NISTIR 8132 

Applied and Computational 

Mathematics Division 

Summary of Activities for Fiscal Year 2015 

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.IR.8132 
 

NISTIR 8132 

Applied and Computational 

Mathematics Division 

Summary of Activities for Fiscal Year 2015 

Ronald F. Boisvert, Editor 

Applied and Computational Mathematics Division 

Information Technology Laboratory 

 This publication is available free of charge from 

http://dx.doi.org/10.6028/NIST.IR.8132 

May 2016 

U.S. Department of Commerce 

Penny Pritzker, Secretary 

National Institute of Standards and Technology 

Willie E. May, Under Secretary of Commerce for Standards and Technology and Director 
 

Summary of Activities for Fiscal Year 2015 i 

Abstract 

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

Information Technology Laboratory at the National Institute of Standards and Technology (NIST). 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 three 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 2014 through December 2015. 

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/. 

Cover Visualization: An image captured by a NIST scanning electron microscope (left), and an enhanced 

version resulting from postprocessing developed by ACMD mathematicians (right). This recently discovered technique for enhancing certain classes of imagery involves an initial adaptive histogram equalization 

of the image, followed by progressive Lévy fractional diffusion smoothing. For details, see page 30. 

Section Visualizations: The word cloud found at the start of each Part of this document was created using 

Wordle, http://www.wordle.net/, using the text of this document as input. 

Acknowledgements: Thanks to Lochi Orr for assisting in the compilation of Parts III and IV of this document. Thanks also to Oliver Slattery and Shahram Orandi who each carefully read the manuscript and 

offered many corrections and suggestions for improvement. 

Disclaimer: Certain commercial entities, equipment, or materials are 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. 
 

 

ii NIST Applied and Computational Mathematics Division 

Contents 

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

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

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

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

Technology Transfer and Community Engagement ............................................................................................. 7
 

Staff News .......................................................................................................................................................... 10
 

Recognition ........................................................................................................................................................ 11
 

PART II: FEATURES ................................................................................................................................................... 13
 

A Strong Loophole-Free Test of Local Realism ................................................................................................. 15
 

Uncertainty Quantification in Molecular Dynamics for Aerospace Polymers................................................18
 

The Resilience of the Internet to Colluding Country Induced Connectivity Disruptions ..............................21
 

PART III: PROJECT SUMMARIES ................................................................................................................................ 25
 

Mathematics of Metrology ................................................................................................................................... 27
 

Computational Tools for Shape Measurement and Analysis ............................................................................. 27
 

Computation of Shape Distances ....................................................................................................................... 29
 

Enhancement of Nanoscale Scanning Electron Microscope Imagery ...............................................................30
 

Molecular Movies: Imaging Femtosecond Motion during Electrochemical Transitions ..................................30
 

A Thousand-Fold Performance Leap in Ultrasensitive Cryogenic Detectors ...................................................31
 

Clutter Measurements Pilot Project: Toward Evaluating Communications Spectrum Sharing Proposals .......32
 

Quantitative MRI ............................................................................................................................................... 32
 

Uncertainty Calculations for Building Engineering .......................................................................................... 34
 

Simulation and Optimization in Cryobiology .................................................................................................... 35
 

Stochastic Regression in Chemometrics ............................................................................................................ 35
 

Modeling Magnetic Fusion ................................................................................................................................ 36
 

Parallel Adaptive Refinement and Multigrid Finite Element Methods.............................................................. 36
 

Stable Explicit Time Marching in Ill-Posed Initial Value Problems for Partial Differential Equations...........38
 

Numerical Solutions of the Time Dependent Schrödinger Equation .................................................................. 41
 

Advanced Materials.............................................................................................................................................. 43
 

Uncertainty Quantification in Molecular Dynamics Workflows for Aerospace Polymers ................................43
 

Bayesian Calibration of Coarse-Grained Forces .............................................................................................. 44

 Micromagnetic Modeling .................................................................................................................................. 45
 

OOF: Finite Element Analysis of Material Microstructures ............................................................................. 46
 

Determination of Diffusion Coefficients in Alloys ............................................................................................. 48
 

Verification and Validation of Finite Element Method-based Solutions............................................................ 49
 

Inversion of the Abel Transform by Truncated Singular Components Method ..................................................50
 

High Performance Computing and Visualization.............................................................................................. 52
 

High Precision Calculations of Fundamental Properties of Few-Electron Atomic Systems.............................52
 

Nano-structures, Nano-optics, and Control of Exciton Fine Structure with Electric and Magnetic Fields ......53
 

Rheology of Dense Suspensions......................................................................................................................... 54
 
 

 

Summary of Activities for Fiscal Year 2015 iii 

HydratiCA: A Parallelized Numeric Model of Cement Hydration .................................................................... 58
 

Network Simulation Visualization ..................................................................................................................... 60
 

Image-based WebVR Graphics .......................................................................................................................... 61
 

High End Visualization Software: Software Tests to Maintain System Reliability ........................................... 62
 

Optical Characterization for Advanced Immersive Displays ............................................................................ 64
 

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

Quantum Information ......................................................................................................................................... 66
 

Quantum Information Science ........................................................................................................................... 66
 

Quantum Estimation Theory and Applications.................................................................................................. 67
 

Phase Retrieval and Quantum Tomography...................................................................................................... 68
 

Device Independently Secure Randomness from Loophole-Free Bell Tests ...................................................... 69
 

Performance of Adiabatic Optimization Algorithms ......................................................................................... 71
 

Computational Complexity of Quantum Field Theory ...................................................................................... 71
 

Knot Theory and Quantum Physics................................................................................................................... 72
 

One-Time Programs Using Isolated Qubits ...................................................................................................... 72
 

Post-Quantum Cryptography ............................................................................................................................ 73
 

High-Speed Error Correction Codes for Quantum Key Distribution ................................................................ 74
 

Towards a Quantum Repeater........................................................................................................................... 75
 

Joint Center for Quantum Information and Computer Science......................................................................... 76
 

Foundations of Measurement Science for Information Systems...................................................................... 78
 

Graph Theoretic Applications to Network Security and Security Metrics ......................................................... 78
 

A Game Theoretic Model of Zero-Day Attack Propagation .............................................................................. 79
 

Security of Complex, Interdependent Systems................................................................................................... 80
 

Measurement Science for Systemic Risk ............................................................................................................ 81
 

Identifying the Best Nodes in a Network for Fast Communication.................................................................... 82
 

Measuring Networks: Monte Carlo Sampling to Approximate the Chromatic Polynomial .............................. 82
 

Fast Sequential Network Model Building .......................................................................................................... 83
 

An Algebraic Formulation for the Analysis and Visualization of Network Graphs .......................................... 84
 

Counting the Number of Linear Extensions of a Partially Ordered Set ............................................................ 85
 

Extremal Theorems for Degree Sequence Packing and the 2-Color Discrete Tomography Problem............... 86
 

Combinatorial Methods in Software Testing ..................................................................................................... 86
 

Can Micro Energy Harvesters Be Used to Power Up Wearable Sensors? ....................................................... 88
 

A Study of the Energy Detection Threshold in the Body Area Network Standard CSMA/CA Protocol............. 89
 

Mathematical Knowledge Management............................................................................................................. 92
 

Digital Library of Mathematical Functions ...................................................................................................... 92
 

Visualization of Complex Functions Data ......................................................................................................... 93
 

DLMF Standard Reference Tables on Demand ................................................................................................. 95
 

Natural Language Processing of Mathematics ................................................................................................. 96
 

NIST Digital Repository of Mathematical Formulae ........................................................................................ 98
 

Fundamental Solutions and Expansions for Special Functions and Orthogonal Polynomials ....................... 100
 

PART IV: ACTIVITY DATA .................................................................................................................................. 103
 

Publications ........................................................................................................................................................ 105
 

Appeared ......................................................................................................................................................... 105
 

Refereed Journals ....................................................................................................................................... 105
 
iv NIST Applied and Computational Mathematics Division 

Journal of Research of NIST....................................................................................................................... 107
 

Book Chapters............................................................................................................................................. 107
 

In Conference Proceedings ......................................................................................................................... 108
 

Technical Magazine Articles ....................................................................................................................... 110
 

Technical Reports ....................................................................................................................................... 110
 

Accepted ........................................................................................................................................................... 110
 

In Review ......................................................................................................................................................... 111
 

Presentations ....................................................................................................................................................... 112
 

Invited Talks ..................................................................................................................................................... 112
 

Conference Presentations ................................................................................................................................ 114
 

Poster Presentations ........................................................................................................................................ 116
 

Web Services ....................................................................................................................................................... 117
 

Software Released............................................................................................................................................... 117
 

Conferences, Minisymposia, Lecture Series, Courses..................................................................................... 118
 

ACMD Seminar Series..................................................................................................................................... 118
 

Shortcourses ................................................................................................................................................ 119
 

Conference Organization ................................................................................................................................. 119
 

Leadership ................................................................................................................................................... 119
 

Committee Membership .............................................................................................................................. 119
 

Session Organization ................................................................................................................................... 120
 

Other Professional Activities............................................................................................................................. 120
 

Internal ............................................................................................................................................................ 120
 

External ............................................................................................................................................................ 120
 

Editorial ...................................................................................................................................................... 120
 

Boards and Committees .............................................................................................................................. 121
 

Community Outreach .................................................................................................................................. 121
 

Thesis Direction .......................................................................................................................................... 122
 

Awards and Recognition.................................................................................................................................... 122
 

Grants Received .................................................................................................................................................. 122
 

Grants Awarded ................................................................................................................................................. 122
 

External Contacts............................................................................................................................................... 122
 

PART V: APPENDIX ................................................................................................................................................... 125
 

Staff ...................................................................................................................................................................... 127
 

Glossary of Acronyms ........................................................................................................................................ 130
 
Part I: Overview

Summary of Activities for Fiscal Year 2015 1 

Part I 

Overview 
2 NIST Applied and Computational Mathematics Division 
Summary of Activities for Fiscal Year 2015 3 

Introduction 

Founded in 1901, the National Institute of Standards and Technology (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 encompassing physics, electrical engineering, nanotechnology, materials science, 

chemistry, bioscience, engineering, fire research, and information technology. 

The Information Technology Laboratory (ITL) is one of seven major laboratories and user facilities at 

NIST. ITL’s overarching goal is to maximize the benefits of information technology to society through a 

balanced measurement science and standards portfolio. To accomplish this, ITL seeks to 

 accelerate innovation in information technology (IT) through the development and application of 

measurements and related technology and tools, 

 develop the essential foundations of computer science, mathematics, and statistics that contribute to 

ITL’s role in IT and measurement science broadly, and 

 ensure the products of our research are available to all to promote U.S. innovation and industrial 

competitiveness, enhance economic security, and improve our quality of life. 

The Applied and Computational Mathematics Division (ACMD) is one of seven 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 computational science and engineering, including analytical methods, numerical and symbolic algorithms, advanced computing and 

communications architectures and applications, and high performance scientific visualization; 

	 engage in peer-to-peer collaborations in the application of mathematical and computational technologies to NIST problems; 

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

 work with internal groups and external organizations to develop standards, test procedures, reference 

implementations, and other measurement technologies for advanced scientific computation on current and future architectures. 

Division staff is organized into four groups: 

Mathematical Analysis and Modeling Group (Timothy Burns, Leader) 

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

analysis for application to measurement science.
 

Mathematical Software Group (Michael Donahue, Leader) 

Performs research and maintains expertise in the methodology and application of mathematical algorithms
 

and software in support of computational science within NIST as well as in industry and academia.
 

Computing and Communications Theory Group (Ronald Boisvert, Acting Leader; Isabel Beichl and Xiao 

Tang, Project Leaders) 

Performs research and maintains expertise in the fundamental mathematics, physics, and measurement science necessary to enable the development and analysis of current and future computing and 

communications systems.
 

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

Performs research and maintains expertise in the methodologies and tools of high performance scientific 

computing and visualization for use in measurement science.
 

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

Project descriptions in Part III of this document are organized according to these broad themes. 
 

 

 

4 NIST Applied and Computational Mathematics Division 

Division Thematic Areas 

Mathematics of Metrology. Mathematics plays an important role in the science of metrology. Mathematical 

models are needed to understand how to design effective 

measurement systems, and to analyze the results they produce. Mathematical techniques are used to develop and 

analyze idealized models of physical phenomena to be 

measured, and mathematical algorithms are necessary to 

find optimal system parameters. Finally, mathematical and 

statistical techniques are needed to transform measured 

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

develop fundamental mathematical methods and analytical 

tools necessary for NIST to continue as a world-class metrology institute, and to apply them to critical 

measurement science applications. 

Advanced Materials. Delivering technical support to the 

nation’s manufacturing industries as they strive to out-innovate and out-perform the international competition has 

always been a top priority at NIST. This has also emerged 

as a major White House priority in recent years, in which 

NIST is playing an increasingly central role. Mathematical 

modeling, computational simulation, and data analytics are 

key enablers of emerging manufacturing technologies. This 

is most clearly evident in the Materials Genome Initiative, 

an interagency program with the goal of significantly reducing the time from discovery to commercial deployment of 

new materials through the use of modeling, simulation, and 

informatics. ACMD’s role in advanced manufacturing centers on the development and assessment of modeling and 

simulation tools, with emphasis on uncertainty quantification, as well as support of NIST Laboratory efforts in such 

areas as materials modeling and smart manufacturing. 

High Performance Computing and Visualization. Computational capability is advancing rapidly, with the result 

that modeling and simulation can be done with greatly increased fidelity (e.g., higher resolution and more complex 

physics). However, developing the requsite large-scale parallel applications remains highly challenging, requiring 

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

techniques must constantly be developed. We are developing and applying such expertise for application to NIST 

problems. In addition, computations and laboratory experiments often produce large volumes of scientific data, 

which cannot be readily comprehended without some 

form of visual analysis. We are developing the infrastructure necessary for advanced visualization of scientific data, 

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

develop the 3D immersive environment into a true interactive measurement laboratory. 

Quantum Information. An emerging discipline at the intersection of physics and computer science, quantum 

information science 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 behavior of quantum systems to enable phenomenal increases in information storage and 

processing capability, as well as communication channels 

with 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 demonstration and assessment of 

technologies for quantum communication. 

Foundations of Measurement Science for Information 

Systems. Modern information systems are astounding in 

their complexity. Software applications are built from 

thousands of interacting components. Computer networks 

interconnect millions of independently operating nodes. 

Large-scale networked applications provide the basis for 

services of national scope, such as financial transactions 

and power distribution. In spite of our increasing reliance 

on such systems, our ability to build far outpaces our ability 

to secure. Protocols controlling the behavior of individual 

nodes lead to unexpected macroscopic behavior. Local 

power anomalies propagate in unexpected ways leading to 

large-scale outages. Computer system vulnerabilities are 

exploited in viral attacks resulting in widespread loss of 

data and system availability. The actual resilience of our 

critical infrastructure is simply unknown. Measurement science has long provided a basis for the understanding and 

control of physical systems. Such deep understanding and 

insight is lacking for complex information systems. We 

seek to develop the mathematical foundations needed for 

a true measurement science for complex networked information systems. 

Mathematical Knowledge Management. We work with 

researchers in academia and industry to develop 

technologies, tools, and standards for representation, 

exchange, and use of mathematical data. Of particular 

concern are semantic-based representations which can 

provide the basis for interoperability of mathematical 

information processing systems. We apply this to the development and dissemination of reference data for applied 

mathematics. The centerpiece of this effort is the Digital 

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

information on the properties of the special functions of 

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

Summary of Activities for Fiscal Year 2015 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. Further details are provided in Part II (Features) and Part III (Project Summaries). 

Mathematics of Metrology. ACMD is working with scientists from the NIST Physical Measurement 

Laboratory (PML) to develop and analyze computational procedures for determining energies, with uncertainties, of individual photons arriving in rapid succession to transition-edge-sensor (TES) 

microcalorimeters for the situation in which detector nonlinearity can be neglected. Such a capability will 

enable more rapid characterization of energy spectra, for scientific and forensic investigations enabled by 

x-ray and gamma ray sources, with the exquisite energy resolution of these devices. Software implementing 

this capability, dubbed multi-pulse fitting, has been developed and evaluated on data collected by a 60­

detector array of TES in experiments at the National Synchrotron Light Source (Brookhaven National Laboratory) as well as at NIST. The new technique, which obtains a least-squares fit of many pulses in a 

stream, rather than filtering pulses individually, outperforms existing record-based processing, in both energy resolution and throughput. See page 31. 

Advanced Materials. While computer simulations have become a common R&D tool in many industrial 

settings, the demands for high-throughput can often push simulations to the limits of their validity. Motivated by these observations, ACMD staff, working with researchers at Boeing, have developed a series of 

uncertainty-quantification tools for molecular dynamics simulations of thermoset polymers, a key component of carbon-composites used by the aerospace industry. Such tools are meant to assess the validity and 

predictive power of simulations; thus, our analysis helps industrial engineers know when and to what extent 

their models are useful for decision-making. Details of this analysis applied to molecular dynamic predictions of the glass-transition temperature have been accepted for publication. See page 18. 

High Performance Computing and Visualization. ACMD completed a major upgrade of its Immersive 

Visualization Environment (IVE) hardware, known as a Cave Automatic Virtual Environment (CAVE), 

this year. The IVE hardware underwent a major upgrade providing a significant improvement in visual 

quality. The new IVE has a larger display area and greater graphics resolution. It is also brighter and has 

greater contrast. In addition, it has a three-way host display switch that allows the selection of one of three 

computers to be the CAVE host at the touch of a button. This capability provides for a primary, backup and 

experimental host to be available to run applications as needed. Full flexibility of video routing allows easy 

selection of special case configurations. System reliability for the CAVE is very important. Included with 

the hardware procurement, a custom software component for self-monitoring of the hardware was specified 

and delivered. Combined with existing system tests it is now possible to run automated tests nightly to 

confirm correct operation of many CAVE subsystems and components. While certain tests require human 

observation, the automated self-test software provides a high level of confidence for ongoing system availability. See page 62. 

We are using the ACMD CAVE to provide insight in a variety of ongoing NIST projects, including 

 Flow of suspensions in pipe systems composed of spherical particles in a fluid matrix, with application to the pumping of concrete and slurries. See page 54. 

 Complex chemical kinetics, with application to cement hydration. See page 58. 

 Spatial distribution of spins in semiconductor nano-scale systems such as quantum dots, with application to the understanding and control of optical properties. See page 53. 
 

6 NIST Applied and Computational Mathematics Division 

Mathematical Knowledge Management. ACMD took important steps this year to ensure the future vitality of the Digital Library of Mathematical Functions (DLMF) project. The DLMF is an online resource 

on the properties of the special functions of applied mathematics1

. In particular, a restructuring of the management of the project was undertaken in order to ensure active maintenance and development of the DLMF 

for the future. In addition, a new set of Senior Associate Editors, who will advise NIST management on the 

future evolution of the project, was put in place. On November 9-10, 2015 the Senior Associate Editors 

assembled at NIST to discuss the possibility of a second edition of the DLMF with significant new content 

and features. Finally, Associate Editors were identified for each existing DLMF chapter. They will work 

with the DLMF Mathematics Editor in responding to user queries about current chapter content, as well as 

developing minor updates. For further details, see page 92. 

Quantum Information. Quantum theory has properties that seem surprising and strange from the perspective of classical physics and everyday intuition. The most profound divide between classical physics and 

quantum physics is that classical physics obeys the principle of local realism, but quantum physics does 

not. Since the mid 1960s, when John Bell proposed an experimental test of this property, physicists have 

performed a series of experiments suggesting violation of local realism, but all have suffered from loopholes, and thereby have not definitively ruled out this principle. This year ACMD researchers participated 

in a loophole-free test of local realism, rejecting the hypothesis that the universe obeys local realism with a 

very high level of statistical significance and ending a decades long quest of foundational physics. This 

work has received a great deal of attention, including being named as number nine in the top 25 science 

stories of 2015 by Science News. See page 15. 

NIST and the University of Maryland (UMD), with the support and participation of the Research 

Directorate of the National Security Agency/Central Security Service (NSA/CSS), inaugurated a new joint 

venture, the Joint Center for Quantum Information and Computer Science (QuICS) on October 31, 2014. 

Scientists at the center will conduct basic research to understand how quantum systems can be effectively 

used to store, transport and process information. QuICS has quickly established itself as a substantial research presence in quantum information science. Newly recruited to the UMD Computer Science 

Department, Andrew Childs, a well-known quantum information theorist, began his tenure as QuICS CoDirector in November. Two postdocs given the distinction of Hartree Postdoctoral Fellows, as well as two 

additional outstanding postdoctoral researchers, also began their tenures in the fall of 2014; others have 

since joined. QuICS Fellows have recruited a total of 11 graduate students into the Center. The technical 

work of QuICS has also seen a strong start, with 65 papers submitted for publication in calendar 2015 alone. 

QuICS has indeed made an impressive start. See page 76. 

Foundations of Measurement Science for Information Systems. ACMD staff have developed an efficient algorithm for estimating the coefficients of the chromatic polynomial P(G,x). P gives the number 

of colorings of a graph G as a function of the number of colors x. The chromatic polynomial is a fundamental metric for the characterization of abstract networks. As such it plays an important role in scheduling and 

assignment problems, such as the allocation of frequencies to communications providers. In addition, it has 

a role in graph analytics as applied to big data, as well as to the q-state Potts model in statistical physics, 

because it gives a measure of graph or network invariants. Computing P is known to be #P hard, in general. 

Division staff devised wo algorithms to estimate the coefficients of the chromatic polynomial of a graph. 

We have compared our methods with other approximation methods and found we have more accuracy in 

less time. A technical article has been submitted for publication. See page 82. 

This year ACMD, working with the NIST Computer Security Division and the Army Research 

Laboratory, completed a study of an internet weakness which has been long suspected, but rarely studied 

quantitatively. This weakness takes the form of the potential of colluding countries deliberately inhibiting 

Internet access of other countries. In this study, we analyzed the scenario in which a group of countries 

disconnect two other countries, isolate a set of countries from the Internet, or break the Internet into noncommunicative clusters. We find that despite the potential for these attacks, the Internet as a whole has 

become increasingly resilient over the period of examination from 2008 to 2013. However, the gains in 

1 http://dlmf.nist.gov/ 
       

 

Summary of Activities for Fiscal Year 2015 7 

robustness and resilience are primarily concentrated in well-connected countries, which form an extremely 

resilient core. See page 21. 

Technology Transfer and Community Engagement 

The volume of technical output of ACMD remains high. During the last 18 months, Division staff members 

were (co-)authors of 49 articles appearing in peer-reviewed journals, 44 papers in conference proceedings, 

and 16 published in other venues. Ten additional papers were accepted for publication, while 30 others are 

undergoing review. Division staff gave 46 invited technical talks and presented 42 others in conferences 

and workshops. 

ACMD continues to maintain an active website with a variety of information and services, most 

notably the Digital Library of Mathematical Functions, though legacy services that are no longer actively 

developed, like the Guide to Available Mathematical Software, the Matrix Market, and the SciMark Java 

benchmark still see significant use. During calendar year (CY) 2015, the division web server satisfied more 

than 5.5 million requests for pages during more than 1.1 million user visits. Another indication of the successful transfer of our technology is references to our software in refereed journal articles. For example, 

our software system for nano-magnetic modeling (OOMMF) was cited in 163 such papers published in CY 

2015 alone; see page 45. 

Members of the Division are also active in professional circles. Staff members hold a total of 13 

editorial positions in peer-reviewed journals. For example, 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 17 organizing/steering/program committees. Of note, ACMD 

played an important role as sponsor or (co-)organizer of several significant events this year, including the 

following: 

	 Dynamics of and on Networks2

. Santa Fe Institute, NM. December 1-5, 2014. 

A NIST grant provided partial funding for this event. This workshop moved beyond the static structure of networks to understand two kinds of dynamics: dynamics “of” a network, where the topology 

changes over time, and dynamics “on” a network, where the topology is fixed on relevant timescales, 

and discrete or continuous variables on nodes and edges evolve. 

	 Reinventing the Grid: Designing Resilient, Adaptive and Creative Power Systems3

. Santa Fe Institute, NM. April 13-17, 2015. 

A NIST grant provided partial funding for this event, whose goal was to catalyze collaborations and 

new approaches to address fundamental questions surrounding the evolution of electricity service. 

It gathered together experts in electric power and ecological systems, along with local Santa Fe 

Institute experts. In addition, we included members of the global “Maker” movement to motivate 

creative thinking about energy problems. We also had significant industry involvement, with participants from local utilities and solar power companies. 

	 13th International Symposium on Orthogonal Polynomials, Special Functions and Applications 

(OPSFA-13)4

. NIST, Gaithersburg, MD. June 1-5, 2015. (D. Lozier, Co-Organizer and H. Cohl, 

Member of the Program Committee). 

Only the second instance of this biennial conference to be held in North America, the meeting was 

co-sponsored by ACMD and the Society for Industrial and Applied Mathematics (SIAM). Conferences in this series provide a forum for mathematicians, physicists, computational scientists, and 

application scientists in other fields to communicate recent research results on mathematical functions that play an essential role in analytical and computational investigations in all areas in science 

2 http://www.santafe.edu/gevent/detail/science/1739/ 

3 http://www.santafe.edu/gevent/detail/science/1953/ 

4 http://www.siam.org/meetings/opsfa13/ 
 

8 NIST Applied and Computational Mathematics Division 

and engineering. The OPSFA community provides the technical basis for the NIST Digital Library 

of Mathematical Functions (DLMF), an online source of reference information on this topic. Some 

200 attendees from 34 countries participated in this event. The symposium featured 10 invited plenary lectures, 22 organized minisymposia of 4-12 talks each, as well as 8 contributed paper sessions. 

Three ACMD staff members made technical presentations. 

 Conference on Intelligent Computer Mathematics (CICM)5

. Washington, DC. July 13-17, 2015. (B. 

Miller and A. Youssef, Co-Organizers) 

The 8th such conference in the series, and the first to be held in the US, CICM brought together 

researchers who seek to advance the use of computers and communication systems in mathematical 

research. During the week-long event, more than 65 participants from 15 countries shared recent 

advances on such topics as digital mathematical systems and libraries, mathematical knowledge 

management, and automated theorem proving. Three ACMD staff members made technical presentations. The proceedings of the conference have appeared as volume 9150 in the Springer series 

Lecture Notes in Artificial Intelligence. 

 Workshop on Uncertainty Quantification in Materials Modeling6

, Purdue University, West Lafayette, IN. July 28-31, 2015. (A. Dienstfrey and P. Patrone, Co-Organizers) 

Organized into six half-day sessions, each of which included a background tutorial followed by 

hands-on computational exercises, the event provided working scientists with exposure to techniques and tools for assessing the results of computational simulations in materials science, thus 

reflecting an important goal of the Materials Genome Initiative. The 40 participants included staff 

from a variety of academic and industrial institutions. 

 Numerical Reproducibility at Exascale7

, at SC158, Austin, TX. November 20, 2015. (M. Mascagni 

and Walid Keyrouz, Co-Organizers) 

A cornerstone of the scientific method is experimental reproducibility. As computation has grown 

into a powerful tool for scientific inquiry, the assumption of computational reproducibility has been 

at the heart of numerical analysis in support of scientific computing. With ordinary CPUs, supporting a single, serial, computation, the ability to document a numerical result has been a 

straightforward process. However, as computer hardware continues to develop, it is becoming harder 

to ensure computational reproducibility, or to even completely document a given computation. This 

workshop explored the current state of computational reproducibility in high performance computing, and sought to organize solutions at different levels. 

 Inference on Networks: Algorithms, Phase Transitions, New Models and New Data9

, Santa Fe Institute, NM, December 14-18, 2015. 

A NIST grant provided partial funding for this event. Networks provide a rigorous representation 

for both modeling and understanding the structure and function of complex systems. Over the past 

10 years, researchers working in statistical inference and statistical physics have developed powerful 

new algorithms for understanding network data, and have revealed new phenomena in the behavior 

of these algorithms. This workshop brought together experts in network science, statistical inference, 

and statistical physics to present recent advances in inference on networks and to organize future 

efforts on developing a deeper mathematical understanding of probability on networks, messagepassing algorithms, and random matrices, on developing new models to handle new sources of rich 

data, and on applying these ideas to key questions in complex systems. 

5 http://cicm-conference.org/2015/cicm.php?event=&menu=general
 

6 http://www.ima.umn.edu/2014-2015/SW7.28-31.15/
 

7 http://www.nist.gov/itl/ssd/is/numreprod2015.cfm
 

8 The International Conference for High Performance Computing, Networking, Storage and Analysis, http://sc15.supercomputing.org/
 

9 http://www.santafe.edu/gevent/detail/science/2154/
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 9 

Service within professional societies is also prevalent among our staff. For example, Barry Schneider served 

as Chair of the Division of Computational Physics of the American Physical Society (APS). Geoffrey 

McFadden serves as Member-at-Large of the Council of the Society for Industrial and Applied Mathematics 

(SIAM). Faculty appointee Michael Mascagni is a Member of the Board of Directors of the International 

Association for Mathematics and Computers in Simulation (IMACS). Ronald Boisvert continues to serve 

as a member of the Publications Board of the Association for Computing Machinery (ACM). Staff members are also active in a variety of working groups. For example, Ronald Boisvert and Andrew Dienstfrey 

serve as members of the International Federation for Information Processing (IFIP) Working Group 2.5 on 

Numerical Software, Donald Porter is a member of the Tcl Core Team, Bruce Miller is a member of W3C’s 

Math Working Group, and Sandy Ressler is a member of the Web3D Consortium. Barry Schneider represents NIST on the High End Computing (HEC) Interagency Working Group of the Federal Networking and 

Table 1. Undergraduate and graduate student interns in ACMD. 

Name From Program Mentor Topic 

Achim, Tudor Stanford U. G NPSC J. Terrill Analysis of cement hydration data with artificial intelligence tools 

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

Chen, Weijan Washington U. St Louis G FGR X. Tang Quantum memory technology 

Hadiji, Hedi Ecole Polytechnique, 

Sophia Antipolis 

G FGR M. Mascagni Probabilistic techniques for solving partial 

differential equations 

Jablonski, Kim Jacobs U. Bremen G FGR B. Miller Mathematical knowledge management 

Keith, Adam U. of Colorado Boulder G PREP E. Knill Quantum measurement analysis 

Kohlhause, Lukas Jacobs U. Bremen G FGR B. Miller Mathematical knowledge management 

Mayer, Karl U. of Colorado Boulder G PREP E. Knill Protocols for quantum optics 

Peng, Bo Washington U. St Louis G FGR X. Tang Generation of correlated photon pairs in 

on-chip high-q WGM resonators 

Schubotz, Moritz Technische U. Berlin G FGR H. Cohl Digital Repository of Mathematical Formulae project development 

Van Meter, James U. of Colorado Boulder G PREP E. Knill Quantum measurement of space-time 

Wills, Peter U. of Colorado Boulder G PREP E. Knill Statistical analysis for quantum info 

Zhang, Guohao UMBC G DGR J. Terrill Scientific visualization 

Zhang, Lizhong ISIMA, France G FGR S. Langer Software development for OOF3D 

Zhao, Henan UMBC G DGR J. Terrill Scientific visualization 

Berger, Isabelle George Washington U. U SURF H. Cohl CAS search and verification for orthogonal 

polynomial generating functions 

Dang, Thinh American University U SURF H. Cohl Fundamental solutions for PDEs on Riemannian manifolds of constant curvature 

Davis, Kyle The College of NJ U SURF S. Ressler Integrating Oculus VR headset with Web 

3D graphics and Leap motion tracker 

Jackson, Alauna Bowie State U. U SURF J. Terrill Integrating Oculus VR headset with Web 

3D graphics and Leap motion tracker 

Park, Zoe Georgetown U. U SURF B. Cloteaux Software for graph theory algorithms 

Rabiega, Daniel Millersville U. PA U SURF M. Mascagni Computing solutions to problems in materials science using Monte Carlo methods 

Traini, Catherine Hood College U SURF H. Cohl CAS search and verification for orthogonal 

polynomial generating functions 

Weller, Ryan U. of Colorado Boulder U SURF S. Langer Software development for OOF3D 

Youssef, Raef UMBC U SURF J. Terrill Integrating Oculus VR headset with Web 

3D graphics and Leap motion tracker 

Zimmerman, 

Jason 

Millersville U. PA U SURF J. Terrill Integrating Oculus VR headset with Web 

3D graphics and Leap motion tracker 

Legend G Graduate student PREP 

U Undergraduate FGR 

NPSC 

DGR 

SURF 

Professional Research Experience Program (Boulder) 

Foreign Guest Researcher 

National Physical Sciences Consortium Fellow 

Domestic Guest Researcher 

Summer Undergraduate Research Fellowship 
 

 

 

 

 

10 NIST Applied and Computational Mathematics Division 

Table 2. High school interns in ACMD. 

Name From Program Mentor Topic 

Agrawal, Neil Poolesville HS SVP H. Cohl Literature search for formula proofs in the Zeta 

Functions Chapter of the DLMF 

Agrawal, Nina Poolesville HS SVP H. Cohl Literature search for formula proofs in the Zeta 

Functions Chapter of the DLMF 

Americianaki, Yusuf Quince Orchard HS SVP H. Cohl MediaWiki development for DRMF 

Cohen, Hannah Magruder HS SVP H. Cohl Literature Search in DLMF 

Gandla, Divya Poolesville HS SVP H. Cohl Digital Repository of Mathematical Formulae 

Kapoor, Yash Clarksburg, HS SVP H. Cohl Mathematical formula research 

Madhu, Shraeya Poolesville HS SVP H. Cohl Digital Repository of Mathematical Formulae 

Nair, Sean Montgomery Blair 

HS 

SVP H. Cohl Dual Bessel function definite integrals using the 

method of integral transforms 

Psurek, Aleksander Thomas S. Wootton 

HS 

SHIP J. Terrill Immersive Visualizations 

Shah, Akash Northwest HS SHIP H. Cohl Mathematical formulae interface and search tools 

Sharma, Ankita Poolesville HS SVP H. Cohl Digital repository of mathematical functions 

Xu, Wenqing Montgomery Blair 

HS 

SVP H. Cohl Generalizations of generating functions of q-hypergeometric orthogonal polynomials 

Zhou, Sabrina Montgomery Blair 

HS 

SVP H. Cohl Digital Repository of Mathematical Formulae 

Seeding and Development 

Zou, Cherry Ying Poolesville HS SVP H. Cohl Digital repository of mathematical functions 

Zou, Claude Poolesville HS SVP H. Cohl Incorporation of semantics in LaTeX expressions 

Legend HS High school SHIP 

SVP 

Summer High school Internship Program 

Student Volunteer Program 

Information Technology Research and Development (NITRD) Program. Further details can be found in 

Part IV of this report. For further details, see Section IV, Activity Data. 

Staff News 

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

Arrivals 

Peter Bierhorst joined ACMD on January 15, 2015 as a NIST Fellow Postdoc working with Manny Knill. 

Peter received a Ph.D. in mathematics from Tulane University in 2014. At NIST Peter is performing research in quantum information theory, focusing on statistical analysis of quantum experiments. 

Paul Patrone, who works in the areas of material modeling and uncertainty quantification, joined ACMD’s 

Mathematical Analysis and Modeling Group on August 24, 2015. Paul received a Master’s degree in Applied Mathematics (2012) and a Ph.D. in physics (2013) from the University of Maryland. He was most 

recently an Industrial Postdoc at the Institute for Mathematics and its Applications at the University of 

Minnesota. As part of that program, he spent a year working at the Boeing Company in Seattle, where he 

worked on uncertainty quantification in the modeling of aerospace composites 

Lochi Orr joined ACMD on December 14, 2015 to provide administrative support to the Mathematical 

Analysis and Modeling Group and the Mathematical Software Group. Lochi, who has a degree in Criminal 

Justice, was most recently employed by the Drug Enforcement Administration in Baltimore. 

Departures 

Yvonne Kemper, who began a stay in ACMD as a NIST National Research Council (NRC) Postdoctoral 

Associate in December 2013, moved on in July 2015 to a second postdoc position in the Mathematics 
 

 

 

Summary of Activities for Fiscal Year 2015 11 

Figure 1. 2015 Department of Commerce Bronze Medal winners from ACMD. Left: Kamran Sayrafian. Right: Xiao Tang, Oliver Slattery, 

Paulina Kuo and Barry Hershman. 

Department at the University of Vienna. She received a Ph.D. in mathematics from the University of California at Davis in 2013, where she wrote a thesis on structural measurements of simplicial complexes and 

convex polytopes. At NIST she worked with Isabel Beichl on methods for approximating the chromatic 

polynomial. 

In August 2015 James Shook, an NRC Postdoctoral Associate in ACMD since 2011, took a permanent 

position in the NIST Computer Security Division. While in ACMD James worked with Isabel Beichl and 

others on problems in combinatorics and graph theory. 

Students 

During FY 2015 ACMD was able to support the work of 42 student interns, including 15 graduate students, 

10 undergraduates, and 15 high school students. See Table 2 and Table 1 for a complete listing. 

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

advisers and as members of thesis committees. For a complete list, see page 120. 

Recognition 

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

below. 

Manny Knill was honored with the 2015 Samuel Wesley Stratton Award “for pioneering research in 

the field of quantum information science and engineering.” The Stratton Award, one of the most prestigious 

awards conferred by NIST, was first presented in 1962. It is granted for outstanding scientific or engineering achievements in support of NIST objectives. 

Kamran Sayrafian received a 2015 Department of Commerce (DOC) Bronze Medal “for leadership 

in the advancement of body-area network technologies that will enable innovations in personal health care 

delivery and telemedicine.” Examples of his current research work in this area can be found on pages 88 

and 89. 

Barry Hershman, Paulina Kuo, Oliver Slattery and Xiao Tang also received a 2015 DOC Bronze 

medal this year. They were cited “for the development of upconversion single photon detectors and spectrometers for use in quantum information research and measurement science.” The team’s current work on 

quantum communications is described on page 75. 
 

 

 

12 NIST Applied and Computational Mathematics Division 

In the fall of 2014, Raghu Kacker received a Department of Commerce Silver Medal “for enabling 

unprecedented levels of software reliability through development of innovative software testing methodologies 

and tools.” The medal recognizes the accomplishments of 

the combinatorial testing project whose current activities 

are described on page 86. D. Richard Kuhn of the ITL 

Computer Security Division was a joint honoree. 

ACMD staff members and associates garnered three 

of the five annual ITL awards presented in 2015: 

 Outstanding Contribution to ITL: Scott Glancy, for 

technical and analytical excellence in the advancement of 

quantum tomography and its application to quantum optics experiments with light and microwaves. 

 Outstanding Journal Paper: James Sims, for excellence in research and exposition in the paper “HylleraasConfiguration-Interaction Nonrelativistic Energies for 

the 1 S Ground States of the Beryllium Isoelectronic Sequence,” which was published in the Journal of Chemical 

Physics in 2014.10 

	 Outstanding Conference Paper: Yi-Kai Liu, for excellence in research and exposition in the paper 

“Single-Shot Security for One-time Memories in the Isolated Qubits Model,” which was published 

in the Proceedings of the 34th Annual Cryptology Conference held in Santa Barbara, CA in 

August 2014.11 

Finally, in December 2015, Oliver Slattery, a member of ACMD’s quantum communications team, was 

awarded a Ph.D. degree in physics from the University of Limerick in December 2015. 

Figure 2. Yi-Kai Liu describes his work on one-time memories 

in the isolated qubits model at the annual QCrypt Conference. 

10 http://dx.doi.org/10.1063/1.4881639 

11 http://dx.doi.org/2010.1007/978-3-662-44381-1_2 
Part II: Features 

 

 

Summary of Activities for Fiscal Year 2015 13

Part II 

Features 
14 NIST Applied and Computational Mathematics Division 
 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 15 

A Strong Loophole-Free Test of Local Realism
 

Quantum theory has properties that seem surprising and 

strange from the perspective of classical physics and 

everyday intuition. These include unavoidable randomness, systems existing in superpositions of states, and 

entanglement between systems. The most profound divide between classical physics and quantum physics is 

that classical physics obeys the principle of local realism, but quantum physics does not. This divide was 

discovered by John S. Bell in 1964 [1]. Since then, physicists have performed a series of experiments suggesting 

violation of local realism, but all have suffered from 

loopholes, and thereby have not definitively ruled out 

this principle. This year ACMD researchers participated in a loophole-free test of local realism, rejecting 

the hypothesis that the universe obeys local realism with 

a very high level of statistical significance and ending a 

decades long quest of foundational physics [2]. 

Scott Glancy 

Compared with the world of our everyday experience, 

quantum theory may seem strange. Objects can exist 

simultaneously in two configurations. This is known as 

a superposition of states. For example, a photon can exist in an equal superposition of horizontal and vertical 

polarizations, which we write as |H+|V. Measurements 

performed on objects in superpositions give random results, but superpositions are fundamentally different 

from familiar probabilities because they can take negative (or even complex) values. We say that multiple 

objects in a correlated superposition are entangled. For 

example, the two-photon entangled state |HH-|VV has 

50 % probability that both are horizontal and 50 % probability that both are vertical. If one of the photons is 

measured to be horizontal, the state of the other photon 

immediately collapses to |H, even if they are separated 

by a great distance12. These features have inspired pithy 

quotes13 seemingly endless philosophical debate, the invention of paradoxes, experiments realizing paradoxes, 

resolutions of the paradoxes, and the science of quantum 

information theory. 

During the early development of quantum theory in 

the late 1920’s, a small group of physicists speculated 

that the apparently fundamental randomness might be 

explained by a system of hidden variables. If we were 

able to measure the hidden variables, we would be able 

to predict with certainty all measurement outcomes, but 

unfortunately the hidden variables are forever hidden 

from us. If hidden variable theory were true, then we 

could attribute many of the strange features of quantum 

12 Whether this collapse is a real physical process or a mathematical 

manipulation is still a subject of heated debate among physicists. 

source sA s A B B 

Alice Bob 

Figure 3. Basic diagram of an experiment to test local realism. A 

source sends a pair of particles to measurement stations “Alice” 

and “Bob.” They randomly choose measurement settings sA and sB, 

which determine what property of the particles Alice and Bob measure. They obtain measurement results A and B. If the particles obey 

the principle of local realism, the probability distribution of (sA, sB, 

A, B) is constrained by Bell inequalities. The experiment is designed 

to observe violation of one of the inequalities. In our experiment, 

the source makes entangled photon pairs, which travel to Alice and 

Bob along optical fibers. Alice and Bob choose an angle along 

which to measure the photons’ polarization, and detect the photons 

with high efficiency superconducting-nanowire single-photon detectors. 

mechanics and its paradoxes to hidden processes that 

would better conform to our everyday intuitions. 

To illustrate, consider the entangled photon pair 

|HH-|VV. If both photons were measured to be horizontal, the hidden variable explanation would be that 

they had both been horizontal, and the measurement 

only revealed this fact. According to this perspective, a 

process that is thought to create the entangled state 

|HH-|VV is actually a process that sometimes creates 

two H photons and at other times creates two V photons. 

Hidden variable theories obey the principle of realism, 

according to which the results of all possible measurements exist as hidden variables before the measurements 

occur. The measurements reveal the hidden variables. 

According to the theory of relativity, the hidden variables should obey a further principle of local realism, 

which says that each particle carries its own hidden variables with results of all possible measurements that 

might be performed on that particle, and the hidden varialbes of separated particles can communicate with one 

another no faster than the speed of light. 

John S. Bell’s great discovery was that one can perform experiments to test whether the universe obeys the 

principle of local realism. A basic diagram of such an 

experiment is given in Figure 3. A source creates a pair 

of particles (photons in our experiment) and sends them 

to two separated laboratories, labeled “Alice” and 

“Bob”. Alice and Bob each randomly choose one of two 

measurements to make on the particle and then measure 

the particle. In our experiment, the two choices are to (1) 

measure polarization along the horizontal/vertical axes 

or (2) measure polarization along a slightly rotated pair 

of axes. Bell proved that if the particles obey local realism, the probability distribution of measurement results 

13 E.g., “God does not play dice.” and “spooky action at a distance” 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

16 NIST Applied and Computational Mathematics Division 

Figure 4. Locations of source (S), Alice (A), and Bob (B) in NIST 

Building 1 of the Boulder campus. The shaded regions represent 

extremely conservative uncertainty regions for the locations of the 

source, Alice, and Bob. If all three are actually located within regions of a given shading, then the corresponding p-value for local 

realism applies. The bottom left of the figure shows expanded views 

of Alice’s and Bob’s labs specifying the locations of their random 

number generators (RNG) and detectors. 

must obey a set of inequalities (the Bell inequalities). 

However, Bell also showed that if the source makes entangled particles, then quantum theory predicts that the 

measurement probabilities can violate these inequalities. 

Bell’s work provided a clear outline for an experiment to test local realism (and local hidden variable 

theory) in the laboratory. Since then many research 

groups have performed various experiments to test local 

realism. However, previous experiments have all allowed means by which a local realistic system could (at 

least in principle) appear to violate the Bell inequality 

being tested. We say that such experiments contain loopholes. The three most technically challenging loopholes 

have been (1) the measurement inefficiency loophole, 

(2) the communication loophole, and (3) weak-analysis 

loopholes. While some past experiments have closed 

some (but not all) of these loopholes, no experiment had 

closed all loopholes until this year. 

Measurement Inefficiency Loophole. If the efficiency 

of transmission and measurement of the entangled particles is less than 2/3, even quantum systems are unable 

to violate Bell’s inequalities. To demonstrate violation, 

past experiments have simply discarded all events in 

which two particles were not detected, implicitly assuming that the measurement probabilities for detected 

particles is the same as the probabilities for lost particles. 

However, that assumption may not be strictly true, and 

one can engineer local realistic systems that can show 

Bell inequality violation for the subset of detected particles. This loophole was first closed in an experiment 

performed by NIST’s Ion Storage Group in 2001 [3]. To 

14 a measure of statistical significance 

close the measurement inefficiency loophole in our experiment, we used high efficiency superconducting 

nanowire single-photon detectors, developed in NIST’s 

PML [4]. We also engineered the source to produce entangled photons that could efficiently enter optical fibers 

for transmission to the Alice and Bob measurement stations. 

Communication Loophole. If information about Alice’s random measurement choice reaches Bob before 

he completes his measurement (or vice-versa), a local 

realistic system could use that information to produce 

correlations between measurement results that in the absence of communication would be impossible for local 

realistic systems. To be certain that communication is 

impossible, we locate Alice and Bob ≈130 m from the 

source and perform the measurements so quickly that a 

signal traveling at the speed of light cannot travel from 

Alice to Bob or vice versa before the measurement is 

complete. The locations of the labs within NIST Building 1 of the Boulder campus are shown in Figure 4. 

High-speed photon detectors, electronics, and random 

number generators were developed to complete the 

measurements in the allowed time. 

Weak Analysis Loophole. A test of the hypothesis of 

local realism deserves a rigorous statistical analysis of 

the experimental data. However, previous experiments 

have been analyzed using methods that required the invocation of assumptions about the data that were 

unjustified and, in some cases, false. These assumptions 

have introduced loopholes that would allow local realistic systems to appear to violate a Bell’s inequality or to 

inflate the statistical significance of a violation. Often it 

has been impossible to interpret reported results as clear 

statements about statistical significance or probabilities. 

For several years, ACMD researchers have been developing methods to calculate p-values14 for tests of local 

realism [5-10]. We have removed assumptions that the 

data from the experiment is independent and identically 

distributed, that the violation of the inequality is normally distributed, and others, so that no analysis 

loopholes remain. Only the null hypothesis of local realism is tested. For this experiment, ACMD researchers 

also designed rigorous data collection and analysis protocols and performed various consistency checks. 

Several data sets were recorded during the NIST 

experiment, the best of these yielded a p-value of 

5.810-9, which is the probability that a local-realistic 

system would violate the Bell inequality by as much as 

we observed in our experiment or more. Similar 

experiments were performed this year at the Technical 

University of Delft [11] and at the University of Vienna 

[12]. Together these experiments firmly refute the 

hypothesis that our universe obeys the principle of local 
 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 17 

realism and confirm fundamental predictions of 

quantum mechanics. 

NIST’s experimental apparatus that was testing local realism will soon have a new job: generation of 

secure random numbers. Just as no local-realistic system 

can mimic the data from the experiment, no hacker can 

control or predict the experimental record (provided that 

the random number generators Alice and Bob use for 

their measurement choices are secure). Such a source of 

secure, unpredictable random numbers can be used for 

various cryptographic tasks or incorporated into NIST’s 

Randomness Beacon15. 

References 

[1]	 J. S. Bell, On the Einstein-Podolsky-Rosen Paradox, 

Physics 1 (1964), 195-200. 

[2]	 L. K. Shalm et al., A Strong Loophole-free Test of Local 

Realism, Physical Review Letters 115 (2015), 250402. 

[3]	 M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. 

M. Itano, C. Monroe, and D. J. Wineland, Experimental 

Violation of a Bell’s Inequality with Efficient Detection, 

Nature 409 (2001), 791-794. 

[4]	 F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. 

Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. 

Shaw, R. P. Mirin, and S. W. Nam, Detecting Single Infrared Photons with 93 % System Efficiency, Nature 

Photonics 7 (2013), 210–214. 

[5]	 Y. Zhang, S. Glancy, and E. Knill, Asymptotically Optimal Data Analysis for Rejecting Local Realism, Physical 

Review A 84 (2011), 062118. 

[6]	 Y. Zhang, S. Glancy, and E. Knill, Efficient Quantification of Experimental Evidence Against Local Realism, 

Physical Review A 88 (2013), 052119. 

[7]	 P. Bierhorst, A Rigorous Analysis of the Clauser–Horne– 

Shimony–Holt Inequality Experiment When Trials Need 

Not Be Independent, Foundations of Physics 44 (2014), 

736-761. 

[8]	 E. Knill, S. Glancy, S. W. Nam, K. Coakley, and Y. 

Zhang, Bell Inequalities for Continuously Emitting 

Sources, Physical Review A 91 (2015), 032105. 

[9]	 P. Bierhorst, A Robust Mathematical Model for a Loophole-Free Clauser–Horne Experiment, Journal of Physics 

A: Mathematical and Theoretical 48 (2015), 195302. 

[10] B. G. Christensen, A. Hill, P. G. Kwiat, E. Knill, S. W. 

Nam, K. Coakley, S. Glancy, L. K. Shalm, Y. Zhang, 

Analysis of Coincidence-Time Loopholes in Experimental Bell Tests, Physical Review A 92 (2015), 032130. 

[11] B. Hensen et al., Loophole-free Bell Inequality Violation 

Using Electron Spins Separated by 1.3 Kilometres, Nature 526 (2015), 682–686. 

[12] M. Giustina	 et al., Significant-Loophole-Free Test of 

Bell’s Theorem with Entangled Photons, Physical Review 

Letters 115 (2015), 250401. 

Participants 

Peter Bierhorst, Scott Glancy, Emanuel Knill (ACMD); 

Kevin J. Coakley (NIST ITL); Michael S. Allman, Joshua 

C. Bienfang, Shellee D. Dyer, Thomas Gerrits, Carson 

Hodge, Adriana E. Lita, Camilla Lambrocco, Alan L. 

Migdall, Richard P. Mirin, Sae Woo Nam, Lynden K. 

Shalm, Martin J. Stevens, Edward Tortorici, Varun B. 

Verma, Michael A. Wayne (NIST PML); Carlos Abellàn, 

Waldimar Amaya, Morgan W. Mitchell, Valerio Pruneri 

(The Barcelona Institute of Science and Technology, 

Spain), Bradley G. Christensen, Daniel R. Kumor, Paul 

G. Kwiat (University of Illinois at Urbana-Champaign); 

William H. Farr, Francesco Marsili, Matthew D. Shaw, 

Jeffrey A. Stern (Jet Propulsion Laboratory); Deny R. 

Hamel (University of Moncton, Canada); Thomas 

Jennewein, Evan Meyer-Scott, Yanbao Zhang (University of Waterloo, Canada) 

15 http://www.nist.gov/itl/csd/ct/nist_beacon.cfm 
 

 

 

 

 

 

 

 

 

 

 

 

18 NIST Applied and Computational Mathematics Division 

Uncertainty Quantification in Molecular Dynamics for 

Aerospace Polymers 

In the past two decades, computer simulations have become a common R&D tool in the aerospace industry. 

While this strategy holds promise, the high-throughput 

demands of industry can extend simulations toward the 

limits of their validity. Motivated by these observations, 

we have developed a series of uncertainty-quantification 

tools for molecular dynamics simulations of thermoset 

polymers, a key component of carbon-composites used 

by the aerospace industry. Broadly speaking, such tools 

are meant to assess the validity and predictive power of 

simulations; thus, our analysis helps industrial engineers know when and to what extent their models are 

useful for decision-making purposes. Details of this 

analysis applied to molecular dynamic predictions of the 

glass-transition temperature have been accepted for 

publication. We anticipate that our analysis can be extended to other material properties and simulation 

techniques. Industrial stakeholders are actively using 

our methods, some of which have recently been incorporated into commercial software packages. 

Andrew Dienstfrey and Paul Patrone 

In the commercial aerospace industry, advances in computer simulations and modeling have led to a dramatic 

paradigm shift in how airplanes are designed and manufactured. From a macroeconomic perspective, the 

motivations for this are clear: every dollar spent on simulations yields as much as a $9 return-on-investment by 

informing decision-making, reducing excess testing, 

and therefore decreasing development times and costs 

[1,2]. Thus, industrial researchers are increasingly considering ways to integrate simulations more fully into 

the aerospace design process. 

Materials science has been identified as a key area 

where advances in computer modeling are needed [1,3]. 

The principal drivers for this are threefold: (i) new materials are becoming market drivers in several industrial 

sectors; (ii) computers are now sufficiently powerful 

that scientists can consider tailoring materials in silico 

to meet specific needs [1,4]; and (iii) the complex, 

many-body simulations required to model such advanced materials are still relatively new and require 

exhaustive verification and validation of their predictions [1,3]. 

To understand the interplay of these facts, it is sufficient to learn from the success of the Boeing 787 

Dreamliner. Built from more than 50 % advanced and 

composite materials by weight, the 787 boasts significantly improved fuel efficiency that reduces operating 

costs for airline carriers by up to 6 % [5]. Eyeing the 

Figure 5. Unit cell showing cross-linked polymer system (33DDS 

and BisF) containing 2000 atoms. Molecular dynamics evolves all 

atoms by Newtonian dynamics using a potential model to compute 

inter-atomic forces. 

economic implications of rising oil prices and the savings promised by the 787, potential customers in 2006 

all but forced the other global airline manufacturers to 

invest billions in similar composite manufacturing techniques [7]. Research engineers quickly realized that new 

materials were the catalyst driving this change, and the 

market was soon to be saturated with current-generation 

composites. Thus, recent efforts have focused on reducing time-to-market of next-generation materials as a 

means to retain competitive advantage. Simulationbased search for new materials is seen as a key tool for 

enabling this materials-by-design paradigm [7]. 

From a practical standpoint, this strategy must confront the complexity of aerospace composites. Such 

materials are not monolithic entities, but rather a compound mixture of many subcomponents. Modern 

thermoset resins, for example, can include more than 10 

distinct monomer types, which are mixed in varying proportions to balance trade-offs in end-product 

performance. The flexibility offered by this combinatorially large design space reflects both the immense 

potential and difficulty associated with designing polymer systems. 

To address these difficulties, aerospace and other 

composite-based industries are turning to molecular dynamic (MD) simulations as a means of balancing 

accuracy and throughput [1,3]. Broadly speaking, MD 

simulations integrate Newton’s equations of motion forward in time for large, many-body particle dynamics 

problems. A representative system is shown in Figure 

5. For crosslinked polymers used in aerospace composites, the success of MD is largely due to its ability to 
 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 19 

Figure 6. Comparison of density-temperature data for two different amine-cured epoxies. Tg is typically computed as the intersection temperature of two lines fit to the low and high temperature asymptotic regimes. Using hyperbolas, we test for the existence of such regimes by comparing 

the data to asymptotes. The left plot shows a system in which the data clearly samples asymptotic behavior, corresponding to temperatures 

outside of the transition region. The right plot shows a dataset that does not sample asymptotic behavior. 

describe the evolution of complex molecular conformations which govern bulk mechanical properties. Such 

level of detail, however, comes at a price. 

For one, the length and time scales of MD simulations are vastly different than their physical 

counterparts. A representative sample of bulk material 

has a mass of a few grams, and thereby consists of 

O(1023) atoms. Relevant time-scales range from dynamic responses of O(10-5) seconds, to aging processes 

taking place over the many-year lifetime of a component. By comparison, current high-end MD simulations 

treat at most O(106

) atoms for O(10-8) seconds. This 

huge discrepancy in scales is a cause for concern. 

A separate issue arises from the opposite end of the 

length spectrum, namely the details of the interatomic 

force-fields that complete Newton’s equations. While 

such forces could, in principle, be derived from quantum 

mechanical considerations, this approach is not widely 

practiced. Instead, a large variety of parameterized interatomic force-fields have been designed for diverse 

material classes and purposes. These phenomenological 

interactions model interatomic bonds, bond and torsional angles between bonded triplets, and long-range 

electrostatic and van der Waals forces in order to approximate the force on each of the atoms in a system. 

In light of these fundamental concerns it may appear remarkable that atomistic simulations such as MD 

are at all informative of bulk system behavior. However, 

a counter-balancing is provided in that the bridge from 

atomic to macroscale is built on ensemble averages of 

atomistic dynamics. Such statistics have the effect of 

smoothing out fine scale details of the interatomic forcefields, and return average bulk-scale properties with variances that decay proportional to the inverse system size. 

Therein lies the theoretical prospects for the value of the 

MD enterprise. 

In light of these observations, a key task in any MDbased R&D activity is to assess confidence in simulations so as to render their predictions more informative 

for decision making. The growing field of uncertainty 

quantification (UQ) provides a useful foundation from 

which to develop and analyze such techniques. In the 

following we describe research results completed in FY 

2015 toward this goal. 

Uncertainty quantification for glass-transition. 

Building upon work from FY 2014, we developed a systematic UQ workflow to assess data arising from MD 

simulations of the glass-transition temperature Tg. This 

quantity is both an important property for engineers16 

that is also difficult to model; thus it represents a useful 

proving ground upon which to develop UQ methods 

We begin by addressing the question: Is simulated 

data consistent with the definition of Tg? In particular, it 

is common practice to estimate Tg by extrapolating to the 

intersection of two fit-lines characterizing the low and 

high-temperature asymptotic behavior of density-temperature curves. Deciding what constitutes “asymptotic 

behavior” at these extreme temperature regions is left to 

the modeler, and hence widely disparate estimates of Tg 

are possible from hard-to-decide cases. Motivated by 

this, we implemented a non-linear regression analysis 

that estimates a hyperbola model for the entire density16 It determines, for example, the temperature at which a wing becomes soft. 
 

 

 

 

 

 

 

20 NIST Applied and Computational Mathematics Division 

temperature dataset, thereby eliminating the need for supervised intervention and data sub-setting. As an added 

benefit, the resulting hyperbola model may be analyzed 

further to determine whether asymptotic regimes are 

manifest in the simulation data; see Figure 6. Thus we 

present a systematic approach to resolve what was previously left open to user skill. 

Additionally, we developed a pooling analysis that 

estimates bias in the Tg predictions by iteratively 

resampling from collections of datasets. Importantly, 

such approaches can indicate when simulations are too 

small to yield property estimates that are converged as a 

function of system size. 

Finally, we quantified the total uncertainty in the 

simulation-based “measurements” of Tg as the combination of two principal contributions. One represents the 

dispersion due to the uncertainty of the non-linear regression determined in the first phase of the analysis. 

This contribution is estimated using a parameterized 

bootstrap Monte Carlo technique. The second characterizes the dispersion between multiple independent 

simulations of the identical physical system. Physically, 

this second contribution is meant to capture the dispersion due to small system sizes and, thus, limited 

sampling of polymer cross-linking statistics as well as 

possibilities for metastable dynamical equilibrium resulting from local minima in the energy landscape. From 

the statistical perspective our uncertainty analysis is 

closely-related to that which is obtained in metrological 

key-comparison studies [8]. To the best of our 

knowledge this is the first time that such a metrology 

approach has been applied to the uncertainty analysis of 

simulation-based data. 

Details of this work are provided in a publication 

that is currently under review [9]. Industrial stakeholders are also using this workflow in their simulation 

protocol, and the software company Schrodinger has incorporated elements of our analysis into their 

commercially available MD simulation package. Future 

directions include (i) generalizing our analysis to more 

mechanical properties of interest, and (ii) developing additional analysis tools for quantifying the extent to 

which a finite simulation samples the network structure 

of bulk materials. 

In addition to this analysis, we continued outreach 

to the broader computational materials science community as part of the Materials Genome Initiative. In 

particular, from July 28–July 31 2015, in collaboration 

with the Institute for Mathematics and its Applications 

(IMA), Air Force Research Lab and Purdue University 

we organized an IMA Hot Topics Workshop on Uncertainty Quantification in Materials Science at Purdue’s 

nanoHUB. This workshop is described elsewhere in this 

annual report. Response to the workshop was positive, 

and a follow-up is scheduled to be held at IMA in February 2016. 

References 

[1]	 G. Goldbeck, The Economic Impact of Molecular Modelling: Impact of the Field on Research, Industry, and 

Economic Development. Goldbeck Consulting Ltd., St. 

John’s Innovation Centre, Cambridge, United Kingdom, 

2012. 

[2]	 E. C. Joseph, C. Ingle, C. Meunier, S. Conway, G. Cattaneo, and N. Martinez, A Strategic Agenda for European 

Leadership in Supercomputing: HPC 2020 — IDC Final 

Report of the HPC Study for the DG Information Society 

of the European Commission, September 2010. 

[3]	 A. Dienstfrey, F. R. Phelan Jr., S. Christensen, A. Strachan, F. Santosa and R. F. Boisvert, Uncertainty 

Quantification in Materials Modeling, JOM 66:7 (2014), 

1342-1344. 

[4]	 S. Christensen and J. Senger, Distortional Matrix of 

Epoxy Resin and Diamine, U.S. Patent 7,985,808 B2, 

filed April 23, 2010, issued July 26, 2011. 

[5]	 J. Ostrower, Boeing’s Key Mission: Cut Dreamliner 

Costs, The Wall Street Journal, June 10, 2014, B1. 

[6]	 D. Gates, Airplane Kingpins Tell Airbus: Overhaul A350, 

Seattle Times, March 29, 2006. 

[7]	 J. Cotton, R. J. Glamm, D. M. Rosenbladt, E. Pripstein 

and S. Christensen, “Integrated Computational Materials 

Engineering Needs for Aerospace,” TMS ICME Conference, Colorado Springs, CO, June 3, 2015. 

[8]	 A. Rukhin, Weighted Means Statistics in Interlaboratory 

Studies, Metrologia 46:3 (2009), 323-331. 

[9]	 P. N. Patrone, A. Dienstfrey, A. R. Browning, S. Tucker 

and S. Christensen, Uncertainty Quantification in Molecular Dynamics Studies of the Glass Transition 

Temperature, Polymer 87 (2016), 246-259. 

Participants 

Andrew Dientfrey, Paul Patrone (ACMD); Stephen 

Christensen, Andrea Browning, Sam Tucker (The Boeing Company) 
 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 21 

The Resilience of the Internet to Colluding Country Induced 

Connectivity Disruptions
 

The apparent robustness of Internet networking hides 

underlying weaknesses. In this work, we have revealed 

a class of such weaknesses in the form of colluding countries deliberately filtering out other countries. For this 

we have analyzed the scenario in which a group of countries disconnect two other countries, isolate a set of 

countries from the Internet, or break the Internet into 

non-communicative clusters. We find that despite the 

potential for these attacks, the Internet as a whole has 

become increasingly resilient over the period of examination from 2008 to 2013. However, the gains in 

robustness and resilience are primarily concentrated in 

well-connected countries, which form an extremely resilient core. Our study suggests that the less connected 

countries form new links largely with well-connected 

countries, and not to each other, maintaining the centrality of the well-connected countries in the paths 

between the less connected countries on the fringe. Because of this, the resilience of these less connected 

countries has not increased significantly over the time 

period studied. The result is that a small set of countries 

is able to isolate significant portions of the Internet or 

to divide it up into clusters. Individual well connected 

countries are often able to unilaterally isolate network 

dependent neighbors. These weaknesses could be addressed through a focus on establishing links between 

poorly connected countries. This would move the poorly 

connected countries away from dependence on the infrastructure of more highly connected countries. 

Assane Gueye 

The Internet was designed to be robust to disruption due 

to the failure of specific networks or routers [1]. However, events have empirically demonstrated that despite 

this design, single points of failure (e.g., the digging up 

of a fiber optic cable, or the cutting of a submarine line 

by a ship anchor) are capable of disconnecting entire 

countries from the rest of the internet [2]. In this study 

[3], we examine the capability for deliberate disruption 

or filtering enacted on inter-country network routes. In 

particular, we examine to what extent a group of colluding countries can disrupt Internet connectivity for other 

countries by evaluating three Internet connectivity security questions: 

17 http://www.caida.org/ 

18 http://www.routeviews.org/ 

1.	 Cutting Pairwise Communications: What is the 

minimal number of colluding countries required to 

prevent two other countries from communicating? 

2.	 Country Isolation: What is the maximal number of 

countries that can be cut off from the Internet by a 

group of colluding countries? 

3.	 Non-Communicative Clusters: Into how many noncommunicative clusters can a group of colluding 

countries divide the Internet? 

These questions are modeled as countries completely 

cutting off routes to other countries. While this certainly 

can be done, we use this approach to model a large class 

of attacks (possibly as yet undiscovered) whereby selective traffic along country-to-country routes may be 

maliciously handled. 

To evaluate these three questions, we created an interconnectivity map of the worldwide Internet routing 

infrastructure, aggregated at the level of individual 

countries. We did this by using data provided by the 

Cooperative Association for Internet Data Analysis 

(CAIDA)17. CAIDA has a worldwide monitoring network that provides an approximate topological map of 

the Internet at the Internet Protocol (IP) layer. It then 

uses the RouteViews18 Border Gateway Protocol (BGP) 

data to collapse the IP topology into a map of autonomous systems (ASs), approximately the set of Internet 

Service Providers. The worldwide monitoring network 

has a number of monitors that have evolved from 33 in 

2008 to 89 in 2013,19 with some being added, others retired, but with 24 monitors being active in all years. 

The collected data consists of AS connectivity from 

2008 to 2013 inclusive, with links between the ASs. In 

using the data, we first model all direct links as bidirectional since, for our experiments, we are concerned 

about the capability to transmit data as opposed to currently policy-based directionality of traffic flow. We 

then used the AS-to-country mappings to aggregate the 

AS nodes into country nodes where edges represent inter-country connectivity. This mapping assigns ASs to 

their country of registration despite the physical location 

of the ASs servers. One aspect of this approach that deserves special attention is the existence of multinational 

ASs (MOAs) which have points of presence (PoPs) 

within multiple countries and sometimes in different 

continents. For our work, we map MOAs to their home 

country (i.e., country of registration), which implies that 

a MOA is required to implement Internet filtering laws 

19 42 in 2009, 54 in 2010, 59 in 2011, and 65 in 2012 
 

 

 

 

 

 

 

 

 

 

 

22 NIST Applied and Computational Mathematics Division 

or government directives from their home country regardless of the physical location of the routers they own. 

The rationale for this approach comes from the legal literature: “the home country may also have laws that 

attempt to regulate business activities of the company 

that are conducted outside the home country” [4]. 

For each year, we generate two inter-country connectivity graphs. The first graph is created by using the 

information provided by all monitors for that year. This 

graph is useful for evaluating bounds on the resilience 

of a particular year. However, the addition of new monitors with new vantage points, as well as the retiring of 

old monitors, means that the visible portions of the routing graph vary significantly from year-to-year, 

independent of changes in the underlying routing graph 

itself. This makes it difficult to reliably compare the resilience between different years. To enable year to year 

comparisons, we generate a second graph by restricting 

the discovered routes to those visible to a set of 24 monitors that were active in all six years of our evaluation. 

As a result, we get two undirected graphs for each 

year. For each graph, the nodes represent the countries 

with presence in the CAIDA data and the links between 

two nodes represent a connection between an AS registered in the first country and an AS registered in the 

second. We then use graph theory tools to evaluate the 

three questions stated above. 

Cutting Pairwise Communications. The communications of two countries, s and t, are considered prevented 

or cut if the ASs registered to s cease having connectivity the ASs registered to t. To evaluate the cutting of 

pairwise communications, we iterate over all pairs of 

countries (s,t) that are not adjacent and determine the 

minimum, maximum, and mean node connectivity. The 

node connectivity calculation determines the minimum 

number of nodes required to disconnect the graph such 

that s and t end up in separate components. 

Country Isolation. A country is considered cut off 

from the Internet or isolated if the ASs registered to that 

particular country cease having connectivity to the largest remaining connected component of the global 

Internet. In the country isolation problem, we would 

like to know the maximal number of countries that can 

be cut off from the Internet (i.e., the largest remaining 

connected component) by a group of k colluding countries. For fixed k, this problem is known to be in general 

NP-hard [5]. As a consequence, we resort to heuristic 

algorithms to find approximate solutions. To evaluate 

country isolation, we iteratively increase the size k of the 

set of colluding countries and, at each iteration, use our 

heuristic algorithms to choose a specific set of country 

nodes that (approximately) maximizes the number of 

isolated countries. 

Non-Communicative Clusters. The Internet is considered to be broken into non-communicative pieces if the 

ASs registered to a group of countries are connected 

while being disconnected from the rest of the Internet. 

In our country graph, there will be multiple isolated 

clusters (possibly consisting of just single nodes) after 

removing the colluding nodes. In this non-communicative clusters problem, the goal of the colluding countries 

is to maximize the number of non-communicative clusters. This is similar to country isolation except that 

instead of optimizing on the number of isolated countries, the algorithms must optimize on the number of 

isolated clusters. We use the same set of algorithms to 

compute an approximate solution. As in the previous 

case, to evaluate non-communicative clusters, we iteratively increase the size k of the set of colluding countries 

and, at each iteration, we use our algorithms to choose a 

specific set of country nodes that maximizes the number 

of non-communicative clusters. 

The algorithms are iterative in nature and greedily 

exploit well-known features of the network. In the first 

one, we iteratively remove the node with the maximum 

degree in the remaining graph as well as all edges that 

are incident to it. In a second one, we iteratively remove 

the node whose deletion maximizes the number of noncommunicative clusters. In a third approach, we iteratively remove the nodes that bisect the current largest 

cluster in the most even way. For our empirical results, 

Figure 7. Mean Number of Collaborating Countries Needed to Disconnect a Pair of Countries. 

Figure 8. Improvement in Robustness: Comparing 2008 to 2013. 
 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 23 

each data point is analyzed by all approaches but only 

the result that best optimizes the relevant security question is kept. Thus, each presented curve in our analysis 

is made up of answers from all approachess, representing our best available approximation of the true NP-hard 

answer. 

Results. Overall, our experiments have shown that the 

Internet as a whole is becoming more resilient to colluding country induced connectivity disruptions. 

Considering cutting pairwise communications, the 

data shows that it is quite feasible for groups of colluding countries to block communications between pairs of 

countries, although this is becoming more difficult to 

implement over time. For all years and both data sets 

(the one using all monitors and the one using one the 24 

persistent monitors), the minimum pairwise connectivity was 1. This indicates that given the routes visible 

through the CAIDA dataset, there always exists some 

country that by itself can disconnect some other pair of 

countries. However, some non-adjacent pairs of countries are extremely hard to disconnect. As shown in 

Figure 7 on the “all data” line, in 2013 there were nonadjacent pairs of countries that required collusion between a minimum of 68 countries in order to disconnect 

them. Furthermore, the data from the set of persistent 

monitors shows an increasing trend over time. 

With regard to country isolation, we observe a linear increase in the number of isolated countries as the 

number of colluding countries increases from 1 to 

around 60. This is the case for both data sets for all 

years. However, the rate of increase diminishes over 

time indicating that the Internet has become more resilient over the years. This is shown in Figure 8 which 

compares years 2008 and 2013. Another way to see this 

improvement in robustness is to ask: how many colluding countries does it take to isolate a fraction of x % of 

the Internet? Figure 9 shows that over time, more countries need to collude in order to cut off the same fraction 

of countries from the Internet. However, these increases 

are for larger percentages of the countries. The “cost” 

of isolating just 10 % of the countries in the Internet is 

small and relatively stable. This indicates that the Internet is still sensitive to colluding attacks, and suggests 

that a fringe set of countries are not receiving the benefits of increased robustness. 

Finally, the analysis of the number of non-communicative clusters shows a linear increase in the number 

of clusters as more countries collude for each year and 

each data set. However, similar to the previous case, the 

rate of increase diminishes over time indicating that the 

Internet has become more resilient since 2008. This is 

confirmed with the plots of Figure 10 which shows the 

number of colluding countries needed to separate the 

network in differing numbers of connected components. 

With both data sets, the trend is that, over time, more 

countries are required to collude in order to separate the 

Figure 9. Number of Colluding Countries Needed to Isolate a 

Fraction x % of the Nodes as a Function of the Year. “A, 10 %” 

in the Legend, means that the plot is done using the entire data 

set, and the fraction of isolated nodes is 10 %; “P” indicates that 

only the persistent monitor data is used. 

Figure 10. Number of Colluding Countries Needed to Divide the 

Network into x Clusters as a Function of the Year. “A, 10” in the 

Legend, means that the plot is done using the entire data set and 

the number of clusters is 10; “P” indicates that only the persistent 

monitor data is used. 

Internet into some predetermined number of non-communicative clusters for approximately 25 clusters or 

more. For smaller isolated clusters, the number of required countries remains relatively constant. 

A point of commonality among these three findings 

is that they involve the smallest grouping of target countries in our experiment, where those countries were the 

least connected ones in the country-based AS graph. 

This suggests that, for these most vulnerable countries 

(that are most easily cut off from the Internet using the 

fewest colluding countries), their robustness has not noticeably increased over the time period of our analysis. 

This appears to be due to the fact that the majority of 
 

 

 

 

 

 

 

 

 

 

24 NIST Applied and Computational Mathematics Division 

Figure 11. Average Degree of Isolated Nodes per Year. “A, 10 %” 

in the Legend, means that the plot is done using the entire data set, 

and the fraction of isolated nodes is 10 %; “P” indicates that only 

the persistent monitor data is used. 

new edges observed in the country AS graph had at least 

one endpoint on a country that was already highly connected. This “rich get richer” phenomenon has been 

observed in other networks [6], and suggests that countries that cannot offer significant connectivity to 

potential partners will have difficulty obtaining sufficient communicating partners to ensure the robustness 

of their connectivity to the rest of the Internet. 

Figure 11 shows the average degree of the isolated 

nodes per year when some specific percentage of the 

countries in the Internet are being isolated. Note that, 

when just 10 % of the countries are isolated, the average 

degree of the isolated countries is less than 2. As the size 

of the set of isolated countries increases, the average degree of the isolated nodes also increases. In addition, 

while the degree of the isolated nodes for 10 % isolation 

appears relatively constant with respect to year, the degree increases sharply for later years when examining 

the isolation of 65 % of the nodes in the graph, supporting the hypotheses that the majority of new links are 

being formed to the most densely and robustly connected nodes. 

These weaknesses could be addressed through a focus on establishing links between poorly connected 

countries (e.g., through grants to poorer countries or 

through collaboration between coalitions of physically 

adjacent countries). This would move the poorly connected countries away from dependence on the 

infrastructure of the more highly connected countries. It 

would also move the Internet as a whole towards a more 

resilient architecture through the provision of alternate 

geographically diverse pathways. 

20 http://www.wired.co.uk/news/archive/2013-04/3/vulnerableundersea-cables 

Future Work. This study on the security of country 

connectivity graphs is the first of its kind and thus a large 

amount of related work remains to be explored. Most if 

not all of the data needed is already publicly available 

from the CAIDA data sets. One could model all the 

PoPs on the Internet and their connectivity and analyze 

how an attacker could take out sets of PoPs to damage 

the Internet. Another approach could be, instead of mapping ASs to their country of registration, to map the 

PoPs underlying the ASs to the countries in which they 

physically reside. This would enable one to model countries nationalizing the Internet infrastructure within their 

physical boundaries to see what harm could be done. An 

alternative approach could be to rerun our experiments 

without modeling all edges as bidirectional. This would 

show the amount of damage colluding countries could 

do prior to any possible policy changes implemented by 

the ASs. Lastly, one could look at specific geographic 

regions comprising poorer countries to evaluate ways to 

improve their Internet resilience, as in [7]. 

References 

[1]	 W. Willinger and J. Doyle, Robustness and the Internet: 

Design and Evolution, Chapter 10 in Robust Design, a 

Repertoire of Biological, Ecological, and Engineering 

Case Studies (E. Jen, ed.), Oxford University Press, 

2005. 

[2]	 A. Chang, Undersea Cables Are Actually More 

Vulnerable Than You Might Think20, Wired, April 3, 

2013. 

[3]	 P. Mell, R. Harang and A. Gueye, The Resilience of the 

Internet to Colluding Country Induced Connectivity 

Disruptions, in Proceedings of the Workshop on Security of Emerging Networking Technologies (SENT), San 

Diego CA, February 8, 2015. 

[4]	 J. Hawkinson, Guidelines for Creation, Selection, and 

Registration of an Autonomous System (AS)21, Internet 

Engineering Task Force, RFC 1930, March 1996. 

[5]	 T. Bui and C. Jones, Finding Good Approximate Vertex 

and Edge Partitions is NP-hard, Information Processing 

Letters 42:3 (1992), 153-159. 

[6]	 A.-L. Barabási and R. Albert, Emergence of Scaling in 

Random Networks, Science 286:5439 (1999), 509-512. 

[7]	 A. Gueye, P. Mell, D. Banse and Y. Congo, On the 

Internet Connectivity on Africa, in Proceedings of the 

7th EAI International Conference on e‐Infrastructure 

and e‐Services for Developing Countries, Cotonou, 

Benin, December 15-16, 2015. 

Participants 

Assane Gueye, Peter Mell (NIST ITL), Richard Harang 

(Army Research Laboratory) 

21 http://tools.ietf.org/html/rfc1930 
Part III: Project Summaries 

Summary of Activities for Fiscal Year 2015 25

Part III 

Project Summaries 
 

26 NIST Applied and Computational Mathematics Division 
 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 27 

Mathematics of Metrology 

Mathematics plays an important role in the science of metrology. Mathematical models are needed to understand how to design effective measurement systems, and to analyze the results they produce. Mathematical 

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

mathematical algorithms are necessary to find optimal system parameters. Finally, mathematical and statistical techniques are needed to transform measured data into useful information. The goal of this work is to 

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

Computational Tools for Shape 

Measurement and Analysis 

Günay Doğan 

Javier Bernal 

Charles R. Hagwood (NIST ITL) 

The main goal of this project is to develop efficient and 

reliable computational tools to detect geometric 

structures, such as curves, regions and boundaries, from 

given direct and indirect measurements, e.g., 

microscope images or tomographic measurements, as 

well as to evaluate and compare these geometric 

structures or shapes in a quantitative manner. This is 

important in many areas of science and engineering, 

where the practitioners obtain their data as images, and 

would like to detect and analyze the objects in the data. 

Examples are microscopy images for cell biology or 

micro-CT (computed tomography) images of 

microstructures in material science. In Fiscal Year (FY) 

2015, we made advances in the following specific 

components of this project. 

Shape energies for image segmentation. Image 

segmentation is the problem of identifying objects or 

regions and their boundaries in given images. Our 

approach to segmentation is to design shape energies 

incorporating image data and shape regularity criteria 

modeling specific segmentation scenarios. The shape, a 

curve or a surface, is the free variable in these energies, 

and we aim to compute optimal shapes minimizing these 

energies. In this approach, we start with suboptimal 

initial curves, and iteratively deform them towards the 

right object boundaries in the images (see Figure 12 for 

an example). Günay Doğan has been implementing, and 

continued to develop a selection of shape energies 

effective for image segmentation. These are: 

1. The Geodesic Active Contour model, used to detect 

region boundaries characterized by high image 

gradients (see [1]); 

2. A region-based multiphase segmentation shape 

energy (see [2]), which can decompose the image 

into homogeneous regions each defined with a 

distinct mean intensity value (a common scenario in 

material microstructures); and 

3. An anisotropic boundary energy, which improves 

detection of concave regions by aligning curve 

normals with extended image gradient fields. 

Faster shape optimization. Realizing the iterative 

shape optimization solution for the segmentation in an 

effective manner requires a well-thought design and 

integration of multiple critical ingredients. A central 

piece is the discretization of the shape, ensuring good 

resolution of data and geometry without too much 

computational overhead. To reduce computational cost, 

we also need to reduce the number of iterations needed 

to reach optima. For this, Günay Doğan has been 

developing shape-Newton algorithms and customized 

stopping criteria, and his recent work demonstrating the 

efficiency gains for the multiphase segmentation energy 

was published in [3]. He has also been working with 

researchers from George Mason University to leverage 

coarse-to-fine discretizations to further reduce 

computational cost, and to increase likelihood of finding 

global minima. 

Automation of image segmentation. Many users of our 

segmentation software are not expected to have a 

background or experience in image processing. 

Therefore, it is very important to make the segmentation 

algorithms as automated as possible for these users. 

Realistically, almost all algorithms solving any 

significant data problems require some, and possibly 

many, parameters to be set, typically by a domain expert. 

For example, a traditional implementation of the 

Geodesic Active Contour model requires an edge 

indicator function to be defined from the image by 

setting a smoothing parameter and an edge contrast 

parameter. The edge indicator function is integrated over 

a curve to define the shape energy, and the energy may 

not work out if good parameter values are not used in 

the definition. Then the shape energy is minimized by 

taking a specified number of steps at specified step sizes, 

requiring two more parameters governing the iterations, 

and depending on their values, the iterations may take 

too long or terminate prematurely. There are additional 

parameters in the discretization of the geometry and 

related differential geometry as well. One can easily see 
 

 

 

 

 

 

 

 

28 NIST Applied and Computational Mathematics Division 

Figure 12. Example of the energy (denoted J at iteration k) minimization process used to detect objects by iteratively deforming curves, shown 

in the top two rows. The bottom row shows detected boundaries (red) in different images, starting from different initial curves (blue, yellow, 

magenta). 

that it is too much to expect of a user, a material scientist, 

for example, to make good choices under varying 

imaging scenarios without expert help. For this reason, 

Günay Doğan has been developing heuristics and 

algorithmic principles to set such parameters 

automatically in the shape energies and the shape 

optimization procedures. 

Meshing segmented images. An important use of our 

segmentation algorithms is for analysis of material 

microstructure images with the finite element software 

OOF (see page 46). This requires a computational mesh 

capturing the geometric features of the microstructure, 

based on its segmentation. We have previously 

developed a meshing algorithm that extracts the grain 

boundaries from a segmented image, and returns a 

triangulation matching these boundaries. We improved 

this algorithm by developing smoothing and coarsening 

algorithms for the boundaries. This results in more 

natural-looking and compact boundary curves. We then 

use it to generate high-quality triangulations with fewer 

elements than the previous version of the algorithm. 

Computing shape distances. We have been working 

with Javier Bernal and Charles Hagwood to develop 

efficient numerical algorithms to compute an elastic 

shape distance (dissimilarity score) between 2D shapes. 

Our shape distance algorithm resulted in up to two 

orders of magnitude speed gains for large curves, due to 

its subquadratic running times (in contrast with the cubic 

asymptotic complexity of the original elastic shape 

distance algorithm). We have recently developed a fast 

curve alignment algorithm that runs in O(N log N) time 

(down from quadratic time complexity), further 

improving the efficiency of our shape distance 

algorithm. Details of this work are described in a 

separate section on computation of shape distances. 

[1]	 V. Caselles, R. Kimmel, G. Sapiro, Geodesic Active 

Contours, in International Journal of Computer Vision 

22:1 (1997), 61-79. 

[2]	 G. Doğan, An Efficient Curve Evolution Algorithm for 

Multiphase Image Segmentation, in Proceedings of the 

10th International Conference on Energy Minimization 

Methods in Computer Vision and Pattern Recognition 

(EMMCVPR’15), Hong Kong, January 2015. 

[3]	 G. Doğan, An Efficient Curve Evolution Algorithm for 

Multiphase Image Segmentation, in Proceedings of the 

5th International Conference on Scale Space and 

Variational Methods in Computer Vision (SSVM’15), 

Bordeaux, France, May 2015. 
 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 29 

Computation of Shape Distances 

Günay Doğan 

Javier Bernal 

Charles R. Hagwood (NIST ITL) 

In many engineering and scientific applications, experts 

are interested in comparing shapes of objects quantitatively, making inferences based on the shape similarity 

or dissimilarity. Examples of such applications are morphological analysis of cells or cell colonies in biology, 

and object recognition in computer vision. Often such 

applications involve large data sets, and this motivates 

the need for fast shape analysis algorithms. 

The shape of an object is unlike typical data descriptors, such as feature 

vectors, or matrices. These are finite-dimensional quantities, which exist in 

simple vector spaces, whereas mathematical shapes are abstract entities existing on 

infinite-dimensional Riemannian manifolds. This introduces challenges in both 

the representation of shapes and computation of shape dissimilarities or shape 

distances for statistical analyses. 

In this work, we have been developing 

fast algorithms to compute elastic shape 

distances between given 2D closed curves, 

based on the square root velocity function 

(SRVF) formalism of Srivastava et al. [1]. 

The resulting elastic shape distance is a 

useful shape dissimilarity metric that 

matches our intuitive understanding of 

shapes. It is invariant to scaling, rotation Matrix Size Prev. Algo. New Algo and translation, and it is robust to moderate Synthetic (Sy) 6×6 = 36 1 h 12 min changes in local features of the shapes. Cells (CA&CB) 10×10 = 100 2.5 h 4.5 min However, it is computationally very ex- Leaves (Lf) 75×75 = 5625 129 h 12.5 h pensive. The original algorithm in [1] has MPEG7 (M7) 100×100 = 104 240 h 38.5 h 

cubic asymptotic time complexity with respect to N, the number of the curve nodes, Figure 13. An order of magnitude in speed-up by our new algorithm computing pairwise shape distance matrices for different shape data sets for N=256. and slows down considerably when N is 

More recently, we improved the efficiency of our 

algorithm even further. We developed a fast alignment 

algorithm for closed curves, matching their starting 

points and rotation angles in O(N log N) time using the 

Fast Fourier Transform, as opposed to the naïve algorithm with quadratic time complexity [3]. 

We are currently working on the dynamic programming component of our algorithm. Although this 

algorithm is very fast in practice, its asymptotic time 

complexity is quadratic. Our preliminary results show 

that we will be able to reduce this to linear time complexity. This will enable us to handle very large curves 

without performance degradation, making it very suitable for large-scale shape statistics studies. 

increased beyond a few hundreds. 

The main challenge of this computation is to minimize a mismatch energy so as to optimally 

match the SRVF representations of two given curves. 

The variables of this minimization are the rotation angle 

and the starting point for optimal alignment of the curve 

shapes, and a reparameterization function defined on the 

curve to enable elastic matching of curve features. Previously, we developed an iterative optimization 

algorithm that performed this minimization in subquadratic running times; see Figure 13 which demonstrates 

the speed gains by our algorithm. The key ingredients of 

this algorithm were our fast dynamic programming and 

nonlinear constrained optimization procedures. We presented this algorithm in the premier computer vision 

conference CVPR’15 [2]. 

[1]	 Srivastava, E. Klassen, S. Joshi and I. Jermyn, Shape 

analysis of elastic curves in Euclidean space, IEEE Transactions on Pattern Analysis and Machine Intelligence 

33:7 (2011) 1415-1428. 

[2]	 G. Doğan, J. Bernal and C. R. Hagwood, A Fast Algorithm for Elastic Shape Distances between Closed Planar 

Curves, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR’15), 

Boston, MA, June 2015. 

[3]	 G. Doğan, J. Bernal and C. R. Hagwood, FFT-based 

Alignment of 2d Closed Curves with Application to Elastic Shape Analysis, in Proceedings of the 1st 

International Workshop on Differential Geometry in 

Computer Vision for Analysis of Shapes, Images and Trajectories (DiffCV’15), Swansea, United Kingdom, 

September 2015. 
 

 

 

 

 

 

30 NIST Applied and Computational Mathematics Division 

Figure 14. Useful enhancement of nanoscale SEM image using technique discussed in References [1] and [2]. 

Enhancement of Nanoscale Scanning 

Electron Microscope Imagery 

Alfred S. Carasso 

Andras E. Vladar (NIST PML) 

A recently discovered powerful technique for enhancing 

Helium Ion Microscope (HIM) imagery [1], involves an 

initial adaptive histogram equalization of the image, followed by progressive Lévy fractional diffusion 

smoothing. This particular two stage method had previously been developed for enhancements of forensic 

latent fingerprints [2]. Interactive Data Language (IDL) 

software is provided in [1] that can implement this 

method. Surprisingly, this approach is usually not helpful in a wide variety of commonly occurring images, 

such as face images, astronomical images, or medical 

images. However, the method has recently been found 

useful on certain types of scanning electron microscope 

(SEM) images as illustrated in Figure 14. 

This development is highly significant in nanoscale 

microscopy, as there is now considerable interest in low 

dose, low landing energy SEM imaging, which typically 

produces very noisy images. Useful enhancement of 

such imagery may now be feasible using the above NIST 

technique. 

[1]	 A. S. Carasso and A. E. Vladar, Recovery of Background 

Structures in Nanoscale Helium Ion Microscope Imaging, 

Journal of Research of the NIST 119 (2014), 683-701. 

22 JILA is a joint physics institute of the University of Colorado at 

Boulder and NIST. See https://jila.colorado.edu/ 

[2]	 A. S. Carasso, A Framework for Reproducible Latent 

Fingerprint Enhancements, Journal of Research of the 

NIST 119 (2014), 212-226. 

Molecular Movies: Imaging 

Femtosecond Motion during 

Electrochemical Transitions 

Bradley Alpert 

Joel Ullom (NIST PML) 

Chris Cromer (NIST PML) 

Ralph Jimenez (NIST PML)
 

Vital to the development of next-generation nanomaterials, including photovoltaics and industrial catalysts, is 

an understanding gained through measurement of electron release, transport, and transfer in engineered 

nanostructures. This project, completed this year after 

five years of support by a NIST Innovations in Measurement Science (IMS) grant, achieved the first timeresolved x-ray emission and time-resolved x-ray absorption measurements with a table-top laboratory set-up. 

The apparatus enables experiments 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 JILA22, with 
 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 31 

transition-edge sensor (TES) microcalorimeter spectroscopy, intensively developed and refined in the Quantum 

Electronics and Photonics Division, enables these new 

measurement capabilities. The integration of these components, accompanied by a significant increase in 

detector array sizes, to achieve large increases in temporal and spatial resolution while maintaining 

extraordinary TES energy resolution, continues to demand new data modeling and processing techniques. 

These techniques will overcome current limitations by 

 resolving temporal overlap in photon detection while 

achieving energy resolution of temporally isolated 

arrivals, 

 improving efficiency in elimination of low-frequency background noise, and 

 extending multiplexing and reducing cross talk in extracting the signals from 0.1 K to room temperatures. 

Wiener filtering, long used among astronomers for estimating amplitudes of pulses of known shape 

contaminated with noise of known frequency content, is 

suitable for measuring isolated pulses. Novel processing approaches have been developed, characterized, 

and are being extended, that rely on this knowledge but 

are suitable for overlapping pulses. 

Analysis efforts this year (1) successfully completed development of a processing method, dubbed 

multi-pulse fitting, applicable when pulses are poorly 

separated in time but small enough to allow neglect of 

detector response nonlinearity, and (2) achieved initial 

success in treating nonlinear detector response by a 

modified method of independent component analysis 

(ICA), which exploits entropy minimization. 

Multi-pulse fitting relies on a linear detector response model in which the signal is a superposition of 

pulses of a single shape and various amplitudes, noise 

coloring (i.e., its frequency dependence) is corrected, 

and by a pulse-height to photon energy calibration curve 

that corrects for deficiencies of this model. This method 

performs quite well, with low pulse rejection and low 

deterioration in energy resolution with increasing pulse 

rate, up to about 100 counts per second per detector, provided photon energies are a modest fraction of the level 

that saturates the detector. 

Detector nonlinear response, significant at higher 

photon rates and at energies approaching those that saturate the detectors, remains a challenge, but promising 

results have been achieved by detector characterization 

through minimization of the entropy of a measured spectrum. This approach uses a calibration source with 

highly localized spectral features, often present in spectra of interest, to establish calibration curves that 

separate the effect of detector residual energy from energy of a new arrival. The method, based on information 

theory, is under active development. 

[1] J. W. Fowler, B. K. Alpert, W. B. Doriese, D. A. Fischer, 

C. Jaye, Y. I. Joe. G. C. O’Neil and D. S. Swetz, J. N. 

Ullom, Microcalorimeter Spectroscopy at High Pulse 

Rates: a Multi-Pulse Fitting Technique, Astrophysical 

Journal Supplement Series 219 (2015), 35. 

[2] J. W. Fowler, B. K. Alpert, W. B. Doriese, Y. I. Joe, G. 

C. O’Neil, J. N. Ullom and D.S. Swetz, The Practice of 

Pulse Processing, Journal of Low Temperature Physics, 

to appear. 

A Thousand-Fold Performance Leap 

in Ultrasensitive Cryogenic Detectors 

Bradley Alpert 

Joel Ullom (NIST PML) 

Lawrence Hudson (NIST PML) 

Terrence Jach (NIST MML) 

Small arrays of ultrasensitive cryogenic detectors invented and developed at NIST have driven 

breakthroughs in x-ray materials analysis, nuclear forensics, and astrophysics. They have played a part in 

prominent international science collaborations in recent 

years. Despite these successes, NIST’s existing cryogenic sensor technology is inadequate for new 

applications such as in-line industrial materials analysis, 

energy resolved x-ray imaging, and next-generation astrophysics experiments, which all require faster sensors, 

much larger arrays, or both. Last year, new support from 

the NIST Innovations in Measurement Science (IMS) 

was awarded to develop both of these capabilities in pursuit of 1000-fold increase in sensor throughput, through 

completely new sensor readout technique (microwave 

multiplexer) enabling much larger detector arrays and 

through major new, higher throughput, processing capabilities. 

A major project connected to the NIST IMS effort 

is HOLMES [1], now underway in Italy to measure the 

mass of the electron neutrino. This experiment, which 

will use NIST-developed microcalorimeters, superconducting quantum interference device (SQUID) 

amplifiers, and microwave multiplexer readout, relies 

on extreme statistics for the spectrum produced by the 

decay of 163Ho. A principal source of error for microcalorimeter characterization of this spectrum is expected 

to be due to undetected near-simultaneous 163Ho decay 

events (pile-ups). Improvements in processing that 

would allow better detection of nearly coincident pulse 

pairs could radically alter the design space for the detectors of the experiment. 

Alpert this year conducted simulations and developed a novel pile-up detection algorithm using NIST 

detector response models [2], that convinced the Italian 

team, led by Angelo Nucciotti, to consider a region of 

the detector design space (for a slower pulse rise) previously believed unusable for HOLMES. The resulting 

detectors will have reduced pulse rise (or arrival time) 
 

 

 

 

 

32 NIST Applied and Computational Mathematics Division 

distortion and the readout electronics specifications will 

be less extreme, enabling arrays containing more detectors and therefore potentially higher statistics and more 

precise characterization of the neutrino mass. 

[1] B. Alpert, M. Balata, D. Bennett, M. Biasotti, C. Boragno, 

C. Brofferio, V. Ceriale, D. Corsini, P.K. Day, M. De 

Gerone, R. Dressler, M. Faverzani, E. Ferri, J. Fowler, F. 

Gatti, A. Giachero, J. Hays-Wehle, S. Heinitz, G. Hilton, 

U. Kőster, M. Lusignoli, M. Maino, J. Mates, S. Nisi, R. 

Nizzolo, A. Nucciotti, G. Pessina, G. Pizzigoni, A. Puiu, 

S. Ragazzi, C. Reintsema, M. Ribeiro-Gomes, D. 

Schmidt, D. Schumann, M. Sisti, D. Swetz, F. Terranova 

and J. Ullom, HOLMES: The Electron Capture Decay of 

163Ho to Measure the Neutrino Mass with sub-eV Sensitivity, European Physics Journal C 75:3 (2015), 112. 

[2] B. Alpert, E. Ferri, D. Bennett, M. Faverzani, J. Fowler, 

A. Giachero, J. Hays-Wehle, M. Maino, A. Nucciotti, A. 

Puiu, D. Swetz and J. Ullom, Algorithms for Identification of Nearly-Coincident Events in Calorimetric 

Sensors, Journal of Low Temperature Physics, to appear. 

Clutter Measurements Pilot Project: 

Toward Evaluating Communications 

Spectrum Sharing Proposals 

Bradley Alpert 

Chriss Hammerschmidt (NTIA) 

Robert Johnk (NTIA) 

Sarah Streett (NIST ITL)
 

Jack Wang (NIST ITL)
 

The joint NIST-NTIA Center for Advanced Communications (CAC) and the NIST Communications 

Technology Laboratory (CTL) will develop the scientific and engineering capacity and experience for 

technical assessment of spectrum sharing and commercialization proposals. Components of this expertise are 

already present in the NIST Electromagnetics Division, 

Physical Measurement Laboratory, the DOC Public 

Safety Communications Research (PSCR), National 

Telecommunications and Information Administration 

(NTIA), and their collaborative research relationships in 

measurement and modeling within NIST and NTIA. 

Kent Rochford, who leads CAC and CTL, suggested in April, 2014, that the researchers (listed above) 

begin a collaboration to form an initial research bridge 

between NIST and NTIA. Following a successful effort 

by Alpert and Wang for preliminary assessment of the 

uncertainty of in-building Long Term Evolution (LTE) 

cell phone path-loss surveys by Johnk, presented by 

Johnk at the PSCR Public Safety Broadband Stakeholder Conference, June, 2014, NTIA Institute for 

Telecommunication Sciences (ITS) lead Hammerschmidt proposed a one-year pilot project to assess 

communications disruption due to environmental clutter 

(buildings, vegetation, power lines, etc.). Its objectives 

have been (1) collect representative clutter measurement 

data in support of ongoing rulemakings such as the 3.5 

GHz Joint Working Group, (2) perform statistical analysis on these data and determine uncertainties, (3) refine 

the measurement methods in preparation for a comprehensive data collection program, and (4) provide 

measurement data to support refinement of existing 

propagation models. 

Lack of experience of the researchers in evaluating 

uncertainties of communications channel losses, including those due to clutter, has prompted a flurry of initial 

activity to establish the project’s direction. In particular, 

early surveys have suffered from (1) lack of repeatability due to position uncertainty and limited comparability 

between nominally identical surveys, (2) large discrepancy, even in uncluttered areas, between path loss 

surveys and those expected from the ITS Irregular Terrain Model (ITM) of path loss, and (3) lack of a survey 

of environmental clutter, to serve as a potential independent, predictive variable. 

Several field surveys, around Boulder, in Denver, 

and in San Diego were conducted by the ITS researchers 

during the past year. The NIST team evaluated the procedures and made recommendations toward isolating 

different sources of variability and causes of discrepancy between path losses predicted by the ITM and 

those observed in the surveys. These sources include 

precise receiving antenna location and velocity, detailed 

terrain and obstacle shapes as obtained through LiDAR 

and other surveys, moving scatterers, transmitting and 

receiving antenna characterization, and temperature, humidity, and time of day factors. More work is needed to 

demonstrate consistent, repeatable surveys, develop 

more reliable propagation models, and enable predictions with characterized uncertainty. 

A report for the pilot project is in preparation. 

Quantitative MRI 

Zydrunas Gimbutas
 

Andrew Dienstfrey 

Stephen Russek (NIST PML)
 

Katy Keenan (NIST PML)
 

Karl Stupic (NIST PML)
 

Michael Boss (NIST PML)
 

Magnetic resonance imaging (MRI) is maturing as a 

quantitative biomedical imaging technology. For example, imaging facilities routinely report tumor volumes in 

units of mm3

, blood perfusion in units of ml g−1 min−1, 

apparent diffusion coefficient in mm2 s−1

, and temperature in K. However, as of a few years ago the use of 

International System (SI) units for these technologies 

was potentially unwarranted as SI traceability chains 
 

 

 																						

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 33 

signal. Sequences of RF pulses, distinguished with respect to timing, duration, and orientation, have the effect 

of emphasizing distinct terms in the Bloch-Torrey equations. Thus, the MR community speaks of weighted 

, and diffusion-weighted images. ܶଶ , ܶଵ images such as 

Our goal is to transform this qualitative, pictorial understanding into a quantitative analysis returning in vivo, 

volumetric parameter maps, traceable to the SI units. 

Restricting attention to quantitative ܶଶ analysis, a 

specifically designed sequence of RF pulses is delivered 

such that the signal in each voxel may be modeled as a 

simple exponential decay, 

௧ ݏሺr, ݐሻ ൌ ܥexp ቀെ ்మሺrሻ

ቁ.

 array is shown in A series of MR scans of the NIST ܶଶ

ሺ1ሻ

Figure 16. Each sphere in this array is filled with a prescribed concentration of MnCl2 solution resulting in a 

. The grayscale values repre- nominal true value of ܶଶ

Figure 15. NIST-Developed MR system phantom. In addition to senting MR signal intensity should obey the exponential 

geometry, biomedical quantities such as proton density, T1(r), and model (1) with the addition of measurement noise. Re­ T2(r) are defined and characterized by independent means. How cently ACMD staff wrote a computer code to perform accurate are MR-based measurements of these quantities in re- the non-linear inversion which takes noisy samples of 

ሺrሻ. Further- ܶଶ (1) as input, and returns an estimate of 

search and clinical settings? 

supporting these MRI measurement modalities were unclear if not non-existent. More recently NIST and 

partner institutions have made substantial investments to 

develop such traceability chains. In the medical community, standard reference artifacts are referred to as 

more, an uncertainty estimate is derived from a 

parametric bootstrap, Monte Carlo analysis. This Monte 

Carlo uncertainty analysis was found to be within a reasonable factor of the lower-bounds on uncertainty 

determined by unbiased, Cramer-Rao theory. Prelimiphantoms and, in particular, NIST now supports several 

phantoms providing SI-traceable calibration standards 

for MRI scanners. One such phantom is shown in Figure 

nary results are promising, demonstrating the ability to

quantify ܶଶ using the NIST MR scanner with relative expanded uncertainties ranging from 10 % – 20 %. Further 

attempts to reduce this uncertainty revealed systematic 15.
 intensity signals that were not noticed previously in this MRI is governed by solutions to the Bloch-Torrey experiment. We are currently performing further studies equation to identify the sources of these signals. 

 analysis workflow is being developed as a ݀M ܯ௫x This ܶଶ ൌ γM ൈ B െ ݀ݐ

Here, the quantities of medical interest are the tissue-de­

ො ൅ ܯ௬yො

ܶଶ

൅ ሺܯ ଴െ ܯ௭ሻzො

ܶଵ

൅ ׏ܦଶM paradigm for a large, cross-site, multi-modal quantitative MRI phantom study being conducted by NIST in 

collaboration with several external stakeholders. In this 

and the effective ܶଶ , pendent relaxation times ܶଵ

diffusion coefficient ܦ which reflects a combination of 

tissue porosity and anatomical structure. B is the forcing 

magnetization which is further resolved as a sum of gradient and radio-frequency (RF) terms. Finally, the 

study, NIST-designed phantoms are being circulated 

and imaged using tightly prescribed scanning protocols. 

The quantities to be analyzed include: ܶଵ, ܶଶ, proton

density, 3D geometric distortion, geometric resolution, 

and slice profile. Currently there is inadequate undergyromagnetic ratio, γ, is a physical constant and M is the 

magnetic moment arising from collections of nuclear 

standing of the degree to which these quantities can be 

spins. 

measured in clinical MR settings independent of variaBroadly speaking, a magnetic resonance measurebility in location, time, and scanner device. Stable 

ment consists of a preparation stage in which M is 

recovery in the presence of such variables is critical for 

preferentially aligned along a fixed axis. This is follongitudinal studies necessary to provide new quantitalowed by a sequence of RF pulses, represented in the B 

tive foundations for diagnosis, treatment, and long-term 

term above, which rotate M by nominal amounts followmonitoring of a variety of medical conditions such as 

Alzheimer’s, traumatic brain injury, and stroke. We will 

ing the dynamics of the Bloch-Torrey equations. 

Ultimately, the component of M lying transverse to a reinitiate detailed analysis of the round robin study in 

ceiver coil is detected as the primary measurement 

2016. External collaborators include the Department of 

Veterans Affairs, the National Institutes of Health, and 
 

 

 

 

34 NIST Applied and Computational Mathematics Division 

Figure 16. MR scan of NIST T2 array. Each sphere is loaded with MnCl2 solution of different concentrations resulting in a known collection of 

true T2 values. The signal intensity progresses from light to dark following an exponential decay law as in Equation 1. 

a standards subcommittee of the International Society of 

Magnetic Resonance in Medicine, which in turn, contains several academic centers as members. We hope to 

report on this work in the coming year. 

[1]	 H.-L. Cheng, et al., Practical Medical Applications of 

Quantitative MR Relaxometry, Journal of Magnetic Resonance Imaging (2012) 36, 805-824. 

Uncertainty Calculations for 

Building Engineering 

Anthony Kearsley 

Lisa Ng (NIST EL) 

Andy Persily (NIST EL)
 

Calculating flow within confined building spaces is an 

important problem. Unhealthy flow can jeopardize human health and welfare, and may even lead to mortality 

and extreme cases. Flow simulation and modeling is also 

particularly crucial when energy efficiency is a focus of 

building specifications. Such is the case with the Netzero house built here at NIST. 

One important flow calculation involves, essentially, balancing flow from different zones within the 

house, and doing so based on measured quantities, and 

therefore uncertainties. The problem can be formulated 

in terms of tracer analysis where a tracer injection, say 

G, at some instance in time is measured, which gives rise 

to a concentration response, call it C, and a change in 

concentration as a function of time, say C ́. These three 

quantities associated with a collection of zones measured at some instant in time determine an instantaneous 

data set. Given n zones, the data set (C, C ́, G) are three 

n × n matrices. In this case, an energy balance is sought 

such that our matching variables, say W, should have 

row sums that vanish. In practice, one may want to impose simple bounds on the elements wij of W. Taken 

together a solution to 

C WT = T 

is sought, where T is the tracer rate matrix, a sum of 

tracer injection G and an injection correction accumulation term, k C ́, where k is a constant zone specific 

constant. Loosely speaking, T is a matrix of tracer rates. 

This problem is further complicated in that a solution W 

is sought that (approximately) solves the equation above 

(and satisfies constraints not specified here) but is also 

subject to measurement errors. In short, an approximate 

solution W and estimated uncertainties are needed. 

This year we managed to solve the above equation 

with small uncertainties associated with each of the 

measurements. We did so by solving a constrained output-least-squares formulation of the problem together 

with an augmented Lagrangian technique to impose the 

constraints, mostly simple bounds. A local Newtonmethod was formulated and employed to estimate worst 

case estimates and were found to be within the domain 

of validity. 
 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 35 

Simulation and Optimization in 

Cryobiology 

Anthony Kearsley
 

Daniel Anderson (George Mason University)
 

James Benson (Northern Illinois University) 

Mathematical modeling is playing an ever increasing 

role in the understanding cells, tissues, and organs undergoing cryopreservation. The frequency and variety of 

uses of these models is increasing almost daily. Cryopreservation procedures permit cells to be stored 

indefinitely using extremely cold temperatures to suspend all metabolic activities. Cryoprotectants are the 

chemical foundation of cryobiology as they 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 oC. 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), and structural complexity change the freezing procedures employed. For 

example, cells with less cytoplasm, like sperm cells, are 

generally considered to be less difficult to freeze than 

those cells with more cytoplasm, like eggs. Slow freezing or equilibration has been successfully employed to 

freeze and store a wide range cells but research is ongoing to optimize the cryobiology of cells. 

In a series of recent review papers, [1-3] we have 

examined from first principles the thermal transport, 

mass transport and solidification processes of an externally-cooled ternary mixture that surrounds a biological 

cell. We have established a thermodynamic framework 

suitable for cryobiological applications through the 

identification of various forms for the Gibbs Free Energy for chemical systems and forms for chemical 

potential gradients used in the definition of chemical 

fluxes and also reviewed choices for chemical composition variables. We have developed the bulk transport 

models as well as their coupling to both phase-change 

(solidification) boundaries and the semi-permeable cell 

membrane; detailed equations in the bulk and at the 

boundaries were given for multi-species systems. We 

have conducted a thorough study of the partial differential equations and coupled boundary conditions specific 

for a spherical cell geometry surrounded by a ternary solution. Solutions to this free-boundary problem were 

compared to related models in cryobiology that assume 

spatial uniformity of thermal and chemical fields in the 

cell and surrounding fluid. One of our more complicated 

models adds a solidification front encroaching upon the 

cell and effects generated by the associated confinement 

of the fluid and cell. To our knowledge we are the first 

to study this scenario. Our future work [4] seeks to describe the solution strategies and numerical methods for 

this multiple free-boundary problem as well as related 

control problems. 

[1]	 D. M. Anderson, J. D. Benson and A. J. Kearsley, Foundations of Modeling in Cryobiology—I: Concentration, 

Gibbs Energy, and Chemical Potential Relationships, 

Cryobiology 69 (2014) 349–360. 

[2]	 D. M. Anderson, J. D. Benson and A. J. Kearsley, Foundations of Modeling in Cryobiology—II: Heat and Mass 

Transport in Bulk and at Cell Membrane and Ice-Liquid 

Interfaces, in preparation. 

[3]	 D. M. Anderson, J. D. Benson and A. J. Kearsley, Foundations of Modeling in Cryobiology—III: Heat and Mass 

Transport in a Ternary System, in preparation. 

[4]	 D. M. Anderson, J. D. Benson and A. J. Kearsley, Numerical Solution of Inward Solidification of a Dilute 

Ternary Solution towards a Semi-Permeable Spherical 

Cell, in preparation. 

Stochastic Regression in 

Chemometrics 

Anthony Kearsley 

John Curry (NIST PML)
 

William Wallace (NIST MML) 

Stochastic differential equations (SDE) can be used to 

model complex phenomenon including modelling noise 

in chemometrics spectroscopy. Previously our research 

demonstrated that a stochastic regression model can be 

used to successfully separate signal from noise in very 

important chemical spectra (arising in forensics, health 

science, etc.). Spectra can be decomposed into additive 

contributions from signal and from estimated noise. 

With an eye towards developing this mathematical machinery into a method for analyzing patterns in chemical 

spectra we investigated the mean-square stability of a 

stochastic differential equation developed specifically to 

predict a decomposition of chemical spectra into noise 

and signal. Making an assumption of multiplicative 

noise, we observed fascinating numerical behavior that 

suggests that the stochastic regression suggested earlier 

[1] may be even more effective at identifying spectral 

structure than previously expected. 

If one considers a traditional θ-method applied to a 

deterministic problem, it was shown by Saito and Mitsui 

[2] that the deterministic A-stability property of the θmethod does not carry through to the mean-square context in general. In fact, they rigorously demonstrated a 

condition under which unconditional stability holds. 

This suggests an identifiable point which one can compute precisely where unconditional stability is lost. This 

can be thought of as an A(α) stability result. 
 

 

 

 

 

 

 

 

 

36 NIST Applied and Computational Mathematics Division 

We sought to use this result to determine in our stochastic regression where the ratio of noise and signal 

coefficients actually loose stability. Intuition suggests 

that these points would indicate structures of interest, 

say a peak, a trough or an inflection point. A few differences exist between our work in [1] and the more general 

work (e.g., [3]). We regress on the variation in a signal, 

not the actual signal position. Secondly, we have a linear 

deterministic term not present in the standard SDE 

model. We have identified very promising but perplexing numerical results that suggest the work presented in 

[1] does a better job of predicting structures of interest 

than it should when applied to a collection of data taken 

from an electrospray experiment. We plan to continue 

our study of SDE analysis as a chemical structure prediction method. 

[1]	 A. J. Kearsley, Y. Gadhyan and W. E. Wallace, Stochastic Regression Modeling of Chemical Spectra, 

Chemometrics and Intelligent Laboratory Systems 139 

(2014), 26-32. 

[2]	 Y. Saito and T. Mitsui, Stability Analysis of Numerical 

Schemes for Stochastic Differential Equations, SIAM 

Journal of Numerical Analysis 33 (1996), 2254–2267. 

[3]	 D. J. Higham, An Algorithmic Introduction to Numerical 

Simulation of Stochastic Differential Equations, SIAM 

Review 43 (2001), 525-546. 

Modeling Magnetic Fusion 

Geoffrey McFadden 

Antoine Cerfon (New York University) 

A future source of commercial energy may be based on 

the controlled fusion of a hot plasma of hydrogen isotopes that is confined by a strong magnetic field. Quite 

often a toroidal geometry is envisioned in which the ions 

fuse to form helium and release energetic neutrons. A 

number of computational methods to model such magnetic fusion devices have been developed by researchers 

at New York University (NYU) and elsewhere to allow 

effective numerical simulations of the most essential 

features of modern tokomak and stellarator experiments. 

G. McFadden and colleagues at NYU completed a 

benchmarking exercise to compare the simulation results produced by a number of codes that are in use by 

the fusion community [1,2]. The benchmark is based on 

the DIII-D tokomak experiment at General Atomics in 

San Diego, California. The benchmarking exercise was 

organized by researchers at the Princeton Plasma Physics Laboratory and Oak Ridge National Laboratory. 

G. McFadden and colleagues at NYU are currently 

modeling the linear stability of a plasma in an annular 

configuration with an axial distribution of current. In 

this study the results of a conventional magnetohydrodynamic (MHD) model are compared with those from a 

more complicated model that includes effects of particle 

transport. This results in a non-self-adjoint eigenproblem in which the (complex) eigenvalue enters in a 

nonlinear fashion, requiring a non-standard numerical 

treatment. The study should be useful in highlighting 

limitations of the continuum MHD models that are 

widely used to predict the performance of fusion devises. 

[1]	 A. Reiman, A. Cerfon, G. McFadden, et al., Tokamak 

Plasma High Field Side Response to an n = 3 Magnetic 

Perturbation: A Comparison of 3D Equilibrium Solutions 

from Seven Different Codes, Nuclear Fusion 55 (2015) 

063026. 

[2]	 P. R. Garabedian and G. B. McFadden, Design of the 

DEMO Fusion Reactor Following ITER, Journal of Research of the National Institute of Standards and 

Technology 114 (2009) 229-236. 

Parallel Adaptive Refinement and 

Multigrid Finite Element Methods 

William F. Mitchell 

Marjorie A. McClain
 

Eite Tiesinga (NIST PML)
 

Paul Julienne (NIST PML)
 

John Villarrubia (NIST PML) 

Garnett Bryant (NIST PML)
 

Michael Gullans (NIST PML)
 

http://math.nist.gov/phaml 

Finite element methods using adaptive refinement and 

multigrid techniques have been shown to be very efficient for solving partial differential equations (PDEs). 

Adaptive refinement reduces the number of grid points 

by concentrating the grid in the areas where the action 

is, and multigrid methods solve the resulting linear systems in an optimal number of operations. Recent 

research has been with hp-adaptive methods where 

adaptivity is in both the grid size and the polynomial order of approximation, resulting in exponential rates of 

convergence. W. Mitchell has been developing a code, 

PHAML (for Parallel Hierarchical Adaptive MultiLevel), 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, the 

quantum physics of matter, and simulation of scanning 

electron microscopes. 

We have continued to expand the forms of hp-adaptivity available in PHAML. We implemented a new 

strategy this year due to Bürg and Dörfler which solves 

a local residual problem on a small patch of elements for 

each of the candidate refinements to determine which 

candidate is most effective. We also extended four of 
 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 37 

Figure 17. Convergence of a finite element solution as measured by using a reference solution vs. using 

the true solution. 

the hp-adaptive strategies, as well as p-adaptivity, to the 

3D code. We used PHAML to perform a numerical experiment to address the question of how large of a 

polynomial degree is worthwhile in hp and high order 

finite elements, and what type of refinement is best in 

different situations. The study showed that with low accuracy requirements, h-adaptive refinement with 

elements of degree 3 or 4 is sufficient, but with high accuracy requirements it is best to use hp-adaptivity up to 

degree 10. We have created a web site23 to make available a collection of standard benchmark PDEs that are 

suitable for bench-marking and testing adaptive mesh 

refinement algorithms and error estimators. We continue to add new PDEs to this collection to cover 

additional problem characteristics. We also completed 

the implementation of a reference solution module and 

added a reference solution to one problem in the collection for which the exact solution is unknown. We 

performed a study to assess whether or not one can use 

a reference solution as the “true” solution for determining the norm of the error of a less accurate solution, 

examining convergence rates, determining the accuracy 

of an a posteriori error estimate, etc. As shown in Figure 

17, the reference solution is an excellent substitute for 

the true solution until the norm of the error is about a 

factor of 2 or 4 larger than the norm of the error of the 

reference solution. 

23 NIST Adaptive Mesh Refinement Benchmark Problems, 

http://math.nist.gov/amr-benchmark 

There are three major 

collaborative efforts with 

PML that apply PHAML to 

their physical models. In a 

collaboration with Eite 

Tiesinga and Paul Julienne, 

we are using PHAML to 

study the interaction of atoms and molecules held in an 

optical trap. We are using a 

3D model to calculate the 

bound states, scattering properties and dynamics of two 

interacting dipolar molecules. Figure 18 illustrates 

the type of wave functions 

that come from these calculations. The large lobes are due 

to the optical trap, and the 

small lobes in the center are 

due to the atom-atom interaction with the orientation due 

to the dipole moment. We 

are also looking into the use 

of absorbing (non-reflecting) 

boundary conditions on the 

surface of an ellipsoid removed from the domain. We 

have performed calculations to examine how the energy 

levels are effected by the eccentricity of the ellipsoid. 

We are also collaborating with John Villarrubia to 

apply PHAML to the modeling of scanning electron microscope images of samples that contain a mixture of 

conducting and insulating regions. John has a code, 

JMONSEL24, that models electron scattering in materials, secondary electron production, and detection. We 

have coupled this code with PHAML which performs 

the finite element analysis to determine the electric 

fields that affect the image. This year we extended 

PHAML to handle several situations that arise in John’s 

models but were not previously supported by PHAML. 

These include interior Dirichlet constraints which come 

from a grounded piece of metal in the sample, floating 

constraints which come from a charged piece of metal in 

the interior of the sample, and duplicate face elements at 

the interface of two materials. We have also begun to 

experiment with mesh adaptivity. We are developing a 

new physics-based error estimate that reflects the 

amount of error in an electron’s path as it passes through 

an element, rather than the error in the electric potential 

in that element. 

Our collaboration with Garnett Bryant applies 

PHAML to the simulation of quantum dot structures. 

Nanoscale semiconductor quantum dot structures can be 

24 Java Monte Carlo Simulation of Secondary Electrons 
 

 

 

 

 

 

 

 

 

38 NIST Applied and Computational Mathematics Division 

Figure 18. The x-z plane slice of a wave function from a simulation that combines an optical trap, atom-atom interaction and dipole moment. 

modified, controlled, and manipulated by applied electric fields that arise from the local strain in the quantum 

dots. In this collaboration we are using PHAML to determine these applied fields and potentials down to the 

scale of the quantum dots. This year we interfaced 

PHAML with Garnett’s existing codes that describe 

these quantum dot structures. With one of Garnett’s 

post-docs, Michael Gullans, we have begun to use 

PHAML to model a single plasmon SET-donorgraphene device, which has applications to on-chip photodetection, optical signal processing and quantum 

computing with CMOS compatible devices. 

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, continue the development of the adaptive 

mesh refinement benchmark suite, and continue collaborations that use PHAML to solve NIST applications. 

Relevant recent references are provided in [1-8]. 

[1]	 W.F. Mitchell and M.A. McClain, A Comparison of hpAdaptive Strategies for Elliptic Partial Differential Equations, ACM Transactions on Mathematical Software 41:1 

(2014), 2 (39 pages). 

[2]	 W.F. Mitchell, How High a Degree is High Enough for 

High Order Finite Elements? Proceedings of the 2015 International Conference on Computational Science, 

Procedia Computer Science 51 (2015), 246–255. 

[3]	 W.F. Mitchell, 30 Years of Newest Vertex Bisection, in 

review. 

[4]	 W.F. Mitchell and M.A. McClain, “Performance of hpAdaptive Strategies for Elliptic Partial Differential Equations,” International Conference on Numerical Analysis 

and Applied Mathematics, Rhodes, Greece, September 

2014. 

[5]	 W.F. Mitchell, “NIST AMR Benchmarks,” poster, SIAM 

Conference on Computational Science and Engineering, 

Salt Lake City, UT, March 2015. 

[6]	 W.F. Mitchell, “Using Space Filling Curves to Find an 

Element That Contains a Given Point, SIAM Conference 

on Computational Science and Engineering,” Salt Lake 

City, UT, March 2015. 

[7]	 W.F. Mitchell, “How High a Degree is High Enough for 

High Order Finite Elements?” International Conference 

on Computational Science (ICCS), Reykjavik, Iceland, 

June 2015. 

[8]	 W.F. Mitchell, “30 Years of Newest Vertex Bisection,” 

13th International Conference of Numerical Analysis and 

Applied Mathematics (ICNAAM), Rhodes, Greece, September 2015. 

Stable Explicit Time Marching in IllPosed Initial Value Problems for 

Partial Differential Equations 

Alfred S. Carasso 

There is a great deal of current interest in effective numerical methods for solving multidimensdional, 

nonlinear, ill-posed initial value problems in partial differential equations. In environmental forensics, ill-posed 

time-reversed parabolic equations are widely used in locating sources of groundwater contamination [1-2]. In 

geophysics, thermal convection in the Earth’s mantle is 

the principal heat and mass transport mechanism. Numerical computation of the ill-posed time-reversed 

thermal convection problem is an active research topic, 

seeking to reconstruct temperature profiles in the Earth’s 

interior in the geological past [3-4]. Numerous other 

significant applications of ill-posed problems are discussed in [5-7]. 

However, computation of ill-posed initial value 

problems presents formidable difficulties. Conventional 

stepwise time-marching schemes, whether explicit or 

implicit, are necessarily unconditionally unstable, and 

result in explosive noise amplification. Recently, in a 

major breakthrough [8-9], a method was discovered that 

can stabilize explicit marching schemes by applying easily synthesized linear smoothing operators at each time 

step to quench the instability. Smoothing operators S = 

exp{-ε ∆t (-∆)

p

}, based on positive real powers of the 

negative Laplacian (-∆), can be realized efficiently on 

rectangular domains using fast Fourier transform (FFT) 

algorithms. Such stabilization leads to a distortion away 

from the true solution. However, that error is often small 

enough to allow for useful results in many problems of 

interest. This new approach opens the door to relatively 

easy and useful computation of some previously intractable nonlinear problems, and it provides a useful 
 

 

 

 

Summary of Activities for Fiscal Year 2015 39 

Figure 19. Successful backward recovery in nonlinear viscous wave equation applied to 512  512 images. With initial displacement and 

velocity shown in the leftmost column, nonlinear viscous wave equation was solved numerically forward in time up to a positive time T. This 

produced the images shown in the middle column. These data were then used as input in the time-reversed FFT-Laplacian stabilized explicit 

scheme discussed in [9] to produce the deblurred images shown in the rightmost column. 

complement to the quasi-reversibility method [6], whose 

formulation is primarily oriented toward linear problems. 

Viscous wave equation. An instructive survey of prototypical ill-posed initial value problems is given in [6]. 

With positive constants a, b, the classical linear viscous 

wave equation wtt - 2a∆wt - b∆w = 0 is discussed in [6], 

and shown to be ill-posed backward in time. In [9], a 

more general nonlinear version of the same equation is 

considered in a rectangular region. A stabilized explicit 

scheme is then developed and analyzed for the time-reversed problem, and shown to lead to almost bestpossible results in the canonical linear self adjoint case. 

Eight bit gray scale 512  512 pixel images provide ideal 

test problems for inverse reconstruction algorithms, and 

several such images are used in [8-9]. An example of 

successful nonlinear backward in time viscous wave reconstruction is shown in Figure 19. With initial 

displacement and velocity shown in the left most column, a nonlinear viscous wave equation was solved 

numerically forward in time up to some positive time T, 

resulting in the images in the middle column. Using the 

middle column as input data at time T, the stabilized explicit scheme discussed in [9] was run backward in time 

to produce the images in the rightmost column. This example is not tractable by the quasi-reversibility approach 

discussed in [6], owing to the nonlinearity. Moreover, 

even in the linear case, the quasi-reversibility method involves the addition of higher order differential 

operators, and the use of implicit schemes to march 

backward in time. With large multidimensional arrays, 

such implicit schemes would require a computationally 

intensive solution of the resulting algebraic systems of 

difference equations at each time step. This difficulty is 

avoided in the present explicit approach. 
 

 

40 NIST Applied and Computational Mathematics Division 

Figure 20. Relatively painless second order accurate stabilized explicit leapfrog computation in well-posed forward nonlinear parabolic 

equation applied to 1024  1024 image. Second order accuracy using Crank-Nicholson implicit scheme would require solution of nonlinear 

system of difference equations of order 106

 at each time step. 

Figure 21. Accurate nonlinear parabolic blurring of 512  512 Doris Day image is easily achieved with the stabilized leapfrog scheme. 

However, backward leapfrog recovery fails here, while useful reconstruction is provided with the backward pure explicit scheme in [8]. 

failed attempt at numerical weather prediction. How- Stabilizing the leapfrog scheme in parabolic equa­ ever, while highly desirable, the leapfrog scheme is tions. One hundred years ago, L. F. Richardson 

unconditionally unstable in well-posed forward para­ introduced second order accurate explicit centered time bolic equations. Using an approach similar to that used differencing, and used such a “leapfrog” scheme in his in [8], stabilization of the leapfrog scheme was achieved 
 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 41 

for an important class of second order nonlinear parabolic equations. An example of a relatively painless 

second order accurate stabilized explicit leapfrog computation, in a well-posed forward nonlinear parabolic 

equation applied to 1024  1024 image, is given in Figure 20. To obtain the equivalent accuracy using the 

Crank-Nicholson implicit scheme would necessitate the 

solution of a nonlinear system of difference equations of 

order 106

 at each time step. Surprisingly, the stabilized 

leapfrog scheme is much less well-behaved backward in 

time than is the less accurate pure explicit scheme in [8]. 

In Figure 21, the nonlinearly distorted Doris Day image, 

computed accurately by the forward stabilized leapfrog 

scheme, cannot be deblurred by the backward leapfrog 

scheme. Useful reconstruction is feasible however, with 

the backward pure explicit scheme in [8]. 

Future directions. Future work will consider other irreversible systems of partial differential equations such as 

coupled sound and heat flow, and thermoelasticity. An 

approach to problems in nonrectangular regions, based 

on enclosing that region in a larger rectangle, is being 

considered. Also, the anomalous behavior backward in 

time in the stabilized leapfrog scheme will be reexamined, and possibly mitigated. 

[1]	 J. Atmadja and A. C. Bagtzoglou, State of the Art Report 

on Mathematical Methods for Groundwater Pollution 

Source Identification, Environmental Forensics 2 (2001), 

205-214. 

[2]	 T. H. Skaggs and Z. J. Kabala, Recovering The History 

of a Groundwater Contaminant Plume: Method of QuasiReversibility, Water Resources Research 31 (1995), 

2669-2673. DOI 10.1029/95WR02383 

[3]	 Ismail-Zadeh et al., Three Dimensional Forward and 

Backward Numerical Modeling of Mantle Plume Evolution: Effects of Thermal Diffusion, Journal of 

Geophysical Research 111 (2006) B06401. DOI 

10.1029/2005JB003782 

[4]	 A. Ismail-Zadeh et al., Numerical Techniques for Solving 

the Inverse Retrospective Problem of Thermal Evolution 

of the Earth Interior, Computers and Structures 87 

(2009), 802-811. 

[5]	 M. M. Lavrentiev, Some Improperly Posed Problems of 

Mathematical Physics, Springer-Verlag, New York, 

1967. 

[6]	 R. Lattès and J. L. Lions, The Method of Quasi-Reversibility, American Elsevier, New York, 1969. 

[7]	 K. A. Ames and B. Straughan, Non-Standard and Improperly Posed Problems, Academic Press, New York, 1997. 

[8]	 A. S. Carasso, Stable Explicit Time Marching in WellPosed or Ill-Posed Nonlinear Parabolic Equations, Inverse Problems in Science and Engineering, 2015. DOI 

10.1080/17415977.2015.1110150 

[9]	 A. S. Carasso, Stable Explicit Stepwise Marching 

Scheme in Ill-Posed Time-Reversed Viscous Wave Equations, Inverse Problems in Science and Engineering, 

2016, to appear. 

Numerical Solutions of the Time 

Dependent Schrödinger Equation 

Barry I. Schneider
 

Klaus Bartschat (Drake University) 

Xiaoxu Guan (Louisiana State University)
 

We have been collaborating for a number of years to develop numerically robust methods for solving the time 

dependent Schrödinger equation. Although the approaches that have been developed are quite general, the 

applications to date have concentrated on describing the 

single and double ionization of electrons exposed to intense, ultrafast, laser radiation. These attosecond (10-18 

sec) pulses provide a new window to study electronic 

motion in atoms and molecules on their natural timescale. To put this in context, the motion of electrons 

responsible for chemical binding and electron transfer 

processes in nature, have a characteristic timescale of 

about 100 attoseconds. (It takes an electron 152 attoseconds to go around the hydrogen atom). 

Such processes can only be described using time dependent quantum mechanics and, where appropriate, 

need to be coupled to Maxwell’s equations to describe 

macroscopic phenomena. At the end of the day, we wish 

to image quantum phenomena with sub-femtosecond 

temporal and sub-Angstrom spatial resolution, eventually producing “molecular movies” of this motion in 

much the same way as it is done in molecular dynamics 

simulations of heavy particle processes. The basic methodology as applied to atoms and simple diatomic 

molecules has been described in [1-3,5-10], and [4] provides a detailed review of the work. The essential 

aspects have been 

	 development of the finite element discrete variable 

method (FEDVR) to spatially discretize the coordinates of the electrons, and 

	 use of the short iterative Lanczos method to propagate the wavefunction in time. 

The method has been efficiently parallelized using 

the message passing interface (MPI), MPI and scales linearly with the size of the FEDVR basis. Large scale 

calculations have been performed on a number of atoms 

and molecules using resources provided by the National 

Science Foundation (NSF) Extreme Science and Engineering Discovery Environment (XSEDE). The group 

has received a competitively awarded allocation of more 

than 8 million service units for the current fiscal year. 

Intel Co-Processor Study. During the past year, the 

group has concentrated its efforts porting the code to the 

Intel Phi co-processors and studying the behavior of the 

code as a function of the work allocated to the main 

Xeon node and the Intel Phi cores. The study was done 

using the Compiler Assisted Offload mode. In that approach, compiler directives are inserted into the code to 
 

 

 

 

 

 

 

 

 

 

 

 

42 NIST Applied and Computational Mathematics Division 

Figure 22. Comparison of benchmark code on Xeon and Intel Phi 

processors. 

direct the most time consuming part of the computation 

to the Intel Phi co-processors. 

For the current application we studied the structured, sparse matrix-vector multiplies required to solve 

the Schrödinger equation at the next time step. In all of 

the tests, only a single MPI task was launched on any 

Xeon node consisting of 16 (20) cores. Then various 

numbers of threads are launched on either the Xeon host 

or the Intel Phi. The Xeon node is allowed to host up to 

16 (20) OpenMP threads. The Intel Phi can host up to 

250 threads. Only a single Intel Phi card per Xeon node 

was employed in all of the tests. We did not examine the 

case where some threads executed on the Xeon cores 

and some on the Intel Phi. The results are summarized 

in Figure 22. Thus we can see that for one or two nodes, 

the ability to launch 250 threads on the Intel Phi enables 

a performance gain. But, by nine nodes its essentially a 

tie and by sixteen nodes, the Xeon nodes are outperforming the Phi co-processor. Essentially, what we are seeing 

is a tradeoff between the larger speed of the Xeon cores 

and the larger number of threads that can be launched on 

the Phi. Clearly, sixteen Xeon nodes performing 256 

OpenMP tasks is better than sixteen nodes performing 

4000 OpenMP tasks on the Phi. It is also important to 

remember that there are communication costs associated 

with moving data from the Phi back to the host that are 

not present when working entirely on the host. 

Hybrid Gaussian-FEDVR Code. We have begun a 

study to employ a mixed basis of Gaussian functions at 

short range and FEDVR functions at long range to extend our methods to complex polyatomic molecules. 

This approach has several important advantages over using a single basis over all of space. First, the use of 

nuclear centered Gaussians preserves the local atomic 

symmetry around each nucleus and avoids the poor convergence of using a single-center FEDVR basis at all 

distances. Second, once the electron is far enough away 

from the nuclear cusps, a single center expansion converges quickly and importantly, can represent the 

electrons out to very large distances using an approach 

that is very amenable to domain decomposition. The 

major issue is to compute the one and two electron integrals between the two types of basis functions. This is 

currently under active investigation. 

[1]	 J. Feist, S. Nagele, R. Pazourek, E. Persson, B. I. Schneider, L. A. Collins and J. Burgdörfer, Nonsequential TwoPhoton Double Ionization of Helium, Physical Review A 

77, 043420 (2008). 

[2]	 X. Guan, K. Bartschat and B. I. Schneider, Dynamics of 

Two-photon Ionization of Helium in Short Intense XUV 

Laser Pulses, Physical Review A 77 (2008), 043421. 

[3]	 X. Guan, K. Bartschat and B. I. Schneider, Two-photon 

Double Ionization of H2 in Intense Femtosecond Laser 

Pulses, Physical Review A 82 (2010), 041407. 

[4]	 B. I. Schneider, J. Feist, S. Nagele, R. Pazourek, S. Hu, 

L. Collins and J. Burgdörfer, Recent Advances in Computational Methods for the Solution of the TimeDependent Schrödinger Equation for the Interaction of 

Short, Intense Radiation with One and Two Electron Systems, in Dynamic Imaging, Theoretical and Numerical 

Methods Series: CRM Series in Mathematical Physics 

XV (A. Bandrauk and M. Ivanov eds.), 2011 

[5]	 X. Guan, E. Secor, K. Bartschat and B. I. Schneider, Double-slit Interference Effect in Electron Emission from H2

+ 

Exposed to X-Ray Radiation, Physical Review A 85 

(2012), 043419. 

[6]	 X. Guan, K. Bartschat, B. I. Schneider and L. Koesterke, 

Resonance Effects in Two-Photon Double Ionization of 

H2 by Femtosecond XUV Laser Pulses, Physical Review 

A 88 (2013), 043402. 

[7]	 J. Feist, O. Zatsarinny, S. Nagele, R. Pazourek, J. 

Burgdörfer, X. Guan, K. Bartschat and B. I. Schneider, 

Time Delays for Attosecond Streaking in Photoionization, Physical Review A 89 (2014), 033417. 

[8]	 X. Guan, K. Bartschat, B. I. Schneider, and L. Koesterke, 

Alignment and pulse-duration effects in two-photon double ionization of H2 by femtosecond XUV laser pulses, 

Physical Review A 90 (2014), 043416. 

[9]	 B. I. Schneider, L. A. Collins, X. Guan, K. Bartschat and 

D. Feder, Time-Dependent Computational Methods for 

Matter Under Extreme Conditions, Advances in Chemical 

Physics 157, Proceedings of the 240 Conference: Science’s Great Challenges, Volume 157, (A. Dinner, ed.), 

John Wiley and Sons, 2015. 

[10] B. I. Schneider, X. Guan and K. Bartschat, Time Propagation of Partial Differential Equations Using the Short 

Iterative Lanczos Method and Finite-Element Discrete 

Variable Representation, International Advances in 

Quantum Chemistry, to appear. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 43 

Advanced Materials 

Delivering technical support to the nation’s manufacturing industries as they strive to out-innovate and outperform the international competition has always been a top priority at NIST. This has also emerged as a 

major White House priority in recent years, in which NIST is playing an increasingly central role. Mathematical modeling, computational simulation, and data analytics are key enablers of emerging manufacturing 

technologies. This is most clearly evident in the Materials Genome Initiative, an interagency program with the 

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

use of modeling, simulation, and informatics. ACMD’s role in advanced manufacturing centers on the development and assessment of modeling and simulation tools, with emphasis on uncertainty quantification, as well 

as support of NIST Laboratory efforts in such areas as materials modeling and smart manufacturing. 

Uncertainty Quantification in 

Molecular Dynamics Workflows for 

Aerospace Polymers 

Paul Patrone
 

Andrew Dienstfrey 

Stephen Christensen (The Boeing Company)
 

Andrea Browning (The Boeing Company)
 

Sam Tucker (The Boeing Company) 

In computational chemistry, molecular dynamics (MD) 

simulations are becoming a key tool for the discovery of 

next-generation materials [1-2]. For crosslinked polymers used in aerospace composites, this success is 

largely due to the ability of MD to describe the evolution 

of complex molecular conformations, which typically 

govern bulk mechanical properties. Such levels of detail, however, come at a price: MD simulations can only 

model at most O(106

) atoms, 17 orders of magnitude less 

than the bulk systems one usually wishes to study. In 

many cases, this discrepancy has led to considerable uncertainties in the resulting predictions, and consequently 

there is growing need for methods that assess the quality 

of simulated data. 

Building upon work from FY 2014, we developed a 

systematic uncertainty quantification (UQ) workflow to 

assess data arising from MD simulations of the glasstransition temperature Tg. This quantity is both an important property for engineers (since it determines, e.g., 

the temperature at which a wing becomes soft) that is 

also difficult to model; thus it is a useful proving ground 

upon which to develop UQ methods. Details of our 

work are provided in a publication that is currently under 

review [3]. Industrial stakeholders are also using this 

workflow in their simulation protocol, and the software 

company Schrodinger has incorporated elements of our 

analysis into their commercially available package. We 

briefly summarize our main ideas here. 

The workflow proceeds in two stages. Without 

computing uncertainties, the first stage of the analysis 

assesses whether data is of sufficient quality to be used 

for property estimation. We begin by addressing the 

question: is simulated data consistent with the definition 

of Tg? In particular, it is common practice to estimate Tg 

by extrapolating to the intersection of two fit-lines characterizing the low and high-temperature asymptotic 

behavior of density-temperature curves. Motivated by 

this, we implemented a hyperbolic regression analysis 

for determining whether data exhibits such asymptotic 

behavior. Additionally, we developed a pooling analysis that estimates bias in the Tg predictions by iteratively 

resampling from collections of datasets. Importantly, 

such approaches can indicate when simulations are too 

small to yield property estimates that are converged as a 

function of system size. 

Given a collection of datasets that are of sufficient 

quality, the second stage of the analysis estimates Tg and 

its uncertainties. We propose to model the output of the 

i

th simulation via 

ሻ ൅ ܰ ଶ ሻ ሺ0, ݕ ଶ 0, ߪ ൅ ௜ܰሺ ܶ௚ ൌ ത ܶ௚,௜

where N(0,X) is a normal random variable with mean 

zero and variance X, ߪ௜

ଶ is a within-simulation noise associated with thermal fluctuations and limited time 

averaging of the i

th MD simulation, and y2

 is a betweensimulation uncertainty quantifying the extent to which a 

finite-size simulation undersamples the crosslinked network and relevant molecular conformations. Estimation 

of the ߪ௜

ଶ proceeds for each dataset individually by a 

noise-sampling process akin to parametric bootstrap 

and ܶത

௚ via 2 analysis. Given these, we then estimate y

maximum likelihood analysis. Interestingly, this approach leads to a weighted-mean estimator of the form 

ܶ ௜௚, ିଵ 1

ܶത

௜ߪ ൅ ଶݕ ௜ ൨௚ ൎ ൤෍ ෍௜ߪ ൅ ଶݕ ௜ ଶ

ଶ

which is frequently used in key comparison studies of 

fundamental constants. Related quantities can be derived for uncertainties in this estimator. Future 

directions for our work include (i) generalizing our analysis to more mechanical properties of interest, and (ii) 

developing additional analysis tools for quantifying the 
 

 

 

 

 

 

 

 

44 NIST Applied and Computational Mathematics Division 

Figure 23. Comparison of density-temperature data for two different amine-cured epoxies. Tg is typically computed as the intersection temperature of two lines fit to the low and high temperature asymptotic regimes. Using hyperbolas, we test for the existence of such regimes by 

comparing the data to asymptotes. The left plot shows a system in which the data clearly samples asymptotic behavior, corresponding to 

temperatures outside of the transition region. The right plot shows a dataset that does not sample asymptotic behavior. 

extent to which a finite simulation undersamples the network structure of bulk materials. 

In addition to the MD-polymers applications, we 

continued outreach to the broader computational materials science community as part of the Materials 

Genome Initiative. In particular, from July 28 – July 31 

2015, we ran a Hot Topics Workshop on Uncertainty 

Quantification in Materials Science at Purdue University in collaboration with Air Force Research Lab, the 

Institute for Mathematics and Its Applications (IMA), 

and Purdue’s nanoHUB. The main goal of this workshop was to provide a hands-on venue for materials 

scientists in industry and academia to learn UQ methods. 

Over three days, six speakers gave three one hour lectures plus computer tutorials to roughly 40 participants, 

nearly a third of whom were from industry. The last day 

of the workshop was devoted to short talks on hot-topics 

and open problems in UQ of materials science. Response to the workshop was positive, and a follow-up is 

scheduled to be held at IMA in February 2016. 

[1]	 S. Christensen, J. Senger. 2010. Distortional matrix of 

epoxy resin and diamine. U.S. Patent 7,745,549 B2, filed 

December 20, 2006, issued June 29, 2010. 

[2]	 S. Christensen, J. Senger. 2011. Distortional matrix of 

epoxy resin and diamine. U.S. Patent 7,985,808 B2, filed 

April 23, 2010, issued July 26, 2011. 

[3]	 P. N. Patrone, A. Dienstfrey, A. R. Browning, S. Tucker 

and S. Christensen, Uncertainty Quantification in Molecular Dynamics Studies of the Glass Transition 

Temperature, in review. 

Bayesian Calibration of CoarseGrained Forces 

Paul N Patrone 

Thomas Rosch (NIST MML)
 

Frederick Phelan (NIST MML) 

In recent years, the high-throughput capabilities of molecular dynamics (MD) have attracted the interest of 

companies involved in materials research and development. In such settings, simulations are beginning to 

accelerate materials insertion, given their ability to rapidly search design spaces for novel systems that warrant 

further experimental study [1]. While it is generally 

agreed that this procedure can significantly reduce material development costs, however, a key theme has 

repeatedly emerged from practical implementations 

thereof: in order to be useful for commercial applications, computational models require techniques that can 

rapidly calibrate inputs and assess uncertainties in simulated predictions [2]. 

In the context of coarse-grained (CG) MD, this 

theme has proven to be especially germane. In particular, high-throughput applications require the ability to 

rapidly customize the level of coarse-graining for arbitrary systems across a range of state points (e.g. 

temperatures); inexpensive and robust calibration techniques are thus critical for enabling this degree of 

flexibility. Often, the key input to be determined is the 

CG interparticle force field f(r; q) as a function of separation r and state-point q. Many techniques have been 

developed to compute these functions from thermodynamic considerations of atomistic systems. However, 
 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 45 

Figure 24. Density-temperature data comparing atomistic simulations of polystyrene with their coarse-grained counterparts. Red x 

are simulated results from atomistic MD. At each temperature, we 

used the force-matching algorithm [4] to estimate CG forces at 

T=100 K, 200 K, ..., 800 K. For a fixed force computed at an anchor point Ti, we then simulated CG densities at 10 K intervals in 

the domain [Ti – 50 K, Ti + 40 K] (black line). The densities exhibit 

sharp jumps when the force curve changes. Such behavior is unphysical for systems like polystyrene and indicates that a given f is 

unsuitable for simulating the density outside of a small window 

around the temperature at which it was calibrated. 

such methods typically draw information from a limited 

number of state-points, and the resulting forces can yield 

incorrect predictions for even small changes away from 

the calibration conditions (see Figure 24). Thus, the following question remains an important open problem: is 

there a general and inexpensive method for calibrating 

f(r; q) so that a CG simulation yields the same predictions as a corresponding atomistic simulation on a large 

interval of state-points? In this project, we developed a 

coarse-graining workflow, based on ideas from numerical analysis and Bayesian probability, for addressing 

this problem. The main steps in our workflow are 

 building a statistical model to describe the target 

predictions against which to calibrate the CG 

forces; 

 constructing a prior probability for the forces via a 

combination of standard CG techniques and interpolation; and 

 correcting the prior probability distribution via a 

Bayesian algorithm that uses functional derivatives of the CG simulations to systematically 

update the forces. 

Importantly, these functional derivatives are inexpensive to approximate, given that CG simulations are 

orders of magnitudes faster than MD. As a result, we 

were able to show that our workflow overcomes the difficulties of generating transferable forces by rapidly and 

robustly calibrating priors constructed from non-robust 

and cheap interpolations of forces in state space. Using 

polystyrene as a test case, we also demonstrated that our 

approach can calibrate forces over a 700 K range so that 

they yield a target density-temperature curve to within 

statistical error. 

Results of this work are detailed in a paper that has 

been submitted for publication [3]. Future directions for 

this work include showing that Bayesian approaches can 

be used to simultaneously calibrate multiple material 

properties, and developing uncertainty quantification 

techniques for the iterative Boltzmann inversion method 

of coarse-graining. 

[1]	 C. Li and A. Strachan, Molecular Scale Simulations on 

Thermoset Polymers: A Review, Journal of Polymer Science, Part B, 53 (2014), 103–122. 

[2]	 A. Dienstfrey, F. R. Phelan Jr., S. Christensen, A. Strachan, F. Santosa and R. Boisvert, Uncertainty 

Quantification in Materials Modeling, The Journal of the 

Minerals, Metals, and Materials Society (JOM) 66 

(2014), 1342-1344. 

[3]	 P. N. Patrone, T. W. Rosch and F. R. Phelan Jr., Bayesian 

Calibration of Coarse-Grained Forces: Efficiently Addressing Transferability, in review. 

[4]	 S. Izvekov, G. A. Voth, Multiscale Coarse-graining of 

Liquid-state Systems, The Journal of Chemical Physics, 

123 (2005), 134105. 

 Micromagnetic Modeling 

Michael Donahue
 

Donald Porter
 

Robert McMichael (NIST CNST)
 

June Lau (NIST MML)
 

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

Advances in magnetic devices such as recording heads, 

field sensors, spin torque oscillators, and magnetic nonvolatile memory (MRAM) are dependent on an 

understanding of magnetization processes in magnetic 

materials at the nanometer level. Micromagnetics, a 

mathematical model used to simulate magnetic behavior, is needed to interpret measurements at this scale. 

ACMD is working with industrial and academic partners, as well as with colleagues in the NIST Cenetr for 

Nanoscale Science and Technology (CNST), Materials 

Measurement Laboratory (MML), and Physical Measurement Laboratory (PML), to improve the state-of-theart in micromagnetic modeling. 

Michael Donahue and Donald Porter in ACMD 

have developed a widely used public domain computer 

code for doing computational micromagnetics, the Object-Oriented Micromagnetic Modeling Framework 

(OOMMF). OOMMF serves as an open, well-documented environment in which algorithms can be 

evaluated on benchmark problems. OOMMF has a 

modular structure that allows independent developers to 

contribute extensions that add to the basic functionality 

of OOMMF. OOMMF also provides a fully functional 

micromagnetic modeling system, handling both two and 

three-dimensional problems, with sophisticated extensible input and output mechanisms. In FY 2015 alone, the 

software was downloaded more than 6000 times, and 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

46 NIST Applied and Computational Mathematics Division 

use of OOMMF was acknowledged in more than 185 

peer-reviewed journal articles. OOMMF has become an 

invaluable tool in the magnetics research community. 

Key new developments over the last year include 

the following. 

	 Major reworking of non-uniform memory access 

(NUMA) aware memory use along with threading 

improvements to support simulations size of more 

than 100 million spins. 

	 Demonstration test of a one billion spin simulation. 

Using this enhanced capability, completed several 

simulations of archetype magnetization structures at 

0.1 nm spatial resolution. Current work involves analyzing these calculations to make a quantitative 

determination of how computation error relates to 

spatial resolution. 

	 Released OOMMF version 1.2a6 in Sept. 201525. 

	 Began collaboration with staff at the nanoHUB project26 of Purdue University to add OOMMF to the 

collection of software tools available to run on their 

online service. 

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. A new 

standard problem 5, adapted from [1], addressing the 

proper calculation of the spin torque transfer effect was 

released27 in September, 2014. New solutions to standard problem 4 were also released28. Ongoing work 

includes the production of standard problem 5 solutions 

for submission, and development of new standard problems. 

In addition to the continuing development of 

OOMMF, the project also does collaborative research 

using OOMMF. Continued collaboration with the University of California, San Diego on porting OOMMF 

calculations to massively parallel graphical processing 

units (GPUs) has produced an article for publication. 

Collaboration with the University of Maryland has 

demonstrated nanoscale control over magnetic anisotropy in a trans-critical Permalloy thin film via strainmediated coupling to ferroelectric domains in BaTiO3, a 

degree of control helpful in the aim to make compact 

and efficient memory devices. The ACMD micromagnetic project produced one invited talk [2], one 

conference presentation [3], and three manuscripts submitted for publication [4-6] this past year. 

25 http://math.nist.gov/oommf/software-12.html 

26 http://nanohub.org/ 

[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]	 M. J. Donahue, “An Introduction to Micromagnetic Modeling”, March 15, 2015, Orlando, Florida. Part of the 

short course Characterization Techniques for Magnetic 

Materials offered in advance of the annual meeting of 

The Minerals Metals and Materials Society. 

[3]	 M. J. Donahue, “Implementation of a localized fourth order demagnetization tensor,” 59th Annual Magnetism 

and Magnetic Materials, November 5, 2014, Honolulu, 

HI. 

[4]	 S.W. Fackler, M.J. Donahue, T. Gao, P.N.A. Nero, S.-W. 

Cheong, J. Cumings, and I. Takeuchi, Locally Controlled 

Magnetic Anisotropy in Transcritical Permalloy Thin 

Films using Ferroelectric BaTiO3 Domains, Applied 

Physics Letters 105 (November 2014), 212905. 

[5]	 S. Fu, W. Cui, M. Hu, R. Chang, M.J. Donahue, and V. 

Lomakin, Finite Difference Micromagnetic Solvers with 

Object Oriented Micromagnetic Framework on Graphics 

Processing Units, IEEE Transactions on Magnetics, to 

appear. 

[6]	 S. Mitropoulos, V. Tsiantos, K. Ovaliadis, D. Kechrakos, 

and M. Donahue, Stiff Modes in Spin Valve Simulations 

with OOMMF, Physica B, to appear. 

OOF: Finite Element Analysis of 

Material Microstructures 

Stephen A. Langer 

Andrew C.E. Reid (NIST MML) 

Günay Doğan 

Shahriyar Keshavarz (Theiss Research) 

Faical Yannick Palingwende Congo 

Lizhong Zhang 

http://www.ctcms.nist.gov/oof/ 

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 Object-Oriented Finite Elements (OOF) Project, a collaboration 

between ACMD and MML, is developing software tools 

for analyzing real material microstructure. OOF uses 

data from a micrograph of a real or simulated material 

to compute the macroscopic behavior of the material via 

finite element analysis. The OOF user loads images into 

the program, assigns material properties to the features 

of the image, generates a finite element mesh that 

matches the geometry of the features, chooses which 

27 http://www.ctcms.nist.gov/~rdm/std5/spec5.xhtml 

28 http://www.ctcms.nist.gov/~rdm/std4/spec4.html 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 47 

physical properties to solve for, and performs virtual experiments to determine the effect of the microstructural 

geometry on the material. OOF is intended to be a general-purpose tool, applicable to a wide variety of 

microstructures in a wide variety of physical situations. 

There are two versions of OOF, OOF2 and OOF3D, 

freely available on the OOF website. OOF2 starts with 

two dimensional images of microstructures and solves 

two dimensional equations, assuming that the material 

being simulated is either a thin freely suspended film or 

a slice from a larger volume that is unvarying in the third 

dimension (generalizations of plane stress and plane 

strain, respectively). OOF3D starts with three dimensional images and solves equations in three dimensions. 

OOF is used by academic, industrial, and government users world-wide, although exact numbers are hard 

to obtain. OOF2 was downloaded 2500 times this year, 

but those numbers are suspect, because OOF3D was 

downloaded an unbelievable 15000 times. OOF3D was 

downloaded to 1157 unique IP addresses. Discounting 

the 10 sites (all Chinese) that downloaded it more than 

1000 times, a reasonable guess is that the number of actual downloads is in the thousands for both programs. 

Most of the year’s progress was on code development for future releases. However, two papers appeared, 

one on OOF’s graphical user interface (GUI) testing 

procedure [1], and one on applying OOF to a problem in 

planetary geology [2], and two new versions of the programs were released. OOF2 version 2.1.12 included 

parallel computation in parts of the program (but only 

when run on Linux) and bug fixes. OOF3D 3.0.1 fixed 

a number of bugs from the initial 3D release. 

OOF development this year was divided into a number of efforts. Yannick Congo added to the OOF3D test 

suite, and moved the OOF2 source control from a local 

Concurrent Versioning System (CVS) repository to the 

NIST GitHub repository29. He also added improvements to the OOF3D GUI. Lizhong Zhang replaced 

Yannick Congo during the year. He has been optimizing 

OOF2 by finding and fixing inefficient serial code, and 

by converting serial code to parallel. Ryan Weller, a 

SURF student from the University of Colorado, added 

three dimensional graphics widgets to OOF3D. Many 

operations in OOF3D are easier if the user can use a 

mouse to define, move, or rotate objects in three dimensions. This is fundamentally different from the 

equivalent operations in OOF2 simply because 3D 

movement can’t be represented in a straight forward 

manner on a 2D computer screen. Ryan implemented a 

compound widget composed of a plane and an arrow, 

which is perpendicular to the plane. Clicking and dragging the arrow head rotates the arrow and plane around 

the point where they meet. Clicking and dragging the 

plane moves it in its normal direction (along the arrow). 

Clicking and dragging while pressing the control key 

29 http://www.github.com/usnistgov 

moves the arrow on the plane, changing the rotation 

point. The widget can be used to define clipping planes, 

or to delimit sets of selected pixels or mesh elements. 

Andrew Reid and Shahriyar Keshavarz, a new 

MML post-doc and an expert on plasticity, have been 

working on adding crystal plasticity modeling to OOF. 

A significant component of this is that the crystal-plastic 

constitutive rules really do not make sense to implement 

outside of a large-strain displacement scheme, so the 

first order of business is to add this capability to OOF. 

Shahriyar’s participation has helped the rest of the developers gain an outsiders perspective on the material 

property applications programming interface (API) in 

OOF, which is less accessible and well-structured than 

initially believed, making the gaps in the existing documentation more important to remedy. A review and 

documentation update of the property API is now underway in parallel with the implementation of crystal 

plasticity. OOF’s highly-valued generality of scope will 

be retained, and this process will yield a very general 

large-strain and large-displacement extension framework applicable across the full range of constitutive 

laws OOF can implement. 

Günay Doğan has been developing algorithms to 

automate segmentation and meshing of microstructure 

images. His focus has been multiphase images, which 

consists of multiple regions, each approximated by a distinct average value, and images in which the regions are 

separated by well-defined high-gradient boundaries. He 

improved his previous segmentation-to-meshing algorithm, so that it would produce smoother and coarser 

boundaries resulting in more compact triangulations for 

finite element analysis. He also improved several components of the shape optimization algorithm used for 

multiphase segmentation and edge-based segmentation 

for better performance and usability. Although much of 

the development effort went into increasing the efficiency with Newton-type optimization, better step size 

selection and stopping criteria, computational efficiency 

is not the sole issue for a typical OOF user. The user 

usually does not have much image analysis experience, 

and thus can be overwhelmed by the multiple choices 

required to achieve acceptable results with a given segmentation algorithm. For this reason, Günay developed 

principles and approaches to set parameters and initialization methods, and incorporated them into the 

segmentation code (more details can be found in the section on Computational Tools for Shape Measurement 

and Analysis). Currently, he is working on interfacing 

the code with OOF, so that the segmentation software 

can be invoked from OOF, and can be used to analyze 

images loaded into OOF workspace. 

Steve Langer began the year fixing bugs and adding 

missing features to OOF3D, but spent most of the year 

redesigning and reimplementing the algorithm used to 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

48 NIST Applied and Computational Mathematics Division 

compute the volume of the intersection of a tetrahedral 

finite element with a group of voxels (3D pixels). This 

is used to compute the homogeneity of an element with 

respect to the various material properties that have been 

assigned to the voxels. The homogeneity calculation is 

at the heart of OOF3D’s mesh adaptation methods, 

which construct a mesh that is a good approximation to 

the geometry of a microstructure. The calculation is 

subtler than it first appears. The homogeneity calculation must be done quickly, so it’s not possible to 

consider each voxel individually. Instead, all voxels 

with a given material type are grouped, and the faces of 

the aggregate voxel group are determined. Finding the 

intersection of these faces with an element is the difficult 

step, because round-off error can lead the program to 

make the wrong decision about whether a point is inside 

or outside the tetrahedron, or about the ordering of two 

points on the perimeter of a polygon. The round-off 

problem arises when the nodes of the element lie on or 

near a boundary between two types of voxels, and the 

mesh adaptation methods unfortunately work to increase the frequency of these cases, because they 

maximize the homogeneity of the elements. 

One approach tried this year was to use thresholds 

and sloppy arithmetic to determine when points coincided. It was discovered that different thresholds were 

needed in different situations, and that no single set of 

threshold values would work in all situations. A new 

approach is being developed that will avoid the roundoff error problem by retaining more topological information about each intersection point. 

[1]	 S. A. Langer, A. C. E. Reid, F. Y. Congo, R. Lua and V. 

.R. Coffman, gtklogger: A Tool for Systematically Testing Graphical User Interfaces, NIST TN 1862, Aug 2015. 

[2]	 J. L. Molaro, S. Byrne and S.A. Langer, Grain-scale Thermoelastic Stresses and Spatiotemporal Temperature 

Gradients on Airless Bodies, Implications for Rock 

Breakdown, Journal of Geophysical Research: Planets 

120:2 (2015), 255-277. 

Determination of Diffusion 

Coefficients in Alloys 

Geoffrey McFadden 

Anthony Kearsley 

James Filliben (NIST ITL) 

William Boettinger (NIST MML) 

Carelyn Campbell (NIST MML) 

Kil-Won Moon (NIST MML)
 

Robert Sekerka (Carnegie Mellon University)
 

A common technique for the measurement of alloy diffusion coefficients is through the analysis of diffusion 

couples. A diffusion couple consists of two long homogeneous solid samples, each of differing alloy 

Figure 25. Top: Concentration (mole fraction of Aluminum in a ternary Aluminum-Cobalt-Tungsten alloy) versus distance (in meters) 

in a diffusion couple. The initial junction was at x=0. The black 

points are experimental data, and the solid red curve is a numerical 

solution to the ODE using a diffusion coefficient with three degrees 

of freedom that is chosen to fit the data. Bottom: Difference between 

the ODE solution and the experimental data versus distance. 

compositions, which are joined together to form a single 

sample with discontinuous concentration profiles. At 

high enough temperatures significant inter-diffusion 

may occur, allowing the concentrations profiles to relax 

in time. After a long enough time, this diffusion process 

would eventually lead to a homogeneous sample. At intermediate times the sample may be quenched to low 

temperatures, halting the diffusion process, and the spatial distribution of the resulting concentration profiles 

can be measured in detail. The time of measurement is 

ideally chosen so that the diffusion process is confined 

to the vicinity of the initial junction, leaving the far ends 

of the sample undisturbed at their initial concentrations. 

An example is shown in Figure 25. Fick’s law relates the 

flux of solute to the instantaneous concentration gradients at each point; the constants of proportionality are 

known as diffusion coefficients, which are generally 

functions of the local concentration at each point. The 

experimental determination of the diffusion coefficients 

is the goal of the project. Under the right conditions the 

diffusion couple can be modeled as a one-dimensional 

sample of infinite extent in each direction. The diffusion 

process is then modeled as a system of diffusion equations for the individual concentrations. For the idealized 

initial conditions there is a similarity solution due to 

Boltzmann in which the concentrations depend on the 

single independent coordinate (x – x0)/t

1/2, where x0 is the 

position of the initial discontinuity, and t is the elapsed 

time. Under this change of variables, the diffusion equations reduce to coupled nonlinear ordinary differential 

equations (ODEs) with far-field boundary conditions 

given by the initial concentrations in each sample. An 

inverse approach to the determination of diffusion coefficients is then to compare numerical solutions of the 

ODEs with the experimentally measured profiles, iterating on the diffusion coefficients to minimize the 
 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 49 

difference. Typically, we assume a low-order power series for the concentration dependence of the diffusion 

coefficients, using the polynomial coefficients as the unknowns in minimizing the error. An example of the 

resulting fit is shown in Figure 25. More general representations for the concentration dependence are also 

useful, as motivated by thermodynamic arguments. 

In some cases, an analytical approach can be used 

to obtain direct relations between the diffusion coefficients and the concentration profiles. For example, an 

appropriate integration of the ODEs produces a direct 

relation between the solute flux at a point and specific 

integrals of the concentration profiles. We have recently 

extended analyses of this type that pertain to single 

phase binary alloy systems to the more general case of 

multiphase, multicomponent systems [1]. 

[1]	 R. F. Sekerka, G. B. McFadden and W. J. Boettinger, Analytical Derivation of the Sauer-Freise-den Broeder Flux 

Equation for Multicomponent Multiphase Diffusion Couples with Variable Molar Volume, in preparation. 

Verification and Validation of Finite 

Element Method-based Solutions 

Jeffrey T. Fong 

James J. Filliben (NIST ITL)
 

N. Alan Heckert (NIST ITL)
 

Stephen Freiman (NIST MML) 

Li Ma (NIST MML) 

Ward Johnson (NIST MML)
 

Stephen Russek (NIST PML)
 

Karl Stupic (NIST PML)
 

Katherine Keenan (NIST PML) 

Pedro V. Marcal (MPACT Corp.)
 

Robert Rainsberger (XYZ Scientific) 

The finite element method (FEM) and the mathematics 

of the verification and validation (V&V) of its computational results [1, 2] have been of interest to engineers and 

scientists since the 1960s. Difficulties in “correct” modeling and “accurate” computing for large-scale practical 

problems involving complex geometry and uncertainty 

in governing equations and physical parameters have 

created a need to develop efficient methods and subsequently recommended practices of FEM V&V. The 

availability of many commercial FEM codes that are increasingly user-friendly has complicated the problem of 

answering the fundamental question, “is the FEM result 

correct, and what are its confidence bounds?” By considering every FEM solution as the result of a numerical 

experiment and by using a combination of three mathematical methods, we have developed a new approach to 

the V & V of FEM. 

Errors and uncertainties in FEM modeling and computing are known to originate from at least seven 

sources: (1) Numerical algorithm of approximation for 

solving a system of partial differential equations with initial and boundary conditions; (2) the choice and design 

of the finite element mesh and element type; (3) the 

choice of when to stop computing before verification; 

(4) the uncertainty in the geometric parameters; (5) the 

uncertainty in the physical and material property parameters; (6) the uncertainty in the loading parameters, and 

(7) the uncertainty in the choice of a correct model. Examples of developing local and global validation metrics 

for specific classes of problems in scientific computing 

not using FEM have appeared in the literature (see, e.g., 

[3, 4]). Using a fractional factorial orthogonal two-level 

design of experiments [5], we addressed in a 2008 paper 

[6] the FEM uncertainty problem for sources (4), (5), 

and (6). To address source (3), we used a nonlinear least 

squares algorithm and a mathematical function named 

the logistic distribution (after Verhulst [7]), that allows 

a user to fit a sequence of FEM solutions of increasing 

mesh density such that a “plateau” is predicted as the 

right horizontal asymptote representing the extrapolated 

solution at “infinite” degrees of freedom (see Figure 26, 

and [8]). To address sources (1) and (2), we recently 

expanded our 2008 experimental design [6] to check the 

“robustness” of the FEM platform and element type in a 

new design involving both continuous and discrete factors. Source (7) is, of course, addressed by experiments. 

[1]	 O. C. Zienkiewicz and R. L. Taylor, The Finite Element 

Method, Volume 1: The Basis, 5th edition, ButterworthHeinemann, 2000. 

[2]	 W. L. Oberkampf and C. J. Roy, Verification and Validation in Scientific Computing, Cambridge University 

Press, 2010. 

[3]	 M. F. Barone, W. L. Oberkampf and F. G. Blottner, Validation Case Study: Prediction of Compressible 

Turbulent Mixing Layer Growth Rate, AIAA Journal 44:7 

(2006), 1488-1497. 

[4]	 W. L. Oberkampf and M. F. Barone, Measures of Agreement Between Computation and Experiment: Validation 

Metrics, Journal of Computational Physics 217 (2006), 

5-36. 

[5]	 G. E. P. Box, W. G. Hunter and J. S. Hunter, Statistics for 

Experimenters, 1st edition, Wiley, 1978. 

[6]	 J. T. Fong, J. J. Filliben, N. A. Heckert and R. deWit, Design of Experiments Approach to Verification and 

Uncertainty Estimation of Simulations based on Finite 

Element Method, in Proceedings of the Conference of the 

American Society for Engineering Education, June 22-25, 

2008, Pittsburgh, PA, AC2008-2725. 

[7]	 P. F. Verhulst, Recherches Mathematiques sur la Loi 

d’Accroissement de la Population,” [Mathematical Research into the Law of Population Growth Increase], 

1845, re-published in Nouveaux Memoires de l’Academie 

Royaledes Sciences et Belles-Lettres de Bruxelles 18 

(2013), 1-42. 

[8]	 J. T. Fong, J. J. Filliben, N. A. Heckert, P. V. Marcal, R. 

Rainsberger and L. Ma, Uncertainty Quantification of 
 

 

 

 

 

 

50 NIST Applied and Computational Mathematics Division 

Figure 26. Extrapolation of coarse finite element solutions to finer meshes with larger degrees of freedom. 

Stresses in a Cracked Pipe Elbow Weldment using a Logistic Function Fit, a Nonlinear Least Squares Algorithm, 

and a Super-Parametric Method, Procedia Engineering 

130 (2015), 135-149. DOI: 10.1016/j.proeng.2015.12.183 

Inversion of the Abel Transform by 

Truncated Singular Components 

Method 

Timothy J. Burns 

Bert W. Rust 

Despite many years of study, the determination of accurate constitutive response models for the flow stress in 

materials for finite-element simulations of high-speed 

machining operations remains a difficult unsolved problem. Most attempts to model the material response have 

been based on direct methods that fit compression test 

data of small samples of the material of interest to a 

given highly nonlinear constitutive response model. The 

main problem with this approach has been that the conditions under which compression tests can be performed 

are not nearly as extreme as the actual conditions that 

are present in a typical high-speed machining operation 

[1], so that a machining process simulation using the 

nonlinear material response model necessarily requires 

huge extrapolations in order to simulate the cutting conditions. 

One area of machining research in which significant 

progress has been made in the past few years has been 

in the measurement of the 2D temperature distribution 

on the chip–tool interface using infrared thermography. 

In particular, Menon and Madhavan [2] have reported 

high accuracy temperature measurements during highspeed machining of a titanium alloy, using single wavelength thermography with an instrumented transparent 

tool. For their experimental cutting conditions, they 

have obtained a 1D temperature distribution as a function of distance along the rake face of the tool, along an 

internal cross section of the chip–tool interface, with an 

estimated uncertainty of less than 1 %. Motivated by this 

work, we have been investigating a new approach to the 

problem of estimating flow stress in machining that is 

based on an inverse method. By finding an asymptotic 

solution of a convection-diffusion problem that models 

the flux of heat into the chip and the tool during a cutting 

experiment, the temperature distribution along the tool 

face can be shown to satisfy Abel’s equation, a Volterra 
 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 51 

integral equation of the first kind with a weakly singular 

kernel, convolved with the flow stress [3]. Inversion of 

this Abel transform provides an estimate of the distribution of flow stress in the chip material near the tool-chip 

interface. 

Because the temperature data are discrete and experimentally determined, estimation of the flow stress 

by inversion of the Abel transform under these circumstances is an ill-posed problem. This year, we have 

shown that the Truncated Singular Components Method 

(TSCM) of Rust [4], [5], which has been successfully 

used to find approximate numerical solutions of 

Fredholm integral equations of the first kind with noisy 

data, can also be applied to find approximate numerical 

solutions of the Abel equation [6]. The basic idea is to 

discretize the integral equation, and obtain an overdetermined system of linear equations, that is perturbed by 

the measurement errors, which are assumed to be samples from a univariate normal distribution, as is typically 

the case. Using methods that have been developed for 

the statistical analysis of time series, we treat the discrete 

problem as a linear regression problem. The key idea is 

to use the singular value decomposition of the matrix of 

the system to separate signal from noise in the data, prior 

to obtaining an estimate of the desired solution of the 

integral equation. A paper on this work is in preparation. 

[1]	 S. P. Mates, R. L. Rhorer, E. P. Whitenton, T. J. Burns 

and D. Basak, A Pulse-Heated Kolsky Bar Technique for 

Measuring Flow Stress of Metals Subjected to High 

Loading and Heating Rates, Experimental Mechanics 48 

(2008), 799–807. 

[2]	 T. Menon and V. Madhavan, Infrared Thermography of 

the Chip-Tool Interface through Transparent Cutting 

Tools, in Proceedings of the North American Manufacturing Research Institution/SME, Ann Arbor, MI, June 

2014. 

[3]	 T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. Whitenton 

and D. Basak, Inverse Method for Estimating Shear 

Stress in Machining. Journal of Mechanics and Physics 

of Solids 86 (2016), 220–236. 

[4]	 B. W. Rust, Truncating the Singular Value Decomposition for Ill-Posed Problems, NIST IR 6131, July 1998. 

[5]	 B. W. Rust and D. P. O’Leary, Residual Periodograms for 

Choosing Regularization Parameters for Ill-Posed Problems, Inverse Problems 24 (2008), 034005 (30 pages). 

DOI:10.1088/0266-5611/24/3/034005. 

[6]	 T. J. Burns and B. W. Rust, “Estimation of Shear Stress 

in Machining by Approximating the Solution of a 

Volterra Integral Equation of the First Kind,” ASME 

2015 Applied Mechanics and Materials Conference, 

McMAT2015, Seattle, WA, June 2015. 
 

 

 

 

 

 

 

 

 

 

 

 

52 NIST Applied and Computational Mathematics Division 

High Performance Computing and Visualization
 

Computational capability is advancing rapidly, with the result that modeling and simulation can be done with 

greatly increased fidelity (e.g., higher resolution, more complex physics). However, developing the requisite 

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

In addition, the hardware landscape is changing rapidly, so new algorithmic techniques must constantly be 

developed. We are developing and applying such expertise for application to NIST problems. In addition, computations and laboratory experiments often produce large volumes of scientific data, which cannot be readily 

comprehended without some form of visual analysis. We are developing the infrastructure necessary for advanced visualization of scientific data, including the use of 3D immersive environments and applying this to 

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

High Precision Calculations of 

Fundamental Properties of FewElectron Atomic Systems 

James Sims
 

Stanley Hagstrom (Indiana University) 

Maria B. Ruiz (University of Erlangen) 

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

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

as the atomic properties of the elements contained in the 

Periodic Table and the vibrational and electronic energy 

level data for neutral and ionic molecules contained in 

the NIST Chemistry WebBook. Fundamental to this 

endeavor is the ability to predict, theoretically, a 

property more accurately than even the most accurate 

experiments. It is our goal to be able to accomplish this 

for few-electron atomic systems. 

While impressive advances have been made 

throughout the years in the study of atomic structure, at 

both the experimental and theoretical levels, information 

on atomic energy levels remains scarce, especially for 

highly ionized atoms. The availability of high precision 

results tails off as the state of ionization increases, not to 

mention higher angular momentum states. In addition, 

atomic anions have more diffuse electronic 

distributions, thus representing more challenging 

computational targets than corresponding ground states. 

In the past two decades, there have been 

breathtaking improvements in computer hardware as 

well as 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. Our 

contribution in this arena has been undertaking the 

theoretical development of our hybrid Hylleraas-CI 

(Hy-CI) wave function method to bring sub-chemical 

accuracy to atomic systems with more than two 

electrons. Our Hy-CI method has been employed to 

explore its utility for both three electron lithium systems 

and the four electron beryllium (Be) atom. In the case of 

lithium, we have computed four excited states of the 

lithium atom two orders of magnitude more accurately 

than has been done before [1]. 

At the four electron level, to get truly accurate 

chemical properties, such as familiar chemical electron 

affinities and ionization energies, it is important to get 

close to the nanohartree level we achieved for the three 

election atom, a significantly more difficult problem for 

four electrons than for three. By investigating more flexible atomic orbital basis sets and better configuration 

state function filtering techniques to control expansion 

lengths, we have been able to successfully tackle the 

four electron case. Progress to date has included computing the non-relativistic ground state energy of not only 

beryllium, but many members of its isoelectronic series 

to 8 significant digit accuracy. With the results from our 

calculations, and a least squares fit of the calculated energies, we have been able to compute the entire 

beryllium ground state isoelectronic sequence [2]. 

The next step to enabling the calculation, not just 

for the ground singlet S symmetry of the beryllium atom 

and other members of its isoelectronic sequence, but 

higher angular momentum states as well, is to complete 

the process of making the four electron integrals, the real 

bottleneck at the 4 and more electron level, as efficient 

as possible, as well as modifying the codes to be able to 

compute the energy levels of the Be atom for states of 

different spin, angular momentum and N quantum number than the ground state. 

The first part of this code revision has been completed and a paper on the mathematical and 

computational science issues involved in doing Hy-CI 

four electron integrals published [3]. We are currently 

doing a calculation on the first excited Be state of singlet 

S symmetry and plan to do three or four more states of 

the same symmetry. Then our plans are to modify the 

code to handle triplet spin, and treat non-S angular momentum states as well by generalizing our angular 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 53 

momentum projector, currently limited to S states, to 

handle states of any angular momentum symmetry. This 

will enable the calculation of higher angular momentum 

states of the four electron atom and its ions. 

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

Doublet S Ground State of Neutral Lithium and the First 

Five Excited Doublet S States, Physical Review A 80 

(2009), 052507. 

[2]	 J. S. Sims and S. A. Hagstrom, Hylleraas-configurationinteraction Nonrelativistic Energies for the Singlet S 

Ground States of the Beryllium Isoelectronic Series Up 

through Z = 113, Journal of Chemical Physics 140 

(2014), 224312. 

[3]	 James S. Sims and Stanley A. Hagstrom, Mathematical 

and Computational Science Issues in High Precision 

Hylleraas-Configuration Interaction Variational 

Calculations: III. Four-electron Integrals, Journal of 

Physics B: Atomic, Molecular and Optical Physics 48 

(2015), 175003. 

Nano-structures, Nano-optics, and 

Control of Exciton Fine Structure 

with Electric and Magnetic Fields 

James S. Sims
 

Wesley Griffin
 

Judith Terrill 

Garnett W. Bryant (NIST PML) 

Jian Chen (UMBC) 

Henan Zhao (UMBC) 

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 been identified as 

a national priority. Semiconductor nanoparticles, also 

known as nanocrystals and quantum dots (QDs), are one 

of the most intensely studied nanotechnology paradigms. Nanoparticles are typically 1 nm to 10 nm in size, 

consisting of 103

 to 106 atoms. Precise control of particle 

size, shape and composition allows one to tailor charge 

distributions and control quantum effects to obtain properties completely different from the bulk or from small 

clusters. As a result of quantum confinement effects, nanoparticles act as artificial atoms, with discrete 

electronic spectra that can be exploited as light sources 

for enhanced lasers, discrete components in nanoelectronics, qubits for quantum information processing, and 

ultrastable fluorescent labels for biosensors to detect 

pathogens and to do cell biology. 

We are working with the NIST Physical Measurement Lab (PML) 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. In particular, electrical, mechanical, 

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 106

 atoms. High performance computational and visualization tools are critical for obtaining the throughput 

necessary for systematic, comprehensive study. 

As device sizes in silicon (Si) electronics continues 

to decrease, devices are rapidly approaching the atomic 

scale where a change in only a few atoms can make a 

significant change in device performance. At the same 

time, the ability to make Si nanodevices with only a few, 

deterministically placed dopant atoms opens the possibility to create quantum information processing devices 

with these structures. We are currently participating in a 

program which aims to make, characterize, and model 

both traditional and quantum Si devices at this few-dopant atom limit. Atomistic modeling must be used. 

We are currently extending our tight-binding atomistic modeling codes to consider Si structures with just a 

few dopant atoms. This requires an extension to Si, developing and implementing models for dopants, and 

including the effects of potentials provided by gates, 

sources and drains. Work is underway to develop codes 

that provide the needed potentials, develop the visualization tools needed for these simulations, and develop 

the parallelization methods needed to ensure that the atomistic tools remain computationally tractable. 

As part of a continuing NIST grant award, Jian 

Chen and Henan Zhao of UMBC have developed a desktop visualization tool for the numerical simulation 

output in close cooperation with NIST PML collaborator 

Garnett Bryant. The tool employs a novel visualization 

technique developed last year [1]; a paper describing 

this new technique is currently in review [2]. Figure 27 

is a snapshot from the current version of the tool. The 

tool has gone through several iterations as Bryant has 

applied the tool to existing datasets. As part of this iterative process, we designed and validated a coloring 

approach that generates a perceptually uniform scale 

where colors at equal parameter distance have an equal 

perceived color difference. We coupled this with an orientation clustering to show the cosine distances among 

vectors. Orientation of the spatial distribution is an important metric since it determines how to understand and 

engineer spin control. The cosine distance provided 

faster understanding of the 3D structure. We also developed shape clustering methods to automate visual 

pattern finding in orientations, and implemented usercontrollable cutting planes and regions of interest. 

[1]	 J. Chen, H. Zhao, W. Griffin, J. Terrill and G. Bryant, 

Validation of Split Vector Encoding and Stereoscopy for 

Quantitative Visualization of Quantum Physics Data in 

Virtual Environment, poster, IEEE Virtual Reality 

(VR2015), Arles France, March 23-27, 2015. 
 

 

 

 

54 NIST Applied and Computational Mathematics Division 

Figure 27. Visualization of a nanostructure composed of Indium-Arsenic. Clustering is based on magnitude and the legend indicates the clustering. The structure of the data is clearly seen as a “tabletop” with four legs. The Split Vector encoding technique ensures that all of the data 

is visible, even though the range of magnitudes is from 10-16 to 10-3. 

[2]	 H. Zhao, G. Bryant, W. Griffin, J. Terrill and J. Chen, 

Validation of Split Vector Encoding and Stereoscopy for 

Quantitative Visualization of Quantum Physics Data, in 

review. 

Rheology of Dense Suspensions 

William George 

Judith Terrill 

Steven Satterfield 

John Hagedorn 

Marc Olano 

Nicos Martys (NIST EL) 

Chiara Ferraris (NIST EL) 

Pascal Hebraud (CNRS/IPCMS) 

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

suspensions, is of 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. Predicting the flow of such systems is challenging, requiring very 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 [1]. This 

simulator uses a modified version of the dissipative particle dynamics technique [2] for the simulation of 

Newtonian fluids, and the smoothed particle hydrodynamics technique (SPH) [3] for the simulation of nonNewtonian fluids. 

QDPD is highly parallel and has been shown to efficiently scale up to 128 000 processors when running 

on the US Department of Energy (DOE) supercomputer 

Mira (IBM Blue Gene/Q) at the Argonne National Laboratory Leadership Computing Facility. Our goal is to 
 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 55 

Figure 28. A snapshot from a QDPD simulation of a proposed mortar SRM in a 6-blade rheometer with a view from the bottom of the 

rheometer. From this view, the blades are rotating clockwise. The 

suspended spheres are color-coded by their starting section. 

Figure 29. A snapshot from a QDPD simulation of a proposed mortar SRM in a 4-blade rheometer. This is a view from the bottom of 

the rheometer. From this view, the blades are rotating clockwise. 

The suspended spheres are color-coded by their starting quadrant. 

advance our understanding of the flow properties of a 

specific material, fresh concrete, a dense suspension 

composed of cement, water, sand, and rocks. We are 

using this code for two projects: a study of vane rheometers and flow in a pipe system. 

Vane Rheometers. We are currently using this computational approach in the development of standard 

reference materials (SRMs) for the calibration of vane 

rheometers used to measure the flow properties of fresh 

concrete. Figure 28 and Figure 29 show snapshots of 

our rheometer simulations of the proposed mortar SRM 

in a vane rheometer. While concrete flow measurements, using different concrete rheometers, can be found 

to correlate, they usually do not provide identical absolute values. This is a consequence of the complex flow 

patterns that develop in the rheometer combined with 

the non-Newtonian behavior of the mortar or concrete. 

This results in complex local stress and strain/strain rate 

fields that make it difficult to express measurement data 

in terms of fundamental rheological parameters. By 

modeling the flow of an SRM in a vane rheometer, we 

are able to predict what should be measured by an experimentalist. Furthermore, we design our simulations 

to map out many details of the local flow, such as 

stress/strain fields in 3D, in order to provide insight into 

the process. Most research on suspensions has made the 

simplifying assumption that the matrix fluid, that is, the 

fluid supporting the suspended particle, is Newtonian. 

With the use of high-performance computing, we have 

been able to simulate suspensions with non-Newtonian 

fluid matrices, which includes most suspensions of interest to industry. 

Our simulations have demonstrated that the viscosity versus shear rate curves for suspensions having 

various volume fractions can be collapsed onto a single 

universal curve parameterized by the properties of the 

underlying non-Newtonian matrix fluid [4]. This, along 

with other results from our studies, has advanced our understanding of the flow of dense suspensions [5-6]. 

Building on this research, we have begun using simulation in the design process for new standard reference 

Figure 30.. A design drawing for a proposed “double-helix” 

rheometer blade. 
 

 

 

 

 

 

 

 

 

56 NIST Applied and Computational Mathematics Division 

Figure 31. One layer is isolated for a visual speed comparison during animation of the simulation data. 

Figure 32. Velocity profile plots show velocity of the solids near 

the pipe wall is much greater for shear thinning (non-Newtonian) 

case. 

materials (SRMs) which will be used for calibrating 

mortar and concrete rheometers. See Figure 28 and 

Figure 29. The first such SRM will be mortar, which 

should be completed in 2016, followed by concrete a 

year later. 

To support our study, we submitted a proposal for 

supercomputer time to the DOE Advanced Scientific 

Computing Research (ASCR) Leadership Computing 

Challenge (ALCC), in February 2015. This resulted in 

an award of 50 million CPU-hours of supercomputer 

time on the IBM Blue Gene/Q, Mira, at the Argonne 

Leadership Computing Facility. Mira, currently ranked 

5th on the Top 500 list of supercomputer installations,30 

will enable us to perform high fidelity simulations. 

Our simulations in 2016 will focus on the design of 

the blades within the rheometers. The current typical design, with 4 or 6 flat blades, has been shown to be suboptimal [7-8] and other blade designs are under consideration. We will modify our simulator to study newly 

proposed blade designs, such as the “double-helix” 

blade shown in Figure 30. 

Flow in Two Pipe Systems. We have also investigated 

another flow geometry of interest to industry, a 

pipe/channel system. Flows of suspensions through such 

systems are important for a wide variety of applications, 

including pumping of concrete and slurries, micro30 http://www.top500.org 

fluidic devices, and biological systems. Many 

computational experiments were required to develop a 

model of the forces between the wall of the pipe and the 

suspended inclusions, as well as the forces between the 

matrix fluid and the pipe. Although these simulations 

on the NIST cluster, Raritan, are still underway, initial 

results of this study have been submitted for 

presentation at the International Concrete Sustainability 

Conference (SCC2016) scheduled for May 2016 [9]. A 

more complete report will be published once all of our 

pipe-flow simulations have been completed. 

A critical part of the understanding of the two pipe 

system is visualization of the results in the NIST Cave 

Automatic Virtual Environment (CAVE). Specifically, 

a CAVE application was created for comparison of 

Newtonian and non-Newtonian fluids. Two pipe flow 

data sets, one Newtonian and one non-Newtonian, 

produced by numerical simulations are displayed and 

analyzed. The capabilities of the NIST 3D environment 

are used to do a side by side comparison of a Newtonian 

matrix fluid and a non-Newtonian shear thinning matrix 

fluid; see Figure 31. Animation controls allow 

simulation time to be played forward/backward at full or 

single step speeds. One layer can be isolated and 

displayed to visually compare the velocity of the two 

simulations. Quarter sections of both pipe flows may be 

turned on and off to reveal the inner data (flow); see 

Figure 32. Interactive sliders provide flexibility for side 

by side comparison at almost any position (side-by-side, 

overlapping, over/under, front/back). User controlled 

navigation through the 3D space provides viewing from 

any point of view. The virtual models can be scaled from 

hand held objects to human (and larger) sizes. 

The immersive environment has an interactive 

clipping plane tool, which behaves like a “data 

windshield”. It cuts away the data elements between the 

user and the clipping plane. For this project an analysis 

capability was added to this data probe. While the user 

explores the flowing particles with the clipping tool, 

average velocity of the simulated flow is extracted and 

displayed to the user as an xy line plot. By creating a line 

plot, it may be positioned on the clipping tool making it 

visible to the natural line of sight. The view is somewhat 

like a heads-up-display or virtual augmented reality. The 

numerical analysis represented by the line plot can be 

easily studied in the context of the corresponding 

physical location. The plot is dynamically updated 

corresponding to both the simulation time step (frame 

number) and the z layer position used to compute 

average velocity. A novel line plot algorithm was 

created consisting of 3D line segments in virtual 3D 

space. This type of object is also known as a wire-frame 

model. Additionally, to draw numerical values, a pure 

stroke font was needed. The Hershey fonts, originally 

developed in 1967 were utilized for the stroke font. The 
 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 57 

Figure 33. Density profile plots show he density of the solids is greater near the central axis of the tube. 

xy plot wire frame geometry used to render the velocity 

vs radius plot is generally sparse enough to allow 

viewing of both the analysis and the underlying 

geometry. 

Results. Several results are clearly indicated in the 

analysis and visualization of the simulation data. 

	 The shear thinning system flows much more 

quickly than the Newtonian system; see Figure 31. 

	 The velocity of the solids near the pipe wall is 

much greater for shear thinning (non-Newtonian); 

see Figure 32. 

	 For both fluid types, the solid density is greater 

near the central axis of the tube, the effect being 

enhanced for the Newtonian case as supported by 

the density profile graph; see Figure 33. 

[1]	 N. Martys, Study of a Dissipative Particle Dynamics 

Based Approach for Modeling Suspensions, Journal of 

Rheology 49:2 (2005), 401-424. 

[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]	 M. Liard, N. S. Martys, W. L. George, D. Lootens and P. 

Hebraud, Scaling laws for the flow of generalized Newtonian suspensions, Journal of Rheology 58 (2014), 1993. 

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

Hebraud, Stress Propagation in a Concentrated Colloidal 

Suspension under Shear, The European Physical Journal 

E 35:3 (2012), 20. 

[6]	 P. Hebraud, D. Lootens, and N. Martys, “Stress Organization in an Attractive Concentrated Colloidal 

Suspension under Flow”, XVIth International Conference 

on Rheology, Lisbon, Portugal, Aug-2012. 

[7]	 C. Ferraris and L. Brower, eds., Comparison of Concrete 

Rheometers: International Tests at LCPC (Nantes, 

France) in October 2000, NISTIR 6819, September 2001. 

[8]	 C. Ferraris and L. Brower, eds., Comparison of Concrete 

Rheometers: International Tests at MB (Cleveland OH, 

USA) in May 2003, NISTIR 7154, September 2004 

[9]	 N. S. Martys, C. F. Ferraris and W. L. George, Modeling 

of Suspension Flow in a Pipe Geometry and Rheometers, 

in review. 

[10] S. Satterfield, N. Martys, W. George, J. Hagedorn and J. 

Terrill, Suspension Flow in Pipe Systems: Comparison of 

Newtonian and Shear Thinning Fluid, movie presented at 

the NIST Booth at SC15, The International Conference 

for High Performance Computing, Networking, Storage 

and Analysis, November 15-20, 2015. 
 

 

 

 

 

 

 

 

 

 

 

58 NIST Applied and Computational Mathematics Division 

HydratiCA: A Parallelized Numeric 

Model of Cement Hydration 

John Hagedorn 

Judith Terrill 

Wesley Griffin 

Steven Satterfield 

Jeffrey Bullard (NIST EL) 

Joshua Arnold (NIST EL) 

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

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

HydratiCA is a stochastic reaction-diffusion model of 

cement hydration. The hydration that occurs after cement powder is mixed with water transforms the paste 

from a fluid suspension into a hardened solid. This process 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 threedimensional spatial domain. HydratiCA addresses these 

challenges with a computational model that has several 

advantages over other models of cement hydration. 

Parallelization of the model and the visualization of 

the output data are important components of this project. 

With parallelization we can simulate systems that are 

large enough to be realistic, avoiding finite size effects, 

and still be able to complete the simulations in a reasonable amount of time. Visualization of the data volumes 

produced by HydratiCA is important both for validation 

and for understanding of the results. 

HydratiCA discretizes space into a three-dimensional lattice of computational sites, with the material 

composition described at each site. The simulation occurs in a series of time steps, which are typically on the 

order of 1 msec. During each time step, material at a site 

may migrate to a neighboring site to simulate diffusion, 

or react with other materials at the same site to produce 

other materials. Each of these types of events is modeled 

stochastically, assigning a probability to each event 

based on the mobility or the reaction rate constant and 

driving force. Each site is visited during each time step, 

and the material amounts are updated accordingly. 

This year we continued work on HydratiCA with 

significant improvements to the algorithm, the parallel 

implementation, and visualization. We obtained new results from large-scale runs on the Stampede supercomputer at the Texas Advanced Computing Center. We 

also made substantial strides in our visualization results. 

In the next year, we will perform much larger simulations on Stampede, a supercomputer housed at the Texas 

Advanced Computing Center (TACC) through a grant 

from the NSF Extreme Science and Engineering Discovery Environment (XSEDE) program. 

Figure 34. Immersive display of the growth of C3S particles (blue) 

hydrating in a calcium hydroxide solution. Regions of orange are 

where hydration reactions have produced solid calcium hydrate reaction product. 

Figure 35. An example of the 2D quantitative visualization of C3S 

hydration metrics. This display and all interactions are within a web 

browser. 

Parallel Implementation. HydratiCA has been 

parallelized using a spatial block decomposition of the 

three-dimensional array of computational sites. Each 

block is handled by a single processor. Communication 

between processors is necessary for several operations, 

most importantly for the diffusion step during which 

materials migrate to neighboring sites. All interprocess 

communication is accomplished through use of the 

Message Passing Interface (MPI). 

During this year, various changes have been made 

to improve both the accuracy of the algorithm and the 

functionality of the implementation. Algorithm changes 

have centered around the proper handling of problems 

that result from the discretization of space and time. 

Changes to the parallel implementation include bug 

fixes, improvement to the communication schemes, and 

various performance optimizations. In addition, the parallel checkpointing scheme was substantially improved 

both in usability and in robustness. 
 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 59 

initial configuration hydrated 7 hours hydrated 24 hours 

Figure 36. A comparison of the results of the HydratiCA simulation to experimental results. The volume 

of growth of CSH that was found experimentally after seven hours is represented in the center image by 

the transparent surface. 

Visualization. Substantial improvements have been 

made to our visualization software that enables us to understand and interact with results from our HydratiCA 

runs. The current visualization tool is a hybrid 3D immersive and 2D quantitative visualization. Figure 34 and 

Figure 35 show the immersive 3D display and the quantitative 2D display respectively. This hybrid tool enables 

one to track the spatial evolution of phases and solution 

composition. The 2D quantitative graphs are displayed 

in NIST’s immersive visualization environment at the 

same time as the 3D visualization. The graphs and 3D 

visualization change with the time step in sync. The 3D 

and 2D visualizations communicate bi-directionally under user control. Geometric clipping and parameter 

clipping are enabled. One can also probe the data dependencies to begin establishing kinetic relationships 

among members of the reaction network. This is invaluable for discovering new physio-chemical relationships 

during hydration, and will become more powerful for 

analyzing more complicated cement systems. 

Results. Last year we received a grant of computer time 

from NSF’s XSEDE program, enabling us to do large 

scale runs on Stampede at TACC. We have used this resource to do direct comparisons between time-resolved 

3D nanoscale observations of the hydration of tricalcium 

silicate (C3S) and simulations of the same system using 

HydratiCA. In particular, we compared nano-computed 

tomography (nCT) observations of C3S particles hydrating in a calcium hydroxide (CH) solution to HydratiCA 

simulations that duplicate, as nearly as possible, the 

thermal and chemical conditions of the experiment. 

Note that one of the principal products of this hydration 

is calcium silicate hydrate (CSH). 

Figure 36 shows a comparison of the results of the 

experiment with the results of the simulation. The initial 

configuration of materials for the simulation is derived 

directly from the initial nCT 3D image. HydratiCA captures the general trends observed in the nCT 

experimental data, but the 

experiment shows a much 

more voluminous hydration 

product. After seven hours 

of simulated time, the volume of CSH is not nearly as 

large as that observed in the 

nCT image after seven 

hours. After 24 hours of 

simulated time, the CSH 

volume has increased but 

has still not as large that the 

seven-hour experimental 

observation. Possible reasons for this differences are: 

 CSH has a much 

larger effective molar 

volume than previously 

indicated by experiments. 

	 In the experiment, CSH from hydrating particles 

outside the field of view (which are not included in 

the simulation) is migrating to the particles that are 

in the field of view. 

In addition to investigating these discrepancies, our future work will be focused on calculating the timedependent rate of heat release, and on the development 

of the percolating solid network that is responsible for 

the hardening of concrete. We have mapped out a sequence of simulations that use realistic particle size and 

shape distributions that have been measured experimentally. This enables us to closely approximate the initial 

conditions of real cementitious systems so that simulation results and experimental measurements can be 

meaningfully compared. These runs will be accomplished through a grant of an additional 743K CPUhours on Stampede through the NSF XSEDE program. 

[1]	 J. Bullard, T. Ley, J. Hagedorn, R. Desaymons, W. Griffin, J. Terrill, Q. Hu, S. Satterfield and P. Gough, Direct 

Comparisons of 3D Hydration Experiments and Simulations, 6th Advances in Cement-Based Materials 

Conference, July 2015. 

[2]	 J. Hagedorn, J. Bullard, R. Desaymons, W. Griffin, J. 

Terrill, T. Ley, Q. Hu, S. Satterfield and P. Gough, 

HydratiCA: A Parallelized Numeric Model of Cement 

Hydration, XSEDE 2015, July 2015. 

[3]	 W. Griffin, D. Catacora, S. Satterfield, J. Bullard and J. 

Terrill, Incorporating D3.js Information Visualization 

into Immersive Virtual Environments, VR2015 IEEE 

Virtual Reality, March 2015. 

[4]	 J. Stoian, T. Oey, J. W. Bullard, J. Huang, A. Kumar, M. 

Balonis, J. E. Terrill, N. Neithalath and G. Sant, New Insights into the Prehydration of Cement and its Mitigation, 

Cement and Concrete Research, 70, 94-103, April 2015. 
 

 

 

 

 

 

60 NIST Applied and Computational Mathematics Division 

Network Simulation Visualization 

Sandy Ressler 

Phil Gough (CSIRO)
 

Kevin Mills (NIST ITL) 

Christopher Dabrowski (NIST ITL)
 

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

Recent work by Mills and Dabrowski [1] has produced 

a network simulation that examines the effect of realistic 

parameter changes on network performance. NIST 

guest researcher Phil Gough produced an interactive 

visualization tool for network simulation data produced 

by this simulation. This tool allows researchers to 

closely examine the results of simulations and to easily 

identify conditions such as network congestion. 

Produced using D3, a JavaScript based information 

visualization library, it is available online31. 

[1]	 K. L. Mills and C. E. Dabrowski, The Influence of 

Realism on Congestion in Network Simulations, NIST 

TN 1905, January 2016. 

[2]	 P. Gough, “Comparing Visualization Approaches to 

Communicating Science to Non-Scientists,” ACM 

SIGGRAPH, Los Angeles, Aug. 9, 2015. 

Figure 37. Network simulation visualization tool details. There 

are five groups or types of nodes (indicated by color of interior of 

circle). Node congestion or occupancy is indicated by color of 

border of circle. Two small circles inside of node indicates queue 

length of up (top) or down (bottom) queue. This work is effectively 

complete however we anticipate producing some animations illustrating the behavior of the network simulations. 

Figure 38. Network simulation visualization tool. Topology on the left side of the display illustrates queue lengths and congestion state. 

Column type displays on the right side allows a user to select parameter input to simulation and displays congestion for each type of node 

group. The graph on bottom displays congestion and lets user step through the time of simulation. Currently two datasets are available one 

with 250 time steps, the other with 3000 time steps. Simply use the desired number in the URL. 

31 http://math.nist.gov/~SRessler/pjg4/networkVis/?dataset=250 
 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 61 

Image-based WebVR Graphics 

Sandy Ressler 

Tomasz Bednarz (CSIRO) 

Kyle Davis (The College of New Jersey) 

Steve Satterfield
 

WebVR is a form of virtual reality (VR) that displays in 

a web page. Everyone has a web browser and given a 

location (a URL), access to information is 

straightforward and virtually unlimited. Graphics 

presented in web pages has become enhanced with the 

arrival and support of WebGL, a web based version of 

the time-tested OpenGL32 specification. Simply put, if 

you go to a page with WebGL 3D graphics it will be 

displayed correctly in your web browser without the 

need for any browser plug-ins. This means that complex 

3D graphics can be placed into web pages, and the rich 

capabilities of these graphics can be used within a web 

page. Similarly, VR environments can now be placed 

into web pages via the WebVR extension. 

One of the big differences from the VR of 20 years 

ago is the ability to create and use 360-degree video 

environments. These image-based environments offer a 

simple method to bring users and the public to places 

that are inaccessible, dangerous or simply forbidden. 

Our first taste of a widely used method of pseudo imagebased VR is an application such as Google Streetview. 

People have modified Streetview to work with Oculus 

Rift headsets33. Clearly this is just the beginning of more 

image based VR on the web. 

We can work with three types of images: computer 

generated graphics, image-based environments, and 

combinations of the two (which leads to a type of 

augmented reality). Each of these has different 

authoring and interaction requirements. Placing these 

images into web pages presents both opportunities and 

challenges. Much of our web-based 3D graphics has 

been built using the X3D graphics standard. Given our 

desire to work with this material using an immersive 

head-mounted display such as the Oculus Rift [1], our 

summer SURF student Kyle Davis created a tool to 

convert X3D files to files that are usable by the Rift; see 

Figure 39. This tool is able to take X3D files of computer 

graphic scenes and make them viewable as stereo pairs 

with WebGL code that allows for the personal 

adjustment of stereo separation34. In addition, there are 

user interface issues when wearing a helmet. Your hand 

effectively disappears and keyboard actions become 

difficult. One solution is to use additional devices such 

as the Leap motion tracking device which monitors your 

hands and can interpret gestures35; see Figure 40. 

32 https://www.opengl.org/
 

33 http://oculusstreetview.eu.pn/
 34 http://math.nist.gov/~SRessler/kmd3/Oculus/X3DToRiftTool.html
 

Figure 39. X3D to Oculus tool 

Figure 40. Leap gestures in use. 

Figure 41. Producing 360-degree video for embedding to web 

page. 

As a guest scientist at Australia’s Commonwealth 

Scientific and Industrial Research Organization 

(CSIRO) [2,3] for a month in Brisbane Australia, Sandy 

Ressler worked with Tomaz Benarz on immersive 3D 

web based video. They produced a prototype workflow 

and demonstrations of 360-degree videos using CSIRO 

equipment to photograph some interior scenes36. See 

Figure 41. 

A near term goal is to create a set of tools and a 

production path to allow people to author 360-degree 

image based environments with interactive areas. See 

Figure 42. Given appropriately indicated “hot-spots” 

users will be able to obtain additional information about 

objects in the scene, all within a web page. The end user 

35 http://math.nist.gov/~SRessler/kmd3/ 

36 http://math.nist.gov/~SRessler/w3d/CSIROwebvr.html#/ 
 

 

 

 

 

 

62 NIST Applied and Computational Mathematics Division 

Figure 42. Hypothetical production path for web-based immersive video content. 

will simply go to a URL and (while wearing a VR 

headset) look around the environment selecting points 

of interest. For example, an environment of a clean room 

for semiconductor manufacturing, a place with normally 

restricted access, can be explored with the user clicking 

on pieces of equipment getting additional information, 

including supplementary video, about the items of 

interest. 

[1]	 S. Ressler “Using Oculus Rift with your Web Browser for 

Science,” SIGGRAPH 2015 Birds of a Feather, August 

9-13, Los Angeles CA. http://slides.com/sressler/oculuswebsiggraph2015/ 

[2]	 S. Ressler, T. Bednarz, “Image Based WebVR: Creating 

and Publishing Environments for Browsers and HMDs,” 

CSIRO Seminar, Canberra, Australia, February 25, 2015. 

http://math.nist.gov/~SRessler/w3d/CSIROwebvr.html 

[3]	 S. Ressler, “WebVR or What’s That 3D Environment doing in my Web Browser,” Computational and Simulation 

Sciences Conference, Melbourne, Australia, February 13, 

2015. http://math.nist.gov/~SRessler/w3d/aus2015keynote.html/ 

High End Visualization Software: 

Software Tests to Maintain System 

Reliability 

Steven Satterfield 

Judith Terrill 

Alauna Jackson (Bowie State University) 

Aleksander Psurek (Thomas Wootton High School) 

Rael Youseff (UMBC) 

Jason Zimmerman (Millersville University) 

John Hagedorn 

Wesley Griffin 

Terence Griffin 

The High Performance Computing and Visualization 

Group (HPCVG) has operated an immersive virtual 

environment (IVE) since 2000 in support of its mission 

of advanced visualization of scientific data. In our 

applications, the 3D immersive environment functions 

as an interactive measurement laboratory. HPCVG 

collaborates with researchers across all areas of NIST to 

apply the IVE and virtual measurement techniques. 

System availability is very important for ongoing 

collaborations and the need to do demonstrations on 

short notice. We have a proactive approach to system 

reliability through the development of our own hardware 
 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 63 

Figure 43. HPCVG SURF student interns during the summer of 2015. 

tests as well as additional tests obtained as part of the 

recent upgrade of the virtual environment (CAVE). 

Equally important is system and application software 

reliability in the context of evolving software such as 

operating system upgrades, security patches, changing 

requirements of NIST research, as well as GPU and 

driver upgrades. During 2015, we began designing and 

implementing a software testing capability to maintain 

software reliability and correctness. 

Software Stack. The application creation framework 

software for the HPCVG CAVE is named HEV (High 

End Visualization). It consists of a stack of vendorsupplied, Open Source, and in-house developed 

software. At the lowest level, the vendor-supplied 

OpenGL library and Linux device driver renders and 

displays graphics in the graphics cards producing 

images displayed on the CAVE screens. Open 

SceneGraph (OSG) is the next level. It is an open source 

high performance 3D graphics toolkit and library for 

organizing graphics data in a hierarchical structure, 

allowing models to be built, manipulated and rendered 

using OpenGL. 

IRIS (Interpreted Runtime Immersive Scenegraph) 

is above OSG in the stack. It is an HPCVG-developed 

C++ software library. IRIS controls the hardware 

elements of the IVE, reading the tracking data to build 

the user view, and updating the projected images in real 

time. For a CAVE, different 3D stereo images are built 

for each screen such that they combine for the user into 

a 3D immersive view. A key feature of IRIS is the 

displayed scene graph can be modified at run-time by 

external processes (programs and scripts) 

communicating via a standard Linux/Unix facility know 

as a named pipe or a FIFO (first-in first-out). The 

functionality of the FIFO is implemented in a set of 

ASCII commands written to the FIFO. These commands 

can be stored in a file, known as an iris file. Another 

feature of IRIS and HEV as a whole is device 

independence. By isolating the display characteristics 

into specific display shared objects (DSOs), the same 

HEV binary code can run on a full range of devices from 

CAVES to non-immersive desktop and laptop displays. 

IDEA (IRIS Development Environment for 

Applications) is the level above IRIS. It is an HPCVGdeveloped collection of commands, scripts and file 

formats. This collection of software tools, locally known 

as the Army of Ants follows in the tradition of the Unix 

philosophy. Each of the pieces generally focus on one 

simple task useful for a wide variety of applications. 

Applications complete the stack, typically 

implementing an interactive visualization in a specific 

area. These applications are often built with very little 

programming by combining existing ants. When new 

tools are required, they are typically generalized as 

much as possible and added back into the HEV software. 

Source Control and Continuous Integration. A 

significant step implemented during 2015 for this 

project was to transfer the HEV source code into the Git 

version control system. HPCVG now maintains a single 

consistent code repository for building the production 

HEV software used for the CAVE and all supporting 

staff workstations. Utilizing Git, all developers have a 

private working copy for creating and testing without 

stepping on each other’s work. Once new features are 

ready, Git merges the changes back into the production 

software. System reliability is enhanced because a 

CAVE application never depends on a special case 

version of HEV. The introduction of continuous 

integration (CI) further improved reliability 

development. Here, the full HEV source is rebuilt twice 

a day to ensure newly merged changes haven’t 

introduced any compile time errors. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

64 NIST Applied and Computational Mathematics Division 

The implementation of software testing involved 

the design and implementation of a software-testing 

infrastructure that allowed all tests to be run with a 

single command. Each individual test required one or 

more baseline results as well as individual analyses to be 

run to yield a composite pass or fail result. 

This year we completed the design and 

implementation of the software-testing infrastructure. 

We also completed a number of tests, primarily with 

SURF students. See Figure 43. These tests are 

implemented as scripts, named timeline files, that direct 

the system to navigate through a scene, issue 

modification directives (such as on/off directives for 

objects in the scene), and save images all at specific 

times. Following a test, analyses are run and the pass / 

fail output for the tests is issued. Initial results indicate 

that repeated tests with the same GPU, driver, and 

software configuration give the same results, though 

images generated on different GPUs can differ. Most of 

the differences are slight (one RGB color unit at one or 

two channels), however, some can vary wildly. In the 

coming year, we will continue to implement tests. 

Optical Characterization for 

Advanced Immersive Displays 

Judith E. Terrill
 

John Penczek (NIST EL)
 

Paul A. Boynton (NIST EL) 

The human visual system (HVS) is the dominant means 

by which we collect information; it consumes the majority of our brainpower in processing input. The accurate 

visualization of datasets leverages the power of the HVS 

for better understanding, discovery, and innovation. The 

rendering of a data visualization is limited by current 

display technologies, which typically cannot take full 

advantage of HVS capabilities. 

We aim to measure the performance of displays in 

order to better understand their limitations. As display 

technologies make rapid advances, they often require 

new characterization methods. We are developing optical methods that evaluate how well immersive display 

technologies perform. As the display industry migrates 

from large immersive multi-screen systems to relatively 

compact head-worn devices, we are creating new characterization methods that adjust to the unique attributes 

of these new technologies. 

In our previous work, we developed optical characterization methods for immersive Cave Automatic 

Virtual Environment (CAVE) systems [1]. These large 

systems are well suited for team members to interact and 

collaborate inside a data visualization. In order to enhance the visual experience of these large screens, the 

display industry is driving toward brighter images with 

a greater range of colors by turning to light emitting diodes (LED) and laser light sources [2]. But the narrow 

spectral bandwidth of these light sources are substantially different than the incandescent and fluorescent 

sources used in the past. (Previous studies have demonstrated the sensitivity of some light-measuring devices 

to narrow-band filtered light sources [3].) Therefore, it 

is necessary to evaluate the impact of these sources on 

the typical optical detectors used to measure display performance. This work was conducted in support of the 

International Electrotechnical Commission (IEC) standardization work on laser projectors [4]. 

There are currently a wide range of commercial detectors available, with varying capability. Since 

immersive display systems often use 3D front- or rearprojections displays, we limited our study to non-contact 

detectors. Optical detectors that measure the spectral radiance, tristimulus values, or luminance of a small area 

on the screen can be used to measure most of the basic 

display performance characteristics. High performance 

portable spectroradiometers are available that offer absolute spectral measurements, but at substantial cost. 

Filtered colorimeters are a lower cost option, but may 

not be appropriate for new display technologies that use 

narrow band light emitting diode (LED) and laser light 

sources. We compared a variety of commercial spectral 

and filter-based detectors from two manufacturers. 

Our results demonstrate that it is necessary to consider the color and spectral bandwidth when choosing 

the appropriate detector for display measurements. In 

addition, the light produced by the display can have 

other characteristics, such as varying polarization, laser 

speckle, spatial non-uniformity, and temporal modulation, all of which should be considered when choosing 

the appropriate detector. Our results will be included in 

a NIST IR, which will be an expanded version of [1]. 

There is currently strong interest in providing an 

immersive experience to the user by placing a headworn display right in front of the eye. A transparent display can provide the viewer with an augmented reality 

experience that is also immersive. The transparent attribute of these devices creates some metrology 

challenges in evaluating their performance. We investigated this aspect in a complimentary project that 

involved conventional transparent displays, and supports IEC standardization work on transparent liquid 

crystal display (LCD) and organic light emitting diode 

(OLED) displays [5,6]. Our investigation developed 

new measuring methods for determining the transmission properties of these displays, and established a 

general framework for evaluating the transparent display performance under ambient lighting conditions 

[7,8]. This work will be incorporated into an industry 

measurement standard [9]. 

Going forward, we will leverage our work on transparent displays to develop optical metrology for see­
 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 65 

through near-eye displays. This augmented reality technology is expected to experience considerable growth 

for medical and industrial applications, but will need 

sound measurement methods to achieve high quality and 

user acceptance. 

These studies on new light sources, transparent displays, and near-the-eye displays lay the groundwork for 

collaborations focused on virtual reality, augmented reality and usability. 

[1]	 J. Penczek, S. G. Satterfield, E. F. Kelley, T. Scheitlin, J. 

E. Terrill and P. A. Boynton, Evaluating the Visual Performance of Stereoscopic Immersive Display Systems, 

Presence, to appear. 

[2]	 Parameter Values for Ultra-High Definition Systems for 

Production and International Programme Exchange, 

ITU-R BT.2020-2, International Telecommunications 

Union, Geneva, 2015. 

[3]	 P. A. Boynton and E. F. Kelley, Assessment of Colour 

Measurement Systems Using Interference Filters, in Proceedings of the CIE Expert Symposium on Colour 

Standards for Imaging Technology (CIE x014-1998), November 1997, 22-27. 

[4]	 Laser Display Devices—Part 5-1: Measurement of Optical Performance for Laser Front Projectors, IEC 62906­

5-1, International Electrotechnical Commission, Geneva, 

under development. 

[5]	 Organic Light Emitting Diode (OLED) Displays—Part 6­

4: Measuring Methods of Transparent Properties, IEC 

62341-6-4, International Electrotechnical Commission, 

Geneva, under development. 

[6]	 Liquid Crystal Display Devices—Part 5: Optical Measuring Methods of Transmissive Transparent LCD Display 

Panels, IEC 61747-30-5, International Electrotechnical 

Commission, Geneva, under development. 

[7]	 J. Penczek, E.F. Kelley and P.A. Boynton, Optical Measuring Methods for Transparent Displays, SID Symposium 

Digest of Technical Papers 46 (June 2015), 731-734. 

[8]	 J. Penczek, E.F. Kelley and P.A. Boynton, General Metrology Framework for Determining the Ambient 

Performance of Flat Displays, SID Symposium Digest of 

Technical Papers 46 (June 2015), 727-730. 

[9]	 Information Display Measurements Standard, V1.03, International Display Metrology Committee, Society of 

Information Display, 2012. 

Texture Compression Evaluation 

and Optimization 

Wesley Griffin 

Marc Olano 

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

Texture compression is widely used in real-time rendering to reduce storage and bandwidth requirements. 

Hardware-based texture compression has not fundamentally changed since its introduction in 1999. Recently, 

however, interest has grown in improving hardwarebased texture compression. 

Our research has explored new techniques for reducing the bit rate for current fixed bit rate algorithms, 

as well as new variable bit rate algorithms that can be 

efficiently decoded in graphics hardware. This work 

benefits the rendering and visualization communities by 

providing a methodology for evaluating and optimizing 

texture compression. It also can be directly applied to 

existing applications to improve the quality of compressed textures. 

In evaluating texture compression, the most common approach is to use some combination of the mean 

square error (MSE), peak signal-to-noise ratio (PSNR), 

or visual image inspection of the compressed texture. 

Last year we introduced a new evaluation methodology 

that accounts for the two ways in which textures are used 

in rendering for which the MSE and PSNR measures 

cannot account. Our evaluation approach combines final 

image rendering with objective image comparison metrics. 

This year we extended our evaluation work to incorporate additional datasets and also further analysis 

and published these results [1,2]. The most useful insight from this study is that the type of texture, combined 

with how it is used, has an impact on perceived quality 

when rendering with compressed textures. Leveraging 

our evaluation approach, we implemented an optimization framework using a first-choice hill climbing 

algorithm to search the multi-dimensional state space of 

a modern texture compression algorithm. The hillclimbing algorithm attempts to minimize an energy 

function that is a combination of bitrate and two objective image comparison metrics. This research prototype 

proves the feasibility of objectively optimizing texture 

compression using our new evaluation methodology. It 

should also enable automatic texture compression optimization in real-time rendering asset pipelines. 

[1]	 W. Griffin and M. Olano, Objective Image Quality Assessment of Texture Compression, in Proceedings of the 

2014 ACM SIGGRAPH Symposium on Interactive 3D 

Graphics and Games (I3D), San Francisco, CA, March 

2014, 119-126. 

[2]	 W. Griffin and M. Olano, Evaluating Texture Compression Masking Effects using Objective Image Quality 

Assessment Metrics, IEEE Transactions on Visualization 

and Computer Graphics, 21:8 (2015), 970-979. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

66 NIST Applied and Computational Mathematics Division 

Quantum Information
 

An emerging discipline at the intersection of physics and computer science, quantum information science 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 behavior of quantum systems to enable phenomenal increases in information storage and 

processing capability, as well as communication channels with 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 demonstration and assessment of technologies for quantum communication. 

Quantum Information Science 

Scott Glancy
 

Emanuel Knill
 

Peter Bierhorst 

Adam Keith
 

Karl Mayer
 

Jim van Meter 

Peter Wills 

Kevin Coakley (NIST ITL)
 

Sae Woo Nam (NIST PML) 

Dietrich Leibfried (NIST PML) 

David Wineland (NIST PML) 

David Pappas (NIST PML)
 

Gerardo Ortiz (Indiana University)
 

Paul Kwiat (U. of Illinois at Urbana Champaign)
 

A primary goal of quantum information science (QIS) is 

to devise and implement algorithms and protocols that 

exploit quantum mechanical effects to gain an advantage 

over purely classical techniques. Striking examples of 

such advantages are efficient quantum factoring of large 

numbers with quantum computers, information-theoretically secure quantum communication, and quantum 

measurement strategies with precision scaling as N-1 rather than the standard N-1/2. The insights from QIS are 

having a growing influence on other fields, most notably 

fundamental and condensed-matter physics. Our work 

contributes to QIS by developing protocols and analysis 

tools for verifying the performance of quantum devices, 

devising statistical certification strategies for trust in 

quantum information, investigating our ability to control 

quantum systems for storage and computation, and exploring the boundaries of quantum advantages when 

confronted with fundamental physical reality. 

There is a wide variety of protocols to demonstrate 

features of QIS with a small number of qubits. We investigate protocols for testing protection against noise, 

establishing information subsystems and demonstrating 

quantum advantages. One such protocol involves preparing and manipulating a “noiseless” qubit subsystem 

in three physical spin-half systems. This qubit is completely immune to uniform magnetic field noise and has 

three non-trivial robust gates that can be applied by 

simply swapping the spin-halfs. A clear demonstration 

of this qubit would be a first for non-trivial protected 

subsystems. We hope to realize this in ions and atoms. 

This has become possible because of remarkable improvements in one and two ion control over the last few 

years. For more on our contributions to protocols and 

analysis of experimental qubits, see page 67. 

In many settings, high-quality quantum control of a 

small number of qubits is limited to operations and evolutions that cannot distinguish between the qubits. An 

example is the typical experimental configuration in our 

ion traps where there are two or three ions in one trap. 

Easily implementable evolutions are those that involve 

each ion equally. This constraint still permits implementation of non-trivial two and three qubit gates such as the 

unitary evolution that changes the sign of only the |111> 

state, also known as the doubly-controlled sign flip. This 

is a version of the famous doubly-controlled not gate 

(Toffoli gate), which is critical to reversible computations. We have studied the question of how many steps 

of Ju

2

 evolution are needed to implement this gate. A Ju

2 

evolution symmetrically couples each pair of qubits and 

can be viewed as a parallel implementation of commuting gates. The known decompositions of the Toffoli gate 

require six canonical two-qubit gates, so one might hope 

that fewer than six Ju

2

 evolutions might be required. But 

we found numerical evidence that six is necessary and 

sufficient. We hope to prove this observation. 

We continued our work on using so-called test martingales [1] for rejecting hypotheses such as local 

realism and separability in quantum experiments. These 

experiments aim to show that simple classical descriptions do not suffice for explaining the observations. Our 

adaptive test martingale methods involve multiplying 

positive random variables (RVs) of a sequence of trials. 

These RVs have the property that, conditional on the 

past and given the hypotheses to be tested, they have expectations bounded by 1. We have previously shown this 
 

 

 

 

 

Summary of Activities for Fiscal Year 2015 67 

to be a very effective method for certifying failure of local realism in Bell tests [2]. We developed and applied 

a version of this strategy [3] for Bell tests involving long 

(in time) trials, of which there were several well-publicized examples last year; see [4]. With this strategy, we 

obtained strong certificates from data that was previously thought to be useless due to the so-called 

coincidence loophole [5]. 

We started an exploratory project to expand the application of the test martingale methods from hypothesis 

testing to confidence interval determination. For this 

purpose, we are exploring the behavior of the method on 

the toy problem of identifying the bias of a coin flipped 

in sequence many times. We obtained a closed form for 

a particular version of our adaptive test martingale strategy, which enables efficient computations of expected 

performance and direct comparison to traditional methods based on “exact” p-values and Chernoff-Hoeffding 

bounds [6]. This work is still in progress. 

A fundamental issue in quantum information and 

quantum measurement science is how the known fundamental physics based on relativistic quantum field 

theory and its variants affects the future performance of 

quantum devices and achievable measurement precision. Our initial investigations of these issues led to the 

reconsideration of arguments [7] suggesting that there 

are general uncertainty principles limiting the achievable precision for measuring features of space-time. Such 

principles could affect the ultimate usable precision of 

atomic clocks, laser interferometers and gravitational 

wave detection, for example. We further developed the 

mathematical approach based on a category-theoretical 

definition of quantum fields on a fixed gravitational 

background familiar from algebraic quantum field theory. This confirmed and made more precise the relevant 

uncertainty principles. 

There have been many proposals to harvest entanglement from the vacuum, thus exploiting a fundamental 

feature of relativistic quantum fields: any bounded region of space-time is necessarily entangled with the rest 

of space-time. A popular effect related to this is the Unruh effect whereby an accelerating observer experiences 

thermal radiation when coupled to the vacuum. In fact, 

the standard proposal for harvesting entanglement involves two oppositely accelerating observers, but the 

accelerations required are unrealistically high. A recent 

study [8] suggests that acceleration can be simulated 

with stationary detectors having strongly “chirped” energies and/or reference pulses. Motivated by this study, 

we initiated an investigation of how one can measure 

general modes of free (non-interacting) quantum fields. 

The study is still in progress, but we expect to determine 

the practicality of verifying the presence of vacuum entanglement by using stationary detection systems based 

on homodyne measurements. This is a precondition for 

practical entanglement harvesting. 

[1]	 G. Shafer, A. Shen, N. Vereshagin, and V. Vovk, Test 

Martingales, Bayes Factors and p-Values, Statistical Science 26 (2011), 84-101. 

[2]	 J. S. Bell, On the Einstein-Podolsky-Rosen Paradox, 

Physics 1 (1964), 195-200. 

[3]	 E. Knill, S. Glancy, S. W. Nam, K. Coakley and Y. 

Zhang, Bell Inequalities for Continuously Emitting 

Sources, Physical Review A 91 (2015), 032105, 17 pages. 

[4]	 B. Christensen, A. Hill, P. G. Kwiat, E. Knill, S. W. Nam, 

K. Coakley, S. Glancy, L. K. Shalm and Y. Zhang, Analysis of Coincidence-Tie Loopholes in Experimental Bell 

Tests, Physical Review A 92 (2015), 032130, 13 pages. 

[5]	 M. Sandberg, E. Knill, E. Kapit, M. R. Vissers and D. P. 

Pappas, Efficient Quantum State Transfer in an Engineered Chain of Quantum Bits, Quantum Information 

Processing, to appear. 

[6]	 W. Hoeffding, Probability Inequalities for Sums of 

Bounded Random Variables, Journal of the American 

Statistical Association 58 (1963), 13-30. 

[7]	 T. G. Downes, G. J. Milburn and C. M. Caves, Optimal 

Quantum Estimation for Gravitation, arXiv:1108.5220 

(2012). 

[8]	 T. Ralph and N. Walk, Quantum Key Distribution Without Sending a Quantum Signal, arXiv:1409.2061 (2014). 

Quantum Estimation Theory and 

Applications 

Peter Bierhorst 

Scott Glancy
 

Adam Keith
 

Emanuel Knill
 

Jose Aumentado (NIST PML)
 

Manuel Castellanos (NIST PML) 

Kevin Coakley (NIST ITL)
 

Michael DeFeo (NIST PML)
 

John Gaebler (NIST PML)
 

Yiheng Lin (NIST PML) 

Ting Rei Tan (NIST PML)
 

Yong Wan (NIST PML) 

George Barbosa da Silva (Federal U. of Ceara)
 

Hilma Vasconcelos (Federal U. of Cearal)
 

Many emerging technologies will exploit quantum mechanical effects to enhance metrology, computation, and 

communication. Developing these technologies requires 

improved methods to measure the states of quantum systems. Quantum estimation is a statistical problem of 

estimating an underlying quantum state, measurement, 

or process by using a collection of measurements made 

on independently prepared copies of the state or applications of the measurement or process. Accurate 

quantum estimation allows experimentalists to answer 

the question “What is happening in my quantum experiment?” and to characterize uncertainty in that answer. 
 

 

 

 

 

 

 

 

 

 

 

 

68 NIST Applied and Computational Mathematics Division 

Figure 44. Reconstruction of quantum states produced in a superconducting microwave cavity. The figures show estimated Wigner 

functions of two different superpositions of 0 and 1 photon states. 

Negative regions demonstrate quantum character of the states. 

Full quantum estimation can be a demanding task, 

requiring a large number of different measurements to 

be performed on (independently prepared copies) of the 

quantum system and large amounts of computation to 

perform the estimation. One method for reducing these 

costs is to exploit pre-existing knowledge about the state 

being measured. For example, the state could be restricted to a smaller subset of all quantum states, such as 

those states that have Gaussian probability distributions 

for measurement results. Existing algorithms for estimation of Gaussian states often return unphysical 

estimates that violate the Heisenberg Uncertainty Principle. ACMD developed an algorithm that constrains 

estimated states to those that obey the uncertainty principle, and implemented this algorithm in tomography 

software [1]. Enforcing the uncertainty principle constraint allows faithful estimation of states produced in 

high fidelity experiments. 

The NIST/PML Ion Storage Group has pioneered 

one of the world’s most successful quantum computer 

development projects. With their recent advances in 

qubit preparation, logical operation, and measurement 

fidelities, more advanced statistical techniques are required to characterize the resulting trapped ion quantum 

states. (NIST trapped ion experiments have reported a 

fidelity of 99.9998 % for single qubit logic operations 

[2].) This year, in collaboration with the Ion Storage 

Group, ACMD researchers developed tools to estimate 

properties of quantum states for experiments with extremely high fidelity. These include a protocol for 

placing a lower bound on the fidelity with which a single 

qubit state can be prepared given minimal assumptions 

and a single procedure for both calibrating measurements (using data from qubits with known states) and 

estimating the quantum state (of a collection of qubits in 

an unknown state) [3]. Because both measurements and 

the unknown state are estimated together, systematic errors are avoided, statistical uncertainty is reduced, and 

mensional vector x from measurements of the form 

௜ݕ 〉| ൌ௜ ܽ〉| ݔ , ଶ ,

where the vectors ܽ௜

higher fidelity states can be analyzed reliably. These algorithms were used to analyze data from a new trapped 

ion experiment demonstrating entangled state fidelities 

above 0.99 [4]. 

 are chosen by the observer. Such 

measurements arise in a variety of applications, including optical imaging (where one measures the intensity 

In many quantum experiments, the state can be only 

partially inferred from the available measurements. 

However, the available measurements may be able to 

place useful bounds on parameters of interest, even if 

they cannot be inferred exactly. ACMD researchers are 

exploring algorithms to obtain such bounds. Researchers 

in the PML’s Quantum Electronics and Photonics Division are preparing various exotic quantum states with 

new superconducting microwave-cavity technology. 

ACMD researchers provided software and consultation 

on the analysis of these experiments [5]. 

Maximum likelihood quantum state estimation is 

known to suffer from bias. However, the amount and direction of the bias has been poorly understood. In 

collaboration with researchers from the Federal University of Ceara, Brazil, ACMD researchers have used a 

series of numerical experiments to characterize this bias, 

finding clear evidence of significant bias for more pure 

quantum states and finding that some measurement 

schemes can significantly reduce the bias [6]. 

[1]	 S. Glancy, N. Kravitz and E. Knill, Efficient Estimation 

of Gaussian Quantum States, in preparation. 

[2]	 K. R. Brown, A. C. Wilson, Y. Colombe, C. Ospelkaus, 

A. M. Meier, E. Knill, D. Leibfried and D. J. Wineland, 

Single-Qubit-Gate Error Below 10-4 in a Trapped Ion, 

Physical Review A 84 (2011), 030303(R). 

[3]	 A. C. Keith, S. Glancy and E. Knill, Partial Quantum Tomography using Maximum Likelihood Estimation, in 

preparation. 

[4]	 Y. Lin, J. P. Gaebler, F. Reiter, T. R. Tan, R. Bowler, Y. 

Wan, A. Keith, E. Knill, S. Glancy, K. Coakley, A. S. 

Sørensen, D. Leibfried and D. J. Wineland, Preparation 

of Entangled States by Hilbert Space Engineering, in 

preparation. 

[5]	 M. Castellanos, M. P. DeFeo, S. Glancy and J. Aumentado, Tomographic Reconstruction of Itinerant Quantum 

Microwave States of Light, in preparation. 

[6]	 G. B. Silva, S. Glancy and H. M. Vasconcelos, Investigating Bias in Maximum Likelihood Quantum State 

Tomography, in preparation. 

Phase Retrieval and Quantum 

Tomography 

Yi-Kai Liu 

Shelby Kimmel (University of Maryland) 

Felix Krahmer (Technical University of Munich) 

Phase retrieval is the task of learning an unknown n-di­

݅ ൌ 1,2,...,݉,
 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 69 

relaxation of this problem. In certain situations

ܽ௜ instance, when the measurement vectors 

of the light field, but not the phase), and quantum tomography (where one measures the probability, but not 

the complex amplitude, of the wave function). 

Recently, there has been a great deal of work on 

PhaseLift, an algorithm for phase retrieval that was inspired by ideas from compressed sensing. PhaseLift 

works by “lifting” the phase retrieval problem to a rankone matrix recovery problem, and then solving a convex 

— for 

 are chosen 

at random from a Gaussian distribution, PhaseLift is 

guaranteed to recover the unknown vector x, using ݉ ൌ

ܱሺ݊ሻ measurements. 

Unfortunately, in real experiments, it is often difficult to perform measurements using Gaussian random

 that have ܽ௜ . Instead, one must use vectors vectors ܽ௜

some additional structure. How well does PhaseLift perform when one uses these structured measurements? 

This is the question we have sought to answer. 

Broadly speaking, we found that for certain vectors 

x, the use of structured measurements prevents 

PhaseLift from recovering x correctly; but these choices 

of x are rare and in some sense pathological. For most 

choices of x, PhaseLift with structured measurements 

performs well. 

More precisely, we studied two classes of structured 

measurements: so-called Bernoulli random vectors sampled from the hypercube ሼ1, െ1ሽ௡, and vectors sampled 

from spherical and unitary 2-designs. 

Bernoulli random measurements are of theoretical 

interest, as they are perhaps the simplest alternative to 

Gaussian random measurements. When using Bernoulli 

random measurements, we showed that PhaseLift can 

reconstruct all “flat” vectors, i.e., all vectors x that satisfy the condition ‖ݔ‖ஶ ൑ ܿ‖ݔ‖ଶ, where c is some small 

constant [1,2]. Our result also holds more generally, for 

random measurements sampled from sub-Gaussian 

product distributions. 

Measurements using spherical and unitary 2-designs are of interest in quantum tomography, as they can 

be implemented easily in many experimental setups, by 

using stabilizer states and Clifford operations. When using these 2-design measurements, we showed that 

PhaseLift can approximately reconstruct almost all vectors x, where the approximate reconstruction holds up to 

constant additive error, and the restriction to “almost all 

vectors x” is with respect to Haar measure [3]. 

As an application of this result, we have developed 

a method for quantum process tomography that is robust 

to state preparation and measurement (SPAM) errors, 

and is quadratically faster than conventional tomography in the case where the unknown process is a generic 

(Haar-random) unitary. 

[1]	 F. Krahmer and Y.-K. Liu, Phase Retrieval Without 

Small-Ball Probability Assumptions: Stability and 

Uniqueness, in Proceedings of the 2015 International 

Conference on Sampling Theory and Applications 

(SampTA), Washington, DC, May 25-29, 2015, 411-414. 

[2]	 F. Krahmer and Y.-K. Liu, Phase Retrieval Without 

Small-Ball Probability Assumptions: Recovery Guarantees for PhaseLift, in Proceedings of the 2015 

International Conference on Sampling Theory and Applications (SampTA), Washington, DC, May 25-29, 2015, 

622-626. 

[3] S. Kimmel and Y.-K. Liu, Quantum Compressed Sensing 

Using 2-Designs, arXiv:1510.08887, October 2015. 

Device Independently Secure 

Randomness from Loophole-Free 

Bell Tests 

Peter Bierhorst 

Scott Glancy
 

Stephen Jordan 

Emanuel Knill
 

Paulina Kuo 

Yi-Kai Liu 

Alan Mink
 

Xiao Tang 

Michael S. Allman (NIST PML)
 

Lawrence Bassham (NIST ITL) 

Joshua C. Bienfang (NIST PML) 

Harold Booth (NIST ITL)
 

Kevin J. Coakley (NIST ITL) 

Shellee D. Dyer (NIST PML)
 

Thomas Gerrits (NIST PML)
 

Carson Hodge (NIST PML) 

Michaela Iorga (NIST ITL)
 

John Kelsey (NIST ITL) 

Adriana E. Lita (NIST PML) 

Camilla Lambrocco (NIST PML) 

Alan L. Migdall (NIST PML) 

Richard P. Mirin (NIST PML)
 

Murugiah Souppaya (NIST ITL) 

Sae Woo Nam (NIST PML) 

René Peralta (NIST ITL) 

Andrew Rukhin (NIST ITL)
 

Lynden K. Shalm (NIST PML) 

Martin J. Stevens (NIST PML) 

Edward Tortorici (NIST PML)
 

Varun B. Verma (NIST PML) 

Michael A. Wayne (NIST PML) 

Carlos Abellán (Barcelona Inst. of Sci. and Tech.)
 

Waldimar Amaya (Barcelona Inst. of Sci. and Tech.)
 

Bradley G. Christensen (University of Illinois) 

William H. Farr (Jet Propulsion Laboratory)
 

Michael Fischer (Yale University) 

Deny R. Hamel (University of Moncton)
 

Thomas Jennewein (University of Waterloo)
 

Daniel R. Kumor University of Illinois) 

Paul G. Kwiat (University of Illinois)
 
 

 

 

 

 

 

 

 

 

 

 

 

 

70 NIST Applied and Computational Mathematics Division 

Francesco Marsili (Jet Propulsion Laboratory) 

Evan Meyer-Scott (University of Waterloo)
 

Morgan W. Mitchell (Barcelona Inst. of Sci. and Tech.)
 

Valerio Pruneri (Barcelona Inst. of Sci. and Tech.)
 

Matthew D. Shaw (Jet Propulsion Laboratory) 

Jeffrey A. Stern (Jet Propulsion Laboratory)
 

Yanbao Zhang (University of Waterloo)
 

Before the invention of quantum theory, theories of 

physics obeyed the principle of local realism. In theories that obey realism, all possible measurement results 

are determined and fixed before the measurement occurs, though that result might be random and hidden. In 

local realistic theories, the hidden measurement results 

cannot be communicated between entities faster than the 

speed of light. The principle of local realism constrains 

the probability distributions that can be produced by local realistic systems. In 1964, John S. Bell described 

those constraints with a system of inequalities involving 

probabilities of measurement outcomes. 

ACMD researchers have studied the properties of 

this system of inequalities, describing any system that 

violates an inequality as a mixture of a small set of deterministic local realistic distributions and a single 

maximally violating distribution [1]. Bell also showed 

that some entangled quantum systems can violate these 

inequalities, so quantum physics does not obey local realism. During the last 50 years, various experiments 

have demonstrated violation of Bell’s inequalities, but 

all previous experiments have suffered from loopholes 

that would allow local realistic systems to appear to violate Bell’s inequalities. 

This year, ACMD researchers participated in a 

NIST led team that achieved a loophole-free test of local 

realism [2]. The experiment required generation of high 

fidelity entangled photon pairs, distributing each photon 

in opposite directions to its own detector system located 

approximately 100 meters from the source, featuring 

fast switching between polarization measurements and 

high efficiency detection. To ensure that communication between the measurement stations is impossible, 

measurements choices were made, photons detected, 

and measurements recorded in less than 400 ns. ACMD 

developed statistical analysis techniques with which pvalues (measures of statistical evidence) for local realism were computed. P-values as small as 2.3 × 10-7 were 

reported, constituting a rejection of local realism with 

very high statistical significance. 

In 2006 it was discovered that Bell tests could be 

used to generate random bits for cryptographic applications in a device-independent secure manner [3]. This 

means that, given a secure random seed, trust in the unpredictability of the secure string of bits can be derived 

solely from the outcomes of the Bell experiment, without needing to trust the internal workings of the 

37 http://www.nist.gov/itl/csd/ct/nist_beacon.cfm 

Figure 45. Spacetime diagram of test of local realism. An entangled 

photon pair is created at the source, and each photon is sent to 

measurement stations ≈120 m from the source. Measurement 

choices are made by random number generators (RNG) at each 

measurement location. The separation of measurement stations ensures that no signal traveling at light speed from the source can 

influence a measurement and no light speed signal traveling from 

one station’s RNG can influence the other station’s measurement 

result. 

hardware, even under the most pessimistic assumption 

that the hardware was provided by an untrustworthy adversary. 

Potential future work at NIST includes doing the 

necessary engineering to develop the Bell test technology used in [2] into a reliable device that can be operated 

continuously for long periods without human oversight. 

Such a device could be integrated into the NIST Randomness Beacon37, a cryptographic service currently 

being run by the ITL Computer Security Division using 

conventional hardware random bit generators. Some of 

the necessary tools for randomness production using 

Bell tests, such as randomness extraction software for 

postprocessing the experimental data, have already been 

developed as part of this project. 

The NIST Beacon posts bit-strings in blocks of 512 

bits every 60 seconds. Each such value is time-stamped 

and signed, and includes the hash of the previous value 

to chain the sequence of values together. This prevents 

all parties, even the source, from retroactively changing 

an output packet without being detected. The NIST Beacon keeps all output packets. At any point in time, the 

full history of outputs is available to users. These features ensure that the Beacon-generated numbers cannot 

be predicted before they are published and a user application can prove to anybody that it used truly random 

numbers not known before a certain point in time. Furthermore, this proof can be presented offline and at any 

point in the future. A number of beacon-based cryptographic protocols for e-commerce and privacy 
 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 71 

protection have been proposed in the cryptographic theory literature. These can now be put into practice using 

the NIST Beacon. 

As of this writing, the NIST Beacon has been functioning without interruption for more than two years. 

The current generation beacon achieves (conventional, 

device-dependent) security using two independent, 

commercially available sources of randomness, each 

with an independent hardware entropy source and NIST 

Special Publication 800-90 approved components. NIST 

encourages the community at large to research and publish novel ways in which this tool can be used. A few 

examples of applications are unpredictable sampling, 

new authentication mechanisms, and secure multi-party 

computation. 

[1]	 P. Bierhorst, Geometric Decompositions of Bell Polytopes with Practical Applications, arXiv:1511.04127 

(2015). 

[2]	 L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, 

D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. 

Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, 

F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. 

Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. 

Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill and S. W. 

Nam, A Strong Loophole-free Test of Local Realism, 

Physical Review Letters 115 (2015) 250402. 

[3]	 R. Colbeck, Quantum and Relativistic Protocols for Secure Multiparty Computation, PhD Thesis, University of 

Cambridge, arXiv:0911.3814 (2006). 

Performance of Adiabatic 

Optimization Algorithms 

Stephen Jordan 

Michael Jarret (University of Maryland)
 

It is firmly established that quantum computers, if built, 

could factor integers and simulate the dynamics of quantum many-body systems exponentially faster than 

conventional, classical computers. More recently, there 

has been much interest in applying quantum computers 

to a wide variety of optimization problems, ranging from 

job shop scheduling to machine learning. Such algorithms could be run on general-purpose digital quantum 

computers, or they could be run on specialized hardware 

such as is being developed by D-Wave Systems. However, the idea that quantum computers may offer an 

advantage for optimization problems presently rests on 

extremely shaky theoretical foundations. 

Most of the research into quantum optimization focuses on adiabatic quantum computation. This is a 

scheme, somewhat similar in spirit to simulated annealing, in which the solutions to combinatorial optimization 

problems are encoded into the low energy states of a 

physical system. The only rigorously established upper 

bound on the runtime of quantum adiabatic optimization 

algorithms scales as one over the square of the gap between the smallest and second-smallest eigenvalues of 

the system’s Hamiltonian. 

The Hamiltonian of a system with n qubits is a 2n

 × 

2n

 matrix. Thus, numerically computing the eigenvalues 

becomes very rapidly intractable. In this project, we 

seek to develop mathematical tools for proving rigorous 

analytic bounds on the eigenvalue gaps of Hamiltonians 

with the ultimate goal of gaining a better understanding 

as to which optimization problems, if any, are amenable 

to faster solution by quantum adiabatic computation. 

Over the past year we have adapted powerful new 

mathematical techniques from the theory of differential 

operators to the context of the discrete Hamiltonians relevant to quantum adiabatic optimization. In 2011, 

Andrews and Clutterbuck developed a new method for 

analyzing the spectrum of differential operators using 

the heat equation, and using this method proved the 

“fundamental gap conjecture.” Proving this conjecture 

had been an open problem for more than twenty years. 

We have now developed a discrete analogue to this 

method and applied it to some example problems. While 

we have not yet obtained results directly applicable to 

the analysis of adiabatic optimization algorithms for 

computational problems of practical interest, we believe 

the introduction of these powerful mathematical techniques to this topic represents a first step toward 

understanding the performance of these algorithms. 

[1]	 M. Jarret and S. P. Jordan, Modulus of Continuity Eigenvalue Bounds for Homogeneous Graphs and Convex 

Subgraphs with Applications to Quantum Hamiltonians, 

arXiv:1506.08475 (2015). 

Computational Complexity of 

Quantum Field Theory 

Stephen Jordan 

Keith Lee (University of Toronto)
 

John Preskill (Caltech) 

Hari Krovi (BBN)
 

Quantum field theory is needed to describe relativistic 

quantum systems, and forms the basis for theoretical 

particle physics. Unfortunately, quantum field theory is 

notoriously difficult to simulate. Millions of CPU hours 

per year are spent on simulations of quantum field theories in order to yield better understanding of nuclear 

physics and make predictions to compare against experimental results from particle accelerators. However, for 

strongly coupled quantum field theories such as quantum chromodynamics (QCD), which describes nuclei, 

no tractable method is known for computing dynamical 
 

 

 

 

 

 

 

 

 

 

 

 

72 NIST Applied and Computational Mathematics Division 

quantities such as scattering probabilities. Instead, computations are limited to static quantities such as mass 

ratios of composite particles. 

It is natural to ask whether the lack of efficient 

methods for computing dynamical quantities in quantum 

field theories is due to a fundamental barrier, or whether 

we simply haven’t discovered the right algorithm yet. In 

recent work, we have shown that, in certain regimes, 

there are fundamental barriers to the efficient computation of dynamical quantities in quantum field theories, 

which are unlikely ever to be overcome by conventional 

supercomputers. To show that quantum field theories 

are hard to simulate, we have devised a method by which 

arbitrary quantum computations can be encoded into the 

outcomes of scattering processes in quantum field theories. Thus, if the outcomes of these scattering processes 

could be efficiently computed by conventional computers, this would allow classical computers to efficiently 

compute the outcomes of all quantum computations. 

There is a lot of mathematical evidence that classical and quantum computation are not equivalent. In 

particular, there are several problems that quantum computers can solve in polynomial time, such as integer 

factorization, which are not believed to be solvable in 

polynomial time by classical computers. This and other 

evidence has led to a widely-believed mathematical conjecture, known as BQP≠P, which states that the set of 

problems solvable in polynomial time by a quantum 

computer is strictly larger than the set of problems solvable in polynomial time by a classical computer. (Note 

that this is a strictly mathematical statement about idealized models of computation, independent of the 

practical construction of quantum computers.) Thus, assuming the BQP≠P conjecture, our encoding implies 

that efficient classical algorithms do not exist for certain 

problems regarding scattering in quantum field theories; 

the problem is not merely that we haven’t discovered 

such algorithms. Interestingly, these difficulties arise 

even for very simple quantum field theories involving a 

single species of particles in only one spatial dimension. 

[1]	 S. P. Jordan, H. Krovi, K. S. M. Lee and J. Preskill. BQPcompleteness of Scattering in Scalar Quantum Field Theory, in preparation. 

Knot Theory and Quantum Physics 

Stephen Jordan 

Gorjan Alagic (University of Copenhagen)
 

Michael Jarret (University of Maryland)
 

In topology, a knot is an embedding of the circle into 

three dimensional space. If one knot can be smoothly 

transformed into another without any cutting and regluing of the string, then the knots are said to be equivalent. 

Deciding equivalence of knots is the central problem in 

computational knot theory. No efficient (i.e., polynomial-time) algorithm is known for this problem. A 

partial solution is given by knot invariants. These are 

functions that take knots as inputs, and produce as output some easy-to-distinguish objects such as numbers or 

polynomials. For such a function to be a knot invariant, 

equivalent knots taken as input must produce identical 

outputs. The definition does not require distinct knots to 

produce distinct outputs. A knot invariant that takes the 

same value on all knots is said to be trivial, and an invariant that takes distinct values on all distinct knots is 

said to be complete. Known knot invariants lie at various 

places between these extremes. 

Remarkably, many of the strongest knot invariants 

arise within quantum physics. In particular, solutions to 

the Yang-Baxter equation, which arose originally in statistical and quantum physics, can be used to construct 

many of the most important knot invariants, including 

both the Alexander and Jones polynomials. The solutions to the Yang-Baxter equation are matrices, which 

may be interpreted as quantum logic gates with two inputs and two outputs. We recently proved that, for the 

resulting knot invariant to be nontrivial, it is necessary 

that the corresponding quantum gate generate quantum 

entanglement. Thus we find an intriguing connection between quantum entanglement and topological 

entanglement, which remains to be further explored. 

[1]	 G. Alagic, M. Jarret and S. P. Jordan. Yang-Baxter Operators Need Quantum Entanglement to Distinguish Knots, 

Journal of Physics A, to appear. [arXiv:1507.05979] 

One-Time Programs Using Isolated 

Qubits 

Yi-Kai Liu 

One-time programs are a class of tamper-resistant computing devices, which have applications in cryptography 

and computer security. Essentially, a one-time program 

is a computer program that can run once, and then stops 

working. One-time programs can be used to restrict access to information that is under the physical control of 

an adversary such as personal information stored on a 

smartphone that has been subsequently lost or stolen. 

In previous work, we showed that a key component 

of a one-time program, called a one-time memory, can 

be constructed using certain kinds of quantum systems, 

called isolated qubits. Isolated qubits are qubits that can 

be accessed individually, but cannot be entangled. 

We are working to extend this result in various 

ways. First, we would like to construct one-time programs (not just one-time memories) from isolated 

qubits, and prove that they are secure. We have taken 

one step in this direction, by developing privacy amplification techniques that work for one-time memories 
 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 73 

based on isolated qubits [1]. Crucially, these techniques 

are non-interactive, as required for tamper-resistant 

hardware. 

The next step will be to show that our one-time 

memories can be composed securely. This is a difficult 

open problem, as it involves parallel (not sequential) 

composition in the isolated qubits model. In addition, we 

are studying quantum protocols for other cryptographic 

tasks, such as password-based identification, which 

might also be achievable in the isolated qubits model. 

Finally, we are studying possible experimental implementations of isolated qubits. Solid-state nuclear 

spins are one attractive option, as they can be engineered 

so that they have long coherence times, while making it 

difficult to perform entangling gates. In addition, it may 

be possible to demonstrate one-time memories using 

other physical systems, such as trapped ions or semiconductor quantum dots, albeit with weaker security 

guarantees. 

[1]	 Y.-K. Liu, Privacy Amplification in the Isolated Qubits 

Model, in Advances in Cryptology – EUROCRYPT 2015, 

Sofia, Bulgaria, April 26-30, 2015, 785-814. 

Post-Quantum Cryptography 

Stephen Jordan 

Yi-Kai Liu 

Lily Chen (NIST ITL) 

Dustin Moody (NIST ITL)
 

Rene Peralta (NIST ITL) 

Ray Perlner (NIST ITL) 

Daniel Smith-Tone (NIST ITL)
 

Public-key cryptography is a fundamental building 

block of the Internet today. It is an essential technology 

for electronic commerce and cybersecurity. However, 

the development of quantum computers poses a potential threat to the security of the public-key cryptosystems 

we use today. Thus, it is desirable to develop and deploy 

new cryptosystems that will be secure against quantum 

attacks, well before any large quantum computers are 

built. 

ACMD is collaborating with the ITL Computer Security Division on several aspects of this problem. First, 

we are reviewing ongoing research on quantum algorithms and quantum cryptanalysis [1]. It is well known 

that Shor’s algorithm can factor integers and compute 

discrete logarithms in polynomial time, thus breaking 

the RSA cryptosystem, Diffie-Hellman key exchange, 

and elliptic curve cryptography. However, further research is needed to understand the power of quantum 

computers to solve other hard problems of interest to 

38 http://www.nist.gov/itl/csd/ct/post-quantum-crypto-workshop2015.cfm 

cryptography, such as finding short vectors in high-dimensional lattices, solving multivariate quadratic 

systems of equations, and computing isogenies of elliptic curves. 

In addition, we are studying different theoretical 

techniques for modeling a quantum adversary when 

proving the security of a cryptographic protocol. In 

most previous security proofs, only classical adversaries 

are considered. Models that allow quantum adversaries, 

such as the quantum random oracle model, are not as 

well understood. 

We are also reviewing ongoing progress in experimental implementations of quantum computers, using 

technologies such as ion traps and superconducting 

qubits. There have been some predictions that cryptographically-relevant quantum computers could be built 

by the year 2031 [2]. This informs our planning for 

when new post-quantum cryptosystems need to be deployed. 

Finally, we are contributing to ongoing research on 

quantum-resistant public-key cryptosystems, including 

schemes based on lattices, error-correcting codes, multivariate systems of polynomial equations, and one-time 

hash-based signatures. Many of these schemes look 

quite promising, but they still have drawbacks with regard to security, efficiency and usability. NIST 

researchers have contributed several new results in this 

area [3-5]. 

NIST is also taking concrete steps towards standardizing post-quantum cryptography. In the past year 

we have engaged with the broader community, including industry, academic and government organizations. 

In April 2015 we organized a workshop on Cybersecurity in a Post-Quantum World38, and in September 2015 

we participated in discussions at a Dagstuhl workshop 

on Quantum Cryptanalysis. We have also collaborated 

with the Joint Center for Quantum Information and 

Computer Science (QuICS) at the University of Maryland. 

Presently, we are in the process of writing a short 

report describing the current status of post-quantum 

cryptography, and we are making plans for an open and 

public process for developing standards in this area. 

Members of our team will discuss these plans at the Post 

Quantum Cryptography (PQCrypto) conference in February 2016. 

[1]	 S. Jordan, Quantum Algorithm Zoo, 

http://math.nist.gov/quantum/zoo/. 

[2]	 M. Mosca, Cybersecurity in an Era with Quantum Computers: Will We Be Ready? Cryptology ePrint Archive, 

Report 2015/1075, International Association for Cryptologic Research. 
 

 

 

   

 

 

 

 

   

 

 

74 NIST Applied and Computational Mathematics Division 

[3]	 D. Moody and R. Perlner, Vulnerabilities of “McEliece 

in the World of Escher,” PQCrypto 2016, Fukuoka, Japan, February 2016, to appear. 

[4]	 R. Cartor, R. Gipson, D. Smith-Tone and J. Vates, On the 

Differential Security of the HFEv- Signature Primitive, 

PQCrypto 2016, Fukuoka, Japan, February 2016, to appear. 

[5]	 R. Perlner and D. Smith-Tone, Security Analysis and Key 

Modification for ZHFE, PQCrypto 2016, Fukuoka, Japan, February 2016, to appear. 

High-Speed Error Correction Codes 

for Quantum Key Distribution 

Alan Mink 

Anastase Nakassis (NIST ITL) 

Quantum information science incorporates quantum mechanics into information technology. It is an emerging 

field thought to have the potential to cause revolutionary 

advances. One promising early area is quantum cryptography, specifically quantum key distribution (QKD), 

which is a protocol that uses a pair of unsecured communication channels, a quantum channel, and a classical 

channel, to establish a shared secret between two parties, 

Alice and Bob. This shared secret is then used to encrypt 

messages between Bob and Alice. QKD has been proven 

information theoretically secure, unlike classical key 

distribution which relies on computational complexity. 

There are four stages to the QKD protocol. The first 

stage involves quantum mechanics, the other three are 

classical processing. Stage 1 is the transmission of randomly encoded single photons over a lossy quantum 

channel to be measured by Bob to form the initial raw 

random sequence. Stage 2 is where Alice and Bob exchange information over the classical channel to “sift” 

their bit sequences to achieve a common sequence. But, 

that sequence may have errors. Stage 3 is where Alice 

and Bob exchange information over the classical channel to correct errors between their bit sequences without 

exposing the value of their bits. Finally, Stage 4 is where 

Alice and Bob privacy amplify their now identical bit 

sequences through the application of a hash function to 

eliminate any leaked information, yielding a smaller set 

of secret bits between Alice and Bob. The last two stages 

are referred to as post-processing. 

There is a large body of information about error correction (EC) codes, but QKD presents a different 

environment than conventional communication. For example, expected QKD error rates (1 % to 11 % vs. 0.1 % 

or below) are higher, error correction information is sent 

separately over an error free channel, the amount of information that the EC code leaks about the data must be 

minimized and, in particular, kept below a given limit to 

Figure 46. Polar code β efficiency as a function of block size. 

Figure 47. QKD secure (Gamma) yield as a function of block size. 

extract a secret, and quantum data retransmission is not 

possible. 

Our previous work has focused on high speed QKD 

reconciliation and we have obtained a processing rate of 

up to 200 Mbit/s for low density parity check (LDPC) 

one-way EC algorithms [1] implemented on a single 

GPU. Our more recent work has focused on polar EC 

codes and how they can be adapted to QKD protocols 

[2]. While investigating efficient approaches to designing polar codes we developed an interactive version of a 

successive cancellation polar decoder that yielded significantly better EC performance. This was obtained by 

improvement in the frame error rate (FER), which is the 

code failure rate, and in its Shannon efficiency. An additional benefit of our interactive algorithm is that it 

eliminates the need for an initial code design (i.e., the 

selection of a predefined frozen bit set) since the algorithm decides what information is needed as it decodes. 

The downside of such an interactive code is the added 

communication overhead, although parallel and efficient implementations may limit the impact of this 

overhead. Moreover, QKD environments that don’t require high speed reconciliation are appropriate 

applications, such as satellite QKD where the post-processing time period is much longer than the quantum 

exchange period. 

Our error correction performance yields FERs of 

less than 10-4 compared to 1 % to 10 % as reported in the 

QKD literature. Our Shannon efficiency results are also 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 75 

better as shown in Figure 46, where the top curve (2 %) 

is comparable to the bottom curve (J-2 %). The percentages in the legend refer to quantum bit error rate 

(QBER), so the 2 % curve refers to the results for a 2 % 

QBER. Furthermore, the QKD secure yield, where 

p=QBER, is defined as 

Gamma yield = (1-FER)( β(1-h(p)) - h(p) ), 

is a metric normalized across code block sizes, resulting 

in the fraction of secure bits extractable from the initial 

total. Figure 47 shows the improved overall QKD performance (Gamma yield) resulting from using our 

interactive polar decoder algorithm compared to the literature. The top curve (2 %) is comparable to the second 

curve (J-2 %). 

[1]	 A. Mink and A. Nakassis, LDPC Error Correction for 

Gbit/s QKD, in Proceedings of the SPIE: Defense Security and Sensing 9123, Baltimore, MD, May 2014. 

[2]	 A. Nakassis and A. Mink, Polar Codes in a QKD Environment, in Proceedings of the SPIE: Defense Security 

and Sensing 9123, Baltimore, MD, May 2014. 

Towards a Quantum Repeater 

Xiao Tang 

Oliver Slattery 

Lijun Ma 

Paulina Kuo 

Barry Hershman 

Alan Mink 

Future quantum computers will efficiently solve certain 

problems that cannot be solved with even the most powerful classical computers. Just as classical computers are 

linked to form large-scale networks, so too will quantum 

computers be linked to form large-scale quantum networks. Single photons will carry information traveling 

in such networks. Quantum repeaters are needed to extend transmission distances beyond single links limited 

by unavoidable transmission losses. Such repeaters must 

maintain the fidelity of the quantum information carried 

by the photon. Although some essential components for 

a quantum repeater (such as quantum memory, narrow 

linewidth entangled photon sources, and frequency conversion between atomic and telecom wavelengths) have 

been demonstrated in principle, no practical quantum repeater has yet been implemented. 

The quantum communication research project in 

ITL was established in 2000 as a part of a NIST-wide 

quantum key distribution (QKD) collaboration that resulted in the fastest QKD systems in the world at that 

time, as well as the demonstration of a 3-node QKD network [1]. The team then developed novel single photon 

frequency conversion systems based on engineered nonlinear materials. These systems can be used, in principle, 

for entangled photon pair generation, single photon detection and as an interface between the wavelengths of 

transmission and storage, which are essential components for quantum repeaters [2]. 

In FY 2015 we extended this work, focusing on the 

quantum memory and entangled photon pair sources 

suitable for a future quantum repeater. In particular, we 

studied quantum memories based on electromagnetically-induced transparency (EIT), and narrow linewidth 

photon sources, including those at 894.6 nm and 1310 

nm, as well as a polarization entangled photon source 

near 1550 nm. 

Quantum memory is a key component in the implementation of quantum repeaters for quantum 

communications and quantum networks. We have 

demonstrated an EIT quantum memory scheme in a 

warm cesium (Cs) atomic vapor cell. The Cs D1 line at 

894.6 nm corresponds to photon pairs (895 nm and 1310 

nm) generated by our spontaneous parametric down 

conversion (SPDC) source. An EIT quantum memory 

with Cs atomic vapor provides an inexpensive and scalable scheme for quantum repeaters. Our preliminary 

results show photon state storage and retrieval efficiency 

to be similar to that of quantum memories of other 

groups [3]. This will provide the basis for further experiments on quantum communication, such as photon 

interference with quantum memory. We have reduced 

the noise level in our system to a level where we can do 

single-photon-level experiments. We expect this noise 

performance to be further improved, with less noise corresponding to higher fidelity of the quantum system. 

Another ingredient necessary for a quantum repeater is a special entangled photon pair source. To 

ensure high transmission efficiency, the wavelength of 

one photon should be in the low-loss telecommunication 

band (1310 nm in our case), and the other photon should 

match an atomic system of the quantum memory, in 

terms of both linewidth and wavelength. For example, 

the quantum memory we developed this year works at 

the Cs D1 transition (around 894.6 nm), and has subMHz operating bandwidth. The development of such a 

photon source is a very challenging task because (1) the 

required photon bandwidth is extremely narrow; (2) its 

central wavelength must be locked on the atomic transition line for long term stabilization; and (3) the 

wavelengths of the two photons in a pair are far apart. 

In FY 2015, we demonstrated a photon pair source 

at 1310 and 894.6 nm with a linewidth of 28 MHz. The 

wavelength at 894.6 nm is locked on the Cs D1 line for 

long term stabilization. Figure 48 shows a part of our 

experimental setup. The detailed results have been published [4]. However, a linewidth of 28 MHz is still broad 

relative to the desired range of a few MHz or even sub 

MHz. To address this, we have initiated another experiment, in which a micro-toroid with an ultra-high quality 

factor will be used to generate photon pairs based on a 

third-order nonlinear effect, so called spontaneous four­
 

 

 

 

 

 

 

 

76 NIST Applied and Computational Mathematics Division 

Figure 48. Experimental setup for quantum repeater development. 

wave mixing (SFWM). The micro-toroid, developed at 

Washington University in St. Louis, is a very promising 

configuration due to its small mode volume and ultrahigh quality factor. 

The team has also been developing a polarizationentangled photon pair source near 1550 nm by using a 

domain-engineered, type-II, periodically poled nonlinear crystal combined with a 775 nm pump. Preliminary 

results were reported in [5]. This source will serve as a 

testbed for studying polarization entanglement visibility 

and the effects of spectral and temporal distinguishability. We are also working on devices for low-noise 

quantum frequency upconversion of 1550 nm photons 

that can be used to characterize and manipulate the 1550 

nm entangled photon source. We envision the source for 

future use in a quantum repeater and in random number 

generation based on the violation of Bell’s inequality. 

In FY 2015, the team also worked on a few additional tasks. 

	 One of our team members participated in the worldwide standardization activity for QKD coordinated 

by the European Telecommunications Standards 

Institute (ETSI) QKD industry specification group 

(ISG). The activities were reported at a workshop 

in December 2014 [6]. 

	 In recent years, diamond based single photon 

sources have shown great potential for quantum information science and technology applications. In 

FY 2015, we observed single photon emitting spectra from various defect centers, including nitrogen 

vacancies, silicon vacancies and Ni-doped defects 

in diamond films by using a confocal microscope 

built in our lab. The team also initiated a related collaboration with the Center for Integrated Quantum 

Materials at Howard University. This initial study 

may open up new opportunities for our future research. 

[1]	 L. Ma, A. Mink and X. Tang, High Speed Quantum Key 

Distribution over Optical Fiber Network System, Journal 

of Research of the National Institute of Standards and 

Technology 114:3 (2009), 149. 

[2]	 L. Ma, O. Slattery and X. Tang, Single Photon Frequency 

Up-conversion and its Applications, Physics Reports 

521:2 (2012), 69-94. 

[3]	 L. Ma, O. Slattery, P. Kuo and X. Tang, EIT Quantum 

Memory with Cs Atomic Vapor for Quantum Communication, Proceedings of the of SPIE 9615 (2015), 96150D– 

1. 

[4]	 O. Slattery, L. Ma, P. Kuo, and X. Tang, Narrow-Linewidth Source of Greatly Non-Degenerate Photon Pairs 

for Quantum Repeaters from a Short Singly Resonant 

Cavity, Applied Physics B 121 (2015), 413-419. 

[5]	 P. Kuo, J. Pelc, O. Slattery, L. Ma and X. Tang, “Domainengineered PPLN for Generation of Polarization-entangled Photons,” SPIE Photonics West, 9377-34, San 

Francisco, CA, February 7-12, 2015. 

[6]	 R. Alléaume, T. Chapuran, C. Chunnilall, I. Degiovanni, 

N. Lutkenhaus, V. Martin, A. Mink, M. Peev, M. Lucamarini, M. Ward and A. Shields, Worldwide 

Standardization Activity for Quantum Key Distribution, 

in Proceedings of the IEEE GlobeCom Workshop on Telecomm Standards – From Research to Standards, Austin, 

TX, December 8 ,2014, 741-746. 

Joint Center for Quantum 

Information and Computer Science 

Dianne P. O’Leary
 

Ronald F. Boisvert
 

Jacob Taylor (NIST PML)
 

Carl Williams (NIST PML) 

Andrew Childs (University of Maryland) 

https://quics.umd.edu/ 

NIST and the University of Maryland (UMD), with the 

support and participation of the Research Directorate of 

the National Security Agency/Central Security Service 

(NSA/CSS), inaugurated a new joint venture, The Joint 

Center for Quantum Information and Computer Science 

(QuICS) on October 31, 2014. Scientists at the center 

will conduct basic research to understand how quantum 

systems can be effectively used to store, transport and 

process information. 

The new center complements the fundamental 

quantum research performed at the Joint Quantum Institute (JQI), which was established in 2006 by UMD, 

NIST and the NSA. Focusing on one of JQI’s original 

objectives, to fully understand quantum information, 

QuICS will bring together computer scientists—who 

have expertise in algorithm and computational complexity theory and computer architecture—with quantum 

information scientists and communications scientists. In 

particular, the center will bring together researchers 

from the University of Maryland Institute for Advanced 
 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 77 

Figure 49. Michael Jarrett (left), a doctoral student at the University of Maryland, is the recipient of the first Booz Allen Hamilton Quantum 

Information Fellowship at QuICS. Jarrett is working with QuICS Fellow, and ACMD researcher, Stephen Jordan (right) to understand the 

computational power of quantum adiabatic optimization algorithms. (See page 71.) 

Computer Studies (UMIACS); the UMD Departments 

of Physics and Computer Science with NIST’s Information Technology and Physical Measurement 

Laboratories. An orientation for QuICS stakeholders, 

held on Feb. 9, 2015, was attended by some 30 staff 

members from UMD, NIST and the NSA. 

Some of the topics QuICS researchers will initially 

examine include understanding how quantum mechanics informs computation and communication theories, 

determining what insights computer science can shed on 

quantum computing, investigating the consequences of 

quantum information theory for fundamental physics, 

and developing practical applications for theoretical advances in quantum computation and communication. 

QuICS is also expected to train scientists for future 

industrial and academic opportunities and provide U.S. 

industry with cutting-edge research results. By combining the strengths of UMD and NIST, it is hoped that 

QuICS will become an international center for excellence in quantum computer and information science. 

Dianne O’Leary, a Professor of Computer Science 

at UMD and a long-time faculty appointee in ACMD, 

served as a founding Director of QuICS, along with Jacob Taylor of the NIST PML. Andrew Childs, a recent 

hire at UMD, took over as Co-Director upon O’Leary’s 

recent retirement. Stephen Jordan and Yi-Kai Liu, both 

of ACMD, have been named QuICS Fellows. 

QuICS has quickly established itself as a substantial 

research presence in quantum information science. Two 

postdocs given the distinction of Hartree Postdoctoral 

Fellows, as well as two additional outstanding postdoctoral researchers, also began their tenures in the fall of 

2014. QuICS Fellows have recruited a total of 11 graduate students into the Center. The Center has also 

developed a robust visitor program, with more than 50 

external speakers presenting in the QuICS Seminar series since October 2014. On September 28 – October 2, 

2015 QuICS hosted a Workshop on the Frontiers of 

Quantum Information and Computer Science. The 

workshop featured 24 lectures by leading quantum information researchers including Seth Lloyd, Edward 

Farhi and Scott Aaronson (MIT) and Daniel Gottesman 

(Perimeter Institute), as well as a poster session with 

more than 30 contributed posters. QuICS has also been 

selected as the host of the 6th International Conference 

on Quantum Cryptography to be held in Washington, 

DC on September 12-16, 2016. QuICS Fellow and 

ACMD researcher Yi-Kai Liu is the lead local organizer 

of the event and Chair of its international Steering Committee. 

The technical work of QuICS has also seen a strong 

start, with 65 papers released in calendar year 2015 

alone. QuICS has indeed made an impressive start. 
 

 

 

 

 

 

 

 

 

 

78 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 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 actual resilience of our critical infrastructure is simply unknown. Measurement science has 

long provided a basis for the understanding and control of physical systems. Such deep understanding and 

insight is lacking for complex information systems. We seek to develop the mathematical foundations needed 

for a true measurement science for complex networked information systems. 

Graph Theoretic Applications to 

Network Security and Security 

Metrics 

Assane Gueye
 

Richard J. La
 

Peter Mell (NIST ITL)
 

Rich Harang (Army Research Laboratory)
 

Desire Banse (NIST ITL) 

Yannick Congo
 

In this project, we have identified and proposed graphtheoretic metrics to quantify the resilience of network 

topologies under an adversarial environment. Using 

these metrics, we have considered three application 

problems: 

1. Resilience of the internet over time, 

2. Defense-in-depth approach for IPv6 network, and 

3. Connectivity of the African network. 

Internet Resilience. The apparent robustness of Internet 

networking hides underlying weaknesses. In this work, 

using data available from the Center for Applied Internet 

Data Analysis (CAIDA), we have revealed a class of 

such weaknesses in the form of the ability of colluding 

countries to deliberately filter out other countries. 

We analyzed the ability of a group of countries to 

disconnect two other countries, to isolate a set of countries from the Internet, or to break the Internet into noncommunicative clusters. We find that, despite the potential for these attacks, the Internet as a whole has become 

increasingly resilient over the period of examination 

from 2008 to 2013. However, the gains in robustness 

and resilience were primarily concentrated in well-connected countries, which form a very resilient core. We 

found that less connected countries formed new links 

largely with well-connected countries, and not to each 

other, maintaining the centrality of the well-connected 

countries in the paths between the less connected countries on the fringe. Because of this, the resilience of these 

less connected countries did not increase significantly 

over the time period studied. The result is that a small 

set of countries is able to isolate significant portions of 

the Internet or to divide it up into clusters. Individual 

well connected countries are often able to unilaterally 

isolate network-dependent neighbors. 

These weaknesses could be addressed through a focus on establishing links between poorly connected 

countries (e.g., through grants to poorer countries or 

through collaboration between coalitions of physically 

adjacent countries). This would move the poorly connected countries away from dependence on the 

infrastructure of the more highly connected countries. It 

would also move the Internet as a whole towards a more 

resilient architecture through the provision of alternate 

geographically diverse pathways. 

Defense-in-Depth. Networks securely configured with 

Internet Protocol version 6 can be made resistant to network scanning, forcing attackers to propagate along 

existing benign communication paths. We leverage this 

limitation of attacker movements to propose a chokepoint-based defensive approach in which heightened 

security measures are deployed on a selected group of 

chokepoint hosts in order to constrain attacker propagation. Chokepoints are chosen such that, together, they 

connect small isolated clusters of the communication 

graph. Hence, attackers attempting to propagate through 

the network are limited to a small set of potential targets 

or have to penetrate one or more chokepoints. 

To choose the chokepoints, we consider two metrics 

to optimize: (i) minimizing the maximal cluster size and 

(ii) maximizing the mean of the minimum number of 

chokepoints that lie between pairs of nodes. The former 

metric aims to constrain the attacker to as small a cluster 

as possible, and the second seeks to maximize the number of chokepoints that an attacker must penetrate on 

average in order to reach a particular high-value network 

target. The optimal placement of such chokepoints is an 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 79 

NP-hard problem and, as a consequence, we have used 

a set of heuristics to approximate the solution. We have 

tested our approach and algorithms using the data from 

a large operational network consisting of over 15500 

nodes. Our experiments have shown that enhanced security solutions have to be deployed to only 0.65 % of 

the nodes to limit the propagation of a random attack to 

less than 15 % of the nodes in the network. Thus, our 

approach enables a novel defense-in-depth approach 

that complements traditional security approaches. 

African Connectivity. The development of the African 

Internet has lagged behind more developed continents. 

However, in the period from 2010 to 2014, significant 

growth has been observed. In this study, we use data 

available from CAIDA to measure and document the 

growth of Internet connectivity in Africa from 2010 to 

2014 with a focus on inter-country relationships. We 

evaluate both intra-continent connectivity as well as 

connectivity to other continents. An initial analysis reveals a modest increase in the number of participating 

countries but an explosive increase in the number of 

routers and network links. We then form the first country level topology maps of the African Internet and 

evaluate the robustness of the network. This includes a 

study of raw connectivity, pairwise shortest paths, and 

betweeness centrality. We then suggest how improvements can be made to the inter-country African 

connectivity to enhance its robustness without reliance 

on paths traversing multiple continents. 

At a deeper level, our connectivity metrics also reveal a highly scale free nature in the country to country 

Africa connectivity graph. There are many countries of 

low degree and a few of high degree. There is a negative 

assortativity whereby the low degree nodes tend to connect to the high degree nodes and not to each other. The 

connectivity within the center of Africa tends to be low. 

The problem with this model is that it is susceptible to 

node failure. The majority of African countries are dependent upon just a few other African countries for their 

intra-continental Internet access. However, we have 

seen that judicious placement of additional links can reduce the fragility induced by the scale free nature. In 

particular, links among the low degree nodes are 

needed. This translates into the need for direct Internet 

links between countries with less Internet infrastructure 

in order to make the African Internet stronger as a 

whole. 

[1]	 A. Gueye, P. Mell, R. Harang and R. La, Defensive 

Resource Allocations with Security Chokepoints in Highrisk IPv6 Networks, in Lecture Notes in Computer 

Science 9149 (2015), Data and Applications Security and 

Privacy XXIX, Springer, 261-276. 

[2]	 P. Mell, R. Harang and A. Gueye, Measuring Limits on 

the Ability of Colluding Countries to Partition the Internet, International Journal of Computer Science: Theory 

and Application 3:3 (2015), 60-73. 

[3]	 P. Mell, R. Harang and A. Gueye, The Resilience of the 

Internet to Colluding Country Induced Connectivity Disruptions, in review. 

[4]	 A. Gueye, P. Mell, D. Banse and Y. Congo, On the Internet Connectivity in Africa, in review. 

[5]	 P. Mell, R. Harang and A. Gueye, Linear Time Vertex 

Partitioning on Massive Graphs, in review. 

A Game Theoretic Model of ZeroDay Attack Propagation 

Assane Gueye 

Richard J. La 

Peter Mell (NIST ITL) 

The goal of this project is to understand the progress of 

an attacker inside a network, who can use both known 

exploits as well as zero-day exploits. The network is 

protected by a defender (and a defense system) which 

aims to prevent the attacker from reaching a high-value 

target inside the network. Both the attacker and the defender have only partial information/observation about 

their interaction and the progress of the attack. We use a 

Markov Decision (MD) process approach to model the 

attacker and defender’s dynamic decision making and 

use a stochastic game model to study their interaction. 

Partial results of our study show that an optimal 

strategy for the attacker is a threshold policy in which 

the attacker starts by using zero-day exploits until it 

achieves a certain level of success or reaches some point 

along the attack and switches to known exploits to complete the attack. For the defender, our numerical analysis 

suggests that an optimal strategy is also a threshold policy that requires the defender to monitor the number of 

alarms generated by the defense systems (employed for 

known and unknown exploits). When the number of 

alarms is smaller than the threshold value, the defender 

keeps improving its defense systems. When the number 

of alarms exceeds the threshold, the defense performs a 

full system reset. 

Our game-theoretic model can be used to enhance 

attack graph-based analysis. For instance, by using our 

attack process model, one can determine the most likely 

paths in the attack graph. 
 

 

 

 

 

 

 

 

 

 

 

80 NIST Applied and Computational Mathematics Division 

Security of Complex, Interdependent 

Systems 

Richard J. La 

Understanding the security of large, complex interconnected networks and systems has emerged as one of the 

key challenges information system engineers face today. 

Examining the system-level security of complex networks or systems is hindered by the fact that security 

measures adopted by various agents or organizations, or 

lack thereof, produce either positive or negative network 

externalities on others, leading to so-called interdependent security (IDS). 

Many, if not most, of existing studies on IDS focus 

on how the infection of a few agents may spread to a 

large number of other agents through networks (e.g., 

computer networks or social networks). Furthermore, 

they mostly consider scenarios where the agents are passive in that their security measures are pre-selected 

independently of the perceived risks and threats. In 

many scenarios of interest, e.g., cybersecurity and disease outbreaks, however, agents can employ security 

measures that are best suited for their risks, including the 

likelihood of infection. 

In the past two years, our efforts have been aimed 

at examining scenarios where nodes are strategic entities 

interested in optimizing their own objectives. We model 

the interdependence in security among agents, which is 

caused by network externalities, using a dependence 

graph. In this graph, the nodes/vertices are the agents/organizations and an edge between two vertices indicates 

interdependence between them. The goal of this project 

is to understand how the underlying network structure 

and properties affect the choices made by strategic 

agents and influence the network-level security. 

In the first year, we focused on understanding how 

the (weighted) node degree distribution of the dependence graph shapes the security choices of strategic 

agents. To this end, we adopted population game models 

and their Nash equilibria as reasonable approximations 

to expected operating points. Our key finding was that 

as the weighted node degree distribution, where the 

weights are the degrees, becomes stochastically larger, 

the local security measured by the risks seen from a 

neighbor improves in that the average number of attacks 

propagating via a single edge decreases [1]. At the same 

time, somewhat surprisingly, the global network security measured by cascade probability, i.e., the likelihood 

that a single initial infection will lead to a large number 

of infected nodes over time, deteriorates [2]. Moreover, 

the price of anarchy, which measures the worst-case inefficiency of Nash equilibria with respect to the system 

optimum, increases as the weighted node degree distribution gets larger. 

In the past year, we continued our efforts along two 

main directions. First, in our past studies, we assumed 

that the dependence graph was neutral, i.e., there is no 

correlation between the degrees of two interdependent 

nodes. It is well known that many natural and engineered 

networks exhibit non-negligible correlations in the degrees of end nodes. We investigated how network 

mixing or assortativity affects the network-level security 

with strategic agents [3]. Our finding suggests that the 

effects of assortativity are similar to those of the 

weighted node degree distribution studied in the first 

year. To be more precise, it is the effective node degree 

distribution seen by the nodes, which is determined by 

both the actual node degree distribution and network 

mixing, that shapes the security choices of the nodes. 

Secondly, we investigated the issue of convergence 

to Nash equilibria. Many existing studies, including our 

previous studies, assume that the agents can reach a 

(pure-strategy) Nash equilibrium, and hence they focus 

on the properties of Nash equilibria. However, in many 

cases, including our own, it is not immediately clear how 

and/or when the agents will be able to arrive at Nash 

equilibria even when they can interact with each other 

many times. To this end, we examined the convergence 

to a Nash equilibrium when the agents adopt the wellknown better-reply dynamics, i.e., when an agent finds 

at least one better reply that reduces its cost, it switches 

to one of the better replies. We showed that, in a large 

class of games called generalized weakly acyclic games, 

the better-reply dynamics ensure almost certain convergence to a Nash equilibrium, even when the agents 

revise their actions based on delayed, sometimes outdated, payoff information in an asynchronous manner 

[4, 5]. 

[1]	 R. J. La, Effects of Degree Distributions on Network Security and Internalization of Externality, in review. 

[2]	 R. J. La, Interdependent Security with Strategic Agents 

and Global Cascades, IEEE/ACM Transactions on Networking, to appear. 

[3]	 R. J. La, Network Mixing – Is it Good or Bad for Network 

Security?, in preparation. 

[4]	 S. Pal and R. J. La, A Simple Learning Rule in Games 

and its Convergence to Pure-Strategy Nash Equilibria, in 

Proceedings of the American Control Conference, Chicago, IL, July 2015. 

[5]	 S. Pal and R. J. La, A Simple Learning in Weakly Acyclic 

Games and Convergence to Nash Equilibria, in Proceedings of the 53rd Annual Allerton Conference, Monticello 

(IL), September 30 – October 2, 2015. 
 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 81 

Measurement Science for Systemic 

Risk 

Vladimir Marbukh 

The economic and convenience benefits of interconnectivity have driven the current explosive emergence and 

growth of networked systems. However, numerous recent systemic failures in various systems suggest that a 

market economy has difficulty in the accurate estimation 

and pricing of the drawbacks and systemic risks of interconnectivity. Our modeling efforts have the goal of 

developing recommendations on the systemic risk/benefit tradeoff of interconnectivity, where benefits are due 

to local risk mitigation, and systemic risk is due to risk 

exposure to cascading failure. 

We model contagion in networked systems as a 

Markov process with locally interacting components, 

where system “topology” is encoded as a directed graph 

with nodes representing system components, and links 

representing the contagion flow [1-2]. In applications, 

some internal node states represent component failure, 

e.g., overload, and thus can be deemed “vulnerable/ undesirable.” This motivates the definition of the 

individual node risk as the probability of this node being 

in such a state, and systemic risk as the individual risk 

averaged over all the nodes in the system. 

We assume that an increase in the node risk exposure immediately drives adjacent nodes towards higher 

risk exposure, creating a possibility of contagion and undesirable cascades. Direct solution of the Kolmogorov 

equations for the underlying Markov “micro-process” 

with a large number of interacting components N is computationally infeasible due to the astronomically high 

dimension of the Kolmogorov system. This high dimension of micro-description on the one hand, and systemic 

risk being inherently a macroscopic phenomenon on the 

other, suggest the possibility of a macro-description of 

systemic risk. 

Our first step in realizing this possibility is developing mean-field and fluid approximations for the 

Figure 50. A typical system phase diagram. Here x is average investment in node “antifragility,” and d is the average node degree. 

boundary of the operational system equilibrium inside 

the system parameter space. The importance of this region is due to economics, which drives networked 

systems towards the stability boundary of the normal/operational equilibrium. We demonstrate that the 

proposed macro-description is instrumental for classification and management of the emerging instability. In 

particular, we suggest that while maximizing economic 

and convenience benefits of interconnectivity, networked system designers and operators should limit the 

systemic risk of abrupt/discontinuous instability in favor 

of gradual/continuous instability. 

Currently we are extending these results by considering the effect of system topology [3-5]. In particular, 

we compare the following two systemic risk mitigation 

techniques: (a) investing in the component “antifragility,” e.g., by adding extra capacity to withstand adverse 

effects of demand bursts, capacity outages, etc., and (b) 

investing in additional interconnectivity allowing for 

more risk diversification. Figure 50 depicts typical system phase diagram in variables (x,d), where x is a 

properly defined average investment in the node “antifragility,” and d is the average node degree. 

The operational regime without systemic risk is unstable within region V, and is at least locally stable 

outside V. We assume that costs/benefits of system connectivity per node can be quantified by an increasing and 

concave utility function of the average node degree d, 

corresponding Kolmogorov microscopic equations. For 

low exposure to the exogenous risk, the approximate 

closed systems of non-linear, fixed-point equations have 

a “normal/operational” system equilibrium with a low 

systemic risk. As the exogenous risk exposure adiabatically, i.e., “slowly,” increases, the approximate 

equations may experience bifurcation, which results in 

emergence of a high systemic risk solution. Following 

the conventional approach, we interpret multiple soluu(d), and consider the optimization problem 

max ݑሺ݀ሻ െ ݔ. ሺ௫,ௗሻ∉௏

The solution to this problem defines the optimal balance 

between the connectivity d = dopt and investment in the 

component antifragility x = xopt subject to systemic risk 

avoidance. In particular, our results indicate that 

(xopt,dopt ) lies on the boundary BC in Figure 50. 

tions of the approximate equations as describing the 

metastable, i.e., persistent, system states. 

[1] V. Marbukh, Towards Unified Perron-Frobenius Framework for Managing Systemic Risk in Networked 

Since for heterogeneous networked systems, the dimensions of the corresponding approximate 

descriptions grow with N, further dimension reduction [2] is required. We suggest a possibility of a Perron-Frobenius-based “macro-description” near the stability 

Systems, in Proceedings of the annual European Safety 

and Reliability Conference (ESREL), Zurich, Switzerland, September 7-10, 2015. 

V. Marbukh, Towards Managing Systemic Risk in Networked Systems, in Proceedings of the International 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

82 NIST Applied and Computational Mathematics Division 

Conference on Operations Research, Vienna, Austria, 

September 1-4, 2015. 

[3]	 V. Marbukh, “On Managing Cost/Benefit Connectivity 

Tradeoff in a Networked Infrastructure Susceptible to 

Adverse Cascades,” International Conference on Network Science (NetSci), Zaragoza, Spain, June 1-5, 2015. 

[4]	 V. Marbukh, “SDN: Systemic Risks due to Dynamic 

Load Balancing,” Internet Research Task Force, Software 

Defined Networking Research Group, IETF 91, Honolulu, Hawaii, USA, 2014. 

[5]	 V. Marbukh, “Network Evolution by Preferential Rewiring with Infection Risk Mitigation: Work in Progress,” 

Workshop on Dynamics of and on Networks, Santa Fe 

Institute, Santa Fe, NM, December 2, 2014. 

Identifying the Best Nodes in a 

Network for Fast Communication 

Fern Y. Hunt 

The identification of nodes in a network that enable the 

fastest spread of information is an important if not fundamental problem in network control and design. It is 

applicable to the optimal placement of sensors, the design of more secure networks, and the problem of 

network control when network resources are limited. 

Our research centers on a model problem where communication is represented mathematically by random 

walks on an undirected graph. The problem of selecting 

the best nodes is then posed in terms of finding the set 

of nodes on the graph (subject to constraints on the set 

size) that minimizes a random walk hitting time function, representing the time it takes for information to 

reach the entire network. In recent years, research on 

methods for solving combinatorial optimization problems like this have centered on the development of 

solution methods when the function to be optimized is 

bounded and submodular (supermodular). 

F. Hunt has been developing methods for identifying optimal and near optimal sets that use the 

supermodular properties of the hitting time function as 

well as information about the network topology [1]. This 

work is intended to be part of the ongoing modeling and 

simulation research on communication networks and 

protocols going on in ITL. Developments of the past 

year include [3] 

	 showing that these methods are polynomial time in 

the number of nodes, 

	 rigorous comparison of the set obtained by our 

method with the exact solution (performance ratio), 

	 a proof that our approximation is as least as good as 

the result of the classic greedy algorithm (frequently used for such problems) and improves the 

results of the greedy algorithm by a quantity that 

can be calculated once the approximation is known, 

and 

	 an analysis of computational complexity that quantifies the tradeoff between the quality of the 

solution and computation required to achieve it. 

Our ongoing research involves the development of 

methods based on an understanding of the structure of 

optimal sets and its near optimal subsets. We believe the 

results of this effort are key to making the approach feasible for realistic networks. 

[1]	 F.Y. Hunt, The Structure of Optimal and Near Optimal 

Target Sets in Consensus Models, NIST Special Publication 500-303, August 2014 

[2]	 F.Y. Hunt, Optimal Spread in Network Consensus Models, in review 

[3]	 F. Y. Hunt, An Algorithm for Identifying Optimal 

Spreaders in a Random Walk Model of Network Communication, in preparation. 

Measuring Networks: Monte Carlo 

Sampling to Approximate the 

Chromatic Polynomial 

Yvonne Kemper 

Isabel Beichl 

At its heart, a network (or graph) is a collection of points 

(vertices) connected by lines (edges). Networks can be 

used to represent a variety of physical and abstract objects, and measuring characteristics of networks allows 

researchers to uncover and understand information encoded in the network, as well as study the systems it 

represents. 

One example of this relates to a particular labeling 

of a graph G called a coloring: a proper k-coloring of the 

graph is an assignment of the numbers 1, 2 ..., k to the 

vertices so that vertices connected by an edge receive 

different numbers. Amazingly, there exists a polynomial, the chromatic polynomial, ΧG(x), that evaluates to 

the number of k-colorings when x=k. The chromatic polynomial (as well as its largest integral root) has received 

much attention as a result of the now-resolved four-color 

problem, but ΧG(x) is also central in multiple applications, such as scheduling and assignment problems and 

the q-state Potts model in statistical physics. Scheduling 

problems occur in a variety of contexts, from algorithm 

design to factory procedures, and with an approximation 

of ΧG(x) it is possible to estimate the number of possible 

solutions given specific parameters. For the latter, the 

relationship between ΧG(x) and the Potts model connects statistical mechanics and graph theory, allowing 

researchers to study phenomena such as the behavior of 

ferromagnets. The complex roots of ΧG(x) are particularly useful in this area of research. 
 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 83 

Unfortunately, computing ΧG(x) for a general graph 

G is known to be #P-hard, and deciding whether or not 

a graph is k-colorable is NP-hard; the best known algorithm for computing ΧG(x) for an arbitrary graph G with 

n vertices has complexity O(2nnO(1)) [1]. 

Approximation methods, however, have received 

little attention. The goal of these methods is to provide 

an evaluation close to the true answer in a fraction of the 

time. In the last year, we have adapted a Monte Carlo 

method of sequential importance sampling to be the basis of two approximation algorithms [2]. After 

implementing our algorithms in both MATLAB and C, 

we were able to compute approximations of ΧG(x) for 

graphs of much larger size than previously possible. Before, the best exact algorithms were limited to 2|E(G)| + 

|V(G)| < 950 and |V(G)| < 65, where |E(G)| is the number 

of edges, and |V(G)| is the number of vertices. Our largest so far had 500 vertices and 62 323 edges, and larger 

computations are possible. We have shown our methods 

to have small relative error in the cases where we were 

able to compare to the exact polynomial. Moreover, as 

the expected value of our approximation is the precise 

value, we may further reduce error by performing further computations. 

[1]	 A. Bjorklund, T. Husfeldt and M. Kolvisto, Set Partitioning via Inclusion-exclusion, SIAM Journal of Computing 

39 (2009), 546-563. 

[2]	 Y. Kemper and I. Beichl, Monte Carlo Methods to Approximate the Chromatic Polynomial, Congressus 

Numerantium 125 (2015), 127-152. 

Fast Sequential Network Model 

Building 

Brian D. Cloteaux
 

Zoe Park (Georgetown University) 

Creating degree-based models is an important first step 

in the modeling of networks. Until recently, the only 

way to create a random model with a given a degree sequence would be to first create an instance using the 

Havel-Hakimi algorithm, and then perform a walk on a 

Markov chain, i.e. Markov chain Monte Carlo (MCMC), 

of edge switches in the graph. This method is fast, but 

since the entire graph must be kept in memory, the size 

of the graph that can be generated is severely limited. In 

addition, little is known about bounds on the mixing 

time of this walk. Finally, this algorithm is difficult to 

modify for creating graphs with additional given characteristics. 

In 2010, Blitzstein and Diaconis published a sequential importance sampling (SIS) method for 

selecting random graphs with a given degree distribution 

[1]. Unfortunately, their method is very slow compared 

to the MCMC approach. While there has been some 

Figure 51. Comparison of generation times for models. 

work to speed up the general algorithm, the usefulness 

of the algorithm is limited to small networks. 

We proposed a new SIS method for constructing 

random graphs based on degree values [2]. Our algorithm chooses a set of possible edges (or a reduction) for 

a vertex in the graph, and then if that set is not viable, 

adjusts the selection in order to choose a new set. This 

selection process is done iteratively, and is guaranteed 

to converge to a viable selection set. This new result 

gives us the advantages of using SIS, while approaching 

the speed of the MCMC method; see Figure 51. 

Zoe Park, a SURF student, has coded this algorithm 

and we are preparing it for release. Work on how to 

quickly test whether a degree sequence is graphical was 

also published [3]. 

For the Blitzstein-Diaconis algorithm, the main bottleneck in time is a requirement to check whether an 

edge is not allowed in order to create a viable realization. 

We call these edges that are not allowed in any realization of a degree sequence a forbidden sequence. 

Conversely, an edge that must appear in every realization is called a forced edge. 

The presence of forced or forbidden edges for a degree sequence has important structural implications for 

graphs. We have been able to show several new results 

such as the set of forced edges for a degree sequence is 

isomorphic to some threshold graph [4]. Also, if a sequence has forbidden edges, that implies the presence of 

forced edges also. Finally, we showed that the diameter 

of every graph that is a realization of a degree sequence 

with forced edges is no more than 3. 

These results have important algorithmic applications, but additionally they help us to understand the 

forced structure in models that depend on a given degree 

sequence. 

[1]	 J. Blitzstein and P. Diaconis, A Sequential Importance 

Sampling Algorithm for Generating Random Graphs with 

Prescribed Degrees. Internet Mathematics 6:4 (2010), 

489. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

84 NIST Applied and Computational Mathematics Division 

[2]	 B. Cloteaux, Fast Sequential Creation of Random Realizations of Degree Sequences, in review. 

[3]	 B. Cloteaux, Is This for Real? Fast Graphicality Testing, 

Computing in Science and Engineering, 17:6 (2015), 91. 

[4]	 B. Cloteaux. Forced and Forbidden Edges for Degree Sequences, in review. 

An Algebraic Formulation for the 

Analysis and Visualization of 

Network Graphs 

Roldan Pozo 

Characterizing the topological structure of large graphs 

remains an important problem in network science. 

While it is straightforward to visualize small networks 

of hundreds or a few thousands of vertices and edges using conventional graph visualization packages, 

attempting to render large real networks is nearly impossible. This is particularly true for information networks 

and social networks, where the graph sizes number into 

the millions and billions. And with the amount of data 

being generated and gathered from large social media 

sites ever increasing, characterizing larger and larger 

networks is only becoming more challenging. 

Conventional algorithms for graph visualization result in a rendering of very large networks as a solid blot 

of color from which it is difficult to obtain meaningful 

information. This difficulty is strongly influenced by the 

sheer volume of nodes and edges which makes rendering into a reasonable image size for viewing and printing 

impractical. It is exacerbated by the presence of highdegree nodes (hubs) which entangle many parts of the 

graph with itself. 

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 connective properties. In this research area, we focus 

on a particular type of information: the distribution of 

“fringe” communities, i.e., 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 which are often lost with the inclusion 

of more popular nodes. 

Our approach, the Q-matrix of a network, in its fundamental form, is a connected component size 

distribution matrix for a series of degree-limited subgraphs of the original network (or weakly-connected 

component for directed networks.) Thus, Q(i,j) is the 

number of connected components of size j in a subgraph 

where the maximum degree is equal to or less than i. 

Consider, for example, a Web graph, where nodes are 

Figure 52. Non-trivial components of math.nist.gov web graph, 

restricted to nodes with combined degree less than or equal to 25. 

Figure 53. Q-matrix plot of math.nist.gov webgraph (29K vertices, 62K edges) showing the component size distribution of 

degree-limited subgraphs. 

individual pages, and edges are directed hyperlinks between two web pages. Figure 52, for example, 

illustrates connected components of the math.nist.gov 

Web graph, where nodes of degree greater than 25 have 

been removed. The result is a collection of non-trivial 

components of math.nist.gov web graph, restricted to 

nodes with combined degree less than or equal to 25. 

The image reveals various structures, such as ladder, 

star, 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 

largest degree in the original graph, we can form a connected component size distribution, which can be 

encoded as a row of a matrix. This sparse matrix may 

still be too large to view directly, but can be compactly 
 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 85 

rendered by projecting its nonzero values onto the z-axis 

and displaying it as a three-dimensional plot, as shown 

in Figure 53. This Q-matrix plot of the math.nist.gov 

webgraph (29K vertices, 62K edges) shows the component size distribution of degree-limited subgraphs. 

The Q-matrix of a graph can be considered as a generalization of its degree-distribution. However, it 

encodes other properties, such as the formation and 

growth of its giant component, its connected subparts, 

as well as its size parameters. In fact, common network 

metrics (e.g., degree distribution, number of connected 

components, number of vertices and edges) can be extracted from the Q-matrix using simple linear algebra 

operations. 

Among the interesting characteristics of the Q-matrix formulation is that network graphs from similar 

application areas (e.g., social networks, email networks, 

web graphs, peer-to-peer networks, road networks, citation graphs) share similar visual characteristics, creating 

a potential framework for network identification and 

classification. Indeed, we have used the Q-matrix formulation to generate meaningful thumbnail images for 

network data collections. The computation of the Q-matrix is relatively efficient; graphs with millions of 

vertices and edges can be processed in less than one minute. 

This year we extended this framework by developing an important generalized measure that compares Qmatrices of networks in varying sizes and scale. This is 

critical in developing the theory as it allows one to compare vastly different networks and provide a numerical 

similarity between them, and establish a taxonomy classification based on these characteristics. We have also 

provided an extended measure formulated on second 

and third-generation degree distributions, which provides a refined fingerprint of network graphs. To each 

vertex we assign not just its degree (d), but the average 

degree of all its neighbors (d1), average degree of all its 

neighbor’s neighbors (d2), and so on. This replaces a single vertex value with a finite vector (d, d1, d2, ..., dk). 

Such vectors can be arranged in a lexicographical along 

one dimension, creating a much richer profile than the 

conventional degree distribution. 

[1]	 R. Pozo, Q-matrix: An Algebraic Formulation for the 

Analysis and Visual Characterization of Network Graphs, 

Journal of Research of NIST 121:1, 16 pages. 

Counting the Number of Linear 

Extensions of a Partially Ordered Set 

Isabel Beichl 

Francis Sullivan 

Given a partially ordered set (P,lt), a linear extension is 

a linear ordering (P,<) of the elements of P that is consistent with (P,lt), i.e., if p1.lt.p2 then p1< p2. The ability 

to count the number of linear extensions of (P,lt) is central to the theory of sorting, which in turn is extremely 

important in the design of algorithms for advanced computers. A count of linear extensions is also important in 

ranking alternatives in scheduling problems where one 

might want to keep options open as long as possible, and 

in applications that arise in the social sciences where one 

wants to rank products or job candidates from a given 

partial order. It also appears in big data applications 

where one might need to set priorities and yet keep as 

many options open as possible. 

The number of linear extensions is a measure of the 

entropy of a graph. While it is computationally easy to 

generate a single linear extension of (P,lt) it is known 

that counting the number of linear extensions is #P-complete and so one must resort to approximation. One 

Monte Carlo technique, called Monte Carlo Markov 

Chain (MCMC), has been devised and investigated extensively in the literature of theoretical computer science 

[1]. It has been proved that the method does give an 

accurate approximation. However, the method is not 

helpful for practical computation because it requires 

work (n5

) for an n-element partially ordered set. 

To enable more practical computation, we investigated another Monte Carlo method that has been used 

with success in other #P-hard counting problems. The 

alternate method, called sequential importance sampling 

(SIS) uses non-uniform sampling based on an importance function. In this case, the importance is 

derived from the famous Moebius inversion formula. 

We have found the SIS-based algorithm to work extremely well in test cases. In addition, it has led to a 

combined SIS-MCMC method that improves the 

MCMC method from O(n5

) to O(n3). 

[1]	 G. Brightwell and P Winkler, Counting Linear Extensions, Order 8 (1991), 225-242. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

86 NIST Applied and Computational Mathematics Division 

Extremal Theorems for Degree 

Sequence Packing and the 2-Color 

Discrete Tomography Problem 

James Shook
 

Jennifer Diemunsch (St. Vincent College)
 

Michael J. Ferrara (University of Colorado at Denver)
 

Sogol Jahanbekam (University of Colorado at Denver)
 

In tomography, three-dimensional objects are reconstructed using data acquired from two-dimensional 

projections. Tomography has uses in medical imagining, 

data security problems, computer assisted engineering, 

and electron microscopy. For computational purposes, 

the tomography problem is reformulated as the k-color 

discrete tomography problem which in turn can be stated 

as a coloring problem. The goal of the k-color discrete 

tomography problem is that of coloring the entries of an 

m × n matrix using k colors so that each row and column 

receive a prescribed number of entries of each color. 

This problem is equivalent to packing the degree sequences of k-bipartite graphs with parts of sizes m and 

n. The case of practical interest is k=2. Two graphs pack 

if there is a bijection of the vertices so that there are no 

common edges after the vertices of the two graphs have 

been identified with each other. The degree of a particular vertex is the number of edges incident with that 

vertex. A degree sequence is an ordered list of the degrees of all the vertices of the graph. A realization of a 

given degree sequence is a graph that has that degree sequence. 

We approached the 2-color discrete tomography 

problem by proving a more general related result in 

graph packing. We found non-trivial conditions for 

when two degree sequences have realizations that pack. 

We then modified our techniques to prove several theorems that have direct applications to the 2-color discrete 

tomography problem. The first part of our work appears 

in [1]. We are now modifying and improving our techniques for better results. 

[1]	 J. Diemunsch, M. Ferrara, S. Jahanbekam and J. M. 

Shook, Extremal Theorems for Degree Sequence Packing 

and the Two-Color Discrete Tomography Problem, SIAM 

Journal on Discrete Mathematics 29:4 (2015), 2088­

2099. 

Combinatorial Methods in Software 

Testing 

Raghu N. Kacker 

D. Richard Kuhn (NIST ITL)
 

Yu Lei (University of Texas at Arlington)
 

James F. Lawrence
 

Jose Torres-Jimenez (CINVESTAV)
 

Itzel Dominguez-Mendoza (CENAM)
 

Combinatorial testing (CT) is an approach to detecting 

interaction faults, which cause a software-system to fail 

when certain values of some factors occur together. 

Many critical system failures in recent times have been 

traced to interaction faults in the underlying software. 

Combinatorial testing is based on an empirical result, referred to as the interaction rule, that while the behavior 

of a software system may be affected by a large number 

of factors, only a few factors are involved in a failureinducing fault. Analysis of actual faults have demonstrated that most involved one or two factors; however, 

some may involve three, four or more factors (a fault involving more than six factors has not been reported yet). 

NIST has taken the lead to advance technology 

from pair-wise to higher strength interaction testing, to 

make available research tools and techniques for US industry, and to help promote their effective use. CT is a 

versatile and broadly applicable methodology that is 

helping to reduce testing costs in software-based systems for science, commerce, defense and security, and 

electronic medical systems. CT is useful for hardware 

testing as well. CT is now included in software engineering courses taught in more than fifteen U.S. universities. 

A NIST special publication [1] on CT has been downloaded more than 30 000 times. 

ACTS is a research tool, developed by NIST and 

the University of Texas at Arlington (UTA), to generate 

high strength test suites for CT. More than 2 200 users 

have downloaded an executable version of the ACTS 

tool from the NIST CT website39. We allow further distribution of the ACTS tool by its recipients. We are now 

distributing version 2.93 of the ACTS tool. The ACTS 

tool is optimized to support constraints among test settings; in particular, avoiding forbidden combinations of 

test settings efficiently. 

CCM (for Combinatorial Coverage Measurement), 

a new research tool developed jointly by NIST and guest 

researcher Itzel Dominguez-Mendoza, from the Center 

for Metrology of Mexico (CENAM), determines combinatorial coverage of a test suite that may not have been 

developed from a CT viewpoint. The latest version of 

CCM supports constraints. A parallel processing version 

of CCM is also available. The most important use of 

CCM is to assess the coverage of the input space of a 

test suite. Combinatorial deficiency of a test suite can 

39 http://csrc.nist.gov/groups/SNS/acts/index.html 
 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 87 

Figure 54. Combinatorial t-way coverage of a test suite of 7489 tests of 82 variables for t=2, 3, 4, and 5. 

be remedied by additional tests, so CCM can help expand a test suite to satisfy stated combinatorial 

requirements. A graph of combinatorial coverage depicts the percentage (y axis) of the fraction (x axis) of all 

t-way combinations that are covered by the test suite. 

Figure 54 shows combinatorial t-way coverage of a test 

suite of 7489 tests of 82 factors for t = 2, 3, 4, and 5. The 

area under a curve represents the proportion of combinations that are covered by the test suite. Thus, the area 

above the curve represents input values for which correct operation has not been verified. 

On April 13-17, 2015 NIST co-organized 4th International Workshop on Combinatorial Testing (IWCT), 

held in conjunction with the 8th IEEE International Conference of Software Testing, Verification and Validation 

(ICST) in Graz, Austria, to bring together researchers, 

developers, users, and practitioners to exchange ideas 

and experiences with CT methods and tools. IWCT2015 received 29 submissions of which 15 papers were 

selected by the Program Committee [5-9]. IWCT-2016 

is scheduled to be held in conjunction with ICST-2016 

on April 10-15, 2016 in Chicago, IL. 

Test suites for CT are based on mathematical objects called covering arrays. Jose Torres-Jimenez of the 

Mexican National Polytechnic Institute Center for Research and Advanced Studies (CINVESTAV) spent his 

sabbatical year (July 1, 2014 to June 30, 2015) at NIST 

as a member of the CT team, where he worked on optimizing covering arrays [2,6]. 

40 https://www.sba-research.org/ 

SBA-Research40 is a leading Austrian research center for information security. It is a consortium of 

companies and universities which receives half of its 

funding from industry and the rest from the Austrian 

government for research on cybersecurity. We are 

jointly investigating research issues in using combinatorial test methods for cyber-security applications. For 

example, SBA-Research has used the NIST CCM tool 

to analyze the combinatorial coverage of test inputs of 

some open-source cryptographic suites. In most cases, 

combinatorial coverage was low; suggesting that standard test sets for these widely used cryptographic 

packages may provide insufficient testing. 

[1]	 D. R. Kuhn, R. N. Kacker and Y. Lei, Practical Combinatorial Testing, NIST Special Publication 800-142, 

October 2010. 

[2]	 J. Torres-Jimenez, I. Izquierdo-Marquez, R. N. Kacker 

and D. R. Kuhn, Tower of Covering Arrays, Discrete Applied Mathematics 190–191 (2015), 141–146. 

[3]	 D. R. Kuhn, R. N. Kacker and Y. Lei, Combinatorial Coverage as an Aspect of Test Quality, Crosstalk: The 

Journal of Defense Software Engineering 28 

(March/April 2015), 19-23. 

[4]	 J. D. Hagar, T. L. Wissink, D. R. Kuhn and R. N. Kacker, 

Introducing Combinatorial Testing in a Large Organization, IEEE Computer 48:4 (April 2015), 64-72. 

[5]	 D. R. Kuhn, R. Bryce, F. Duan, L. Ghandehari, Y. Lei 

and R. N. Kacker, Combinatorial Testing: Theory and 
 

 

 

 

 

 

 

 

 

 

 

 

 

88 NIST Applied and Computational Mathematics Division 

Practice, in Advances in Computers 99, (A. Memon, ed.), 

Elsevier, 2015, 1-66. 

[6]	 D. R. Kuhn, R. N. Kacker, Y. Lei and J. Torres-Jimenez 

Efficient Verification of Equivalence Classes and Simultaneous Testing Using Two-layer Covering Arrays, in 

Proceedings of 4th International Workshop on Combinatorial Testing, Graz, Austria, April 13-18, 2015. 

[7]	 F. Duan, L. Yu, Y. Lei, R. N. Kacker and D. R. Kuhn 

Improving IPOG’s Vertical Growth Based on a Graph 

Coloring Scheme, in Proceedings of 4th International 

Workshop on Combinatorial Testing, Graz, Austria, April 

13-18, 2015. 

[8]	 L. Ghandehari, J. Chandrasekaran, Y. Lei, R. N. Kacker 

and D. R. Kuhn, BEN: A Combinatorial Testing-Based 

Fault Localization Tool, in Proceedings of 4th International Workshop on Combinatorial Testing, Graz, 

Austria, April 13-18, 2015. 

[9]	 L. Yu, F. Duan, Y. Lei, R. N. Kacker and D. R. Kuhn 

Constraint Handling in Combinatorial Test Generation 

Using Forbidden Tuples, in Proceedings of 4th International Workshop on Combinatorial Testing, Graz, 

Austria, April 13-18, 2015. 

[10] V. Hu, D. F. Ferraiolo, D. R. Kuhn, R. N. Kacker and Y. 

Lei, Implementing and Managing Policy Rules in 

Attribute Based Access Control, in Proceedings of 16th 

IEEE International Conference on Information Reuse 

and Integration (IRI), San Francisco, CA, August 13-15, 

2015. 

Can Micro Energy Harvesters Be 

Used to Power Up Wearable 

Sensors? 

Kamran Sayrafian
 

Dora Budić (University of Zagreb)
 

Dina Simunić (University of Zagreb)
 

Wearable sensors are considered to be a key component 

of next generation health-IT systems. These sensors, 

which enable real-time physiological monitoring, will 

provide interfaces between human and future information and communication technology devices. 

Sophisticated wearable sensors capable of measuring 

neurological or physiological signals, as well as associated wireless communications are emerging daily. 

However, as complexity of these sensors increase, so 

does their energy consumption. Given the small size 

constraints for these sensors, limited energy sources 

(e.g., small batteries) will become a bottleneck in their 

functionality. Therefore, any technology that can prolong the lifetime of these sensors or reduce charging 

frequency will positively impact their market adoption. 

Energy harvesting refers to the process of capturing 

and storing energy from the ambient environment. Light, body heat, and body movement all can be 

harvested for use in a wearable device. Kinetic energy 

Figure 55. Placement of the accelerometer on the body: A: Wrist, 

B: Chest, C: Hip, D: Leg, and Block diagram of the measurement 

system. 

Figure 56. Harvested power from wrist motion for 300 sec measurement intervals (MSD dimension: 15×15×1.5 mm3

, and F = 

17.25×10-3). 

Figure 57. Average harvested power from the human wrist motion 

versus the electrostatic force F in a CFPG architecture. 

harvested from the human body motion seems to be one 

of the most convenient and attractive solutions for wearable wireless sensors [1,2]. 

Miniaturized energy harvesting devices, also 

known as micro-generators, consist of a mass-springdamper (MSD), a transducer, and an interfacing powerprocessing circuit. The transducer converts mechanical 

power into electrical energy. Kinetic micro-generators 

either utilize direct application of force on the device, or 

make use of inertial, ambient forces acting on a proof 

mass. These forces are captured within the MSD component. Unlike micro-generators that utilize a direct 

application of force, their inertial-based counterparts require only one point of attachment to the moving 

structure, allowing for greater mounting flexibility and 

miniaturization that is ideal for wearable devices. 
 

 

 

 

 

 

 

  

   

 

 

 

Summary of Activities for Fiscal Year 2015 89 

In [3] a miniature triaxial accelerometer has been 

used to measure acceleration from human motion during 

various activities. Figure 55 shows the placement of the 

accelerometer on the body where measurements were 

obtained. Measurements were done for several short 

(i.e., 5 min) and long (one hour) intervals during the day. 

Data from these measurements were used as input to a 

Simulink-based micro-harvester model in order to generate output instantaneous power as shown in Figure 56. 

The triaxial accelerometer is capable of measuring acceleration in all 3 axes as defined by the placement of 

the device on the body. Although the current micro-harvester technology can only use one axis for energy 

conversion, in our study we investigated the possible 

amount of average power in each direction. This information will be useful to identify which axis is most 

appropriate for harvesting kinetic energy. We have also 

provided the resulting power from all three axes combined, which is just the summation of the estimated 

power in each direction. Also, as the intended use of 

these harvesters is in very small wearable sensors, we 

only considered micro-harvesters with small sizes (i.e., 

from 100 mm3

 to 800 mm3) to estimate the average 

power. Figure 57 shows sample results for a sensor that 

is attached to the wrist (e.g. a smart watch) during various activities like walking, running or rollerblading. 

In our previous study [4], we showed that there exists an optimal value for the electrostatic force F, a 

parameter in the internal architecture of the CFPG micro-harvester. Figure 57 shows the impact of this 

electrostatic force on the average power. Almost a factor 

of 10 increase in the generated power can be expected 

when a proper value for F is chosen. Although Figure 57 

uses the measurement data obtained through wrist motion during walking to demonstrate the dependency on 

F, similar behavior is also observed for other input data. 

With knowledge of the optimal values of the electrostatic force, a lot more power from the same body 

motions can potentially be harvested. 

The preliminary results in this paper point to the 

promising application of the micro-harvesting technology in wearable sensors [5]. The power consumption of 

a popular wrist-worn device such as a smart watch can 

be as low as 1 mW. Our results show that up to 0.5 mW 

of power can be generated by natural human wrist motion. Therefore, integration of a small micro-harvester in 

a smart watch can increase its battery lifetime up to 

50 %. This is a significant gain which basically leads to 

longer operation of the device or equivalently 50 % less 

frequency of recharge. The power consumption of general wearable sensors heavily depends on their 

functionality, and could range from nanowatt to several 

milliwatts. Sensor location on the human body, its size, 

and typical activity of the person wearing the sensor 

could determine the optimized design and integration of 

the micro-harvester. We plan to continue this research 

by focusing on methodologies that can adaptively optimize the architectural parameters of a micro energy 

harvester based on the input acceleration. 

[1]	 N. Yarkony, K. Sayrafian and A. Possolo, Energy Harvesting from the Human Leg Motion, in Proceedings of 

the 8th International Conference on Pervasive Computing Technologies for Healthcare (Pervasive Health 

2014), Oldenburg, Germany, May 20-23, 2014. 

[2]	 N. Yarkony, K. Sayrafian and A. Possolo, Statistical 

Modeling of Harvestable Kinetic Energy for Wearable 

Medical Sensors, in Proceedings of the IEEE 

International Symposium on World of Wireless Mobile 

and Multimedia Networks (WoWMoM), 2010. 

[3]	 D. Budic, Applicability of Kinetic-Based Energy 

Harvesting for Mobile Phones, Thesis No. 3868, Faculty 

of Electrical Engineering and Computing, University of 

Zagreb, July 2015. 

[4]	 M. Dadfarnia, K. Sayrafian, P. Mitcheson and J. Baras, 

Power of a CFPG Micro Energy-Harvester for Wearable 

Medical “Maximizing Output Sensors”, in Proceedings 

of the 4th International Conference on Wireless Mobile 

Communication and Healthcare, MobiHealth 2014, 

Athens, Greece, November 2014 

[5]	 D.Budic, D. Simunic and K. Sayrafian, Kinetic-Based 

Micro Energy-Harvesting for Wearable Sensors, in 

Proceedings of the 6th IEEE International Conference on 

Cognitive Infocommunications, October 19-21, 2015. 

A Study of the Energy Detection 

Threshold in the Body Area Network 

Standard CSMA/CA Protocol 

Martina Barbi 

Vladimir Marbukh 

John Hagedorn 

Kamran Sayrafian 

Mehdi Alasti 

A body area network (BAN) consists of multiple wearable (or implantable) sensors that can establish two-way 

wireless communication with a controller node that is 

located in the vicinity of the body. Considering the mobile nature of BANs, these networks are expected to 

coexist with other wireless devices that are operating in 

their proximity. However, interference from coexisting 

wireless networks or other nearby BANs could create 

problems with the reliability of the network operation. 

For example, when several body area networks are 

within close proximity of each other, inter-BAN interference may occur since no coordination across multiple 

networks exists in general. For these scenarios, several 

mitigation strategies that are applicable to the PHY layer 

have been proposed and studied [2,3]. In this project, 

we focus on the MAC layer and specifically the operation of the CSMA/CA protocol. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

90 NIST Applied and Computational Mathematics Division 

Figure 58. Average Packet Delay versus Traffic Load for the meeting scenario. 

Figure 59. Packet Drop Rate per link for different Traffic Loads. 

Consider a system comprised of several adjacent 

BANs. Each BAN consists of one coordinator and several sensor nodes in a star topology as outlined in the 

IEEE 802.15.6 standard41 [1]. A CSMA/CA transmission protocol based on the standard is used for 

communication between the coordinator and the body 

sensors. At each BAN, the access to the channel is managed by the coordinator through the establishment of a 

SuperFrame (SF). According to the IEEE 802.15.6 

CSMA MAC protocol, time in a SF is divided into slots 

with duration of 145 μsec. When a node needs to transmit a data packet, a back-off counter (BC) is chosen 

randomly within the interval [1 CW], where CW ∈

[CWmin CWmax]. Then, the channel is sensed for a 

time period pSIFS (Short Inter Frame Spacing) of 75 

μsec to determine whether it is idle. If the channel is determined to be idle for this period, the BC 

(corresponding to the node) is decremented by one for 

each idle slot that follows. Once the BC has reached 

zero, the node transmits the corresponding data packet. 

On the other hand, if the channel is sensed to be busy, 

the BC is locked until the channel becomes idle again 

for the entire duration of a pSIFS. 

41 http://standards.ieee.org/findstds/standard/802.15.6-2012.html 

A node assessment of the transmission channel (i.e., 

idle/free) is done according to the Clear Channel Assessment (CCA) Mode 1 described in the standard document 

[1]. It involves the use of an Energy Detection (ED) 

threshold. If the node’s receiver detects any energy in 

the selected frequency channel above the ED threshold, 

the channel is determined to be busy; conversely, the 

idle channel status corresponds to no energy detection 

above the ED threshold. According to the standard, the 

minimum ED threshold should be set to values such that 

the received power is no less than 10 dB above the receiver sensitivity for the lowest data rate within the band 

of interest. 

Consider a simulation scenario consisting of eight 

BANs (each having three on-body sensors and one coordinator node) that are static and at a fixed distance 

from each other [5]. This is intended to emulate eight 

people (each wearing a BAN) sitting around an ovalshaped table. Similar static scenarios such as people sitting in a bus may also be considered, and it can be shown 

that our results are easily applicable to those scenarios 

as well. Figure 58 shows the average packet delay as a 

function of the traffic load per BAN for this system. 

Here it has been assumed that there are no hidden node 

problems within each BAN. Therefore, simultaneous 

transmissions within the same BAN may occur only if 

sensor nodes set their BC to the same random value. On 

the other hand, simultaneous transmissions at different 

adjacent BANs may indeed occur, and this in fact depends on the ED threshold that has been set for the 

sensor nodes. As observed, the value of an ED threshold 

could have a significant impact on the system performance. For low threshold values (corresponding to the 

range -84 dBm to -75 dBm in our example), the average 

packet delay tends to rapidly increase for relatively 

lower values of the traffic load. This is due to the fact 

that the low values of the ED thresholds make transmitting nodes be more conservative, and therefore, hold off 

on any possible transmissions if they sense even a slight 

amount of inter-BAN interference. This could result in 

large delays (i.e., waiting time in the queue) that each 

packet experiences before it even gets the chance to be 

transmitted. Similarly, for high values of the ED threshold, nodes will become more aggressive and could 

transmit their waiting packets irrespective of the high 

existing inter-BAN interference. This, in turn, will increase the possibility of unsuccessful receptions (e.g., 

collisions) at the receiver which means further retransmissions will be required. Obviously, this will add to the 

total delay experienced by the packet. 

As the results in Figure 58 show, the optimal value 

of the ED threshold is -62 dBm. In general, this optimal 

value depends on the exact scenario details including the 

relative position of each sensor at each BAN, the number of nodes, the channel conditions, etc. However, our 
 

 

 

Summary of Activities for Fiscal Year 2015 91 

argument is that the choice of this value could make a 

significant impact on the quality of service experienced 

by a node. If we consider a bound for the number of 

times that a given packet is allowed to be retransmitted, 

we can see the impact of a static ED threshold on packets 

drop rate. Figure 59 shows this drop rate for the sensor 

nodes in the system when the maximum number of retransmissions is 3. The large standard deviation of the 

packet drop rates across sensors is indicative of the nonuniform quality of service experienced by the nodes. 

The focus of our study is the potential significant 

impact of the ED threshold in the IEEE 802.15.6 standard on the quality of service performance of various 

links across multiple adjacent BANs. We show that 

there exists an optimal choice for the value of this 

threshold for the example of several adjacent BANs. We 

have observed that this optimal value is heavily scenario-dependent. So, in normal operation of a BAN, it 

would be impossible to estimate and adjust the static 

value of this threshold in order to guarantee the optimal 

performance of all links in the system. This is a fundamental problem that is caused by having the same fixed 

ED threshold to sense the channel and make decisions 

on whether to go ahead with packet transmissions. We 

believe that the solution to this problem is through an 

intelligent adaptive threshold scheme for energy detection, where each node can modify their corresponding 

ED threshold based on their assessment of their own 

channels. Several adaptive strategies are currently under 

investigation. Further results have been provided in [4]. 

[1]	 802.15.6 – IEEE Standard for Local and Metropolitan 

Area Networks – Part 15.6: Wireless Body Area 

Networks, IEEE Standards Association. 

[2]	 M. Barbi, K. Sayrafian and M. Alasti, Uncoordinated 

Scheduling Strategies for BAN-to-BAN Interference 

Mitigation, in Proceedings of the 3rd International Black 

Sea Conference on Communications and Networking, 

Constanta, Romania, May 18-21, 2015. 

[3]	 V. Marbukh, K. Sayrafian, M. Barbi and M. Alasti, A Regret Matching Strategy Framework for Inter-BAN 

Interference Mitigation, in Proceedings of the IFIP 8th 

Wireless and Mobile Networking Conference, Munich, 

Germany, October. 5-7, 2015, 231-234. 

[4]	 M. Barbi, K. Sayrafian and M. Alasti, Impact of the Energy Detection Threshold on Performance of the IEEE 

802.15.6 CSMA/CA, in Proceedings of the 2015 IEEE 

Conference on Standards for Communications and Networking, Tokyo, Japan, October 28-30, 2015. 

[5]	 K. Sayrafian, J. Hagedorn, M. Barbi, J. Terrill and M. 

Alasti, A Simulation Platform to Study Inter-BAN Interference, in Proceedings of the 4th IEEE International 

Conference on Cognitive Infocommunicaitons, Budapest, 

Hungary, December 2-5, 2013. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

92 NIST Applied and Computational Mathematics Division 

Mathematical Knowledge Management
 

We work with researchers in academia and industry to develop technologies, tools, and standards for 

representation, exchange, and use of mathematical data. Of particular concern are semantic-based 

representations which can provide the basis for interoperability of mathematical information processing 

systems. We apply this to the development and dissemination of reference data for applied mathematics. The 

centerpiece of this effort is the Digital Library of Mathematical Functions, a freely available interactive and 

richly linked online resource, providing essential information on the properties of the special functions of 

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

Digital Library of Mathematical 

Functions 

Barry I. Schneider 

Daniel W. Lozier 

Adri B. Olde Daalhuis (University of Edinburgh) 

Bruce R. Miller 

Ronald F. Boisvert 

Charles W. Clark (NIST PML) 

Bonita V. Saunders 

Marjorie A. McClain 

Howard S. Cohl 

Brian Antonishek (NIST EL) 

Neil Agrawal (Poolesville High School) 

Nina Agrawal (Poolesville High School) 

Hannah Cohen (Colonel Z. Magruder High School) 

Progress in science has often been catalyzed by advances in mathematics. More recently, developments in 

the physical sciences, such as investigations into string 

theory, have had influence in pure mathematics. This 

symbiotic relationship has been extremely beneficial to 

both fields. Mathematical developments have found numerous applications in practical problem-solving in all 

fields of science and engineering, while cutting-edge 

science has been a major driver of mathematical research. Often the mathematical objects at the 

intersection of mathematics and physical science are 

mathematical functions. Effective use of these tools requires ready access to their many properties, a need that 

was capably satisfied for more than 50 years by the 1964 

National Bureau of Standards (NBS) Handbook of 

Mathematical Functions with Formulas, Graphs, and 

Mathematical Tables [1]. 

The 21st century successor to the NBS Handbook, 

the online Digital Library of Mathematical Functions 

(DLMF)42 together with the accompanying book, NIST 

Handbook of Mathematical Functions [2], both issued 

in 2010, are collectively referred to as the DLMF. The 

DLMF continues to remain the gold standard reference 

for the properties of what are termed the special functions of mathematical physics. The DLMF has 

considerably extended the scope of the original handbook, as well as improved accessibility to the worldwide 

community of scientists and mathematicians. To cite a 

few examples, the new handbook contains more than 

twice as many formulas as the old one, coverage of more 

functions, in more detail, and an up-to-date list of references. The website covers everything in the printed 

NIST Handbook and much more: additional formulas 

and graphics, live zooming and rotation of 3D graphs, 

interactive search, internal links to symbol definitions 

and cross-references, and external links to online references and sources of software. In order to help assess 

the impact of the DLMF project, the NIST library has 

undertaken a project to track citations to the DLMF, as 

well as to the original NBS Handbook. While the original Handbook still receives an enormous number of 

citations (2421 in 2014 alone), citations to the DLMF 

are steadily growing, with 374 citations in 2014. As of 

February 2016, Google Scholar has identified 2087 total 

citations to the new NIST Handbook. 

Today’s DLMF is the product of many years of effort by more than 50 expert contributors. Its appearance 

in 2010, however, was not the end of the project. Corrections to errors, clarifications, bibliographic updates, 

and addition of important new material all continually 

need to be made, and new chapters covering emerging 

subject areas need to be added, so as to assure the continued vitality of the DLMF deep into the 21st century. 

Developments Currently in Progress. During the past 

year, the DLMF project has seen continued progress on 

several fronts. During that period there was only a single new release of the DLMF (version 1.0.10). This was 

a consequence of the large number of changes required 

for this update, which took more time than anticipated. 

An important effort initiated during the current year 

was the verification, completeness and traceability of 

proofs for DLMF formulae. One of the goals of the 

DLMF was to ensure that each equation had either a 

42 http://dlmf.nist.gov/ 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 93 

Principal Editors 

Barry Schneider General Editor 

Daniel Lozier General Editor 

Adri Olde Daalhuis Mathematics Editor 

University of Edinburgh 

Bruce Miller Information Technology Editor 

Bonita Saunders Graphics Editor 

Ronald Boisvert Editor-at-Large 

Charles Clark Applications Editor 

Contributing Developers 

Marjorie McClain Bibliography, LaTeX 

Howard Cohl Mathematics 

Brian Antonishek Graphics 

Senior Associate Editors 

Mark Ablowitz University of Colorado 

George Andrews Penn State University 

Michael Berry University of Bristol 

Annie Cuyt University of Antwerp 

Mourad Ismail University of Central Florida 

James Pitman University of California at Berkeley 

William Reinhardt University of Washington (retired) 

Simon Ruijsenaars University of Leeds 

Nico Temme CWI Amsterdam (retired) 

Stephen Watt University of Waterloo 

Figure 60. DLMF Management and Organization Structure 

short proof for the formula or a reference to a proof for 

the formula, and that each definition also was linked to 

a source. Unfortunately, gaps have been observed in this 

coverage. A systematic audit of Chapters 25 and 27, 

aided by a group of capable high school interns, is now 

underway to determine the extent of the problem, as well 

as to fill in all missing information. We plan to extend 

this effort to the entire DLMF. 

We continue to pursue enhancement to the online 

graphics provided in the DLMF. That work is described 

on 93. 

The past year also saw changes in the Editorial 

Board and a restructuring of the management of the project in order to ensure active maintenance and 

development of the DLMF for the future. Figure 60 lists 

the roles of the current principal DLMF editors and developers. Also listed is the revitalized set of Senior 

Associate Editors (SAE), who will advise NIST management on the future evolution of the project. Finally, 

an Associate Editor (AE) has been identified for each 

existing DLMF chapter. AEs will work with the Mathematics Editor in responding to user queries about current 

chapter content, as well as developing minor updates. 

On November 9-10, 2015 the SAEs assembled at 

NIST to discuss the possibility of a second edition of the 

DLMF with significant new content and features. 

Among the items discussed were 

 Chapters that need major expansions, 

 Potential topics for new chapters, 

 The merits of online versus print, 

43 https://www.khronos.org/webgl/ 

 Numbering of formulae and relation to the first 

edition, 

 Raising awareness of the DLMF, 

 Licensing issues, 

 New semantic-based technologies, and 

 Application programmer interfaces to data. 

A good deal of useful input was obtained, and project 

staff are now beginning to act on it. 

The DLMF has spawned a number of related efforts 

within the Division, which are described elsewhere in 

this document, including the DLMF Standard Reference 

Tables on Demand (page 93), the Digital Repository of 

Mathematical Formulae (page 97), as well as a robust 

research effort on the natural language processing of 

mathematics (page 96). 

[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. 

Visualization of Complex Functions 

Data 

Bonita Saunders 

Brian Antonishek (NIST EL) 

Qiming Wang 

Bruce Miller 

Sandy Ressler 

Though originally motivated by a desire for clear, informative graphs in the NIST Digital Library of 

Mathematical Functions (DLMF), our work has produced cutting edge 3D visualizations that have evolved 

in tandem with technologies for creating and viewing 

3D graphics on the Web. Our first visualizations were 

created using VRML, a special 3D file format for displaying graphics on the Web, but by the release of the 

DLMF in 2010, we also offered X3D, an XML-based 

format touted as the successor to VRML. At the Web3D 

conference in June 2015, Johannes Behr of Fraunhofer 

IGD, one of the developers of X3D, noted that he was 

so impressed with our implementation of cutting planes 

that it motivated him to incorporate a clipping plane feature into the specifications for X3D. 

Unfortunately, both VRML and X3D require users 

to install a special plugin in order to view visualizations. 

However, by taking advantage of work on WebGL by 

the Khronos Group43 and the development of X3DOM 

by Behr et al. [4], we were able to create 
 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

  

94 NIST Applied and Computational Mathematics Division 

Figure 61. DLMF webpage with an embedded visualization of 

|erf (x + iy)|. 

X3DOM/WebGL visualizations for the DLMF that all 

but eliminated the plugin problem. WebGL is a JavaScript application program interface (API) for rendering 

3D graphics in a web browser without a plugin. X3DOM 

is a special framework for creating graphics applications 

on the Web. Basing our WebGL code on X3DOM allowed us to build our WebGL applications around our 

X3D codes. Our visualizations can now be viewed in 

any WebGL-enabled browser on Windows, Mac, and 

Linux platforms as well as on many mobile devices. 

The new X3DOM/WebGL visualizations were released in version 1.0.7 of the DLMF in March 2014. 

Figure 61 shows the graph of the modulus of the error 

function, |erf(x + iy)|, displayed with a phase, or argument, color map. In the new visualizations, color maps 

are more vibrant, cutting plane curves clearer, and the 

interactive movement of surfaces faster and smoother. 

While X3DOM/WebGL is now the default, we continue 

to offer VRML and X3D for users who prefer to continue viewing the graphs in those formats. 

Some of our work is now focused on the creation of 

a continuous surface spin option in our 

X3DOM/WebGL visualizations. This feature would 

permit a user to create a continuous spin in any direction 

by touching and flicking the surface. The speed of the 

spin would vary according to how fast the surface is 

flicked. This would be an effective tool for drawing interest during a talk or for creating an instant animation 

in an exhibit. The feature was available in the early CosmoPlayer VRML plugin designed by Silicon Graphics, 

but it was implemented in few VRML or X3D plugins 

developed subsequently. X3DOM developers have expressed an interest in making the feature part of their 

44 http://www.shapeways.com/ 

standard if our work is successful. Sandy Ressler has 

completed preliminary work, first implementing the feature by coding directly in WebGL and then successfully 

creating a rough X3DOM version by modifying codes 

pieced together from software freely shared by a designer at Shapeways, a 3D printing firm44. A substantial 

amount of work is still needed to streamline, restructure, 

and integrate the code into our visualizations. 

We are also working on the reduction of graphics 

file sizes using adaptive grid generation, looking at 2D 

visualization possibilities, and exploring the feasibility 

of developing an accurate zoom. 

We continually search for opportunities to increase 

the visibility of our work. In version 1.0.10 of the 

DLMF released in August 2015 a List of Figures entry 

was added to the table of contents to give users quicker 

access to the nearly 600 graphs and visualizations available in the DLMF. An animation on the table of contents 

page and a Wikipedia reference are also being explored. 

We published a proceedings paper based on our talk 

given at Web3D 2015 [1] and presented numerous invited and contributed talks throughout the year [5-9]. 

[1]	 B. Saunders, B. Antonishek, Q. Wang and B. Miller, Dynamic 3D Visualizations of Complex Function Surfaces 

Using X3DOM and WebGL, in Proceedings of the 20th 

International Conference on 3D Web Technology 

(Web3D 2015), Crete, Greece, 2015, 219-225. 

[2]	 B. Saunders, Q. Wang and B. Antonishek, Adaptive 

Composite B-Spline Grid Generation for Interactive 3D 

Visualizations, IMACS Series in Computational and Applied Mathematics 18 (2014), Proceedings of 

MASCOT/ISGG 2012, Las Palmas de Gran Canaria, 

Spain, October 22-26, 2012, 241-250. 

[3]	 S. Ressler and B. Antonishek, “New WebGL Graphics in 

the NIST DLMF,” Web3D Emerging Technology Showcase, Virginia Tech Research Center, Arlington, VA, 

March 25, 2014. 

[4]	 J. Behr, P. Eschler, Y. Jung and M. Zollner, 2009. 

X3DOM: a DOM-based HTML5/X3D Integration 

Model, in Proceedings of the 14th International Conference on 3D Web Technology (Web3D ‘09), ACM, S. N. 

Spencer, Ed., 127–135. 

[5]	 B. Saunders, “Slices of 3D Surfaces on the Web Using 

Tensor Product B-Spline Grids,” SIAM Conference on 

Geometric and Physical Modeling (GD/SPM15), Salt 

Lake City Utah, Utah, October 12, 2015. 

[6]	 B. Saunders, “Cutting Edge Information Technology Applied to the NIST Digital Library of Mathematical 

Functions,” Mathematical Association of America MathFest 2015, Washington, D.C., August 8, 2015. 

[7]	 B. Saunders, “X3DOM/WebGL Visualizations in the 

NIST DLMF,” Web3D Showcase, 20th International 

Conference on 3D Web Technology (Web3D 2015), Heraklion, Crete, Greece, June 20, 2015. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 95 

[8]	 B. Saunders, B. Antonishek, Q. Wang and B. Miller, 

“State of the Art Visualizations of Complex Function 

Data,” 2015 International Conference on Orthogonal Polynomials, Special Functions and Applications, NIST, 

Gaithersburg, MD, June 4, 2015. 

[9]	 B. Saunders, “Adaptive Grid Generation, 3D Graphics on 

the Web, and a Digital Library,” Infinite Possibilities 

Conference, Oregon State University, Corvallis, Oregon, 

March 2, 2015. 

DLMF Standard Reference Tables 

on Demand 

Bonita Saunders 

Bruce Miller 

Marjorie McClain 

Daniel Lozier 

Andrew Dienstfrey 

Annie Cuyt (University of Antwerp) 

Stefan Becuwe (University of Antwerp) 

Franky Backeljauw (University of Antwerp) 

Chris Schanzle 

During the development of the NIST Digital Library of 

Mathematical Functions (DLMF) http://dlmf.nist.gov/ 

[1,2] the inclusion of a computational component was 

seen as a desirable goal, but its creation was deferred for 

the future. To begin meeting this objective, and to bring 

the value of reliable computing to the attention of a 

broader audience, NIST and the University of Antwerp 

are collaborating to develop the DLMF Standard Reference Tables (DLMF Tables), an online service that 

allows users to create their own tables of special function values with an error certification. ACMD is 

building the front end user interface while the University 

of Antwerp Computational Mathematics Research 

Group (CMA) is developing the back end computational 

engine based on their MpIeee library. 

Of course, there are many numerical routines for 

evaluating special functions in widely used mathematical software libraries, packages, and systems, but none 

of these produce results with guaranteed error-bounds. 

For a real valued function, the error bound determines 

an interval within which the exact function value is guaranteed to lie [3]. Reliable results of this type, while 

typically too computationally intensive to use directly in 

modeling and simulation, are valuable references for the 

testing and evaluation of mathematical software libraries and systems. 

MpIeee is an IEEE 754/854 compliant C++ library 

for mixed precision floating point arithmetic in base 2௡

or 10௠. IEEE compliance implies, among other things, 

that basic arithmetic operations as well as remainder and 

45 http://dlmftables.uantwerpen.be/ 

Figure 62. Table of contents for DLMF Tables website. 

Figure 63. Input screen for Fresnel integral S(x). 

square root operations are rounded according to specification: round-to-nearest (even), round toward ∞, round 

toward -∞, round toward 0, round away from 0. This 

means the result of the operation is the floating point 

value that would be obtained by first computing the exact mathematical value and then rounding it to its 

floating point representation. IEEE compliance provides 

the foundation for building reliable software. 

MpIeee contains a selection of special functions, using algorithms based on series and continued fraction 

representations, in conjunction with a detailed analysis 

of the rounding errors, to compute results that lie within 

an arbitrarily prescribed relative error. Currently, MpIeee covers real variables only, but CMA is actively 

working to expand its coverage to more functions and 

eventually to complex variables [3-7]. 

A beta version of the site is already in place.45 As 

shown in Figure 62, the table of contents lists the chapters available, with all entries currently corresponding to 

chapters in the DLMF. After a chapter is selected, the 

input screen (Figure 63) for that chapter appears; the 
 

 

 

 

 

 

 

 

 

 

96 NIST Applied and Computational Mathematics Division 

Figure 64. Output for comparison of DLMF Tables computations 

with table of function values submitted by the user. 

user chooses a function and requests either a tabulation 

or comparison. This selection determines what additional user input will be required. Each function 

description contains a link to the definition of the function in the DLMF. 

For a tabulation, a user may request up to 500 output digits and choose an output mode for computation. 

The default is interval mode, where a strict high-precision enclosure (lower and upper bound) is displayed for 

each requested function value. Alternatively, the user 

may choose an exact output rounded to the requested 

number of digits according to one of the standard rounding modes indicated earlier. 

If the user requests a comparison, a user-supplied 

data file must be uploaded. The output table displays 

the reference values, computed in one of the user selected output modes, alternated with the values provided 

by the user. The approximate relative error is also 

shown. Differences between reference values and uploaded values are highlighted in either yellow (warning) 

or red (error) as shown in Figure 64. 

The release of the beta version marks the completion of the first phase of the project. More functions are 

in the pipeline, and additional site enhancements are currently in progress. Links to relevant papers will be added 

along with more user documentation, and the possibility 

of more extensive documentation for programmers is 

being considered. Testing of the site has also begun, but 

the sparsity of systems and software of this type and 

quality make comprehensive testing a challenging task. 

We are in the process of developing a formal structure 

where test results can be duplicated when necessary to 

address problems identified either through our own 

work or from user feedback. Several talks were presented throughout the year [8,9] and a paper on the 

DLMF Tables is in review [10]. 

[1]	 NIST Digital Library of Mathematical Functions. 

http://dlmf.nist.gov/, Release 1.0.10 of 2015-08-07. 

Online companion to [2]. 

[2]	 F. W. J. Olver, D. W. Lozier, R. F. Boisvert and C. W. 

Clark, eds., NIST Handbook of Mathematical Functions. 

Cambridge University Press, New York, NY, 2010. Print 

companion to [1]. 

[3]	 F. Backeljauw, S. Becuwe, A. Cuyt, J. Van Deun and D. 

Lozier, Validated Evaluation of Special Mathematical 

Functions, Science of Computer Programming 10 (2013), 

1016. 

[4]	 M. Colman, A. Cuyt and J. Van Deun, Validated Computation of Certain Hypergeometric Functions, ACM 

Transactions on Mathematical Software 38:2 (January 

2012), 11. 

[5]	 F. Backeljauw, A Library for Radix-independent Multiprecision IEEE-compliant Floating-point Arithmetic, 

Technical Report 2009-01, Department of Mathematics 

and Computer Science, Universiteit Antwerpen, 2009. 

[6]	 A. Cuyt, V. B. Petersen, B. Verdonk, H. Waadeland and 

W. B. Jones, Handbook of Continued Fractions for Special Functions. Springer, New York, 2008. 

[7]	 A. Cuyt, B. Verdonk and H. Waadeland, Efficient and 

Reliable Multiprecision Implementation of Elementary 

and Special Functions, SIAM Journal of Scientific 

Computing 28 (2006), 1437-1462. 

[8]	 B. Saunders, B. Miller, M. McClain, D. Lozier, A. 

Dienstfrey, A. Cuyt, S. Becuwe and F. Backeljauw, 

“DLMF Standard Reference Tables on Demand (DLMF 

Tables),” Minisymposium on Orthogonal Polynomials 

and Special Functions: Computational Aspects, 2015 International Conference on Orthogonal Polynomials, 

Special Functions and Applications, NIST, Gaithersburg, 

MD, June 1, 2015. 

[9]	 B. Saunders, “NIST Projects: Graphics in the Digital Library of Mathematical Functions (DLMF) and DLMF 

Standard Reference Tables on Demand (DLMF Tables),” 

Careers in Mathematical Sciences Workshop for Underrepresented Groups, IMA, University of Minnesota, 

Minneapolis, MN, March 29, 2015. 

[10] B. Saunders, B. Miller, F. Backeljauw, S. Becuwe, M. 

McClain, D. Lozier, A. Cuyt and A. Dienstfrey, DLMF 

Tables: A Computational Resource Inspired by the NIST 

Digital Library of Mathematical Functions, in review. 

Natural Language Processing of 

Mathematics 

Abdou Youssef 

Bruce Miller 

Howard Cohl 

Natural language processing (NLP) has made significant 

strides in recent years, with practical applications and 

deployed software such as part-of-speech tagging (e.g., 

Stanford POS tagger), language translation (e.g. Google 

translate), text analysis, and question answering systems. Mathematics literature, however, presents unique 

challenges due to its abstract nature and its inclusion of 
 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 97 

mathematical equations and expressions. While mainstream NLP applies to some extent to processing math 

texts, considerable changes must be made and new techniques developed to address uniquely mathematical 

challenges and applications. 

This project is a natural next step to the math search 

work that we pioneered at NIST, and that resulted in a 

search system that is deployed as part of the online Digital Library of Mathematical Functions. This project is 

broader than math search, spans several years, and involves many components and applications, which we 

describe below. 

Part-of-Math Tagging. Much as part-of-speech (POS) 

tagging is a fundamental early stage of many NLP tasks, 

part-of-math (POM) tagging is expected to be an essential early stage of many math-NLP tasks. A POM tagger 

will read any math expression/equation, identify its tokens, and label each token as to its math role (e.g., 

variable, function, relation, operation/operator, derivative, integral, logical quantifier, logical connective, 

delimiter, sub/super-scripts, “accent”, etc., along with 

additional attributes that enrich the description of tokens). One key problem is token-sense disambiguation. 

o Techniques: We will use techniques from machine 

learning, standard NLP and text mining, and mathematical parsing, to achieve POM tagging. 

o Potential applications: Automated annotation of 

math documents; richer math search; mathematical 

text-to-speech readers; semantic extraction; etc. 

o Timeline: We have already mapped out the main 

parts of POM tagging, and fully determined the classes of math tokens (and their attributes). In the next 

18 months (on a part-time basis), the essential POM 

tagging algorithms will be developed. Refinements 

and extensions will take a little longer. 

Mathematical Semantic Extraction (MSE). Using 

POM tagging, MSE aims to extract semantics about the 

various components of math expressions and related 

(surrounding) texts in math documents. For example, if 

a token is determined by POM to be a function, the MSE 

module will determine what kind of function it is (e.g., 

its functional class), its mathematical definition, (possibly) its properties and constraints, etc. Similarly, if it is 

a variable, the MSE module will attempt to determine its 

data type, what it signifies if any (e.g., time variable, positional variable), its range, etc. If it is a superscript, the 

semantic module will determine if it is a power, a mere 

index, a derivative, the order of a derivative, etc. 

o Techniques: We will use POM tagging, and machine 

learning techniques for deriving the meaning of each 

mathematical symbol, exploiting textual correlations 

and mathematical notational practices, and mining 

definitions embedded in texts. 

o Potential Applications: Automated annotation of 

math documents; richer semantic search; math question answering; math document summarization; 

proof checking; proof assistants; etc. 

o Timeline: About 12 to18 months after POM tagging. 

Mathematical Question Answering (MQA). Using semantic extraction, we will develop an MQA application 

that can ultimately answer questions like: (1) Given a 

math document D and a math symbol X, is X defined in 

the given document? If so, what is the definition of X? 

If not explicitly defined in D, what is the likely implicit 

meaning of X? (2) Given a math document D, a corpus 

C, and a formula E, Is formula E proved in document D? 

If not, is E proved in the corpus? If so, what/where is the 

proof? Under what constraints does E hold? (3) What is 

the relationship between concept A and concept B in a 

given math document/corpus? (e.g., A could be a special 

case, a generalization, or a prerequisite of B.) 

o Techniques: Semantic extraction; machine learning; 

AI; text mining; and various NLP techniques. 

o Potential Applications: Online math help systems/math assistants for students, mathematicians, 

and scientists; an efficient time-saving way for examining/interrogating large collections of math 

documents; Knowledge discovery in general; etc. 

o Timeline: About 1 to 2 years after the MSE part. 

[1]	 M. Schubotz, A. Youssef, V. Markl and H. S. Cohl, Challenges of Mathematical Information Retrieval in the 

NTCIR-11 Math Wikipedia Task, 38th Annual ACM 

SIGIR Conference, Santiago, Chile, August 9-13, 2015. 

[2]	 M. Schubotz, A. Youssef, V. Markl, H. Cohl, and J. Li, 

Evaluation of Similarity-Measure Factors for Formulae 

based on the NTCIR-11 Math Task, 11th NTCIR Conference and Evaluation of Information Access 

Technologies, Tokyo, Japan, December 9-12, 2014. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

98 NIST Applied and Computational Mathematics Division 

NIST Digital Repository of 

Mathematical Formulae 

Howard S. Cohl
 

Marjorie A. McClain
 

Bonita V. Saunders 

Moritz Schubotz (Technische Universität Berlin) 

Alan P. Sexton (University of Birmingham)
 

Ankita Sharma (Poolesville High School) 

Cherry Zou (Poolesville High School) 

Sabrina Zou (Montgomery Blair High School)
 

Shraeya Madhu (Poolesville High School) 

Divya Gandla (Poolesville High School)
 

Azeem Mohammed (Poolesville High School) 

Jimmy Li (Richard Montgomery High School)
 

Yusuf Ameri (Quince Orchard High School)
 

Akash Shah (Northwest High School)
 

Claude Zou (Poolesville High School) 

Yash Kapoor (Clarksburg High School)
 

Rahul Shah (Clarksburg High School)
 

The NIST Digital Repository of Mathematical Formulae 

(DRMF) is designed for a mathematically literate audience to (1) facilitate interaction among a community of 

mathematicians and scientists interested in compendia 

of formulae data for orthogonal polynomials and special 

functions (OPSF); (2) be expandable, allowing the input 

of new formulae from the literature; (3) provide information about related open data 

projects; (4) represent the contextfree full semantic information concerning individual formulas; (5) 

have a user friendly, consistent, and 

hyperlinkable viewpoint and authoring perspective; (6) contain 

easily searchable mathematics; and 

(7) take advantage of modern 

MathML tools for easy to read, scalably rendered, content driven 

mathematics. 

Our DRMF implementation is 

built using MediaWiki, the software 

used by Wikipedia. See Figure 66 

for a sample DRMF formula home 

page. The DRMF has been described in a series of publications and talks [1-3]. 

A key asset in the development of DRMF contextfree semantic content is the utilization of a set of LaTeX 

macros originally created for the NIST Digital Library 

of Mathematical Functions (DLMF)46. These macros 

were invented by Bruce Miller of ACMD to achieve the 

encapsulation of semantic information within the NIST 

DLMF. These macros give us the capability to tie LaTeX commands unambiguously to mathematical 

46 http://dlmf.nist.gov 

Figure 65. The DRMF logo. 

functions defined in an OPSF context. There are currently 533 DLMF LaTeX macros, as well as an 

additional 156 which have been created specifically for 

the DRMF. All DLMF macros have at least one DLMF 

web page associated with them, and the goal is to have 

definition pages for all additional DRMF macros. The 

committed use of DLMF and DRMF macros guarantees 

a mathematical and structural consistency throughout 

the DRMF. 

DRMF formula seeding is currently focused on 

	 DLMF chapters 5 (Gamma Functions), 15 (Hypergeometric Function), 16 (Generalized Hypergeometric 

Functions and Meijer G-Function), 17 (q-Hypergeometric and Related Functions), 18 (Orthogonal 

Polynomials), and 25 (Zeta and Related Functions); 

	 Koekoek, Lesky, and Swarttouw chapters 1 (Definitions and Miscellaneous Formulas), 9 

(Hypergeometric Orthogonal Polynomials), and 14 

(Basic Hypergeometric Orthogonal Polynomials) 

[4]; 

 Koornwinder KLS addendum LaTeX data [5]; 

 Bateman Manuscript Project (BMP) books [6]; and 

 the Wolfram Computational Knowledge of Continued Fractions Project (eCF).47 

In August, 2014, the DRMF Project obtained permission 

to use BMP material as seed content for the DRMF from 

Caltech. Alan Sexton of the Scientific Document Analysis Group, School of Computer Science, University of 

Birmingham, UK has scanned a 

copy of the BMP (loaned to us by 

Caltech) and is developing software 

to perform mathematical optical 

character recognition to obtain LaTeX source code. 

For the first seed project, the 

DLMF source already has DLMF 

macros inserted. However, for the 

remaining seed projects we are developing Python and node.JS 

software to incorporate DLMF and 

DRMF macros into the corresponding LaTeX source. Our coding 

efforts have also focused on extracting formula data from LaTeX 

source as well as generating DRMF 

Wikitext. We are developing Python software for the 

seeding of the eCF project which involves conversion 

from Mathematica format to DLMF and DRMF macro 

incorporated LaTeX. 

Current and future DRMF MediaWiki development 

projects include the production of formula output representations (such as semantic LaTeX, MathML, 

47 http://blog.wolframalpha.com/2013/05/16/computationalknowledge-of-continued-fractions 
 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 99 

Mathematica, Maple, and Sage); incorporation of sophisticated DLMF and 

DRMF macro-related formula search; 

and the development of capabilities for 

user community formula input. Our current DRMF servers, both public and 

development instances, have been deployed using the Wikitech server of the 

Wikimedia Foundation in San Francisco. 

We use Labs Vagrant and Puppet to upload our Wikitext pages quickly using 

PHP importDump. 

The DLMF Chapter 25 source has 

been uploaded to the Wikitech instances 

as well as the KLS and KLSadd datasets, 

for a total of 1842 Wikitext pages [7]. 

This includes one main page, one bibliography page, one common.css page, 

one DRMF requirements page, two table 

of contents pages, 76 lists of formulas 

pages, 124 definition pages, and 1636 

formula home pages. 

By working with the Artists Rights 

Society of New York, we have received 

permission from Foundation Vasarely, 

to use an image of one of Victor Vasarely’s paintings as a DRMF logo; see 

Figure 65. 

[1]	 H. S. Cohl, M. A. McClain, B. V. Saunders, M. Schubotz and J. C. Williams, 

Digital Repository of Mathematical 

Formulae, Lecture Notes in Artificial Intelligence 8543 (2014), Proceedings of 

the Conferences on Intelligent Computer Mathematics 2014, (S. M. Watt, J. 

H. Davenport, A. P. Sexton, P. Sojka 

and J. Urban, eds.), Coimbra, Portugal, 

July 7-11, 2014, 419-422. 

[2]	 H. S. Cohl, M. A. McClain, B. V. Saunders and M. Schubotz, “Outgrowths of the Digital Library 

of Mathematical Functions Project, Part II: NIST Digital 

Repository of Mathematical Formulae,” Workshop on 

Challenges in 21st Century Experimental Mathematical 

Computation, Institute for Computational and Experimental Research in Mathematics, Providence, Rhode 

Island, July 201448. 

[3]	 H. S. Cohl, M. A. McClain, B. V. Saunders, M. Schubotz, 

A. Danoff, J. Li, J. Migdall, A. Liu, C. Zou, A. Mohammed and S. Madhu, “XSEDE and the NIST Digital 

Repository of Mathematical Formulae,” XSEDE Science 

Gateways Community Series, August 201449. 

[4]	 R. Koekoek, P. A. Lesky and R. F. Swarttouw, Hypergeometric Orthogonal Polynomials and their q-Analogues, 

Springer Monographs in Mathematics, Springer-Verlag, 

Berlin, 2010. 

48 http://icerm.brown.edu/video_archive, see Programs and Workshops 2014 → Summer 2014 → Challenges in 21st Century 

Figure 66. Sample DRMF formula home page. 

[5]	 T. H. Koornwinder, Additions to the Formula Lists in 

“Hypergeometric Orthogonal Polynomials and their qanalogues” by Koekoek, Lesky and Swarttouw, 

arXiv:1401.0815, January 2014. 

[6]	 A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, Vols. I, II, III, 

Robert E. Krieger Publishing Co., Melbourne, FL, 1981. 

[7]	 H. S. Cohl, M. Schubotz, M. A. McClain, B. V. Saunders, C. Y. Zou, A. S. Mohammed and A. A. Danoff, 

Growing the Digital Repository of Mathematical Formulae with Generic LaTeX Sources, Lecture Notes in 

Artificial Intelligence 9150 (2015), Conference on Intelligent Computer Mathematics, (M. Kerber, J. Carette, C. 

Kaliszyk and V. Sorge, eds.), 280-287. 

49 

https://www.youtube.com/watch?v=gAGqr_4AjkI&list=UU6ulv87K 

V32afXMLv6uWTW 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100 NIST Applied and Computational Mathematics Division 

Fundamental Solutions and 

Expansions for Special Functions 

and Orthogonal Polynomials 

Howard S. Cohl
 

Roberto S. Costas-Santos (University of Alcalá)
 

Hans Volkmer (University of Wisconsin-Milwaukee)
 

Gestur Olafsson (Louisiana State University)
 

Michael A. Baeder (Citigroup Inc.) 

Rebekah M. Palmer (Johns Hopkins University) 

Jessica E. Hirtenstein (American University) 

Philbert R. Hwang (University of Maryland)
 

Wenqing Xu (Caltech) 

Sean J. Nair (Montgomery Blair High School)
 

The concept of a function expresses the idea that one 

quantity (the input) completely determines another 

quantity (the output). Our research concerns special 

functions and orthogonal polynomials. A special function is a function that has appeared in the mathematical 

sciences so often that it has been given a name. Green’s 

functions (named after the British mathematician 

George Green, who first developed the concept in the 

1830s) describe the influence of linear natural phenomena such as electromagnetism, gravity, heat and waves. 

For example, in electrostatics, a Green’s function describes the influence of a point charge, called the source, 

over all of space. The inputs for Green’s functions are 

all of space (with the exception of a singular region), and 

the output is the “force” exerted from the point throughout space. Green’s functions are fundamental to the 

study of partial differential equations and provide a 

powerful mechanism for obtaining their solutions. 

We investigate fundamental solutions (Green’s 

functions) of linear partial differential equations on 

highly symmetric Riemannian manifolds (harmonic, 

rank-one symmetric spaces) such as real, complex, quarternionic, and octonionic Euclidean, hyperbolic, and 

projective spaces. Our recent focus has been on applications of fundamental solutions for linear elliptic partial 

differential operators on spaces of constant curvature. 

For instance, we have recently submitted a paper which 

derives fundamental solution expansions (azimuthal 

Fourier and Gegenbauer) with applications to Newtonian potential theory on d-dimensional spaces of 

constant positive curvature, namely hyperspherical geometry [1]. We have also recently had success in 

constructing closed-form expressions of a fundamental 

solution for the Helmholtz equation is d-dimensional 

spaces of constant negative curvature, namely the hyperboloid model of hyperbolic geometry, in terms of 

associated Legendre functions. We continue our ongoing discussion on the harmonic analysis of fundamental 

solutions for Laplace’s equation on rank one symmetric 

spaces of compact and noncompact type with Gestur 

Olafsson (Louisiana State University). 

In [2] we derived eigenfunction expansions for a 

fundamental solution of Laplace’s equation in 3-dimensional Euclidean space in one of the most general 

orthogonal asymmetric confocal cyclidic coordinate 

systems which admit solutions through separation of 

variables, 5-cyclide coordinates. The harmonics in this 

coordinate system are given by products of solutions of 

second-order Fuchsian ordinary differential equations 

with five elementary singularities. The Dirichlet problem for the global harmonics in this coordinate system 

is solved using multiparameter spectral theory in the regions bounded by the asymmetric confocal cyclidic 

coordinate surfaces. 

In the following sequence of papers, we derive specializations and generalizations of generalized and basic 

hypergeometric orthogonal polynomial generating functions as well as corresponding definite integrals using 

orthogonality. 

	 In [3] we derive generalized generating functions for 

continuous hypergeometric orthogonal polynomials, 

namely Wilson, continuous Hahn, continuous dual 

Hahn, and Meixner-Pollaczek polynomials. 

	 In [4] we presented an open problem on a very-wellpoised 9F8 generalized hypergeometric series which 

was presented at OPSFA12. 

	 In [6] we present the power collection method for hypergeometric orthogonal polynomials, and 

summarize for which orthogonal polynomials in the 

Askey and q-Askey schemes, it can be applied. We 

apply the power collection method to Meixner polynomials and compute a series of connection and 

connection-type relations for these orthogonal polynomials. We also apply these connection and 

connection-type relations to generating functions for 

Meixner and Krawtchouk polynomials. 

	 In [7] we present contour integral orthogonality relations for the Al-Salam-Carlitz polynomials which is 

valid for arguments in the complex plane and complex-valued parameters. We also compute 

generalized generating functions for the Al-SalamCarlitz polynomials using connection relations for 

these polynomials. 

	 In [8] we derive definite integrals for Bessel functions of the first kind by applying the method of 

integral transforms (Hankel transform) to know definite integrals which are found in famous compendia 

of definite integrals. 

	 In [9] we derive explicit bounds of convergence for 

an integral addition theorem due to Magnus which 

expresses a Kummer confluent hypergeometric function of the second kind U(x+y) as an integral over a 

product of U with argument x and U with argument 

y. We also show how this integral addition theorem 

can also be expressed in terms of modified parabolic 

cylinder functions, Hankel, Macdonald, and Bessel 
 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 101 

functions of the first and second kind with order zero 

and one. 

There are several connections with conferences for 

this project. For instance, Cohl served on both the scientific and local organizing committees for the 13th 

International Symposium on Orthogonal Polynomials, 

Special Functions and Applications which was held on 

June 1-5, 2015 at NIST. Cohl is also serving on the Scientific and Local Organizing committees for the 

Orthogonal Polynomials and Special Functions Summer 

School 6 (OPSF-S6) workshop to be held on June 17­

23, 2016 at the Norbert Wiener Center for Harmonic 

Analysis and Applications at the University of Maryland. The OPSF-S6 summer school is being coorganized with Daniel Lozier, Mourad Ismail, Kasso 

Okoudjou, John Benedetto, Stephen Casey, Erik Koelink, Ahmed Zayed and Willard Miller, Jr. 

[1]	 H. S. Cohl and R. M. Palmer, Fourier and Gegenbauer 

Expansions for a Fundamental Solution of Laplace’s 

Equation in Hyperspherical Geometry, Symmetry, Integrability and Geometry: Methods and Applications, 

11:015 (2015). 

[2]	 H. S. Cohl and H. Volkmer, Expansions for a Fundamental Solution of Laplace’s Equation on R3 in 5-cyclidic 

Harmonics, Analysis and Applications 12:6 (2014), 613­

633. (Special Issue Dedicated to the Memory of Frank 

Olver). 

[3]	 M. A. Baeder, H. S. Cohl and H. Volkmer, Generalizations of Generating Functions for Higher Continuous 

Hypergeometric Orthogonal Polynomials in the Askey 

Scheme, Journal of Mathematical Analysis and Applications 427:1 (2015), 377-398. 

[4]	 C. Berg, M. J. Atia and H. S. Cohl, A. Swaminathan and 

W. Van Assche, Open problems at OPSFA-12 Sousse, 

Tunisia, Integral Transforms and Special Functions 26:2 

(2015), 90-95. 

[5]	 H. S. Cohl, R. S. Costas-Santos and P. R. Hwang, Generalizations of Generating Functions for Basic 

Hypergeometric Orthogonal Polynomials, in review. 

[6]	 H. S. Cohl, R. S. Costas-Santos, and W. Xu, The Power 

Collection Method for Connection Relations: Meixner 

Polynomials, in review. 

[7]	 H. S. Cohl, R. S. Costas-Santos and W. Xu, The orthogonality of Al-Salam-Carlitz Polynomials for Complex 

Parameters, in review. 

[8]	 H. S. Cohl, S. J. Nair and R. M. Palmer, Some Dual Definite Integrals for Bessel Functions, in review. 

[9]	 H. S. Cohl, J. E. Hirtenstein and H. Volkmer, Convergence of Magnus Integral Addition Theorems for 

Confluent Hypergeometric Functions, in preparation. 
 

102 NIST Applied and Computational Mathematics Division 
 

Part IV: Activity Data 

 

Summary of Activities for Fiscal Year 2015 103 

Part IV

 Activity Data 
104 NIST Applied and Computational Mathematics Division 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 105 

Publications 

Note: Names of (co-)authors with a Division affiliation 

during this reporting period are underlined. 

Appeared 

Refereed Journals 

1.	 B. Alpert, M. Balata, D. Bennett, M. Biasotti, C. 

Boragno, C. Brofferio, V. Ceriale, D. Corsini, P.K. 

Day, M. De Gerone, R. Dressler, M. Faverzani, E. 

Ferri, J. Fowler, F. Gatti, A. Giachero, J. HaysWehle, S. Heinitz, G. Hilton, U. Köster, M. 

Lusignoli, M. Maino, J. Mates, S. Nisi, R. Nizzolo, 

A. Nucciotti, G. Pessina, G. Pizzigoni, A. Puiu, S. 

Ragazzi, C. Reintsema, M. Ribeiro-Gomes, D. 

Schmidt, D. Schumann, M. Sisti, D. Swetz, F. Terranova and J. Ullom, HOLMES: The Electron 

Capture Decay of 163Ho to Measure the Neutrino 

Mass with sub-eV Sensitivity, European Physics 

Journal C 75:3 (2015), 112. DOI: 10.1140/epjc/s10052‐

015‐3329‐5

2.	 D. A. Anderson, J. D. Benson, A. J. Kearsley, Foundations of Modeling in Cryobiology-I: 

Concentration, Gibbs Energy, and Chemical Potential Relationships, Cryobiology, 69 (2015), 349­

360. DOI: 10.1016/j.cryobiol.2014.09.004 

3.	 A. Anandkumar, D. P. Foster, D. Hsu, S. M. Kakade 

and Y.-K. Liu, A Spectral Algorithm for Latent Dirichlet Allocation, Algorithmica 72:1 (2015), 193­

214. DOI: 10.1007/s00453-014-9909-1 

4.	 M. A. Baeder, H. S. Cohl and H. Volkmer, Generalizations of Generating Functions for Higher 

Continuous Hypergeometric Orthogonal Polynomials in the Askey Scheme, Journal of Mathematical 

Analysis and Applications 427:1 (2015), 377-398. 

DOI: 10.1016/j.jmaa.2015.01.074 

5.	 C. Berg, M. J. Atia, H. S. Cohl, A. Swaminathan 

and W. Van Assche, Open Problems, Special Issue 

on OPSFA12, Sousse, Tunisia, Integral Transforms 

and Special Functions 26:2 (2015), 90-95. DOI: 

10.1080/10652469.2014.973193 

6.	 I. Brezinova, A. U. J. Lode, A. I. Streltsov, L. S. 

Cederbaum, O. E. Alon, L. A Collins, B. I. Schneider and J. Burgdörfer, Elastic Scattering of a BoseEinstein Condensate at a Potential Landscape, Journal of Physics: Conference Series 488 (2014), 

012032. DOI: 10.1088/1742-6596/488/1/012032 

7.	 T. Burns, S. P. Mates, R. L. Rhorer, E. P. Whitenton 

and D. Basak, Inverse Method for Estimating Shear 

Stress in Machining, Journal of the Mechanics and 

Physics of Solids, 86 (2016), 220-236. DOI: 

10.1016/j.jmps.2015.10.008 

8.	 A. S. Carasso, Stable Explicit Time Marching in 

Well-posed or Ill-posed Nonlinear Parabolic Equations. Inverse Problems in Science and 

Engineering, 2015, 21 pages. DOI: 

10.1080/17415977.2015.1110150 

9.	 B. G. Christensen, A. Hill, P. G. Kwiat, E. Knill, S. 

W. Nam, K. Coakley, S. Glancy, L. K. Shalm and 

Y. Zhang, Analysis of Coincidence-time Loopholes 

in Experimental Bell Tests, Physical Review A 92:3 

(2015), 032130. DOI: 10.1103/PhysRevA.92.032130 

10.	 H. S. Cohl and R. M. Palmer, Fourier and Gegenbauer Expansions for a Fundamental Solution of 

Laplace’s Equation in Hyperspherical Geometry, 

Symmetry, Integrability and Geometry: Methods 

and Applications 11:015 (2015). DOI: 

10.3842/SIGMA.2015.015 

11. H. S. Cohl and H. Volkmer, Expansions for a Fundamental Solution of Laplace's Equation on R3

 in 5­

cyclidic Harmonics, Analysis and Applications 12:6 

(2014), 613-633.	DOI:	10.1142/S0219530514500407

12.	 J. Diemunsch, M. Ferrara, S. Jahanbekam and J. 

Shook, Extremal Theorems for Degree Sequence 

Packing and the Two-Color Discrete Tomography 

Problem, SIAM Journal on Discrete Mathematics 

29:4 (2015), 2088-2099. DOI: 10.137/140987912 

13.	 A. Eberle, N. Martys, L. Porcar, S. Kline, W. 

George, J. Kim, P. Butler and N. Wagner, Shear 

Viscosity and Structural Scalings in Model Adhesive Hard-Sphere Gels, Physical Review E, 89, 

050302R (2014). DOI: 10.1103/PhysRevE.89.050302

14.	 S. Fackler, M. Donahue, T. Gao, P. N. A. Nero, S. 

W. Cheong, J. Cumings and I. Takeuchi, Locally 

Controlled Magnetic Anisotropy in Transcritical 

Permalloy Thin Films Using Ferroelectric, Applied 

Physics Letters 105 (2014), 212905. DOI: 

10.1063/1.4902809 

15.	 C. Ferraris, N. Martys and W. George, Development of Standard Reference Materials for 

Rheological Measurements of Cement-Based Materials, Cement and Concrete Composites 54 

(2014), 29-33. DOI: 10.1016/j.cemconcomp.2014.01.008 

16.	 J. W. Fowler, B. Alpert, W. B. Doriese, D. A. 

Fischer, C. Jaye, Y. I. Joe, G. C. O’Neil, D. S. Swetz 

and J. N. Ullom, Microcalorimeter Spectroscopy at 

High Pulse Rates: a Multi-Pulse Fitting Technique, 

Astrophysical Journal Supplement Series 219 

(2015), 35. DOI: 10.1088/0067-0049/219/2/35 

17.	 Z. Gimbutas and L. Greengard, Computational 

Software: Simple FMM Libraries for Electrostatics, 

Slow Viscous Flow, and Frequency-Domain Wave 

Propagation, Communications in Computational 

Physics, 18:2 (2015), 516-528. DOI: 

10.4208/cicp.150215.260615sw 
 

 

 

 

 

 

 

 

 

 

 

 

 

106 NIST Applied and Computational Mathematics Division 

18.	 Z. Gimbutas and L. Greengard, A Fast Multipole 

Method for The Evaluation of Elastostatic Fields in 

a Half-Space with Zero Normal Stress, Advances in 

Computational Mathematics, 42:1 (2016), 175 ­

198. DOI: 10.1007/s10444-015-9416-1 

19.	 Z. Gimbutas, L. Greengard and S. Veerapaneni, 

Simple and Efficient Representations for the Fundamental Solutions of Stokes Flow in a Half-space, 

Journal of Fluid Mechanics, 776 (2015), R1, 10 

pages. DOI: 10.1017/jfm.2015.302 

20.	 W. Griffin and M. Olano, Evaluating Texture Compression Masking Effects Using Objective Image 

Quality Assesment Metrics, IEEE Transactions on 

Visualization and Computer Graphics, 21:8 (2015), 

970-979. DOI: 10.1109/TVCG.2015.2429576 

21.	 X. Guan, K. Bartschat, L. Koesterke and B. I. 

Schneider, Effects of Autoionizing States on TwoPhoton Double Ionization of the H2 Molecule, Journal of Physics: Conference Series 488 (2014), 

032015. DOI: 10.1088/1742-6596/488/3/032015 

22.	 R. Kacker, Probability Distributions and Coverage 

Probability in GUM, JCGM Documents and Statistical Inference, Measurement 65 (2015), 61-70. DOI: 

10.1016/j.measurement.2014.12.056 

23.	 A. J. Kearsley, Y. Gadhyan, W. E. Wallace, Stochastic Regression Modeling of Chemical Spectra, 

Chemometrics and Intelligent Laboratory Systems 

139, pp. 26-32 (2015). DOI: 10.1016/j.chemolab.2014.08.002 

24.	 Y. Kemper and I. Beichl, Monte Carlo Methods to 

Approximate the Chromatic Polynomial, Congressus Numerantium 125 (2015), 127-152. 

25.	 E. Knill, S. Glancy, S. W. Nam, K. Coakley and Y. 

Zhang, Bell Inequalities for Continuously Emitting 

Sources, Physical Review A 91:3 (2015), 032105. 

DOI: 10.1103/PhysRevA.91.032105 

26.	 H. S. Ku, W. F. Kindel, F. Mallet, S. Glancy, K. D. 

Irwin, G. C. Hilton, L. R. Vale and K. W. Lehnert, 

Generating and Verifying Entangled Itinerant Microwave Fields with Efficient and Independent 

Measurements, Physical Review A 91:4 (2015), 

042305. DOI: 10.1103/PhysRevA.91.042305 

27.	 J. Lawrence, R. Kacker, R. Kessel, Obtaining a 

Trapezoidal Distribution, Communications in Statistics Theory and Methods 44:21 (2015), 4586 ­

4599. DOI: 10.1080/03610926.2013.833239 

28.	 M. Liard, N. Martys, W. George, D. Lootens and P. 

Hebraud, Scaling Laws for the Flow of Generalized 

Newtonian Suspensions, Journal of Rheology 58 

(2014), 1993-2015. DOI: 10.1122/1.4896896 

29.	 A. Luna, G. B. McFadden, M. I Aladjem and K. W. 

Kohn, Predicted Role of NAD Utilization in the 

Control of Circadian Rhythms During DNA Damage Response, PLOS Computational Biology, 11 

(2015), 1004144. DOI: 10.1371/journal.pcbi.1004144 

30.	 H. Mahboubi, K. Moezzi, A. Aghdam and K. Sayrafian, Distributed Deployment Algorithms for 

Efficient Coverage in a Network of Mobile Sensors 

with Nonidentical Sensing Capabilities, IEEE 

Transactions of Vehicular Technology, 63:8 (2014), 

3998-4016. DOI: 10.1109/TII.2013.2280095 

31.	 P. Mell, R. Harang and A. Gueye, Measuring Limits 

on the Ability of Colluding Countries to Partition 

the Internet, International Journal of Computer Science: Theory and Application 3:3 (2015), 60-73. 

32.	 Y. Mishin, G. B. McFadden, R. F. Sekerka and W. 

J. Boettinger, A Sharp Interface Model of Creep 

Deformation in Crystalline Solids, Physical Review 

B 92 (2015), 064113. DOI: 10.1103/PhysRevB.92.064113 

33.	 W. F. Mitchell and M. A. McClain, A Comparison 

of hp-Adaptive Strategies for Elliptic Partial Differential Equations, ACM Transactions on 

Mathematical Software 41:1 (2014). DOI: 

10.1145/2629459 

34.	 J. L. Molaro, S. Byrne, S. A. Langer, Grain-scale 

Thermoelastic Stresses and Spatiotemporal Temperature Gradients on Airless Bodies, Implications 

for Rock Breakdown, Journal of Geophysical Research: Planets, 120:2 (2015), 255-277. DOI: 

10.1002/2014JE004729 

35.	 A. K. Nurse, S. Colbert-Kelly, S. R. Coriell and G. 

B. McFadden, Equilibrium and Stability of Axisymmetric Drops on a Conical Substrate under 

Gravity, Physics of Fluids 27 (2015), 084101. DOI: 

10.1063/1.4927697 

36.	 J. Penczek, S. Satterfield, E. Kelley, T. Scheitlin, J. 

Terrill and P. Boynton, Evaluating the Visual Performance of Stereoscopic Immersive Display 

Systems, Presence: Teleoperators and Virtual Environments, 24:4 (2015). 

37.	 A Reiman, A. Cerfon, G. B. McFadden, et al., A 

Cross-Benchmarking and Validation Initiative for 

Tokamak 3D Equilibrium Calculations, Nuclear 

Fusion 55 (2015), 063026. DOI: 10.1088/0029­

5515/55/6/063026 

38.	 L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. 

Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, 

S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, 

C. Lambrocco, E. Tortorici, A. L. Migdall, Y. 

Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. 

Shaw, J. A. Stern, C. Abellán, W. Amaya, V. 

Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, 

J. C. Bienfang, R. P. Mirin, E. Knill, S. W. Nam, A 
 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 107 

Strong Loophole-free Test of Local Realism, Physical Review Letters 115:25 (2015), 250402. DOI: 

10.1103/PhysRevLett.115.250402

39.	 J. Sifuentes, Z. Gimbutas and L. Greengard, Randomized Methods for Rank-Deficient Linear 

Systems, Electronic Transactions on Numerical 

Analysis, 44 (2015), 177-188. URL: 

http://etna.mcs.kent.edu//vol.44.2015/pp177-188.pdf 

40.	 J. Sims and S. Hagstrom, Mathematical and Computational Science Issues in High Precision 

Hylleraas-Configuration Interaction Variational 

Calculations: III Four-Electrol Integrals, Journal of 

Physics B: Atomic, Molecular and Optical Physics 

48:17 (2015), 175003. DOI: 10.1088/0953­

4075/48/17/175003 

41.	 O. Slattery, L. Ma, P. Kuo and X. Tang, Narrowlinewidth Source of Greatly Non-degenerate Photon Pairs for Quantum Repeaters from a Short 

Singly Resonant Cavity, Applied Physics B 121 

(2015), 413-419. DOI: 10.1007/s00340-015-6198-6 

42.	 J. Stoian, T. Oey, J. Huang, A. Kumar, J. Bullard, 

M. Balonis, S. Satterfield, J. Terrill, N. Neithalath 

and G. Sant, New Insights into the Prehydration of 

Cement and its Mitigation, Cement and Concrete 

Research, 70 (2015), 94–103. DOI: 10.1016/j.cemconres.2015.01.012 

43.	 A. Streib, N. Streib, I. Beichl and F. Sullivan, Stratified Sampling for the Ising Model – A Graph 

Theoretic Approach, Computer Physics Communications 191 (2015), 1-8. DOI: 10.1016/j.cpc.2015.01.005 

44.	 J. Torres-Jimenez, I. Izquierdo-Marquez, R. Kacker 

and D. R. Kuhn, Tower of Covering Arrays, Discrete Applied Mathematics (2015), 141–146. DOI: 

10.1016/j.dam.2015.03.010 

45.	 J. Torres-Jimenez, N. Rangel-Valdez, R. Kacker 

and J. Lawrence, Combinatorial Analysis of Diagonal, Box, and Greater-Than Polynomials as Packing 

Functions, Applied Mathematics and Information 

Sciences 9 (2015), 2757-2766. 

46.	 J. Torres-Jimenez, I. Izquierdo-Marquez, A. Garcia-Robledo, A. Gonzalez-Gomez, J. Bernal and R. 

Kacker, A Dual Representation Simulated Annealing Algorithm for the Bandwidth Minimization 

Problem on Graphs, Information Sciences 303 

(2015), 33–49. DOI: 10.1016/j.ins.2014.12.041 

47.	 F. Vico, M. Ferrando, L. Greengard and Z. Gimbutas, The Decoupled Potential Integral Equation for 

Time-Harmonic Electromagnetic Scattering, Communications on Pure and Applied Mathematics, 

(2015), 42 pages. DOI: 10.1002/cpa.21585 

48.	 S. Weiss, A. Boliong and H. S. Cohl, Measurement 

and Analysis of the Lowest Resonant Mode of a 

Spherical Annular-Sector Patch Antenna, IET Microwaves, Antennas & Propagation 9:2 (2015), 95­

100. DOI: 10.1049/iet-map.2014.0163 

49.	 D. H. Yeo and F. A. Potra, Sustainable Design of 

Reinforced Concrete Structures Through CO2 

Emission Optimization, Journal of Structural Engineering 141:3-4 (2015), B4014002, 07015002. DOI: 

10.1061/(ASCE)ST.1943-541X.0000888 

Journal of Research of NIST 

1.	 J. Bernal and J. Torres-Jimenez, SAGRAD: A Program for Neural Network Training with Simulated 

Annealing and the Conjugate Gradient Algorithm, 

Journal of Research of the NIST 120 (2015), 113­

128. DOI: 10.6028/jres.120.009 

2.	 A. S. Carasso and A. E. Vladar, Recovery of Background Structures in Nanoscale Helium Ion 

Microscope Imaging, Journal of Research of the 

NIST 119 (2014), 683-701. DOI: 10.6028/jres.119.030 

3.	 A. K. Nurse, S. R. Coriell and G. B. McFadden, On 

the Stability of Rotating Drops, Journal of Research 

of the NIST 120 (2015), 74-101. DOI: 

10.6028/jres.120.007 

Book Chapters 

1.	 R. Datla and R. Kacker, Calibration Traceability, 

Measurement Uncertainty, and Verification and 

Validations, Chapter 3 in NIST Handbook 157: 

Guidelines for Radiometric Calibration of ElectroOptical Instruments for Remote Sensing, (J. Tansock, ed.), April 2015, 17-30. DOI: 

10.6028/NIST.HB.157 

2.	 H. Mahboubi, A. Aghdam and K. Sayrafian, Area 

Coverage in a Fixed-Obstacle Environment Using 

Mobile Sensor Networks, Control and Systems Engineering: A Report on Four Decades of 

Contributions, Springer Publishing, 2015. 

3.	 D. Richard Kuhn, R. Bryce, F. Duan, L. 

Ghandehari, Y. Lei and R. Kacker, Combinatorial 

Testing: Theory and Practice, Chapter 1 in Advances in Computers, Vol. 99, (A. Memon, ed.) 

Academic Press, Elsevier Inc., 2015. 

4.	 B. I. Schneider, L. A. Collins, X. Guan, K. 

Bartschat and D. Feder, Time-Dependent Computational Methods for Matter Under Extreme 

Conditions, in Advances in Chemical Physics 157, 

Proceedings of the 240 Conference: Science’s Great 

Challenges (A. Dinner, ed.), John Wiley and Sons, 

2015. 

5.	 R. F. Sekerka, S. R. Coriell and G. B. McFadden, 

Morphological Stability, Chapter 14 in Handbook 
 

 

 

 

 

 

108 NIST Applied and Computational Mathematics Division 

of Crystal Growth, 2nd ed. (T. Nishinaga, ed.), 

Elsevier, 2015, 595-630. 

In Conference Proceedings 

1.	 R. Alléaume, T. Chapuran, C. Chunnilall, I. Degiovanni, N. Lutkenhaus, V. Martin, A. Mink, M. 

Peev, M. Lucamarini, A. Shields and M. Ward, 

Worldwide Standardization Activity for Quantum 

Key Distribution, in Proceedings of IEEE 

GlobeCom Workshop on Telecomm Standards, 

From Research to Standards, Austin, TX, December 8, 2014, 741-746. DOI: 

10.1109/GLOCOMW.2014.7063507 

2.	 M. Barbi, K. Sayrafian and M. Alasti, Inter-BAN 

Interference Mitigation Using Uncoordinated 

Transmission Scheduling Strategies, in Proceedings of COST IC1004, TD(15), Dublin, Ireland, 

January 28-30, 2015, 12035. 

3.	 M. Barbi, K. Sayrafian and M. Alasti, Uncoordinated Scheduling Strategies for BAN-to-BAN 

Interference Mitigation, in Proceedings of the 2015 

IEEE International Conference on Communications and Networking (BlackSeaCom), Constanta, 

Romania, May 18-21, 2015. DOI: 

10.1109/BlackSeaCom.2015.7185121 

4.	 M. Barbi, K. Sayrafian and M. Alasti, Impact of the 

Energy Detection Threshold on Performance of the 

IEEE 802.15.6 CSMA/CA, in Proceedings of the 

IEEE Conference on Standards for Communications & Networking (CSCN’15), Tokyo, Japan, 

October 28-30, 2015. 

5.	 T. Bednarz, J. Taylor, W. Huang, W. Griffin, S. Satterfield, J. Hagedorn and J. Terrill, HighPerformance Visualization in Science and Research, in Electronic Proceedings of the IEEE Vis 

2014, Paris, France, November 9-14, 2014. 

6.	 D.Budic, D. Simunic and K. Sayrafian, KineticBased Micro Energy-Harvesting for Wearable Sensors, in Proceedings of the 6th IEEE International 

Conference on Cognitive infocommunications, 

(IEEE CogInfocom), Gyor, Hungary, October 19­

21, 2015. 

7.	 J. Bullard, M. Ley, J. Hagedorn, R. Desaymons, W. 

Griffin, J. Terrill, Q. Hu, S. Satterfield, and P. 

Gough, Direct Comparisons of 3D Hydration Experiments and Simulations, in Proceedings of the 6th 

Advances in Cement-based Materials: Characterization, Processing, Modeling and Sensing, 

Manhattan, Kansas, July 20, 2015. 

8.	 S. D. Casey and H. S. Cohl, UWB Signal Processing: Projection, B-Splines, and Modified 

Gegenbauer Bases, in Proceedings of the 11th International Conference on Sampling Theory and 

Applications (SampTA), 2015. 

9.	 H. S. Cohl, M. Schubotz, M. A. McClain, B. V. 

Saunders, C. Y. Zou, A. S. Mohammed and A. A. 

Danoff, Growing the Digital Repository of Mathematical Formulae with Generic LaTeX Sources in 

Proceedings of the Conference on Intelligent Computer Mathematics, Lecture Notes in Artificial 

Intelligence 9150 (2015), (M. Kerber, J. Carette, C. 

Kaliszyk and V. Sorge, eds.), 280-287. 

10.	 J. Chen, H. Zhao, W. Griffin, J. Terrill and G. Bryant, Validation of SplitVector Encoding and 

Steroscopy for Quantitative Visualization fo Quantum Physics Data in Virtual Environments, in 

Proceedings of the IEEE Virtual Reality 2015 Conference, Arles, France, March 23 – 27, 2015. 

11.	 M. Dadfarnia, K. Sayrafian, P. Mitcheson and J. Baras, Maximizing Output Power of a CFPG Micro 

Energy-Harvester for Wearable Medical Sensors, in 

Proceedings of the 4th International Conference on 

Wireless Mobile Communication and Healthcare 

(MobiHealth 2014), Athens, Greece, November 

2014. 

12.	 G. Dogan, An Efficient Curve Evolution Algorithm 

for Multiphase Image Segmentation, in Proceedings of the 10th International Conference of Energy 

Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR’15), Hong Kong, 

January 2015. 

13.	 G. Dogan, An Efficient Curve Evolution Algorithm 

for Multiphase Image Segmentation, in Proceedings of the 5th International Conference on Scale 

Space and Variational Methods in Computer Vision 

(SSVM’15), Bordeaux, France, May 2015. 

14.	 G. Dogan, J. Bernal and C. Hagwood, A Fast Algorithm for Elastic Shape Distances between Closed 

Planar Curves, in Proceedings of CVPR 2015 (IEEE 

Conference on Computer Vision and Pattern 

Recognition), Boston, MA, June 7-12, 2015, 4222­

4230. 

15.	 G. Dogan, J. Bernal and C. Hagwood, FFT-based 

Alignment of 2D Closed Curves with Application 

to Elastic Shape Analysis, in Proceedings of 1st International Workshop on Differential Geometry in 

Computer Vision for Analysis of Shapes, Images 

and Trajectories (DIFF-CV) 2015, British Machine 

Vision Conference (BMVC) 2015, Swansea, 

Wales, UK, September 7-10, 2015, 12.1-12.10. 

16.	 F. Duan, L. Yu, Y. Lei, R. Kacker and D. R. Kuhn, 

Improving IPOG’s Vertical Growth Based on a 

Graph Coloring Scheme, in Proceedings of 4th International Workshop on Combinatorial Testing in 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 109 

Junction with 8th IEEE International Conference 

on Software Testing, Verification and Validation 

(ICST 2015), Graz, Austria, April 13-18, 2015. 

17.	 J. T. Fong, J. J. Filliben, N. A. Heckert, P. V. Marcal 

and R. Rainsberger, Uncertainty Quantification of 

Stresses in a Cracked Pipe Elbow Weldment using 

a Logistic Function Fit, a Nonlinear Least Squares 

Algorithm, and a Super-parametric Method, in Proceedings of the 14th International Conference on 

Pressure Vessel Technology (ICPVT-14), Shanghai, China, September 23-26, 2015. 

18.	 J. T. Fong, N. A. Heckert, J. J. Filliben, P. V. Marcal 

and R. Rainsberger, Uncertainty of FEM Solutions 

Using a Nonlinear Least Squares Fit Method and a 

Design of Experiments Approach, Proceedings of 

the 2015 International COMSOL Users’ Conference, Boston, MA, Oct. 7-9, 2015. 

19.	 L. Ghandehari, J. Chandrasekaran, Y. Lei, R. 

Kacker and D. R. Kuhn, BEN: A Combinatorial 

Testing-Based Fault Localization Tool, in Proceedings of 4th International Workshop on 

Combinatorial Testing in Junction with 8th IEEE 

International Conference on Software Testing, Verification and Validation (ICST 2015), Graz, 

Austria, April 13-18, 2015. 

20.	 W. Griffin, D. Catacora, S. Satterfield, J. Bullard 

and J. Terrill, Incorporating D3.js Information Visualization into Immersive Virtual Environments, in 

Proceedings of the IEEE Virtual Reality 2015 Conference, Arles, France, March 23-27, 2015. 

21.	 A. Gueye, P. Mell, R. Harang, R. La. Defensive 

Resource Allocations with Security Chokepoints in 

High-risk IPv6 Networks, in Proceedings of the 

29th Annual IFIP WG 11.3 Working Conference on 

Data and Applications Security and Privacy, Fairfax, VA, July 13-15, 2015. 

22.	 J. Hagedorn, J. Bullard, R. Desaymons, W. Griffin, 

J. Terrill, T. Ley, Q. Hu, S. Satterfield and P. 

Gough, HydratiCA: A Parallelized Numeric Model 

of Cement Hydration, in Proceedings of the Extreme Science Engineering Discovery Environment 

2015 Conference (XSEDE’15), St. Louis, Missouri, 

July 26-30, 2015. 

23.	 V. Hu, D. F. Ferraiolo, D. R. Kuhn, R. Kacker and 

Y. Lei, Implementing and Managing Policy Rules 

in Attribute Based Access Control, in Proceedings 

of 16th IEEE International Conference on Information Reuse and Integration (IRI 2015), San 

Francisco, CA, August 13-15, 2015. 

24.	 F. Krahmer and Y. K. Liu, Phase Retrieval Without 

Small-Ball Probability Assumptions: Stability and 

Uniqueness, in Proceedings of the 2015 International Conference on Sampling Theory and 

Applications (SampTA), Washington, DC, May 25­

29, 2015. 

25.	 D. R. Kuhn, R. Kacker, Y. Lei and J. TorresJimenez, Efficient Verification of Equivalence 

Classes and Simultaneous Testing Using Two-layer 

Covering Arrays, in Proceedings of 4th International Workshop on Combinatorial Testing in 

Junction with 8th IEEE International Conference 

on Software Testing, Verification and Validation 

(ICST 2015), Graz, Austria, April 13-18, 2015. 

26.	 R. J. La, Role of Network Topology in Cybersecurity, in Proceedings of the IEEE Conference on 

Decision and Control (CDC), Los Angeles, CA, 

December 15-17, 2014. 

27.	 M. Liard, N. Martys, W. George, D. Lootens and P. 

Hebraud, Scaling Laws for the Flow of Non-Newtonian Suspensions, in Proceedings of the 86th 

Annual Meeting of the Society of Rheology, Philadelphia, Pennsylvania, October 5-9, 2014. 

28.	 Y. K. Liu, Privacy Amplification in the Isolated 

Qubits Model, Advances in Cryptology -

EUROCRYPT 2015, Sofia, Bulgaria, April 26-30, 

2015. 

29.	 Li Ma, M. Stoudt, L. Levine and J. T. Fong, Effect 

of Grain Size and Grain Boundary Microstructure 

on Fatigue Crack Nucleation in FCC Polycrystalline Materials, Proceedings of the 2015 Three 

Materials Society (TMS) 144th Annual Meeting and 

Exhibition, Walt Disney World, FL, March 15-19, 

2015. 

30.	 Lijun Ma, O. Slattery, P. Kuo and X. Tang, EIT 

Quantum Memory with Cs Atomic Vapor for Quantum Communication, in Proceedings of SPIE, Vol. 

9615, 96150D–1 (2015). 

31.	 Li Ma, J. T. Fong, B. Lane, S. Moylan, J. J. Filliben, 

N. A. Heckert and L. Levine, Using Design of Experiments in Finite Element Modeling to Identify 

Critical Variables for Laser Powder Bed Fusion, in 

Proceedings of the 26th Annual International Solid 

Freeform Fabrication Symposium: An Additive 

Manufacturing Conference, University of Texas, 

Austin, Texas, August 10-12, 2015. 

32.	 V. Marbukh, Towards Managing Systemic Risk in 

Networked Systems, in Proceedings of the International Conference on Operations Research, Vienna, 

Austria, September 1-4, 2015. 

33.	 V. Marbukh, Towards Unified Perron-Frobenius 

Framework for Managing Systemic Risk in Networked Systems, in Proceedings of the annual 

European Safety and Reliability Conference 

(ESREL), Zurich, Switzerland, September 7-10, 

2015. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

110 NIST Applied and Computational Mathematics Division 

34.	 V. Marbukh, K. Sayrafian, M. Barbi and M. Alasti, 

A Regret Matching Strategy Framework for InterBAN Interference Mitigation, in Proceedings of 8th 

IFIP Wireless and Mobile Networking Conference 

(WMNC), Munich, Germany, October 5-7, 2015. 

35.	 P. V. Marcal, J. T. Fong, R. Rainsberger and L. Ma, 

Finite Element Analysis of a Pipe Elbow Weldment 

Creep-Fracture Problem Using an Extremely Accurate 27-node Tri-Quadratic Shell and Solid Element 

Formulation, in Proceedings of the 14th International Conference on Pressure Vessel Technology 

(ICPVT-14), Shanghai, China, September 23-26, 

2015. 

36.	 P. Mell, R. Harang and A. Gueye, The Resilience of 

the Internet to Colluding Country Induced Connectivity Disruptions, in Proceedings of the Workshop 

on Security of Emerging Networking Technologies 

(SENT), San Diego CA, February 8, 2015. 

37.	 W. F. Mitchell, How High a Degree is High Enough 

for High Order Finite Elements? in Proceedings of 

the 2015 International Conference on Computational Science, Reykjavίk, Iceland, June 1-3, 2015. 

DOI: 10.1016/j.procs.2015.05.235 

38.	 S. Pal and R. J. La, A Simple Learning Rule in 

Games and Its Convergence to Pure-Strategy Nash 

Equilibria, in Proceedings of the American Control 

Conference, Chicago, IL, July 1-3, 2015. 

39.	 S. Pal and R. J. La, A Simple Learning in Weakly 

Acyclic Games and Convergence to Nash Equilibria, in Proceedings of the Annual Allerton 

Conference on Communication, Control, and Computing, Monticello, IL, September 30 – October 2, 

2015. 

40.	 B. Saunders, B. Antonishek, Q. Wang and B. Miller, Dynamic 3D Visualizations of Complex 

Function Surfaces Using X3DOM and WebGL, in 

Proceedings of the 20th International Conference 

on 3D Web Technology (Web3D 2015), Crete, 

Greece, ACM and New York, 2015. 

41.	 M. Schubotz, A. Youssef, V. Markl, H. S. Cohl and 

J. J. Li, Evaluation of Similarity Measure Factors 

for Formulae based on the NTCIR-11 Math Task, 

in Proceedings of the 11th NTCIR Conference, Tokyo, Japan, December 9-12, 2014. 

42.	 M. Schubotz, A. Youssef, V. Markl, and H. S. Cohl, 

Challenges of Mathematical Information Retrieval 

in the NTCIR-11 Math Wikipedia Task, 2015, in 

Proceedings of the 38th Annual ACM Special Interest Group on Information Retrieval Conference 

(SIGIR 2015), Santiago, Chile, August 9-13, 2015. 

43.	 O. Slattery, L. Ma, P. Kuo and X. Tang, Comparing 

the Linewidths from Single-Pass SPDC and SinglyResonant Cavity SPDC, in Proceedings of SPIE, 

Vol. 9615, 961507–1 (2015). 

44.	 L. Yu, F. Duan, Y. Lei, R. Kacker and D. R. Kuhn, 

Constraint Handling in Combinatorial Test Generation Using Forbidden Tuples, in Proceedings of 4th 

International Workshop on Combinatorial Testing 

in Junction with 8th IEEE International Conference 

on Software Testing, Verification and Validation 

(ICST 2015), Graz, Austria, April 13-18, 2015. 

Technical Magazine Articles 

1.	 B. Cloteaux, Is This for Real? Fast Graphicality 

Testing, Computing in Science & Engineering 17:6 

(2015), 91-95. DOI: 10.1109/MCSE.2015.125 

2.	 B. I. Schneider, The Impact of Heterogenous Computer Architectures on Computational Physics, 

Computing in Science & Engineering 17:2 (2015), 

9-13. DOI: 10.1109/MCSE.2015.39 

3.	 D. R. Kuhn, R. Kacker and Y. Lei, Combinatorial 

Coverage as an Aspect of Test Quality, Crosstalk: 

the Journal of Defense Software Engineering, 28, 

(March/April 2015), 19-23. 

4.	 J. D. Hagar, T. L. Wissink, D. R. Kuhn and R. 

Kacker, Introducing Combinatorial Testing in a 

Large Organization, IEEE Computer (April 2015), 

64-72. DOI: 10.1109/MC.2015.114 

Technical Reports 

1.	 J. Bernal, NEURBT: A Program for Computing 

Neural Networks for Classification using Batch 

Learning, NISTIR 8037, February 2015. DOI: 

10.6028/NIST.IR.8037 

2.	 R. F. Boisvert (ed.), Applied and Computational 

Mathematics Division, Summary of Activities for 

Fiscal Year 2014, NISTIR 8056, April 2015. DOI: 

10.6028/NIST.IR.8056 

3.	 S. Kimmel and Y. K. Liu, Quantum Compressed 

Sensing Using 2-Designs, Arxiv preprint, October 

2015. DOI: 1510.08887v1 

4.	 S. A. Langer, A. C. E Reid, F. Y. Congo, R. Lua, V. 

R. Coffman, gtklogger: A Tool for Systematically 

Testing Graphical User Interfaces, NIST TN 1862, 

August 2015. DOI: 10.6028/NIST.TN.1862 

Accepted 

1.	 B. Alpert, E. Ferri, D. Bennett, M. Faverzani, J. 

Fowler, A. Giachero, J. Hays-Wehle, M. Maino, A. 

Nucciotti, A. Puiu, D. Swetz and J. Ullom, Algorithms for Identification of Nearly-Coincident 
 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 111 

Events in Calorimetric Sensors, Journal of Low 

Temperature Physics. DOI: 10.1007/s10909-015-1402-y 

2.	 A. S. Carasso, Stable Explicit Stepwise Marching 

Scheme in Ill-Posed Time-Reversed Viscous Wave 

Equations, Inverse Problems in Science and Engineering. DOI: 10.1080/17415977.2015.112429 

3.	 J. W. Fowler, B. Alpert, W. B. Doriese, Y. I. Joe, 

G. C. O'Neil, J. N. Ullom, D. S. Swetz, The Practice 

of Pulse Processing, Journal of Low Temperature 

Physics. DOI: 10.1007/s10909-015-1380-0 

4.	 R. J. La, Interdependent Security with Strategic 

Agents and Global Cascades, IEEE/ACM Transactions on Networking. DOI: 10.1109/TNET.2015.2408598 

5.	 J. Lawrence, R. Kacker and R. Kessel, Obtaining a 

Trapezoidal Distribution, Communications in Statistics: Theory and Methods. DOI: 

10.1080/03610926.2013.833239 

6.	 F. A. Potra, Sufficient Weighted Complementarity 

Problems, Computational Optimization and Applications. DOI: 10.1007/s10589-015-9811-z 

7.	 K. Sayrafian and K. Yazdandoost, Toward 5G 

Emerging Technologies: Selected Papers from 

IEEE PIMRC 2014, International Journal of Wireless Information Networks. 

8.	 R. Rossini and K. Sayrafian, MAC and Upper Layers in Body Area Networks, in Cooperative Radio 

Communications for Green Smart Environments. 

9.	 K. Sayrafian, Implant Channel Models in Body 

Area Networks, in Cooperative Radio Communications for Green Smart Environments. 

10.	 B. I. Schneider, X. Guan and K. Bartschat, Time 

Propagation of Partial Differential Equations Using 

the Short Iterative Lanczos Method and Finite-Element Discrete Variable Representation, Advances 

in Quantum Chemistry. 

11.	 J. C. Wu, A. F. Martin and R. Kacker, Validation of 

Nonparametric Two-sample Bootstrap in ROC 

Analysis on Large Datasets, Communications in 

Statistics: Simulation and Computation. DOI: 

10.1080/03610918.2015.1065327 

In Review 

1.	 D. Anderson, J. Benson, A. Kearsley, Foundations 

of Modeling in Cryobiology-II: Heat and Mass 

Transport in Bulk and at Cell Membrane and IceLiquid Interfaces. 

2.	 D. Anderson, J. Benson, A. Kearsley, Foundations 

of Modeling in Cryobiology-III: Heat and Mass 

Transport in a Ternary System. 

3.	 B. Cloteaux, Fast Sequential Creation of Random 

Realiozations of Degree Sequences. 

4.	 B. Cloteaux, Forced and Forbidden Edges for Degree Sequences. 

5.	 H. S. Cohl, J. Hirtenstein and H. Volkmer, Convergence of Magnus Integral Addition Theorems for 

Confluent Hypergeometric Functions. 

6.	 H. S. Cohl, R. S. Costas-Santos and P. R. Hwang, 

Generalizations of Generating Functions for Basic 

Hypergeometric Orthogonal Polynomials. 

7.	 H. S. Cohl, R. S. Costas-Santos and W. Xu, The 

Power Collection Method for Connection Relations: Meixner Polynomials. 

8.	 H. S. Cohl, S. J. Nair and R. M. Palmer, Some Dual 

Definite Integrals for Bessel Functions. 

9.	 H. S. Cohl, R. S. Costas-Santos and W. Xu, The Orthogonality of Al-Salam-Carlitz Polynomials for 

Complex Parameters. 

10.	 S. Colbert-Kelly, G. B. McFadden, D. Phillips and 

J. Shen, A Spectral-Galerkin Method for a Generalized Ginzburg-Landau Equation in a Circular 

Geometry. 

11.	 S. Fu, W. Cui, M. Hu, R. Chang, M. Donahue, and 

V. Lomakin, Finite Difference Micromagnetic 

Solvers with Object Oriented Micromagnetic 

Framework on Graphics Processing Units. 

12.	 A. Gueye, P. Mell, D. Banse and Y. Congo, On the 

Internet Connectivity in Africa. 

13.	 F. Y. Hunt, Optimal Spread in Network Consensus 

Models. 

14.	 F. Y. Hunt, An Algorithm for Identifying Optimal 

Spreaders in a Random Walk Model of Network 

Communication. 

15.	 R. Kacker, R. Kessel and J. Lawrence, Removing 

Divergence of JCGM Documents from the GUM 

(1993). 

16.	 R. J. La, Effects of Degree Distributions on Network Security and Internalization of Externality. 

17.	 J. Lawrence and R. Kacker, The Pair of Distributions that Brackets a Trapezoidal Distribution. 

18.	 F. Maggioni, F. A. Potra and M. Bertocchi, A Scenario-Based Framework for Supply Planning Under 

Uncertainty: Stochastic Programming Versus Robust Optimization Approaches. 

19.	 H. Mahboubi, W. Masoudimansour, A. Aghdam 

and K. Sayrafian, An Energy-Efficient Target 

Tracking Strategy for Mobile Sensor Networks. 
 

 

 

 

 

 

 

112 NIST Applied and Computational Mathematics Division 

20.	 H. Mahboubi, W. Masoudimansour, A. Aghdam 

and K. Sayrafian, Maximum Lifetime Strategy for 

Target Monitoring with Controlled Node Mobility 

in Sensor Networks with Obstacles. 

21.	 H. Mahboubi, A. Aghdam and K. Sayrafian, Toward Autonomous Mobile Sensor Networks 

Technology. 

22.	 P. Mell, R. Harang and A. Gueye, Linear Time Vertex Partitioning on Massive Graphs. 

23.	 S. Mitropoulos, V. Tsiantos, K. Ovaliadis, D. 

Kechhhrakos and M. Donahue, Stiff Modes in Spinvalve Simulations with OOMMF. 

24.	 S. Pal and R.J. La, Better Reply Dynamics – Convergence under Information Delays and Erroneous 

Payoff Information. 

25.	 P. N. Patrone, A. Dienstfrey, A. R. Browning, S. 

Tucker and S. Christensen, Uncertainty Quantification in Molecular Dynamics Studies of the Glass 

Transition Temperature. 

26.	 P. N. Patrone, T. W. Rosch and F. R. Phelan, Bayesian Calibration of Coarse-Grained Forces: 

Efficiently Addressing Transferability. 

27.	 C. G. Petra and F. A. Potra, A Homogeneous Model 

for Monotones Mixed Horizontal Linear Complementarity Problems. 

28.	 R. Pozo, Q-matrix: An Algebraic Formulation for 

the Analysis and Visual Characterization of Network graphs. 

29.	 B. Saunders, B. Miller, F. Backeljauw, S. Becuwe, 

M. McClain, D. Lozier, A. Cuyt and A. Dienstfrey, 

DLMF Tables: A Computational Resource Inspired 

by the NIST Digital Library of Mathematical Functions. 

30.	 H. Zhao, G. Bryant, W. Griffin, J. Terrill and J. 

Chen, Validation of SplitVector Encoding and Stereoscopy for Quantitative Visualization of 

Quantum Physics Data. 

Presentations 

Invited Talks 

1.	 R. F. Boisvert, “The Role of Publishers in Reproducibility,” Panel on Reporting Results and Sharing 

Study Data, Workshop on Statistical Challenges in 

Assessing and Fostering the Reproducibility of Scientific Results, National Research Council 

Committee on Applied and Theoretical Statistics, 

Washington, DC, February 27, 2015. 

2.	 R. F. Boisvert, “Reproducibility in Computing: The 

Role of Professional Societies,” Bluenose Applied 

and Computational Mathematics Days Workshop, 

St. Mary’s University, Halifax, NS, Canada, July 

11, 2015. 

3.	 A. S. Carasso, “Stabilized Explicit Time-Marching 

Schemes in Ill-Posed Nonlinear Backward Parabolic Equations,” 2015 Inverse Problems 

Symposium, Michigan State University, East Lansing, MI, May 31 - June 2, 2015. 

4.	 H. S. Cohl, “Fundamental Solutions, Generalized 

Expansions, and Formulae for Orthogonal Polynomials and Special Functions at NIST,” Department 

of Mathematics, University of Macau, Macau, December 9, 2014. 

5.	 G. Dogan, J. Bernal and C. R. Hagwood, “Fast Algorithms for Shape Analysis of Planar Objects,” 

SIAM Conference of Comptuational Science and 

Engineering, Salt Lake City, UT, March 14, 2015. 

6.	 G. Dogan, “Lagrangian Shape Optimization for 

Segmentation of Mulitphase Images,” AMMCSCAIMS Congress of Applied Mathematics, Modeling and Computational Science, Waterloo, Canada, 

June 11, 2015. 

7.	 M. Donahue, “An Introduction to Micromagnectic 

Modeling,” Orlando, Florida, March 15, 2015. 

8.	 J. T. Fong, “Optimal Design of a Magnetic Resonance Imaging (MRI) Radio Frequency (RF) Coil 

using Finite Element Method (FEM) and Statistical 

Design of Experiments (DOE),” Department of 

Electrical Engineering Seminar, University of 

Northern Texas, Denton, TX, October 3, 2014. 

9.	 J. T. Fong, “A Design-of-Experiments Approach to 

FEM Uncertainty Analysis for Optimizing Magnetic Resonance Imaging RF Coil Design,” 2014 

International COMSOL Users’ Conference, Boston, MA, October 9, 2014. 

10.	 J. T. Fong, “Introduction to Statistical Design of 

Experimetns with a Software Tool,” Department of 

Electrical Engineering, University of Northern 

Texas, Denton, TX, January 28-30, 2015. 

11.	 J. T. Fong, “Experience in Uncertainty Estimation 

of FEM Solutions using COMSOL Structural Mechanics, MEMS, and RF Modules,” COMSOL 

Government Symposium, McLean, VA, May 6, 

2015. 

12.	 J. T. Fong, “Model-based POD and Fatigue Life 

Modeling using Modern Statistical Tool,” 2015 

IEEE 12th Far East Forum on Nondestructive Evaluation and Testing (FENDT), Zhuhai, China, May 

29, 2015. 
 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 113 

13.	 J. T. Fong, “Multiaxial Composites Failure Criteria, 

Uncertainty Propagation, and Estimation of A-basis 

and B-basis Design Allowables,” ASME Applied 

Mechanics and Materials Division Joint Conference, McMat2015, Seattle, WA, July 1, 2015. 

14.	 J. T. Fong, “Structural Reliability Theory and Software Tools for Composites Design,” 10th 

Composites Design Workshop (CDW-10), Department of Aeronautics and Astronautics, Stanford 

University, Stanford, CA, July 17, 2015. 

15.	 J. T. Fong, “Uncertainty Quantification of Finite Element Simulations for Creep, Fracture, Fatigue and 

Crystal Viscoplasticity,” Metallurgy Research Laboratories of the French Atomic Energy 

Commission (CEA), Saclay, France, July 31, 2015. 

16.	 J. T. Fong, “A Fail-Safe Design and Operation 

Methodology based on a Near-Zero Failure Probability and NDE-informed Damage Tolerance Limit 

Approach,” International Structural Mechanics in 

Reactor Technology (SMiRT) Conference, Manchester, United Kingdom, August 11, 2015. 

17.	 J. T. Fong, “Uncertainty Quantification of Stresses 

in a Cracked Pipe Elbow Weldment using a Logistic 

Function Fit, a Nonlinear Least Squares Algorithm, 

and a Super-parametric Method, 14th International 

Conference on Pressure Vessel Technology 

(ICPVT-14), Shanghai, China, September 24, 2015. 

18.	 Z. Gimbutas and A. Dienstfrey, “A Fast Algorithm 

for Decaying Complex Exponential Sums,” Applied Mathematics & Statistics Colloquium, 

Colorado School of Mines, Golden, Colorado, 

March 20, 2015. 

19.	 S. Glancy, “Quantum Information and Statistics at 

NIST Boulder,” US-Korea Workshop on Quantum 

Information Applications, Los Angeles, CA, November 17, 2014. 

20.	 S. Glancy, “Analysis of Coincidence-Time Loopholes in Experimental Bell Tests,” Quantum 

Theory: from Foundations to Technologies, Växjö, 

Sweden, June 8, 2015. 

21.	 S. Glancy, “Bell Inequalities for Continuously 

Emitting Sources,” Joint Center for Quantum Information and Computer Science Seminar, College 

Park, MD, October 28, 2015. 

22.	 F.Y. Hunt, “An Algorithm for Identifying Optimal 

Spreaders in a Random Walk Model of Network 

Communication,” Probability Seminar, Mathematics Department, University of Delaware, November 

1, 2015. 

23.	 A. J. Kearsley, “Measurement Science at NIST,” 

SIAM Mid-Atlantic Regional Conference, George 

Mason University, March 21, 2015. 

24.	 Y. Kemper, “Approximating the Chromatic Polynomial,” George Mason University, February 20, 

2015. 

25.	 Y. Kemper, “From Broken Circuits to Monte Carlo: 

Approximating the Chromatic Polynomial and its 

Friends”, Workshop on New Directions for the 

Tutte Polynomial: Extensions, Interrelations, and 

Applications, Royal Holloway University of London, Egham, England, July 11, 2015. 

26.	 R. J. La, “Convergence of a Class of Simple Learning Rules to Pure-strategy Nash Equilibria,” 

Department of Electrical Engineering, University of 

Southern California, Los Angeles (CA), January 

2015. 

27.	 R. J. La, “Convergence to Pure-Strategy Nash Equilibria under Simple Learning Rules and Selection of 

Resilient Pure-Strategy Nash Equililbria,” Department of Electrical Engineering and Computer 

Science, University of Michigan, Ann Arbor (MI), 

April 2015. 

28.	 Y. K. Liu, “Tamper-Resistant Cryptographic Hardware in the Isolated Qubits Model,” US-Korea 

Workshop on Quantum Information, Los Angeles, 

CA, November 17-19, 2014. 

29.	 Y. K. Liu, “Tamper-Resistant Cryptographic Hardware in the Isolated Qubits Model,” Southwest 

Quantum Information and Technology (SQuInT) 

workshop, Berkeley, CA, February 20, 2015. 

30.	 Lijun Ma, O. Slattery, P. Kuo and X. Tang, “EIT 

Quantum Memory with Cs Atomic Vapor for Quantum Communication”, SPIE: Optics and Photonics, 

Quantum Communications and Quantum Imaging 

Xlll, San Diego, CA. August 09, 2015. 

31.	 Li Ma and J. T. Fong, “Effect of Grain Size and 

Grain Boundary Microstructure on Fatigue Crack 

Nucleation in FCC Polycrystalline Materials,” The 

2015 Three Materials Society (TMS) 144th Annual 

Meeting and Exhibition, Walt Disney World, FL, 

March 16, 2015. 

32.	 V. Marbukh, “SDN: Systemic Risk Due to Dynamic Load Balancing,” Software Defined 

Networking Internet Research Task Force Working 

Group (SDN IRTF WG), Honolulu, Hawaii, November 9-14, 2014. 

33.	 W. F. Mitchell, “The NIST Adaptive Mesh Refinement Benchmark Suite”, Mathematics Department 

Numerical Analysis Seminar, University of Maryland, College Park, MD, February 24, 2015. 

34.	 W. F. Mitchell, “30 Years of Newest Vertex Bisection”, Thirteenth International Conference of 

Numerical Analysis and Applied Mathematics, 

Rhodes, Greece, September 23, 2015. 
 

 

 

 

 

 

 

 

 

 

 

 

114 NIST Applied and Computational Mathematics Division 

35.	 D. G. Porter, “State of Tcl”, 21st Annual Tcl/Tk 

Conference, Portland, OR, November 13, 2014. 

36.	 R. Pozo, “A Network Measure the Analysis and 

Visualization of Large-scale Graphs,” SIAM Workshop on Network Science, Snowbird, UT, May 17, 

2015. 

37.	 S. Ressler, “360 Image Creation,” CSIRO Conference, Brisbane, Australia, March 2, 2015. 

38.	 S. Ressler, “Image Based WebVR: Creating and 

Publishing Environments for Browsers and 

HMDs,” Queensland University of Technology, 

School of Design, February 27, 2015. 

39.	 S. Ressler, “Image Based WebVR: Creating and 

Publishing Environments for Browsers and 

HMDs,” CSIRO, Canberra and Brisbane, Australia, 

2015. 

40.	 B. Saunders, B. Miller, M. McClain, D. Lozier, A. 

Dienstfrey, A. Cuyt, S. Becuwe and F. Backeljauw, 

“DLMF Standard Reference Tables on Demand 

(DLMF Tables),” Minisymposium on Orthogonal 

Polynomials and Special Functions: Computational 

Aspects, 2015 International Conference on Orthogonal Polynomials, Special Functions and 

Applications, NIST, Gaithersburg, MD, June 1, 

2015. 

41.	 B. Saunders, “NIST Projects: Graphics in the Digital Library of Mathematical Functions (DLMF) and 

DLMF Standard Reference Tables on Demand 

(DLMF Tables),” Careers in Mathematical Sciences Workshop for Underrepresented Groups, 

IMA, University of Minnesota, Minneapolis, MN, 

March 29, 2015. 

42.	 B. Saunders, “A Historical Perspective on the 2015 

Winner of the Dr. Etta Z. Falconer Award for Mentoring and Commitment to Diversity—Dr. 

Genevieve Knight,” Infinite Possibilities Conference, Oregon State University, Corvallis, Oregon, 

March 2-3, 2015. 

43.	 K. Sayrafian, “Internet of Things – How to Break 

the Barriers for Business Development?” IEEE 

BlackSeaCom, Constanta, Romania, May 20, 2015. 

44.	 J. Shook, “Matrix Scaling: A New Heuristic for the 

Directed Feedback Vertex Set Problem”, Institute 

for Defense Analysis Center for Computing Sciences, Bowie, MD, November 11, 2014. 

45.	 O. Slattery, L. Ma, P. Kuo and X. Tang, “A Narrowband Source of Correlated Non-degenerate 

Photon Pairs,” SPIE: Optics and Photonics, Quantum Communications and Quantum Imaging Xlll, 

San Diego, CA. August 09, 2015. 

46.	 O. Slattery, “Status of Narrow Linewidth Source for 

Quantum Communication Applications,” University of Limerick, Department of Physics and 

Energy, Limerick, Ireland. July 19th, 2015. 

Conference Presentations 

1.	 T. J. Burns and B. W. Rust, “Estimation of Shear 

Stress in Machining by Approximating the Solution 

of a Volterra Integral Equation of the First Kind,” 

ASME 2015 Applied Mechanics and Materials 

Conference, McMAT2015, Seattle, WA, June 

2015. 

2.	 S. D. Casey and H. S. Cohl, “UWB Signal Processing: Projection, B-Splines, and Modified 

Gegenbauer Bases,” Sampling Theory and Applications 2015 (SampTA 2015), American University, 

Washington DC, May 25, 2015. 

3.	 H. S. Cohl, “Overview of Digital Mathematics Libraries and the NIST Digital Repository of 

Mathematical Formulae,” 13th International Symposium on Orthogonal Polynomials, Special 

Functions and Applications, National Institute of 

Standards and Technology, Gaithersburg, Maryland, June 4, 2015. 

4.	 H. S. Cohl, “Generalizations of generating functions for hypergeometric and q-hypergeometric 

orthogonal polynomials,” International Conference 

on Applied Mathematics, in honour of Professor 

Roderick S. C. Wong's 70th birthday, City University of Hong Kong, Hong Kong, China, December 

1, 2014. 

5.	 H. S. Cohl, “Newtonian Potential Theory on Hyperspheres,” International Conference on Applied 

Mathematics, in honour of Professor Roderick S. C. 

Wong's 70th birthday, City University of Hong 

Kong, Hong Kong, China, December 4, 2014. 

6.	 H. S. Cohl, “Newtonian Potential Theory and Superintegrable Potentials on Hyperspheres,” 

International Conference on Orthogonal Polynomials and q-Series, University of Central Florida, 

Orlando, Florida, May 10, 2015. 

7.	 G. Dogan, J. Bernal and C. Hagwood, “FFT-based 

Alignment of 2D Closed Curves with Application 

to Elastic Shape Analysis,” 1st International Workshop on Differential Geometry in Computer Vision 

for Analysis of Shapes, Images and Trajectories 

(DIFF-CV) 2015, British Machine Vision Conference (BMVC) 2015, Swansea, Wales, UK, 

September 10, 2015. 

8.	 G. Dogan, “An Efficient Curve Evolution Algorithm for Muliphase Image Segmentation,” 10th 

International Conference of Energy Minimization 
 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 115 

Methods in Computer Vision and Pattern Recognition (EMMCVPR’15), Hong Kong, January 13, 

2015. 

9.	 G. Dogan, J. Bernal, C. R. Hagwood, “A Fast Algorithm to Compute Shape Dissimilarity of 2d 

Curves,” DelMar Numerics Day, US Naval Academy, Annapolis, MD, May 9, 2015. 

10.	 M. Donahue, “Implementation of a Localized 

Fourth Order Demagnetization Tensor,” Magnetism and Magnetic Materials Conference, 

Honolulu, Hawaii, November 5, 2014. 

11.	 A. Gueye, P. Mell, R. Harang and R. La, “Defensive 

Resource Allocations with Security Chokepoints in 

High-risk IPv6 Networks,” 29th Annual IFIP WG 

11.3 Working Conference on Data and Applications 

Security and Privacy, Fairfax, VA, July 13-15, 

2015. 

12.	 Y. Kemper, “Approximating the Chromatic Polynomial”, 46th Southeastern International 

Conference on Combinatorics, Graph Theory, and 

Computing, March 2, 2015. 

13.	 M. Liard, N. Martys, W. George, D. Lootens and P. 

Hebraud, “Scaling Laws for the Flow of Non-Newtonian Suspensions,” 86th Annual Meeting of the 

Society of Rheology, Philidelphia, Pennsylvania, 

October 5-9, 2014. 

14.	 V. Marbukh, “Network Evolution by Preferential 

Rewiring with Infection Risk Mitigation: Work in 

Progress,” Dynamic Off & On Networks workshop, 

Santa Fe Complex Systems Institute, December 1­

5, 2014. 

15.	 V. Marbukh, “Towards Managing Systemic Risk in 

Networked Systems, International Conference on 

Operations Research,” Vienna, Austria, September 

1-4, 2015. 

16.	 V. Marbukh, “Towards Unified Perron-Frobenius 

Framework for Managing Systemic Risk in Networked Systems, Annual European Safety and 

Reliability Conference (ESREL)”, Zurich, Switzerland, September 7-10, 2015. 

17.	 S. Mates, E. Vax, R. Rhorer, M. Kennedy, E. 

Whitenton, S. Banovic, T. Burns, “Dynamic Flow 

Stress Measurements for Machining Applications”, 

2014 Annual Conference on Experimental and Applied Mechanics, Greenville, SC, June 2-5, 2014. 

18.	 W. F. Mitchell, “Using Space Filling Curves to Find 

an Element That Contains a Given Point”, SIAM 

Conference on Computational Science and Engineering, Salt Lake City, UT, March 18, 2015. 

19.	 W. F. Mitchell, “How High a Degree is High 

Enough for High Order Finite Elements?”, International Conference on Computational Science, 

Reykjavίk, Iceland, June 2, 2015. 

20.	 P. N. Patrone, “A Method for Simulated Annealing 

of Cross-linked Polymers,” The Composites and 

Advanced Materials Expo (CAMX 2015), Dallas 

Texas, October 28, 2015. 

21.	 S. Ressler, “WebVR What’s It All About,” Web3D 

2015, Heraklion, Greece, June 18-21, 2015. 

22.	 S. Ressler, “Web3D Cultural and Natural Heritage 

Working Group,” Web3D 2015, Heraklion, Greece, 

June 18-21, 2015. 

23.	 S. Ressler, “Web3D 20 Year History,” Web3D 

2015, Heraklion, Greece, June 18-21, 2015. 

24.	 S. Ressler, “Web3D Cultural and Natural Heritage 

Working Group,” SIGGRAPH 2015, Los Angeles, 

California, August 9-13, 2015. 

25.	 S. Ressler, “Using Oculus Rift with your Web 

Browser for Science,” SIGGRAPH 2015, Los Angeles, California, August 9-13, 2015. 

26.	 B. W. Rust, “The Metrology of Type Ia Supernova 

Lightcurves,” 225th Meeting of the American Astronomical Society, Seattle, WA, January 5, 2015. 

27.	 B. W. Rust, M. Pruzhinskaya and B. J. Thijsse, 

“Calibrating the Decline Rate – Peak Luminosity 

Relation for Type Ia Supernovae,” XXIX General 

Assembly fo the International Astroniomical Union, Honolulu, HI, August 2015. 

28.	 B. Saunders, “Slices of 3D Surfaces on the Web Using Tensor Product B-Spline Grids,” SIAM 

Conference on Geometric and Physical Modeling 

(GD/SPM15), Salt Lake City, Utah, October 12, 

2015. 

29.	 B. Saunders, “Cutting Edge Information Technology Applied to the NIST Digital Library of 

Mathematical Functions,” MAA MathFest 2015, 

Washington, D.C., August 8, 2015. 

30.	 B. Saunders, B. Antonishek, Q. Wang and B. Miller, “Dynamic 3D Visualizations of Complex 

Function Surfaces Using X3DOM and WebGL,” 

20th International Conference on 3D Web Technology (Web3D 2015), Crete, Greece, June 20, 2015. 

31.	 B. Saunders, “X3DOM/WebGL Visualizations in 

the NIST DLMF,” Web3D Showcase, 20th International Conference on 3D Web Technology (Web3D 

2015), Crete, Greece, June 20, 2015. 

32.	 B. Saunders, B. Antonishek, Q. Wang and B. Miller, “State of the Art Visualizations of Complex 

Function Data,” 2015 International Conference on 
 

 

 

 

 

 

 

 

 

 

116 NIST Applied and Computational Mathematics Division 

Orthogonal Polynomials, Special Functions and 

Applications, NIST, June 4, 2015. 

33.	 B. Saunders, “Adaptive Grid Generation, 3D 

Graphics on the Web and a Digital Library,” Infinite Possibilities Conference, Oregon State 

University, Corvallis, Oregon, March 2, 2015. 

34.	 K. Sayrafian, “Kinetic-Based Micro Energy-Har6th vesting for Wearable Sensors,” IEEE 

International Conference of Cognitive Infocommunications, Gyor, Hungary, October 19-21, 2015. 

35.	 K. Sayrafian, “A Regret Matching Strategy Framework for Inter-BAN Interference Mitigation,” 8th 

Wireless and Mobile Networking Conference, Munich Germany, October 5-7, 2015. 

36.	 K. Sayrafian, “Impact of the Energy Detection 

Threshold on Performance of the IEEE 802.15.6 

CSMA/CA,” 2015 IEEE Conference of Standards 

for Communications & Networking, Tokyo, Japan, 

October 28-30, 2015. 

37.	 K. Sayrafian, “Inter-BAN Interference Mitigation 

Using Uncoordinated Transmission Scheduling 

Strategies,” COST IC1004, Dublin, Ireland, January 28-30, 2015. 

38.	 K. Sayrafian, “Uncoordinated Scheduling Strategies for BAN-toBAN Interference Mitigation,” 

IEEE BlackSeaCom 2105 Conference, Constanta, 

Romania, May 18-21, 2015. 

39.	 K. Sayrafian, “Maximizing Output Power of a 

CFPG Micro Energy-Harvester for Wearable Medical Sensors,” 4th International Conference on 

Wireless Mobile Communication and Healthcare, 

November 2-5, 2014. 

40.	 B. I. Schneider, “Novel Numerical Approaches to 

Solving the Time-Dependent Schrödinger’s Equation,” Concepts of Mathematical Physics in 

Chemistry, Playa del Carmen, Quintana Roo, 

México, December 10, 2014. 

41.	 M. Schubotz, H. S. Cohl, M. A. McClain, B. V. 

Saunders, C. Y. Zou, A. S. Mohammed and A. A. 

Danoff, “Growing the Digital Repository of Mathematical Formulae with Generic LaTeX Sources,” 

Conference on Intelligent Computer Mathematics, 

Washington DC, July 17, 2015. 

42.	 J. Shook, “Matrix Scaling: A New Heuristic for the 

Directed Feedback Vertex Set Problem,” 2015 Joint 

Mathematics Meetings, San Antonio, Texas, January 13th, 2015. 

Poster Presentations 

1.	 B. Alpert, E. Ferri, D. Bennett, M. Faverzani, J. 

Fowler, A. Giachero, J. Hays-Wehle, M. Maino, A. 

Nucciotti, A. Puiu and J. Ullom, “Algorithms for 

Identification of Nearly-Coincident Events in Calorimetric Sensors,” 16th International Workshop on 

Low Temperature Detectors, July 21, 2015, Grenoble, France. 

2.	 T. Bednarz, J. Taylor, W. Huang, W. Griffin, S. Satterfield, J. Hagedorn and J. Terrill, HighPerformance Visualization in Science and Research, IEEE Vis 2014, Paris, France, November 9­

14, 2014. 

3. J. Bullard, T. Ley, J. Hagedorn, R. Desaymons, W. 

Griffin and J. Terrill, “Direct Comparisions of 3D 

Hydration Experiments and Simulations,” 6th Advances in Cement Based Materials Conference, 

Manhattan, KS, July 20-22, 2015. 

4.	 G. Dogan, “A Pyton Toolbox for Shape Optimization in Image Processing,” 10th International 

Conference on Energy Minimization Methods in 

Computer Vision and Pattern Recognition 

(EMMCVPR’15), Hong Kong, January 13, 2015. 

5.	 G. Dogan, “A Python Toolbox for Shape Optimization in Imaging and Data Analysis,” SIAM 

Conference on Computational Science and Engineering, Salt Lake City, UT, March 14, 2015. 

6.	 G. Dogan, J. Bernal and C. Hagwood, “Fast Computation of Elastic Shape Distances between 2D 

Objects,” Bioimage Informatics Conference 2015, 

NIST, October 15, 2015. 

7.	 G. Dogan, “Fast Minimization of Region-based Ac5th tive Contours Using Shape Hessian,” 

International Conference of Scale Space and Variational Methods in Computer Vision (SSVM’15), 

Bordeaux, France, June 3, 2015. 

8.	 G. Dogan, J. Bernal and C. R. Hagwood, “A Fast 

Algorithm for Elastic Shape Distances Between 

Closed Planar Curves,” IEEE Conference on Computer Vision and Pattern Recognition (CVPR’15), 

Boston, MA, June 9, 2015. 

9.	 S. Glancy, “Maximum Likelihood Estimation of 

Gaussian Quantum States,” Southwest Quantum Information Technology Workshop, Berkeley, CA, 

February 19, 2015. 

10.	 W. Griffin, D. Catacora, S. Satterfield, J. Bullard 

and J. Terrill, “Incorporating 3D Information Visualization into Immersive Virtual Environments,” 

VR2015 IEEE Virtual Reality, Arles, Camargue, 

Provence France, March 23-27, 2015. 

11.	 J. Hagedorn, J. Bullard, R. Desaymons, W. Griffin, 

J. Terrill, T. Ley, Q. Hu, S. Satterfield and P. 

Gough, “HydratiCA: A Parallelized Numeric 
 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 117 

Model of Cement Hydration,” XSEDE 2015 Extreme Science Engineering Discovery 

Environments, St. Louis, MO, July 26-30, 2015. 

12.	 F. Y. Hunt, “An Optimization Problem Arising 

from a Random Walk on an Undirected Graph,” 

Workshop on Convexity and Optimization: Theory 

and Applications, Institute for Mathematics and its 

Applications, University of Minnesota, Minneapolis, MN, February 24, 2015. 

13.	 P. Kuo, J. S. Pelc, O. Slattery, L. Ma and X. Tang, 

“Domain-engineered PPLN for Generation of Polarization-entangled Photons,” 2015 SPIE 

Photonics West, San Francisco, CA, February 11, 

2015. 

14.	 V. Marbukh, “On Managing Cost/Benefit Connectivity Tradeoff in a Networked Infrastructure 

Susceptible to Adverse Cascades,” International 

Conference on Network Science (NetSci), Zaragoza, Spain, June 1-5, 2015. 

15.	 W. F. Mitchell, “NIST AMR Benchmarks”, SIAM 

Conference on Computational Science and Engineering, Salt Lake City, UT, March 15, 2015. 

16.	 O. Slattery, L. Ma, P. Kuo and X. Tang “Narrow 

Source of Greatly Non-degenerate Correlated Photon Pairs from a Singly Resonant Cavity,” 7th 

Single Photon Workshop, University of Geneva, 

Geneva, Switzerland, July 14, 2015. 

17.	 X. Tang, “An Overview of Quantum Repeater Research at NIST,” Workshop for Quantum Repeaters 

and Networks, Pacific Grove, California, May 15­

17, 2015. 

18.	 X. Tang, O. Slattery, L. Ma, P. Kuo, A. Mink, 

“Quantum Repeater Research at NIST”, SPIE Optics and Photonics 2015, (9615-32) San Diego, 

California, 9-13 August 2015. 

Web Services 

1.	 Adaptive Mesh Refinement Benchmark Problems50: 

a collection of partial differential equations suitable 

for testing and benchmarking adaptive mesh refinement algorithms and software. 

50 http://math.nist.gov/amr-benchmark 51 http://dlmf.nist.gov/ 52 http://dlmftables.uantwerpen.be/ 53 http://gams.nist.gov/ 54 http://math.nist.gov/matrixmarket/ 55 http://www.ctcms.nist.gov/~rdm/mumag.org.html 

56 http://math.nist.gov/quantum/zoo/ 57 http://math.nist.gov/scimark/ 

2.	 Digital Library of Mathematical Functions51: a repository of information on the special functions of 

applied mathematics. 

3.	 DLMF Standard Reference Tables on Demand52: an 

online service providing tables of values for special 

functions, with guaranteed accuracy to high precision. 

4.	 Guide to Available Mathematical Functions53: a 

virtual repository of mathematical software components. (dormant) 

5.	 Matrix Market54: a repository of matrices for testing 

of algorithms and software for numerical linear algebra. (dormant) 

6.	 μMAG55: a collection of micromagnetic reference 

problems and submitted solutions 

7.	 Quantum Algorithm Zoo56: a comprehensive catalog of quantum algorithms 

8.	 SciMark57: a benchmark for scientific computing in 

Java. (dormant) 

Software Released 

1.	 CCM Combinatorial coverage measurement58: Java 

version with support of constraints. D. R. Kuhn, R. 

Kacker 

2.	 PHAML59: Solution of elliptic partial differential 

equations using finite elements, hp-adaptive refinement, and multigrid methods. Version 1.15.0. W. F. 

Mitchell 

3.	 OOF260: Two dimensional finite element analysis 

of materials with complex microstructures. Version 

2.1.12. S.A. Langer, A.C.E. Reid, F.Y. Congo, L. 

Zhang. 

4.	 OOF3D61: Three dimensional finite element analysis of materials with complex microstructure. 

Version 3.0.1. S.A. Langer, A.C.E. Reid, F.Y. 

Congo, L. Zhang. 

5.	 OOMMF62: Micromagnetics software suite. Version 1.2a6. M. Donahue and D. G. Porter 

6.	 Tcl/Tk63: Extensible scripting language and GUI 

toolkit. Versions 8.5.17, 8.5.18, 8.6.3, 8.6. D. G. 

Porter 

58 http://csrc.nist.gov/groups/SNS/acts/coverage_measure.html 

59 http://math.nist.gov/phaml/ 

60 http://www.ctcms.nist.gov/oof/oof2/ 

61 http://www.ctcms.nist.gov/oof/oof3d/ 

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

63 https://www.tcl.tk/software/tcltk/ 
 

 

 

 

 

 

 

 

 

118 NIST Applied and Computational Mathematics Division 

7.	 Itcl: C++ inspired Object Oriented commands for 

Tcl. Versions 3.4.2, 4.0.2, 4.0.3. D. G. Porter. 

8.	 Thread64: Thread management commands for Tcl. 

Version 2.7.2. D. G. Porter. 

9.	 TDBC: Database connection commands for Tcl. 

Versions 1.0.2, 1.0.3. D. G. Porter. 

10.	 sqlite365: Bindings to the SQLite database engine 

for Tcl. Versions 3.8.7.1, 3.8.8.3, 3.8.9, 3.8.10, 

3.8.11.1. D. G. Porter 

11.	 trofs66: Read-only archive system for Tcl virtual 

filesystems. Version 0.4.8 D. G. Porter 

Conferences, Minisymposia, 

Lecture Series, Courses 

ACMD Seminar Series 

Brian Cloteaux served as Chair of the ACMD Seminar 

Series. There were 36 talks presented during this period; all talks are listed chronologically. 

1.	 J. Edmonds, University of Waterloo, “The 

Traveling Salesman Problem and P vs. NP: Some 

1960s Theoretical Work at NIST On the 

Complexity of Mathematical Algorithms,” October 

10, 2015. 

2.	 S. Hartke, University of Nebraska-Lincoln, 

“Computational Combinatorics: Uniquely Krsaturated Graphs,” October 20, 2014. 

3.	 D. Kahaner, Asian Technology Information 

Program, “High Performance Computing 

Development in China,” October 21, 2014. 

4.	 Y. Li, Old Dominion University, “Revisit of Monte 

Carlo Methods on Solving Large-Scale Linear 

Systems,” November 4, 2015. 

5.	 E. Gobet, Ecole Polytechnique, “Rare Event 

Simulation Using Reversible Shaking 

Transformations,” November 13, 2014. 

6.	 D. Kelly, Courant Institute of Mathematical 

Sciences, New York University, “Filter divergence 

and EnKF,” December 11, 2014. 

7.	 B. Schneider, ACMD, “The Finite Element 

Discrete Variable Method (FEDVRM) for Solving 

the Time-Dependent Schroedinger Equation 

(TDSE),” December 16, 2014. 

8.	 J. E. Johnson, University of South Carolina, “A 

Proposed Standard for Representing Numerical 

64 https://www.tcl.tk/ 

65 http://sf.net/projects/tcl/files/Tcl/ 

Information & A Mathematical Foundation for 

Networks with Clustering Analysis,” January 13, 

2015. 

9.	 W. Keyrouz, NIST/ITL Software and Systems 

Division, “A Hybrid CPU-GPU System for 

Stitching Large Scale Optical Microscopy Images,” 

February 3, 2015. 

10.	 R. Nochetto, University of Maryland, “Discrete 

ABP Estimate and Rates of Convergence for Linear 

Elliptic PDEs in Non-Divergence Form,” February 

18, 2015. 

11.	 V. Braverman, Johns Hopkins University, 

“Approximating Large Frequency Moments with 

O(n1-2/k

) Bits,” February 24, 2015. 

12.	 V. Lomakin, University of California San Diego, 

“High-Performance Micromagnetic Simulators,” 

March 2, 2015. 

13.	 K. K. Irikura, NIST/MML Chemical Sciences 

Division, “Attaching Uncertainties to Predictions 

from Quantum Chemistry Models,” March 3, 2015. 

14.	 S. Rump, Hamburg University of Technology, 

“INTLAB - The Matlab Toolbox for Reliable 

Computing,” March 12, 2015. 

15.	 F. Hunt, ACMD, “A New Approach to Finding 

Influential Spreaders in a Network,” March 24, 

2015. 

16.	 R. Mullen, University of South Carolina, 

“Uncertainty Quantification of Structures with 

Unknown Probabilistic Dependency,” April 3, 

2015. 

17.	 S. Margulies, US Naval Academy, “Hilbert's 

Nullstellensatz and Linear Algebra: An Algorithm 

for Determining Combinatorial Infeasibility,” April 

7, 2015. 

18.	 W. Cai, UNC Charlotte, “A Highly Scalable 

Communication-free Domain Decomposition BIEWOS (Boundary Integral Equation-Walk on 

Spheres) Method for Laplace Equations,” April 16, 

2015. 

19.	 H. Elman, University of Maryland, “Reduced Basis 

Collocation Methods for Partial Differential 

Equations with Random Coefficients,” April 22, 

2015. 

20.	 J. Shook, ACMD, “Degree Sequence Packing with 

Applications to Discrete Tomography,” April 28, 

2015. 

21.	 E. Otarola, University of Maryland, “A PDE 

66 http://math.nist.gov/~DPorter/tcltk/trofs/ 
 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 119 

Approach to Fractional Diffusion,” May 7, 2015. 

22.	 M. Ferrara, University of Colorado Denver, 

“Realization Problems for Graphic and 

Hypergraphic Sequences,” May 12, 2015. 

23.	 R. Costas-Santos, Universidad de Alcala, 

“Discovering Discrete Classical Polynomials: First 

Steps,” May 19, 2015. 

24.	 A. Bertozzi, UCLA, “Geometric Graph-Based 

Methods for High Dimensional Data,” May 26, 

2015. 

25.	 S. Flammia, University of Sydney, Sparse Quantum 

Codes with (Almost) Good Distance,” June 18, 

2015. 

26.	 C. Puelz, Rice University, “Reduced Blood Flow 

Models: Numerical Methods and Applications,” 

June 25, 2015. 

27.	 M. Mascagni, ACMD, “Convergence Analysis of 

Monte Carlo Linear Solvers Using the Ulam-Von 

Neumann Algorithm: Necessary and Sufficient 

Conditions,” June 30, 2015. 

28.	 A. Moorthy, University of Guelph, “Guts, Bugs, 

and Dietary Fiber - A Mathematical Approach to 

Studying a Complex Biophysical System,” June 17, 

2015. 

29.	 P. Diniz, USC Information Science Institute, 

“Managing Application Resilience: A 

Programming Language Approach,” July 21, 2015. 

30.	 M. Schubotz, Technische Universitat Berlin, “The 

NIST Digital Repository of Mathematical Formulae 

and Scalable Math Search,” July 24, 2015. 

31.	 C. Witzgall, ACMD, “Determining Primitive 

Roots,” September 15, 2015. 

32.	 D. Simos, SBA Research, “Combinatorial Security 

Testing: Combinatorial Testing Meets Information 

Security,” September 22, 2015. 

33.	 P. Krajcevski, University of North Carolina, “GPU 

Focused Image Compression Techniques,” October 

19, 2015. 

34.	 A. S. Carasso, ACMD, “Taming Explosive 

Computational Instability: Compensated Explicit 

Time-Marching Schemes in Multidimensional, 

Nonlinear, Well-Posed or Ill-Posed Initial Value 

Problems for Partial Differential Equations,” 

October 29, 2015. 

35.	 R. Evans, Department of Mathematical Sciences, 

University of Delaware, “Multiple-Component 

Reactions in Optical Biosensors,” November 17, 

67 http://www.ima.umn.edu/2014-2015/SW7.28-31.15/ 

2015. 

36.	 K. Mills, NIST/ITL Advanced Network 

Technologies Division, “The Influence of Realism 

on Congestion in Network Simulations,” December 

1, 2015. 

Shortcourses 

1.	 T. Achim, Summer Lectures in Machine Learning, 

NIST, Gaithersburg, MD, July-August 2015. 

Conference Organization 

Leadership 

1.	 H. S. Cohl and D. Lozier, Co-Organizers, Orthogonal Polynomials and Special Functions Summer 

School 6 (OPSF-S6), Norbert Wiener Center for 

Harmonic Analysis and Applications, University of 

Maryland, July 11-15, 2016. 

2.	 W. Griffin, Chair, 2015 ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, San 

Francisco, CA, February 27 – March 1, 2015. 

3.	 R. Kacker, Co-Organizer, 4th International Workshop on Combinatorial Testing (IWCT 2015) in 

Conjunction with ICST 2015, Graz, Austria April 

13-18, 2015. 

4.	 Y.-K. Liu, Chair, Steering Committee, International 

Conference on Quantum Cryptography (QCrypt), 

2016. 

5.	 D. Lozier, Co-Chair, Scientific Committee, 13th International Symposium on Orthogonal 

Polynomials, Special Functions, and Applications 

(OPSFA-13), Gaithersburg, MD, June 1-5, 2015. 

6.	 B. Miller and A. Youssef, Co-Organizers, 3th International Symposium on Orthogonal Polynomials, 

Special Functions and Applications (OPSFA), 

Washington, DC. July 13-17, 2015. 

7.	 P. Patrone and A. Dienstfrey, Co-Organizers, 

Workshop on Uncertainty Quantification in Materials Modeling67, Purdue University, West Lafayette, 

IN. July 28-31, 2015. 

8.	 S. Ressler, Chair and Member, Organizing Committee, Web3D 2015, Crete, Greece, June 18 – 21, 

2015. 

Committee Membership 

9.	 H. S. Cohl, Member, Scientific Committee, 13th International Symposium on Orthogonal 
 

 

 

 

 

120 NIST Applied and Computational Mathematics Division 

Polynomials, Special Functions, and Applications 

(OPSFA-13), Gaithersburg, MD, June 1-5, 2015. 

10.	 F. Y. Hunt, Member, Organizing and Awards Committees, Infinite Possibilities Conference, Oregon 

State University, Corvallis, OR, March 1-3, 2015. 

11.	 R. Kacker, Member, Program Committee, 8th IEEE 

International Conference on Software Testing, Verification and Validation, (ICST 2015), Graz, 

Austria, April 13-18, 2015. 

12.	 P. Kuo, Member, Program Committee (CLEO S&I 

4: Nonlinear Optical Technologies), CLEO Conference, May 10-15, 2015. 

13.	 Y.-K. Liu, Member, Program Committee, International Conference on Post-Quantum Cryptography 

(PQCrypto), 2016. 

14.	 W. F. Mitchell, Member, Scientific Committee, 

Thirteenth International Conference of Numerical 

Analysis and Applied Mathematics, (ICNAAM), 

Rhodes, Greece, September 23-29, 2015. 

15.	 X. Tang, Member, Program Committee, SPIE Conference 9615: Quantum Communications and 

Quantum Imaging XIII, San Diego, CA. August 09, 

2015. 

Session Organization 

16.	 T. Bednarz and J. Terrill, Co-Organizers, Bird’s of 

a Feather Session on Immersive Visualization for 

Science and Research International, 42nd International Conference and Exhibition on Computer 

Graphics and Interactive Technologies, Los Angeles, CA, August 10, 2015. 

17.	 Y. Parker and J. Terrill, Co-Organizers, NIST 

Booth, 2014 International Conference for High Performance Computing, Networking, Storage and 

Analysis, New Orleans, LA, November 17-20, 

2014. 

18.	 B. Saunders, Chair, Session on Spline Surfaces, 

SIAM Conference on Geometric and Physical Modeling (GD/SPM15), Salt Lake City, Utah, October 

12, 2015. 

Other Professional Activities 

Internal 

1.	 R. Boisvert, Member, ITL Diversity Committee. 

2.	 B. Cloteaux, Member, Washington Editorial Review Board. 

3.	 C. Schanzle, Member, Scientific Computing Steering Group. 

4.	 I. Beichl, ITL Co-Director, NIST Summer Undergraduate Research Fellowship Program. 

5.	 S. Glancy, Member, NIST Boulder SURF Committee. 

6.	 S. Glancy, Member, ITL Diversity Committee. 

External 

Editorial 

1.	 R. F. Boisvert, Associate Editor, ACM Transactions 

on Mathematical Software. 

2.	 R. F. Boisvert, Area Editor (Numerical Analysis, 

Mathematical Software, and Computational Engineering, Finance, and Science), Computing 

Research Repository. 

3.	 I. Beichl, Member, Editorial Board, Computing in 

Science & Engineering. 

4.	 H. S. Cohl, Co-Editor, OP-SF NET, The Electronic 

News Net of the SIAM Activity Group on Orthogonal Polynomials and Special Functions. 

5.	 H. S. Cohl, Guest Editor, Special Issue on Orthogonal Polynomials, Special Functions and 

Applications, Symmetry, Integrability and Geometry: Methods and Applications. 

6.	 Z. Gimbutas, Member, Editorial Board, Advances 

in Computational Mathematics. 

7.	 W. F. Mitchell, 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, Department Editor, Your Homework Assignment column, Computing in Science & 

Engineering. 

10.	 F. A. Potra, Regional Editor for the Americas, Optimization Methods and Software 

11.	 F. A. Potra, Associate Editor, Journal of Optimization Theory and Applications 

12.	 F. A. Potra, Associate Editor, Numerical Functional 

Analysis and Optimization 

13.	 F. A. Potra, Associate Editor, Optimization and Engineering 

14.	 K. Sayrafian, Associate Editor, International Journal of Wireless Information Networks 

15.	 K. Sayrafian, Section Editor, Cooperative Radio 

Communications for Green Smart Environments 
 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 121 

16.	 K. Sayrafian, Guest Editor, IEEE Wireless Communications, Special Issue: Mobile Wearable 

Communications. 

17.	 K. Sayrafian, Guest Editor, International Journal 

on Wireless Information Networks, Special Issue: 

Toward 5G Emerging Technologies: Selected Papers from IEEE PIMRC 2014. 

18.	 B. I. Schneider, Department Editor (Computer Simulations), Computing in Science & Engineering. 

Boards and Committees 

1.	 R. F. Boisvert, Member, ACM Publications Board. 

2.	 R. F. Boisvert, Member, International Federation 

for Information Processing (IFIP) Working Group 

2.5 (Numerical Software). 

3.	 R. F. Boisvert, Member, External Advisory Committee, Department of Computer Science, George 

Washington University. 

4.	 W. George, Member, Argonne National Laboratory, Leadership Computing Facility User Advisory 

Committee. 

5.	 G. B. McFadden, Member, SIAM Kleinman Prize 

Selection Committee. 

6.	 G. B. McFadden, Member-at-Large, SIAM Council. 

7.	 D. P. O’Leary, Founding Co-Director, Joint University of Maryland and NIST Center for Quantum 

Information and Computer Science (QuICS), 2013­

2015. 

8.	 D. G. Porter, Member, Tcl Core Team. 

9.	 S. Ressler, Member, Web3D Consortium. 

10.	 S. Ressler, Member, W3C, Declaritive 3D for the 

WebArchitecture Community Group. 

11.	 B. Saunders, Member, Advisory Board for Degree 

Programs in Mathematics and Statistics, American 

University, Washington, D.C. 

12.	 B. Saunders, Member, NSF Panel Selection Committee for Presidential Awards for Excellence in 

Mathematics and Science Teaching. 

13.	 B. Saunders, Member, MAA Business, Industry, 

and Government (BIG) Committee. 

14.	 B. Saunders, Webmaster, SIAM Activity Group on 

Orthogonal Polynomials and Special Functions. 

15.	 B. Saunders, OP-SF Talk listserv Moderator, SIAM 

Activity Group on Orthogonal Polynomials and 

Special Functions. 

16.	 K. Sayrafian, Co-Chair and Co-Organizer, IEEE 

BSN 2015. 

17.	 K. Sayrafian, Member, Quantum Medical Device 

Interoperablility Project. 

18.	 K. Sayrafian, Member, Wireless Medical Technology Working Group. 

19.	 K. Sayrafian, Member, Advisory Board, National 

Center for Wearable Technology in Rehabilitation 

Research. 

20.	 B. I Schneider, Chair, Division of Computational 

Physics, American Physical Society. 

21.	 B. I Schneider, Member, High End Computing Interagency Working Group, Federal Networking and 

Information Technology R&D (NITRD) Program. 

22.	 J. Terrill, Co-Organizer, 42nd International Conference and Exhibition on Computer Graphics and 

Interactive Technologies. 

23.	 J. Terrill, Member, High End Computing Research 

and Development and Infrastructure Interagency 

Working Groups, Networking and Information 

Technology R & D. (NITRD) Program. 

Community Outreach 

1.	 A. J. Kearsley, Panelist, Industrial Day, SIAM MidAtlantic Regional Conference, George Mason University, March 21, 2015. 

2.	 D. P. O’Leary, Mentor, Association for Women in 

Mathematics Mentor Network. 

3.	 B. Saunders, Judge (Mathematics), Siemens 

Competition in Math, Science and Technology, 

October 9-11, 2015 at Discovery Communications, 

Silver Spring, MD. 

4.	 B. Saunders, Organizer, Virginia Standards of 

Learning Tutoring Program, Northern Virginia 

Chapter (NoVAC) of Delta Sigma Theta Sorority, 

Inc. and the Dunbar Alexandria-Olympic Branch of 

the Boys and Girls Clubs of Greater Washington, 

January-May, 2015. 

5.	 B. Saunders, Mentor, Careers in Mathematical 

Sciences: Workshop for Underrepresented Groups, 

Institute for Mathematics and Its Applications, 

University of Minnesota, Minneapolis, MN March 

26-29, 2015. 

6.	 B. Saunders, Mentor, International Baccalaureate 

Middle Years Program, Francis Scott Key Middle 

School, Silver Spring, MD, May 21, 2015. 

7.	 D. P. O'Leary, Mentor, Association for Women in 

Mathematics Mentor Network. 
 

 

 

 

 

 

 

 

 

122 NIST Applied and Computational Mathematics Division 

Thesis Direction 

1.	 Z. Gimbutas, Member, Ph.D. Thesis Committee, 

Sija Hao, Applied Mathematics, University of Colorado, Boulder. Title: Numerical Methods for 

Solving Linear Elliptic PDEs: Direct Solvers and 

High Order Accurate Discretization. Completed 

2015. 

2.	 K. Sayrafian, Member, Ph.D. Thesis Committee, 

Mehdi Dadfarnia, University of Maryland. 

3.	 K. Sayrafian, Member, Ph.D. Thesis Committee, 

Bojan Lukovac, University of Zagreb. 

4.	 K. Sayrafian, Member, Ph.D. Thesis Committee, 

Hamid Mahboubi, Concordia University. 

5.	 X. Tang, Ph.D. Thesis Supervisor, Oliver Slattery, 

University of Limerick, Ireland. 

6.	 J. Terrill, Member, Thesis Committee, Henan Zhao, 

University of Maryland Baltimore County. 

Awards and Recognition 

1.	 S. Glancy, ITL Outstanding Contribution Award, 

NIST Information Technology Laboratory, 2015. 

2.	 R. Kacker, Silver Medal (joint award), Department 

of Commerce, December 10, 2014. 

3.	 E. Knill, Samuel Wesley Stratton Award, NIST, 

December 2015. 

4.	 Y. K. Liu, ITL Outstanding Conference Paper 

Award, NIST Information Technology Laboratory, 

June 15, 2015. 

5.	 D. P. O’Leary, A Celebration in Honor of Dianne 

P. O’Leary on the Occasion of her Retirement, Minisymposium and Banquet, SIAM Conference on 

Applied Linear Algebra, Atlanta, GA, October 29, 

2015. 

6.	 B. Saunders, recognized for 12 years of service as a 

math tutor, Boys and Girls Clubs of Greater Washington, GEICO and the Washington Wizards, 

Washington Wizards Basketball game, Verizon 

Center, December 5, 2014. 

7.	 K. Sayrafian, Bronze Medal, US Department of 

Commerce, December 2015. 

8.	 X. Tang, O. Slattery, P. Kuo and B. Hershman, 

Bronze Medal, US Department of Commerce, December 2015. 

Grants Received 

1.	 W. George, M. Olano, S. Satterfield, J. Terrill, N. 

Martys, C. Ferraris and D. Lootens, Rheometer Design for Large-particle Dense Suspensions, DOE 

Advanced Scientific Computing Research Leadership Computing Challenge, 50 million hours of 

computer time, IBM Blue Gene Q system (Mira) at 

Argonne National Laboratory. 

2.	 B. I. Schneider, K. Bartschat and X. Guan, Numerical Solutions to the Time-independent and Timedependent Schrödinger Equation, NSF XSEDE 

Program, 8M service units of computer time, Texas 

Advanced Computer Center Stampede and San Diego Supercomputer Center Comet supercomputers. 

Grants Awarded 

ACMD awards a small amount of funding through the 

NIST Measurement Science Grants Program for projects that make direct contributions to its research 

programs. Often such grants support direct cooperation 

between an external awardee and ACMD. This year the 

following new cooperative agreements were initiated. 

1.	 University of Edinburgh: Rigorous and Presentable 

Asymptotics for Special Functions and Orthogonal 

Polynomials, $687,640 (5 years). PI: Prof. Adri 

Olde Daalhuis. 

2.	 University of Texas at Arlington: Combinatorial 

Testing for Big Data Software, $375,624 (3 years), 

PI: Prof. Yu Lei. (Jointly funded by the ITL Computer Security Division.) 

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 

ActiveState 

Boeing Company 

CEA Leti (France) 

Center for Intergration of Medicine & Innovative Tech 

Citigroup, Inc. 

FlightAware 

Ford Motor Company 

Fraunhofer Institute for Computer Graphics Research 

(Germany) 

Jet Propulsion Laboratory 

Lockheed Martin 

Mechdyne 

Memorial Sloan Kettering Cancer Center 
 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 123 

Mentor Graphics 

Microsoft 

One World Terrain Standards Development 

Raytheon 

Rockwell-Collins 

SAS Institute 

Schrodinger 

Siemens 

SIKA Technology (Switzerland) 

SINTEF (Norway) 

Suisse d’Electronique et Microtechnique (Switzerland) 

Synopsys 

Government/Non-profit Organizations 

Air Force Office of Scientific Research 

American Institute of Physics 

Argonne National Laboratory 

Army Research Laboratory 

Association for Computing Machinery 

Barcelona Institute of Science and Technology (Spain) 

Canadian Institute for Advanced Research (Canada) 

CENAM, National Metrology Center (Mexico) 

Center for Research and Advanced Studies of the National Polytechnic Institute (Mexico) 

Centrum Wiskunde & Informatica (Netherlands) 

China Special Equipment Inspection and Res. Inst. 

Commonwealth Scientific & Ind. Res. Org. (Australia) 

Defense Advanced Research Projects Agency 

Department of Energy 

Electric Power Research Institute 

Food and Drug Administration 

IDA Center for Computing Sciences 

IDA Center for Communications Research 

IEEE Computer Society 

IPCMS Strasborg (France) 

Johns Hopkins University Applied Physics Lab 

Lawrence Livermore National Laboratory 

MIT Lincoln Labs 

Montgomery County, Maryland 

NASA - Cassini MSS Project 

NASA Glenn Research Center 

NASA Ind. Verification and Validation Facility 

National Center for Scientific Research (France) 

National Institutes of Health 

National Oceanic and Atmospheric Administration 

National Physical Laboratory (United Kingdom) 

National Renewable Energy Laboratory 

National Science Foundation 

National Security Agency 

Naval Facilities Engineering Command 

Nuclear Regulatory Commission 

Oak Ridge National Laboratory 

Princeton Plasma Physics Laboratory 

Pacific Northwest National Laboratory 

Sandia National Laboratories 

SBA-Research (Austria) 

Leibniz-Zentrum für Informatik (Germany) 

Smithsonian Institution 

Southwest Research Institute 

US Army Research Laboratory 

U.S. Marine Corps 

Web3D Consortium 

Universities 

American University 

Arizona State University 

Beijing Institute of Technology (China) 

California Institute of Technology 

Carnegie Mellon University 

China University of Petroleum (China) 

City University of Hong Kong (China) 

Colorado State University 

Concordia University (Canada) 

Dalian University of Technology (China) 

Dartmouth College 

Drake University 

Duke University 

East Carolina University 

East China University of Science and Tech. (China) 

Federal University of Rio Grande do Norte (Brazil) 

Federal University of Ceará (Brazil) 

George Mason University 

Georgetown University 

George Washington University 

Hampton University 

Howard University 

Imperial College (United Kingdom) 

Indiana University 

Iowa State University 

Khallikote College (India) 

Kings College (United Kingdom) 

Lanzhou University of Technology (China) 

Linköping University (Sweden) 

Linnaeus University (Sweden) 

Louisiana State University 

Lund University (Sweden) 

Mahidol University (Thailand) 

McLennan Community College 

Nanyang University (Singapore) 

National University of Singapore (Singapore) 

Naval Postgraduate School 

Ningbo University (China) 

New York University 

Northern Illinois Univerisity 

Northwestern University 

Oregon State University 

Oslo University (Norway) 

Polytechnic University of Valencia (Spain) 

Queensland University of Technology (Australia) 

Rochester Institute of Technology 

Shandong University (China) 

Stanford University 

Technical University of Berlin (Germany) 

Technical University of Delft (Netherlands) 
 

 

 

 

 

124 NIST Applied and Computational Mathematics Division 

Technical University of Munich (Germany) 

Three Gorges University (China)
 

Tohoko University (Japan) 

Tsinghua University (China) 

Tulane University
 

University of Alcala (Spain) 

University of Antwerp (Belgium)
 

University of Bologna (Italy) 

University of British Columbia (Canada) 

University of California San Diego 

University of California Santa Barbara 

University of Campinas (Brazil) 

University of Colorado 

University of Copenhagen (Denmark) 

University of Edinburgh (Scotland) 

University of Erlangen-Nuremberg (Germany) 

University of Hong Kong (China) 

University of Houston 

University of Illinois Urbana-Champaign
 

University of Indiana, Bloomington
 

Univeristy of Innsbruck (Austria)
 

University of Iowa
 

University of Limerick (Ireland)
 

University of Lisbon (Portugal) 

University of Maryland, College Park 

University of Maryland, Baltimore County 

University of Miami 

University of Michigan 

University of Moncton (Canada) 

University of Nebraska 

University of Northern Texas 

University of Oulu (Finland) 

University of South Carolina 

University of Surrey (United Kingdom) 

University of Texas, Arlington 

University of Toronto (Canada) 

University of Waterloo (Canada) 

University of Windsor (Canada) 

University of Wisconsin-Milwaukee 

University of Zagreb (Croatia) 

Virginia Polytechnic Institute and State University 

Washington University, St. Louis 

Worcester Polytechnic University 

Yale University 

Yokohama National University (Japan) 
 

Part V: Appendix 

 

Summary of Activities for Fiscal Year 2015 125 

Part V 

Appendix 
 

 

126 NIST Applied and Computational Mathematics Division 
 

 

Summary of Activities for Fiscal Year 2015 127 

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 non-student 

appointments held during any portion of the reporting period (October 2014 – December 2015). For students and interns, see Staff News on page 10. (*) Denotes staff at NIST Boulder. 

Division Staff 

Ronald Boisvert, Chief, Ph.D. (Computer Science), Purdue University, 1979 

Catherine Graham, Secretary 

Ginger White, Administrative Assistant, M.B.A., University of Maryland, 2014. 

Lochi Orr, Administrative Assistant, Associate (Criminal Justice), Grantham University, 2009 

Alfred Carasso, Ph.D. (Mathematics), University of Wisconsin, 1968 

Roldan Pozo, Ph.D. (Computer Science), University of Colorado at Boulder, 1991 

Kamran Sayrafian-Pour, Ph.D. (Electrical and Computer Engineering), University of Maryland, 1999 

Christopher Schanzle, B.S. (Computer Science), University of Maryland Baltimore County, 1989 

Mathematical Analysis and Modeling Group 

Timothy Burns, Leader, Ph.D. (Mathematics), University of New Mexico, 1977 

*Bradley Alpert, Ph.D. (Computer Science), Yale University, 1990 

*Andrew Dienstfrey, Ph.D. (Mathematics), New York University, 1998 

Jeffrey Fong, Ph. D. (Applied Mechanics and Mathematics), Stanford University, 1966 

*Zydrunas Gimbutas, Ph.D. (Applied Mathematics), Yale University, 1999 

Fern Hunt, Ph.D. (Mathematics), New York University, 1978 

Raghu Kacker, Ph.D. (Statistics), Iowa State University, 1979 

Anthony Kearsley, Ph.D. (Computational and Applied Mathematics), Rice University, 1996 

Geoffrey McFadden, NIST Fellow, Ph.D. (Mathematics), New York University, 1979 

Paul Patrone, Ph.D. (Physics), University of Maryland, 2013 

Bert Rust, Ph.D. (Astronomy), University of Illinois at Urbana-Champaign, 1974 

 Faculty Appointee (Name, Degree / Home Institution)
 

Daniel Anderson, Ph.D. / George Mason University
 

Dianne O’Leary, Ph.D. / University of Maryland College Park 

Michael Mascagni, Ph.D. / Florida State University 

Florian Potra, Ph.D. / University of Maryland Baltimore County 

Guest Researchers (Name, Degree / Home Institution)
 

Sean Colbert-Kelly, Ph.D. / Noblis 

Michael Cromer, Ph.D. / Rochester Institute of Technology 

David Gilsinn, Ph.D. / NIST (retired) 

Yu (Jeff) Lei, Ph.D. / University of Texas at Arlington 

Itzel Dominquez Mendoza / Centro Nacional de Metrología, Mexico
 

Asha Nurse, Ph.D. 

Jose Torres-Jimenez, Ph.D / CINVESTAV, Mexico 

Christoph Witzgall, Ph.D. / NIST Scientist Emeritus 

Mathematical Software Group 

Michael Donahue, Leader Ph.D. (Mathematics), Ohio State University, 1991 

Javier Bernal, Ph.D. (Mathematics), Catholic University, 1980 
 

 

 

 

128 NIST Applied and Computational Mathematics Division 

Howard Cohl, Ph.D. (Mathematics), University of Auckland, 2010 

Stephen Langer, Ph.D. (Physics), Cornell University, 1989 

Daniel Lozier, Ph.D. (Applied Mathematics), University of Maryland, 1979 

Marjorie McClain, M.S. (Mathematics), University of Maryland College Park, 1984 

Bruce Miller, Ph.D. (Physics), University of Texas at Austin, 1983 

William Mitchell, Ph.D. (Computer Science), University of Illinois at Urbana-Champaign, 1988 

Donald Porter, Ph.D. (Electrical Engineering), Washington University, 1996 

Bonita Saunders, Ph.D. (Mathematics), Old Dominion University, 1985 

Barry Schneider, Ph.D. (Physics), University of Chicago, 1969 

Faculty Appointees (Name, Degree / Home Institution) 

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 

Leonard Maximon, Ph.D. / George Washington University 

Mark Pederson, Ph.D. / DOE Office of Science 

Jianwei Sun, Ph.D. / Temple University 

Qiming Wang / NIST (retired) 

Computing and Communications Theory Group 

Ronald Boisvert, Acting Leader, Ph.D. (Computer Science), Purdue University, 1979 

Isabel Beichl, Project Leader, Ph.D. (Mathematics), Cornell University, 1981 

Brian Cloteaux, Ph.D. (Computer Science), New Mexico State University, 2007 

*Scott Glancy, Ph.D. (Physics), University of Notre Dame, 2003 

Barry Hershman, A.A. (Electronics Engineering), Capitol College, 1979 

Stephen Jordan, Ph.D. (Physics), Massachusetts Institute of Technology, 2008 

 *Emanuel Knill, NIST Fellow, Ph.D. (Mathematics), University of Colorado at Boulder, 1991 

Paulina Kuo, Ph.D. (Physics), Stanford University, 2008 

 Yi-Kai Liu, Ph.D. (Computer Science), University of California, San Diego, 2007

 Vladimir Marbukh, Ph.D. (Mathematics) Leningrad Polytechnic University, 1986 

James Shook, Ph.D. (Mathematics), University of Mississippi, 2010 

Oliver Slattery, Ph.D. (Physics), University of Limerick, 2015 

Xiao Tang, Project Leader, Ph.D. (Physics), Chinese Academy of Sciences, 1985 

NRC Postdoctoral Associates 

Yvonne Kemper, Ph.D. (Mathematics), University of California at Davis, 2013 

Contractors (Name, Degree / Home Institution)
 

Alan Mink, Ph.D. / Wagner Resources 

Faculty Appointees (Name, Degree / Home Institution)
 

James Lawrence, Ph.D. / George Mason University 

Guest Researchers (Name, Degree / Home Institution)
 

*Peter Bierhorst, Ph.D. / University of Colorado 

*Bryan Eastin, Ph.D. / Northrup Grumman
 

Assane Gueye, Ph.D. / University of Maryland 

Richard La, Ph.D. / University of Maryland 

Lijun Ma, Ph.D. / Theiss Research
 

Francis Sullivan, Ph.D. / IDA Center for Computing Sciences 
Summary of Activities for Fiscal Year 2015 129 

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 

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 

Guest Researchers (Name, Degree / Home Institution) 

Tomasz Bednarz, Ph.D. / CSIRO, Australia 

Jian Chen, Ph.D. / University of Maryland Baltimore County 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

130 NIST Applied and Computational Mathematics Division 

Glossary of Acronyms 

2D two-dimensional 

3D three-dimensional 

ACM Association for Computing Machinery 

ACMD NIST/ITL Applied and Computational Mathematics Division 

ACTS Advanced Combinatorial Testing System 

AFOSR Air Force Office of Scientific Research 

ALCC Advanced Leadership Computing Center 

API application programmer’s interface 

APS American Physical Society 

arXiv preprint archive housed at Cornell University (http://arxiv.org/) 

AS autonomous system 

ASCE American Society of Civil Engineers 

ASCR Advanced Scientific Computing Research 

BAN body area network 

BC back-off counter 

BGP boarder gateway protocol 

BMP Bateman Manuscript Project 

BQP bounded-error quantum polynomial time 

CAC NIST-NTIA Center for Advanced Communications 

CAIDA Center for Applied Internet Data Analysis 

Caltech California Institute of Technology 

CAVE Cave Automatic Virtual Environment 

CCA clear channel assessment 

CCM Combiatorial Coverage Measurement 

CENAM Center for Metrology of Mexico 

CFPG Coulomb force parametric generator 

CG coarse-grained 

CI configuration interaction 

CICM Conference on Intelligent Computer Mathematics 

CINVESTAV Center for Research and Advanced Studies of the National Polytechnic Institute (Mexico) 

CMA University of Antwerp Computational Mathematics Research Group 

CMOS complementary metal-oxide semiconductor 

CNRS Centre National de la Recherche Scientifique (France) 

CNST NIST Center for Nanoscale Science and Technology 

CPU central processing unit 

CSH calcium silicate hydrate 

CT combinatorial testing 

CT computed tomography 

CTL NIST Communications Technology Laboratory 

CY calendar year 

CVS a source code control system 

DLMF Digital Library of Mathematical Functions 

DNA deoxyribonucleic acid 

DOC Department of Commerce 

DOE U.S. Department of Energy 

DPD dissipative particle dynamics 

DRMF digital repository of mathematical functions 

DSO display shared object 

EC error correction 

ED energy detection 

EIT electromagnetically induced transparency 

EL NIST Engineering Laboratory 

ETSI European Telecommunications Standards Institute 

FEDVR finite element discrete variable method 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Activities for Fiscal Year 2015 131 

FEM finite element method 

FFT fast Fourier transform 

FIFO first-in first-out 

FY fiscal year 

GPU graphics processing units 

GUI graphical user interface 

HEC High End Computing 

HEV high end visualization 

HIM helium ion microscope 

HOLMES a physics experiment 

HPCVG ACMD High Performance Computing and Visualization Group 

HTML hypertext markup language 

HVS human visual system 

Hy-CI Hylleraas-Configuration Interaction technique 

ICA independent component analysis 

ICST International Conference of Software Testing 

IDEA IRIS Development Environment for Applications 

IDL Interactive Data Language 

IDS interdependent security 

IEC International Electrotechnical Commission 

IEEE Institute of Electronics and Electrical Engineers 

IFIP International Federation for Information Processing 

IMA Institute for Mathematics and Its Applications 

IMACS International Association for Mathematics and Computers in Simulation 

IMS Innovations in Measurement Science 

IP internet protocol 

IRIS Interpreted Runtime Immersive Scenegraph 

ISG industry specification group 

ISGG International Society for Grid Generation 

ISIMA Institut Supérieur d’Informatique, de Modélisation et de leurs Applications (France) 

ITL NIST Information Technology Laboratory 

ITM irregular terrain model 

ITS NTIA Instritute for Telecommunication Sciences 

IVE immersive visualization environment 

JILA joint NIST-University of Colorado physics research institute 

JMONSEL simulation code used to model electron scattering in materials 

JQI Joint Quantum Institute 

KLS Koekoek, Lesky and Swarttouw 

LaTeX a math-oriented text processing system 

LDPC low density parity check 

LiDAR light detection and ranging 

LTE long-term evolution 

MAA Mathematical Association of America 

MathML Mathematical Markup Language (W3C standard) 

MCMC Monte Carlo Markov Chain 

MD molecular dynamics 

MEMS micro-electro-mechanical system 

MHD magnetohydro-dynamic 

MIT Massachusetts Institute of Technology 

MML NIST Material Measurement Laboratory 

MOAs Multinational ASs 

MPI Message Passing Interface 

MQA mathematical questions answering 

MRAM magneto-resistive random access memory 

MRI magnetic resonance imaging 

MSD mass-spring damper 

MSE mean squared error 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

132 NIST Applied and Computational Mathematics Division 

muMAG Micromagnetic Activity Group 

NASA National Aeronautics and Space Administration 

NBS National Bureau of Standards 

nCT nano computed tomography 

NIST National Institute of Standards and Technology 

NISTIR NIST Internal Report 

NITRD Networking and Information Technology Research and Development 

NLP natural language processing 

NPSC National Physical Science Consortium 

NRC National Research Council 

NSA National Security Agency 

NSF National Science Foundation 

NTIA National Telecommunications and Information Administration 

NYU New York University 

ODEs ordinary differential equations 

OLED organic light emitting diode 

OOF Object-Oriented Finite Elements (software) 

OOMMF Object-Oriented Micromagnetic Modeling Framework (software) 

OPSF orthogonal polynomials and special functions 

OSG Open SceneGraph 

PDE partial differential equation 

PHAML Parallel Hierarchical Adaptive Multi Level (software) 

PML NIST Physical Measurement Laboratory 

POM part of math 

PoPs Points of Presence 

POS part of speech 

PPLN periodically poled lithium niobate 

PSCR NTIA Public Safety Communications Research 

PSNR peak signal-to-noise ratio 

QBER quantum bit error rate 

QCD quantum chromodynamics 

QD quantum dot 

QDPD quarternion-based dissipative particle dynamics 

QIS quantum information science 

QKD quantum key distribution 

QuICS UMD-NIST Joint Center for Quantum Information and Computer Science 

R&D research and development 

RF radio frequency 

RSA a public-key cryptosystem 

SAE senior associate editor 

SDE stochastic differential equation 

SEM scanning electron microscope 

SFWM spontaneous four-wave mixing 

SHIP NIST Summer High School Internship Program 

Si Silicon 

SIAM Society for Industrial and Applied Mathematics 

SIGGRAPH ACM Special Interest Group on Graphics 

SIS sequential importance sampling 

SPAM state preparation and measurement 

SPDC spontaneous parametric down-conversion 

SPH smoothed particle hydrodynamics 

SPIE International Society for Optical Engineering 

SQUID superconducting quantum interference device 

SRM standard reference material 

SRVF square root velocity function 

SURF Student Undergraduate Research Fellowship 

TACC Texas Advanced Computing Center 
 

 

 

 

Summary of Activities for Fiscal Year 2015 133 

TES transition edge sensor 

TSCM truncated singular components method 

UMBC University of Maryland Baltimore County 

UMD University of Maryland 

UMIACS University of Maryland Institute for Advanced Computer Studies 

UQ uncertainty quantification 

VR virtual reality 

VRML virtual reality modeling language 

W3C World Wide Web Consortium 

WebGL Web-based Graphics Library 

X3D Extensible 3D 

X3DOM an open-source framework for integrating X3D and HTML5 

XSEDE NSF eXtreme Science and Engineering Discovery Environment 

XML Extensible Markup Language