation Backward in Time in Nonlinear Parabolic 

Equations and an Experiment in Deblurring Nonlinearly Blurred Imagery,” December 4, 2012.

29. Amanda P. Streib (ACMD), “Mixing Times of 

Self-Organizing Lists and Biased Permutations,”

December 12, 2012.

Conference Committees

1. Wesley Griffin, Publicity Chair, ACM 

SIGGRAPH Symposium on Interactive 3D 

Graphics and Games, 2013.

2. A. Gueye, Technical Program Chair, 3rd

Conference on Decision and Game Theory for 

Security, (GameSec2012), 2012.

3. A. Gueye, Member, Organizing Committee, 2nd

Conference on Decision and Game Theory for Security (GameSec2011), 2011.

4. F. Hunt, Co-Chair, Steering Committee, Infinite 

Possibilities Conference, University of Maryland, 

Baltimore County, March 30-31, 2012.

5. R. Kacker, Co-Chair, First International Workshop 

on Combinatorial Testing (IWCT) in conjunction 

with the 5th IEEE International Conference on 

Software Testing, Verification and Validation 

(ICST), Montreal Canada, April 17-21, 2012.

6. S. Jordan, Member, Program Committee, Quantum 

Information Processing, (QIP) 2013.

7. A. Kearsley, Member, Organizing Committee, 2nd 

IEEE Conference on Control, Systems & Industrial Informatics, 2012.

8. V. Marbukh, Co-Organizer, Second NIST – Alcatel/Lucent Bell Labs Workshops on Large-Scale 

Geometry of Complex Networks, NIST,

Gaithersburg, MD, March 14, 2012. 

9. W. F. Mitchell, Member, Scientific Committee, 

International Conference of Numerical Analysis 

and Applied Mathematics (ICNAAM 2012), Kos, 

Greece, September 19-25, 2012.

10. D. P. O’Leary, Member, Program Committee, 

NAACL-HLT 2012 Workshop on Evaluation Metrics and System Comparison for Automatic 

Summarization, Montreal, Quebec, Canada, June 

8, 2012.

11. D. P. O’Leary, Member, Organizing Committee, 

SIAM Conference on Applied Linear Algebra 

(LA12), Valencia, Spain, June 18-22, 2012.

12. Sandy Ressler, Tutorial Chair, 18th International 

Conference on 3D Web Technology, 2013.

13. Sandy Ressler, Member, Program Committee, 

WWW2012 Workshop on Declarative 3D for the 

Web Architecture, 2012.

14. K. Sayrafian, Member, Organizing Committee and

Track Chair, 22nd Annual IEEE International Symposium on Personal, Indoor and Mobile Radio 

Communications (PIMRC), Sept. 11-14, 2011.

15. K. Sayrafian, Member, Organizing Committee and

Track Chair, 7th International Conference on Body 

Area Networks (BodyNets), Sept. 24-26, 2012.

16. K. Sayrafian, Member, Steering Committee, NSF 

Planning Workshop on Medical Device Innovation 

Using Cyber Physical Systems, July 18-19, 2012.

17. K. Sayrafian, Member, Technical Program Committee, 6th International Symposium on Medical 

Information and Communication Technology 

(ISMICT), March 26-29, 2012.

18. K. Sayrafian, Member, Technical Program Committee and International Advisory Board, 4th 

International Symposium on Applied Sciences in 

Biomedical and Communication Technologies

(ISABEL), October 26-29, 2011.
Summary of Activities for Fiscal Year 2012 113

Other

1. J. T. Fong, Instructor, Modern Statistics, Data 

Analysis and Specimen/Structural Reliability 

Modeling, One-day Shortcourse, American Ceramic Society Fall Conference, Columbus, OH, 

October 16, 2011.

2. F. Hunt, Instructor, Stochastic Processes, Howard 

University, Fall 2012.

3. R. Kacker and Y. Lei, Presenters, Workshop on 

Combinatorial Testing for Software and Systems 

in conjunction with the International Conference 

on Quality and Reliability Engineering (ICQRE2011) organized by the Indian Statistical Institute, 

Bangalore, India, December 22, 2011.

4. A. J. Kearsley, Mentor, Mathematical Modeling in 

Industry XVI -- A Workshop for Graduate Students, University of Calgary, Canada, June 18-27, 

2012.

5. Y. Parker and J. Terrill, Co-Organizers, NIST 

booth, SC11, the 2011 International Conference 

for High Performance Computing, Networking, 

Storage and Analysis, Seattle, WA, November 13-

19, 

6. 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. 

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, President, Boulder Commerce Children’s Center Association.

6. W. Mitchell, ITL Awards Committee.

7. A. O’Gallagher, ITL Diversity Committee.

8. 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.33

4. A. Dienstfrey, Associate Editor, International 

Journal of Uncertainty Quantification.

5. A. Kearsley, Member, Editorial Board, ISRN 

Journal on Applied Mathematics.

6. D. Lozier, Associate Editor, Journal of Numerical 

Analysis, Industrial and Applied Mathematics.

7. W. Mitchell, Associate Editor, Journal of Numerical Analysis, Industrial and Applied Mathematics.

8. D. P. O’Leary, Editor-in-Chief, SIAM Journal on 

Matrix Analysis and Applications.

9. D. P. O’Leary, Member, Editorial Board, Education Section, SIAM Review.

10. D. P. O’Leary, Member, Editorial Board, SIAM 

Books.

11. D. P. O’Leary, Department Editor, Your Homework Assignment, Computing in Science & 

Engineering.

12. F. Potra, Regional Editor for the Americas, Optimization Methods and Software.

13. F. Potra, Associate Editor, Journal of Optimization 

Theory and Applications.

14. F. Potra, Associate Editor, Numerical Functional 

Analysis and Optimization.

15. F. Potra, Associate Editor, Optimization and Engineering.

16. R. Pozo, Associate Editor, ACM Transactions on 

Mathematical Software. 

17. K. Sayrafian, Guest Editor, International Journal 

on Wireless Information Networks (IJWIN), Special Issue on Wireless Technologies in Healthcare, 

Volume 19, Issue 3, 2012.

18. K. Sayrafian, Guest Editor, International Journal 

of Ultra Wideband Communications and Systems, 

Special Issue on Applications of Ultra Wideband 

 

33 http://www.arXiv.org/
114 NIST Applied and Computational Mathematics Division

Technology in Healthcare, Volume 2, Issue 2, 

2011.

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, Chair, 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 

Technology, National Science and Technology 

Council.

9. A. Dienstfrey, Member, International Federation 

for Information Processing’s (IFIP) Working 

Group 2.5 (Numerical Software).

10. F. Hunt, Member, Advisory Board, National Institute of Mathematical Biological Synthesis,

University of Tennessee, Knoxville, Tennessee.

11. E. Knill, Member, Technical Advisory Panel, 

Quantum Computer Science Program, IARPA.

12. D. Lozier, Member, Steering Committee, Painleve 

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, Member, Release Manager, Tcl Core 

Team.

19. S. Ressler, Member, Declarative 3D for the Web 

Architecture Community Group34.

20. B. Saunders, Member, MAA Committee on Business, Industry and Government Mathematics.

21. B. Saunders, Member, Advisory Group for NSF 

CoSMIC Scholars Program, Towson University. 

22. B. Saunders, Webmaster, SIAM Activity Group on 

Orthogonal Polynomials and Special Functions.

23. B. Saunders, OP-SF Talk listserv Moderator,

SIAM Activity Group on Orthogonal Polynomials 

and Special Functions.

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, Wireless Medical Technologies Working Group, National Institute for 

Biomedical Imaging and Bioengineering 

(NIBIB/NIH).

27. K. Sayrafian, Member, Thesis Defense Committee, Worcester Polytechnic Institute (Pranay Swar, 

Ph.D., May 30th, 2012, Yunxing Ye, M.Sc., July 

31, 2012)

28. J. Terrill, Member, High End Computing Research 

and Development and Infrastructure Interagency 

Working Groups, Networking and Information 

Technology R&D (NITRD) Program.

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 research grants were awarded.

1. Concordia University: Energy Efficient Robust 

Control of Mobile Sensors in Environments with 

 

34 http://www.w3.org/community/declarative3d/
Summary of Activities for Fiscal Year 2012 115

Obstacles, $99,000 (3 years). PI: Dr. Amir Aghdam.

2. National Physical Sciences Consortium: NIST-ITL, 

National Physical Science Consortium Project, 

$297,000 (3 years). PI: Dr. James Powell.

3. Santa Fe Institute: Innovative Workshop Program 

in Network Science, Biologically Inspired Computation, and Computer Security, $300,000 (5 years). 

PIs: Dr. Chris Wood and Drs. Chris Wood and 

Cris Moore.

4. University of California at San Diego: Micromagnetic Finite Difference Simulators on GPUs, 

$180,000 (3 years). PI: Vitaliy Lomakin.

5. University of Edinburgh: Special Functions: Next 

Steps for the DLMF, $173,513 (3 years). PI: Dr. 

Adri Olde Daalhuis.

6. University of Minnesota: Uncertainty Quantification for Molecular Dynamics Simulations for Bulk 

Behavior of Advanced Composites, $283,387 (3 

years). PI: Dr. Fadil Santosa.

7. University of Texas at Arlington: Combinatorial 

Testing for Complex Systems, $330,384 (3 years). 

PI: Dr. Yu Lei.

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

ASSET InterTech

CLO Virtual Fashion, Inc. 

Foray Technologies

IBM India, Bangalore, India

Infosys Technologies, Bangalore, India

Mentor Graphics

Microsoft Research New England

MPACT Corporation

Northrup Grumman

NVIDIA 

Orbital Sciences Corporation

OSI Systems

Palantir Technologies 

Philips Research Asia Bangalore, India

Schwarz Forensic Enterprises

Walt Disney Animation Studios 

Watson Adventures

Government/Non-profit Organizations

Air Force Office of Scientific Research

Argonne National Laboratory

Army Research Laboratory

American Society for Mechanical Engineering

Association for Computing Machinery 

Basque Center for Applied Mathematics (Spain)

CEA (France)

CENAM (National Metrology Institute of Mexico)

Center for Integration of Medicine and Innovative 

Technology

China Special Equip. Inspection and Res. Inst. (China)

CNRS/ESPCI, France

Department of Energy

Electric Power Research Institute

Federal Communications Comission

Food and Drug Administration

IARPA

IDA Center for Computing Sciences

IEEE

Indian Statistical Institute (India)

International Federation for Information Processing

Internet Research Task Force

Lawrence Livermore National Laboratory

Lieber Institute

NASA Ames Research Center 

NASA Indep. Verification and Validation Facility

Nat. Inst. for Biomedical Imaging and Bioengineering

National Institutes of Health

National Institute of Information and Communication 

Technology (Japan)

NOAA

National Physical Laboratory (UK)

National Physical Sciences Consortium

National Renewable Energy Laboratory

National Science Foundation

Nuclear Regulatory Commission

Oak Ridge National Laboratory

Pacific Northwest National Laboratory

Perimeter Institute (Canada)

Physikalisch-Technische Bundesanstalt (Germany)

Sandia National Laboratories

Santa Fe Institute

Savanah River National Laboratory

Society for Industrial and Applied Mathematics

Southwest Research Institute

Swedish Defense Research Agency (Sweden)

Theiss Research

West Health Institute

World Wide Web Consortium 

Universities

Adam Mickiewicz University (Poland)

AGH University of Science and Technology (Poland) 

Beijing Institute of Technology (China)

Boston University

Brown University

Budapest University of Technology and Economics

(Hungary)
116 NIST Applied and Computational Mathematics Division

California Institute of Technology

Carnegie Mellon University

China University of Petroleum (China)

Chinese Culture University (China)

City University of Hong Kong (China)

College of William and Mary

Concordia University (Canada)

Cornell University

Courant Institue of Mathematical Sciences

Dalian University of Technology (China)

East China University of Sci. and Technology (China)

Ecole Polytechnique de Montreal (Canada)

ETH, Zurich (Switzerland)

Federal University of Rio Grande do Norte (Brazil)

Freiburg Institute for Advanced Studies (Germany)

Freie Universität Berlin

George Mason University

George Washington University

Georgia Institute of Technology 

Georgia State University

Gothenburg University (Sweden) 

Hanoi Institute of Mathematics (Vietnam)

Howard University

IGBMC, Strasbourg (France)

Illinois Institute of Technology 

Imperial College, London (UK)

Indiana University 

Institut Supérieur d’Informatique de Modélisation et de 

leurs Applications (ISIMA) (France)

Institute for Computational and Experimental Math.

Institute for Mathematics and Its Applications

Iowa State University

Istituto per le Applicazioni del Calcolo (Italy)

Jacobs University Bremen (Germany)

Johns Hopkins University

Kansas State University

Karlsruhe Institute of Technology (Germany)

Louisiana State University

Macquarie University (Australia)

Montana State University

Morgan State University

Nanyang University (Singapore)

National University of Singapore (Singapore)

New York University

Northern Illinois University

Ningbo University, Ningbo (China)

Northwestern University

Old Dominion University

Open University (UK)

Oregon State University

Oslo University (Norway)

Purdue University

Shandong University (China)

Stanford University

Technical University of Berlin (Germany)

Tel Aviv University (Israel)

The College of William and Mary

Tokyo Institute of Technology (Japan)

Towson University

Tsinghua University (China)

Tulane University

UCLA

University of Alabama at Birmingham

University of Antwerp (Belgium)

University of Bologna (Italy) 

University of Colorado

University of British Columbia

University of California at Berkeley

University of California at Davis 

University of California at Irvine

University of California at San Diego

University of California at Santa Cruz

University of Campinas (Brazil)

University of Cantabria (Spain)

University of Central Florida

University of Colorado at Denver

University of Edinburgh (UK)

University of Erlangen (Germany)

University of Florida 

University of Freiburg

University of Hong Kong (China)

University of Illinois

University of Indiana

University of Maryland

University of Maryland Baltimore County 

University of Metz (France)

University of Miami

University of Minnesota

University of Mississippi

University of New Mexico 

University of Oulu (Finland)

University of Pennsylvania

University of Pittsburgh

University of Rochester

University of South Carolina

University of Sydney (Australia)

University of Tennessee

University of Texas at Arlington

University of Utah 

University of Waikato (New Zealand)

University of Washington

University of Waterloo (Canada)

University of Wisconsin

University of West Bohemia (Czech Republic)

University of Zagreb (Croatia)

Virginia Tech 

Worcester Polytechnic Institute

Wroclaw University (Poland)

Yokohama National University (Japan)
Summary of Activities for Fiscal Year 2012 117

Part V: Appendix

 Part V

Appendix
118 NIST Applied and Computational Mathematics Division

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 2011 – December 2012). 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

Robin Bickel, Secretary

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

David Gilsinn, Ph.D. (Mathematics), Georgetown University, 1969

Fern Hunt, Ph.D. (Mathematics), New York University, 1978

Raghu Kacker, Ph.D. (Statistics), Iowa State University, 1979

Anthony Kearsley, Ph.D. (Computational and Applied Mathematics), Rice University, 1996

Peter Ketcham. M.S. (Mathematics), University of Minnesota, 1997

Geoffrey McFadden, NIST Fellow, Ph.D. (Mathematics), New York University, 1979

*Agnes O’Gallagher, M.S. (Applied Mathematics), University of Colorado at Boulder, 1991

Bert Rust, Ph.D. (Astronomy), University of Illinois at Urbana-Champaign, 1974

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

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)

*Daniel Kaslovsky, Ph.D. / University of Colorado

Yu (Jeff) Lei, Ph.D. / University of Texas at Arlington

P. Aaron Lott, Ph.D. / Lawrence Livermore National Laboratory

Itzel Dominquez Mendoza / Centro Nacional de Metrología, Mexico
Summary of Activities for Fiscal Year 2012 119

Bruce Murray, Ph.D. / SUNY Binghamton

Santanu Sarkar, Ph.D. / Indian Statistical Institute

Christoph Witzgall, Ph.D., NIST Scientist Emeritus

Mathematical Software Group

Daniel Lozier, Leader, Ph.D. (Applied Mathematics), University of Maryland, 1979 

Michael Donahue, Acting Leader Ph.D. (Mathematics), Ohio State University, 1991

Javier Bernal, Ph.D. (Mathematics), Catholic University, 1980

Stephen Langer, Ph.D. (Physics), Cornell University, 1989

Marjorie McClain, M.S. (Mathematics), University of Maryland College Park, 1984

Bruce Miller, Ph.D. (Physics), University of Texas at Austin, 1983 

William Mitchell, Ph.D. (Computer Science), University of Illinois at Urbana-Champaign, 1988

Donald Porter, Ph.D. (Electrical Engineering), Washington University, 1996

Bonita Saunders, Ph.D. (Mathematics), Old Dominion University, 1985 

NRC Postdoctoral Associates

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

Guest Researchers (Name, Degree / Home Institution)

Gunay Dogan, Ph.D. / Theiss Research

Adri Olde Daalhuis, Ph.D. / University of Edinburgh

Qiming Wang / NIST (retired)

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), Massachussetts Institute of Technology, 2008

 *Emanuel Knill, NIST Fellow, Ph.D. (Math), University of Colorado at Boulder, 1991

 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

Elizabeth Moseman, Ph.D. (Mathematics), Dartmouth College, 2007

James Shook, Ph.D. (Mathematics), University of Mississippi, 2010

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
120 NIST Applied and Computational Mathematics Division

Contractors

Lijun Ma, Ph.D. (Optical Engineering), Tsinghua University, 2001

Alan Mink, Ph.D. (Electrical Engineering), University of Maryland, 1980

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

Paulina Kuo, Ph.D. / Joint Quantum Institute, 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

John Kelso, M.S. (Computer Science), George Washington University, 1984

*Adele Peskin, Ph.D. (Chemical Engineering), University of Colorado at Boulder, 1985

Sandy Ressler, M.F.A. (Visual Arts), Rutgers University, 1980

Steven Satterfield, M.S. (Computer Science), North Carolina State University, 1975

James Sims, Ph.D. (Chemical Physics), Indiana University, 1969

Faculty Appointees (Name, Degree / Home Institution)

Marc Olano, Ph.D. / University of Maryland Baltimore County
Summary of Activities for Fiscal Year 2012 121

Glossary of Acronyms

2D two dimensions

3D three dimensions

A&S Abramowitz & Stegun (NBS Handbook of Mathematical Functions, 1964)

ACM Association for Computing Machinery

ACMD NIST/ITL Applied and Computational Mathematics Division

ACTS Advanced Combinatorial Testing System

AIP American Institute of Physics

AISI American Iron and Steele Institute

ALCF Argonne Leadership Computing Facility

AMS American Mathematical Society

ANSI American National Standards Institute

ANTD ITL Advanced Networking Technology Division

APD avalanche photo diode (photon detector)

ARRA American Recovery and Reinvestment Act

arXiv preprint archive housed at Cornell University (http://arxiv.org/)

ASCE American Society of Civil Engineers

ASME American Society of Mechanical Engineers

ASTM ASTM International, formerly known as the American Society for Testing and Materials

BAN body area network

Caltech Californial Institute of Technology

CENAM Centro Nacional de Metrología (Mexico)

CI configuration interaction

CMOS complementary metal-oxide semiconductor

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

CSD ITL Computer Security Division

CT combinatorial testing

CT computed tomography

CVSS Common Vulnerability Scoring System

CY calendar year

DARPA DOD Defense Advanced Research Projects Agency

DLMF Digital Library of Mathematical Functions

DNA deoxyribonucleic acid

DOC Department of Commerce

DOD U.S. Department of Defense

DOE U.S. Department of Energy

DOM Document Object Model

DPD dissipative particle dynamics

ECG electrocardiogram

EL NIST Engineering Laboratory

EM expectation maximization

ESPCI École Supérieure de Physique et Chimie Industrielles de la Ville de Paris (France)

FASTER Faster Administration of Science and Technology Education and Research

FDA Food and Drug Administration

FEM finite element method

FFT fast Fourier transform

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
122 NIST Applied and Computational Mathematics Division

HEC high-end computing

HU Hounsfield units

HTML hypertext markup language

HPCV ACMD’s High Performance Computing and Visualization Group

Hy-CI Hylleraas-Configuration Interaction technique

IAD ITL Information Access Division

IARPA Intelligence Advanced Research Projects Agency

ICT information and communication technologies

IDA Institute for Defense Analysis

IEEE Institute of Electronics and Electrical Engineers

IFIP International Federation for Information Processing

IMA Insitute for Mathematics and Its Applications

IMS Innovations in Measurement Science

INCITE Innovative and Novel Computational Impact on Theory and Experiment (DOE Program)

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)

LaTeX a math-oriented text processing system

LaTeXML LaTeX to MathML translator

LDA latent Dirichlet allocation

LDPC low density parity check

MAA Mathematical Association of America

MathML Mathematical Modeling Language (W3C standard)

MCG multi-crack growth

MCMC Markov Chain Monte Carlo

MD molecular dynamics

MGI Materials Genome Initiative

MIT Massachusetts Institute of Technology

MKM mathematical knowledge management

MLE maximum likelihood estimation

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

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

NPSC National Physical Science Consortium

NRC National Research Council

NRC Nuclear Regulatory Commission

NSF National Science Foundation

NUMA non-uniform memory access

NVD National Vulnerability Database

ODE ordinary differential equation

OOF Object-Oriented Finite Elements (software)
Summary of Activities for Fiscal Year 2012 123

OOMMF Object-Oriented Micromagnetic Modeling Framework (software)

PDE partial differential equation

PHAML Parallel Hierarchical Adaptive Multi Level (software)

PML NIST Physical Measurement Laboratory

PREP Professional Research Experience Program

PSNR peak signal-to-noise ratio

QDPD quarternion-based dissipative particle dynamics

QIBA Quantitative Imaging Biomarkers Alliance

QIS quantum information science

QKD quantum key distribution

R&D research and development

REGEN software for modeling of cryocoolers

RF radio frequency

SAR specific absorption rate

SBIR Small Business Innovative Research

SCO NIST Standards Coordination Office

SED ITL Statistical Engineering Division

SHIP NIST Summer High School Internship Program

SIAM Society for Industrial and Applied Mathematics

SIGGRAPH ACM Special Interest Group on Graphics

SparseLib++ software for spare linear algebra in C++

SPIE International Society for Optical Engineering

SRM standard reference material

SSD ITL Software and Systems Division

STEP NIST Student Temporary Employment Program

SUNY State University of New York

SURF Student Undergraduate Research Fellowship

SVG scalable vector graphics

TCIA The Cancer Imaging Archive

TNT Template Numerical Toolkit (software)

TPAC W3C Technical Plenary Advisory Committee

TV total variation

UK United Kingdom

UMBC University of Maryland Baltimore County

UWB ultra-wide band

VRML virtual reality modeling language

W3C World Wide Web Consortium

WAS Washington Academy of Sciences

WebGL Web-based Graphics Library

X3D Extensible 3D

X3DOM an open-source frameword for integrating X3D and HTML5

XML Extensible Markup Language